2

Section 8

REINFORCED CONCRETE*

Part AGENERAL REQUIREMENTS AND MATERIALS

8.1 APPLICATION

8.1.1 General

The specifications of this section are intended for de-sign of reinforced (nonprestressed) concrete bridge mem-bers and structures. Bridge members designed as pre-stressed concrete shall conform to Section 9.

8.1.2 Notations

a = depth of equivalent rectangular stress block(Article 8.16.2.7)

ab = depth of equivalent rectangular stress blockfor balanced strain conditions, in. (Article8.16.4.2.3)

av = shear span, distance between concentratedload and face of support (Articles 8.15.5.8and 8.16.6.8)

A = effective tension area, in square inches, ofconcrete surrounding the flexural tension re-inforcement and having the same centroid asthat reinforcement, divided by the number ofbars or wires. When the flexural reinforce-ment consists of several bar or wire sizes, thenumber of bars or wires shall be computed asthe total area of reinforcement divided by thearea of the largest bar or wire used. For cal-culation purposes, the thickness of clear con-crete cover used to compute A shall not betaken greater than 2 inches.

Ab = area of an individual bar, sq. in. (Article8.25.1)

A, = area of core of spirally reinforced compres-sion member measured to the outside diame-ter of the spiral, sq. in. (Article 8.18.2.2.2)

Acv = area of concrete section resisting shear trans-fer, sq. in. (Article 8.16.6.4.5)

Af = area of reinforcement in bracket or corbel re-sisting moment, sq. in. (Articles 8.15.5.8 and8.16.6.8)

A g = gross area of section, sq. in.Ah = area of shear reinforcement parallel to flex-

ural tension reinforcement, sq. in. (Articles8.15.5.8 and 8.16.6.8)

An = area of reinforcement in bracket or corbel re-sisting tensile force N, (N„.), sq. in. (Articles8.15.5.8 and 8.16.6.8)

A, = area of tension reinforcement, sq. in.AS = area of compression reinforcement, sq. in.A sf = area of reinforcement to develop compres-

sive strength of overhanging flanges of I- andT-sections (Article 8.16.3.3.2)

Ask = area of skin reinforcement per unit heightin one side face, sq. in. per ft. (Article8.17.2.1.3).

Ast = total area of longitudinal reinforcement(Articles 8,16,4.1.2 and 8.16.4.2.1)

Av = area of shear reinforcement within a dis-tance s

Avf = area of shear-friction reinforcement, sq. in.(Article 8.15.5.4.3)

Aw = area of an individual wire to be developed orspliced, sq. in. (Articles 8.30.1.2 and8.30.2)

A, = loaded area (Articles 8.15.2.1.3 and 8.16.7.2)A Z = maximum area of the portion of the support-

ing surface that is geometrically similar toand concentric with the loaded area (Articles8.15.2.1.3 and 8.16.7.2)

b = width of compression face of memberbo = perimeter of critical section for slabs and

footings (Articles 8.15.5.6.2 and 8.16.6.6.2)by = width of cross section at contact surface

being investigated for horizontal shear (Arti-cle 8.15.5.5.3)

*The specifications of Section 8 are patterned after and are in general conformity with the provisions of ACI Standard 318 for reinforced concrete de-sign and its commentary, ACI 318 R, published by the American Concrete Institute.

189

190 HIGHWAY BRIDGES 8.1.2

b,

Cm

d

d'

d"

db

d,

= web width, or diameter of circular section(Article 8.15.5.1.1)

= distance from extreme compression fiber toneutral axis (Article 8.16.2.7)

= factor relating the actual moment diagramto an equivalent uniform moment diagram(Article 8.16.5.2.7)

= distance from extreme compression fiber tocentroid of tension reinforcement, in. Forcomputing shear strength of circular sections,d need not be less than the distance from ex-treme compression fiber to centroid of ten-sion reinforcement in opposite half of mem-ber. For computing horizontal shear strengthof composite members, d shall be the dis-tance from extreme compression fiber to cen-troid of tension reinforcement for entire com-posite section.

= distance from extreme compression fiber tocentroid of compression reinforcement, in.

= distance from centroid of gross section, ne-glecting the reinforcement, to centroid of ten-sion reinforcement, in.

= nominal diameter of bar or wire, in.= distance measured from extreme tension

t = tensile stress in reinforcement at serviceloads, psi (Article 8.15.2.2)

fs = stress in compression reinforcement at bal-anced conditions (Articles 8.16.3.4.3 and8.16.4.2.3)

ft = extreme fiber tensile stress in concrete at ser-vice loads (Article 8.15.2.1.1)

fs, = specified yield strength of reinforcement, psih = overall thickness of member; in.hf = compression flange thickness of I- and T-

sectionsI, = moment of inertia of cracked section trans-

formed to concrete (Article 8.13.3)le = effective moment of inertia for computation

of deflection (Article 8.13.3)Ig = moment of inertia of gross concrete section

about centroidal axis, neglecting reinforce-ment

= moment of inertia of reinforcement aboutcentroidal axis of member cross section

= effective length factor for compression mem-bers (Article 8.16.5.2.3)

= additional embedment length at support or atpoint of inflection, in. (Article 8.24.2.3)

= development length, in. (Articles 8.24through 8.32)

= development length of standard hook in ten-sion, measured from critical section to out-side end of hook (straight embedment lengthbetween critical section and start of hook(point of tangency) plus radius of bend andone bar diameter), in. (Article 8.29)

= fhb X applicable modification factor= basic development length of standard hook in

tension, in.= unsupported length of compression member

(Article 8.16.5.2.1)= computed moment capacity (Article 8.24.2.3)= maximum moment in member at stage for

which deflection is being computed (Article8.13.3)

= nominal moment strength of a section at bal-anced strain conditions (Article 8.16.4.2.3)

= moment to be used for design of compressionmember (Article 8.16.5.2.7)

= cracking moment (Article 8.13.3)= nominal moment strength of a section= nominal moment strength of a section in the

direction of the x axis (Article 8.16.4.3)= nominal moment strength of a section in the

direction of the y axis (Article 8.16.4.3)= factored moment at section

fiber to center of the closest bar or wire infahinches. For calculation purposes, the thick-

ness of clear concrete cover used to computed, shall not be taken greater than 2 inches.

E, = modulus of elasticity of concrete, psi (Article8.7.1)

EI = flexural stiffness of compression member fdh(Article 8.16.5.2.7)

fhbE, = modulus of elasticity of reinforcement, psi

(Article 8.7.2) fufb = average bearing stress in concrete on loaded

area (Articles 8.15.2.1.3 and 8.16.7.1) M

t = extreme fiber compressive stress in concrete Maat service loads (Article 8.15.2.1.1)

C = specified compressive strength of concrete,psi

= square root of specified compressive strengthMb

of concrete, psi MCfit = average splitting tensile strength of light-

weight aggregate concrete, psi Mirff = fatigue stress range in reinforcement, ksi (Ar- M.

ticle 8.16.8.3) Mnxf,,,;n = algebraic minimum stress level in reinforce-

ment (Article 8.16.8.3) M,,,fr = modulus of rupture of concrete, psi (Article

8.15.2.1.1) M.

9.1.2 DIVISION I—DESIGN 191

M UX = factored moment component in the directionof the x axis (Article 8.16.4.3)

M, = factored moment component in the directionof the y axis (Article 8.16.4.3)

Mib = value of smaller end moment on compressionmember due to gravity loads that result in noappreciable sidesway calculated by conven-tional elastic frame analysis, positive if mem-ber is bent in single curvature, negative ifbent in double curvature (Article 8.16.5.2.4)

M 2b = value of larger end moment on compressionmember due to gravity loads that result in noappreciable sidesway calculated by conven-tional elastic frame analysis, always positive(Article 8.16.5.2.4)

M2s = value of larger end moment on compressionmember due to lateral loads or gravity loadsthat result in appreciable sidesway, definedby a deflection 0, greater than f U

/1500, cal-culated by conventional elastic frame analy-sis, always positive. (Article 8.16.5.2)

n = modular ratio of elasticity = EJE, (Article8.15.3.4)

N = design axial load normal to cross section oc-curring simultaneously with V to be taken aspositive for compression, negative for ten-sion and to include the effects of tension dueto shrinkage and creep (Articles 8.15.5.2.2and 8.15.5.2.3)

Nc = design tensile force applied at top of bracketof corbel acting simultaneously with V, to betaken as positive for tension (Article 8.15.5.8)

N U = factored axial load normal to the cross sec-tion occurring simultaneously with V. to betaken as positive for compression, negativefor tension, and to include the effects of ten-sion due to shrinkage and creep (Article8.16.6.2.2)

NUS = factored tensile force applied at top ofbracket or corbel acting simultaneously withVu, to be taken as positive for tension (Arti-cle 8.16.6.8)

Pb = nominal axial load strength of a section at bal-anced strain conditions (Article 8.16.4.2.3)

P, = critical load (Article 8.16.5.2.7)Po = nominal axial load strength of a section at

zero eccentricity (Article 8.16.4.2.1)Pn = nominal axial load strength at given eccen-

tricityPnx = nominal axial load strength corresponding to

MnX , with bending considered in the directionof the x axis only (Article 8.16.4.3)

P, = nominal axial load strength corresponding to

Mnp with bending considered in the directionof the y axis only (Article 8.16.4.3)

P nxy = nominal axial load strength with biaxial load-ing (Article 8.16.4.3)

PU = factored axial load at given eccentricity

r = radius of gyration of cross section of a com-pression member (Article 8.16.5.2.2)

s = spacing of shear reinforcement in directionparallel to the longitudinal reinforcement, in.

s W = spacing of wires to be developed or spliced,

in.S = span length, ftV = design shear force at section (Article

8.15.5.1.1)v = design shear stress at section (Article

8.15.5.1.1)V, = nominal shear strength provided by concrete

(Article 8.16.6.1)V, = permissible shear stress carried by concrete

(Article 8.15.5.2)van = design horizontal shear stress at any cross

section (Article 8.15.5.5.3)vb = permissible horizontal shear stress (Article

8.15.5.5.3)V„ = nominal shear strength (Article 8.16.6.1)Vnb = nominal horizontal shear strength (Article

8.16.6.5.3)V, = nominal shear strength provided by shear re-

inforcement (Article 8.16.6.1)VU = factored shear force at section (Article

8.16.6.1)WC = weight of concrete, lb per cu fty t = distance from centroidal axis of gross sec-

tion, neglecting reinforcement, to extremefiber in tension (Article 8.13.3)

z = quantity limiting distribution of flexural rein-forcement (Article 8.16.8.4)

a (alpha) = angle between inclined shear reinforcementand longitudinal axis of member

of = angle between shear-friction reinforcementand shear plane (Articles 8.15.5.4 and8.16.6.4)

Pb (beta) = ratio of area of reinforcement cut off to totalarea of reinforcement at the section (Article8.24.1.4.2)

R~ = ratio of long side to short side of concentratedload or reaction area; for a circular concen-trated load or reaction area, P c = 1.0 (Articles8.15.5.6.3 and 8.16.6.6.2)


Ra = absolute value of ratio of maximum deadload moment to maximum total load mo-ment, always positive

(3, = ratio of depth of equivalent compressionzone to depth from fiber of maximum com-pressive strain to the neutral axis (Article8.16.2.7)

= correction factor related to unit weight forconcrete (Articles 8.15.5.4 and 8.16.6.4)

µ ( mu) = coefficient of friction (Article 8.15.5.4.3)p (rho) = tension reinforcement ratio = A S /b wd, A,Ibdp ' = compression reinforcement ratio = A ' IbdPb = reinforcement ratio producing balanced strain

conditions (Article 8.16.3.1.1)PS = ratio of volume of spiral reinforcement to

total volume of core (out-to-out of spirals) ofa spirally reinforced compression member(Article 8.18.2.2.2)

p w = reinforcement ratio used in Equation (8-4)and Equation (8-48)

8 b = moment magnification factor for membersbraced against sidesway to reflect effects ofmember curvature between ends of compres-sion member

8 s = moment magnification factor for membersnot braced against sidesway to reflect lateraldrift resulting from lateral and gravity loads

(phi) = strength reduction factor (Article 8.16.1.2)

8.1.3 Definitions

The following terms are defined for general use inSection 8. Specialized definitions appear in individualArticles.

Bracket or corbel—Short (haunched) cantilever thatprojects from the face of a column or wall to support aconcentrated load or beam reaction. See Articles 8.15.5.8and 8.16.6.8.

Compressive strength of concrete (f,)—Specifiedcompressive strength of concrete in pounds per squareinch (psi).

Concrete, structural lightweight—A concrete contain-ing lightweight aggregate having an air-dry unit weight asdetermined by "Method of Test for Unit Weight of Struc-tural Lightweight Concrete" (ASTM C 567), not exceed-ing 115 pcf. In this specification, a lightweight concretewithout natural sand is termed "all-lightweight concrete"and one in which all fine aggregate consists of normalweight sand is termed "sand-lightweight concrete."

Deformed reinforcementDeformed reinforcing bars,deformed wire, welded smooth wire fabric, and weldeddeformed wire fabric.

Design load—All applicable loads and forces or theirrelated internal moments and forces used to proportionmembers. For design by SERVICE LOAD DESIGN, de-sign load refers to loads without load factors. For designby STRENGTH DESIGN METHOD, design load refersto loads multiplied by appropriate load factors.

Design strength—Nominal strength multiplied by astrength reduction factor, (~.

Development length—Length of embedded reinforce-ment required to develop the design strength of the rein-forcement at a critical section.

Embedment length—Length of embedded reinforce-ment provided beyond a critical section.

Factored load—Load, multiplied by appropriate loadfactors, used to proportion members by the STRENGTHDESIGN METHOD.

Nominal strength—Strength of a member or cross sec-tion calculated in accordance with provisions and as-sumptions of the STRENGTH DESIGN METHOD be-fore application of any strength reduction factors.

Plain reinforcement—Reinforcement that does notconform to the definition of deformed reinforcement.

Required strength—Strength of a member or cross sec-tion required to resist factored loads or related internalmoments and forces in such combinations as are stipu-lated in Article 3.22.

Service loadLoads without load factors.Spiral reinforcement—Continuously wound reinforce-

ment in the form of a cylindrical helix.Splitting tensile strength (f,,)—Tensile strength of con-

crete determined in accordance with "Specifications forLightweight Aggregates for Structural Concrete,"AASHTO M 195 (ASTM C 330).

Stirrups or ties—Lateral reinforcement formed of in-dividual units, open or closed, or of continuously woundreinforcement. The term "stirrups" is usually applied tolateral reinforcement in horizontal members and the term"ties" to those in vertical members.

Tension tie member—Member having an axial tensileforce sufficient to create tension over the entire cross sec-tion and having limited concrete cover on all sides. Ex-amples include: arch ties, hangers carrying load to anoverhead supporting structure, and main tension elementsin a truss.

Yield strength or yield point (fy ) —Specified minimumyield strength or yield point of reinforcement in poundsper square inch.

8.2 CONCRETE

The specified compressive strength, f,, of the con-crete for each part of the structure shall be shown on

8 . 2 DIVISION I—DESIGN 193

the plans. The requirements for f' shall be based on tests ofcylinders made and tested in accordance with Section 4—Division 11.

8.3 REINFORCEMENT

8.3.1 The yield strength or grade of reinforcement shallbe shown on the plans.

8.3.2 Reinforcement to be welded shall be indicated onthe plans and the welding procedure to be used shall bespecified.

8.3.3 Designs shall not use a yield strength, fy, in excess

of 60,000 psi.

8.3.4 Deformed reinforcement shall be used except thatplain bars or smooth wire may be used for spirals andties.

8.3.5 Reinforcement shall conform to the specifica-tions listed in Division 11, Section 5, except that, forreinforcing bars, the yield strength and tensile strengthshall correspond to that determined by tests on full-sizedbars.

Part BANALYSIS

8.4 GENERAL

All members of continuous and rigid frame structuresshall be designed for the maximum effects of the loadsspecified in Articles 3.2 through 3.22 as determined by thetheory of elastic analysis.

8.5 EXPANSION AND CONTRACTION

8.5.1 In general, provisions for temperature changesshall be made in simple spans when the span length ex-ceeds 40 feet.

8.5.2 In continuous bridges, the design shall provide forthermal stresses or for the accommodation of thermalmovement with rockers, sliding plates, elastomeric pads,or other means.

8.5.3 The coefficient of thermal expansion and contrac-tion for normal weight concrete may be taken as 0.000006per deg F.

8.5.4 The coefficient of shrinkage for normal weightconcrete may be taken as 0.0002.

8.5.5 Thermal and shrinkage coefficients for light-weight concrete shall be determined for the type of light-weight aggregate used.

8.6 STIFFNESS

8.6.1 Any reasonable assumptions may be adopted forcomputing the relative flexural and torsional stiffnesses ofcontinuous and rigid frame members. The assumptionsmade shall be consistent throughout the analysis.

8.6.2 The effect of haunches shall be considered both indetermining moments and in design of members.

8.7 MODULUS OF ELASTICITY ANDPOISSON'S RATIO

8.7.1 The modulus of elasticity, E c , for concrete may betaken as w1-

133 V

-f,-' in psi for values of wc between 90

and 155 pounds per cubic foot. For normal weight con-crete (w, = 145 pcf), E, may be considered as 57,000 f7'.

8.7.2 The modulus of elasticity, E5 , for nonprestressedsteel reinforcement may be taken as 29,000,000 psi.

8.7.3 Poisson's ratio may be assumed as 0.2.

8.8 SPAN LENGTH

8.8.1 The span length of members that are not built in-tegrally with their supports shall be considered the clearspan plus the depth of the member but need not exceed thedistance between centers of supports.


8.8.2 In analysis of continuous and rigid frame mem-bers, distances to the geometric centers of members shallbe used in the determination of moments. Moments atfaces of support may be used for member design. Whenfillets making an angle of 45° or more with the axis of acontinuous or restrained member are built monolithic withthe member and support, the face of support shall be con-sidered at a section where the combined depth of themember and fillet is at least one and one-half times thethickness of the member. No portion of a fillet shall beconsidered as adding to the effective depth.

8.8.3 The effective span length of slabs shall be as spec-ified in Article 3.24.1.

8.9 CONTROL OF DEFLECTIONS

8.9.1 General

Flexural members of bridge structures shall be de-signed to have adequate stiffness to limit deflections orany deformations that may adversely affect the strength orserviceability of the structure at service load plus impact.

8.9.2 Superstructure Depth Limitations

The minimum depths stipulated in Table 8.9.2 are rec-ommended unless computation of deflection indicates thatlesser depths may be used without adverse effects.

8.9.3 Superstructure Deflection Limitations

When making deflection computations, the followingcriteria are recommended.

8.9.3.1 Members having simple or continuous spanspreferably should be designed so that the deflection due toservice live load plus impact shall not exceed Y6 of the span,except on bridges in urban areas used in part by pedestrianswhereon the ratio preferably shall not exceed %000.

8.9.3.2 The deflection of cantilever arms due to ser-vice live load plus impact preferably should be limited to%oo of the cantilever arm except for the case includingpedestrian use, where the ratio preferably should be %,5.

8.10 COMPRESSION FLANGE WIDTH

8.10.1 TGirder

8.10.1.1 The total width of slab effective as a T-girder flange shall not exceed one-fourth of the spanlength of the girder. The effective flange width overhang-ing on each side of the web shall not exceed six times the

TABLE 8.9.2 Recommended Minimum Depths forConstant Depth Members

Minimum Depthin Feet'

Superstructure Type Simple Spans Continuous Spans

Bridge slabs with mainreinforcement parallelto traffic 1.2(S + 10)/30 (S + 10)/30 ? 0.542

T-Girders 0.070S 0.065S

Box-Girders 0.0605 0.055S

Pedestrian StructureGirders 0.033S 0.033S

' When variable depth members are used, values may be adjusted toaccount for change in relative stiffness of positive and negative mo-ment sections.

S = span length as defined in Article 8.8 in feet.

thickness of the slab or one-half the clear distance to thenext web.

8.10.1.2 For girders having a slab on one side only, theeffective overhanging flange width shall not exceed %12 ofthe span length of the girder, six times the thickness of theslab, or one-half the clear distance to the next web.

8.10.1.3 Isolated T-girders in which the T-shape isused to provide a flange for additional compression areashall have a flange thickness not less than one-half thewidth of the girder web and an effective flange width notmore than four times the width of the girder web.

8.10.1.4 For integral bent caps, the effective flangewidth overhanging each side of the bent cap web shall notexceed six times the least slab thickness, or %io the spanlength of the bent cap. For cantilevered bent caps, the spanlength shall be taken as two times the length of thecantilever span.

8.10.2 Box Girders

8.10.2.1 The entire slab width shall be assumedeffective for compression.

8.10.2.2 For integral bent caps, see Article 8.10.1.4.

8.11 SLAB AND WEB THICKNESS

8.11.1 The thickness of deck slabs shall be designed inaccordance with Article 3.24.3 but shall not be less thanspecified in Article 8.9.

8.11.2 The thickness of the bottom slab of a box girdershall be not less than %6 of the clear span between girder


webs or 5 % inches, except that the thickness need not begreater than the top slab unless required by design.

8.11.3 When required by design, changes in girder webthickness shall be tapered for a minimum distance of 12times the difference in web thickness.

8.12 DIAPHRAGMS

8.12.1 Diaphragms shall be used at the ends of T-girderand box girder spans unless other means are providedto resist lateral forces and to maintain section geometry.Diaphragms may be omitted where tests or structuralanalysis show adequate strength.

8.12.2 In T-girder construction, one intermediate di-aphragm is recommended at the point of maximum posi-tive moment for spans in excess of 40 feet.

8.12.3 Straight box girder bridges and curved box girderbridges with an inside radius of 800 feet or greater do notrequire intermediate diaphragms. For curved box girderbridges having an inside radius less than 800 feet, inter-mediate diaphragms are required unless shown otherwiseby tests or structural analysis. For such curved box gird-ers, a maximum diaphragm spacing of 40 feet is recom-mended to assist in resisting torsion.

8.13 COMPUTATION OF DEFLECTIONS

8.13.1 Computed deflections shall be based on thecross-sectional properties of the entire superstructure sec-tion excluding railings, curbs, sidewalks, or any elementnot placed monolithically with the superstructure sectionbefore falsework removal.

8.13.2 Live load deflection may be based on the as-sumption that the superstructure flexural members act to-gether and have equal deflection. The live loading shallconsist of all traffic lanes fully loaded, with reduction inload intensity allowed as specified in Article 3.12. The

live loading shall be considered uniformly distributed toall longitudinal flexural members.

8.13.3 Deflections that occur immediately on applica-tion of load shall be computed by the usual methods orformulas for elastic deflections. Unless stiffness valuesare obtained by a more comprehensive analysis, immedi-ate deflections shall be computed taking the modulus ofelasticity for concrete as specified in Article 8.7 for nor-mal weight or lightweight concrete and taking the mo-ment of inertia as either the gross moment of inertia, Ig, orthe effective moment of inertia, Ie as follows:

Ie =Ma )3

I g + 1–Ma

1" I g (8 -1)

where:

M ir = fri g/yl (8-2)

and f, = modulus of rupture of concrete specified in Arti-cle 8.15.2.1.1.

For continuous members, effective moment of inertiamay be taken as the average of the values obtained fromEquation (8-1) for the critical positive and negative mo-ment sections. For prismatic members, effective momentof inertia may be taken as the value obtained from Equa-tion (8-1) at midspan for simple or continuous spans, andas the value at the support for cantilevers.

8.13.4 Unless values are obtained by a more compre-hensive analysis, the long-time deflection for both normalweight and lightweight concrete flexural members shallbe the immediate deflection caused by the sustained loadconsidered, computed in accordance with Article 8.13.3,multiplied by one of the following factors:

(a) Where the immediate deflection has been based onIg, the multiplication factor for the long-rime deflectionshall be taken as 4.(b) Where the immediate deflection has been based onIe , the multiplication factor for the long-time deflectionshall be taken as 3 – 1.2(A,/AB ) >_ 1.6.

Part CDESIGN

8.14 GENERAL

8.14.1 Design Methods

8.14.1.1 The design of reinforced concrete membersshall be made either with reference to service loads and

allowable stresses as provided in SERVICE LOAD DE-SIGN or, alternatively, with reference to load factors andstrengths as provided in STRENGTH DESIGN.

8.14.1.2 All applicable provisions of this specifica-tion shall apply to both methods of design, except Articles

196 HIGHWAY BRIDGES 8.14.1.2

3.5 and 3.17 shall not apply for design by STRENGTHDESIGN.

8.14.1.3 The strength and serviceability require-ments of STRENGTH DESIGN may be assumed to besatisfied for design by SERVICE LOAD DESIGN if theservice load stresses are limited to the values given inArticle 8.15.2.

8.14.2 Composite Flexural Members

8.14.2.1 Composite flexural members consist of pre-cast and/or cast-in-place concrete elements constructed inseparate placements but so interconnected that all ele-ments respond to superimposed loads as a unit. When con-sidered in design, shoring shall not be removed until thesupported elements have developed the design propertiesrequired to support all loads and limit deflections andcracking.

8.14.2.2 The entire composite member or portionsthereof may be used in resisting the shear and moment.The individual elements shall be investigated for all criti-cal stages of loading and shall be designed to support allloads introduced prior to the full development of the de-sign strength of the composite member. Reinforcementshall be provided as necessary to prevent separation of theindividual elements.

8.14.2.3 If the specified strength, unit weight, orother properties of the various elements are different, theproperties of the individual elements, or the most criticalvalues, shall be used in design.

8.14.2.4 In calculating the flexural strength of a com-posite member by strength design, no distinction shall bemade between shored and unshored members.

8.14.2.5 When an entire member is assumed to resistthe vertical shear, the design shall be in accordance withthe requirements of Article 8.15.5 or Article 8.16.6 as fora monolithically cast member of the same cross-sectionalshape.

8.14.2.6 Shear reinforcement shall be fully anchoredinto the interconnected elements in accordance with Arti-cle 8.27. Extended and anchored shear reinforcement maybe included as ties for horizontal shear.

8.14.2.7 The design shall provide for full transfer ofhorizontal shear forces at contact surfaces of intercon-

nected elements. Design for horizontal shear shall be inaccordance with the requirements of Article 8.15.5.5 orArticle 8.16.6.5.

8.14.3 Concrete Arches

8.14.3.1 The combined flexure and axial loadstrength of an arch ring shall be in accordance with theprovisions of Articles 8.16.4 and 8.16.5. Slenderness ef-fects in the vertical plane of an arch ring, other than tiedarches with suspended roadway, may be evaluated by theapproximate procedure of Article 8.16.5.2 with the un-supported length, fu, taken as one-half the length of thearch ring, and the radius of gyration, r, taken about an axisperpendicular to the plane of the arch at the quarter pointof the arch span. Values of the effective length factor, k,given in Table 8. 14.3 may be used. In Equation (8-41), C,,,shall be taken as 1.0 and (~ shall be taken as 0.85.

8.14.3.2 Slenderness effects between points of lateralsupport and between suspenders in the vertical plane of atied arch with suspended roadway, shall be evaluated by arational analysis taking into account the requirements ofArticle 8.16.5.1.1.

8.14.3.3 The shape of arch rings shall conform, asnearly as is practicable, to the equilibrium polygon for fulldead load.

8.14.3.4 In arch ribs and barrels, the longitudinal re-inforcement shall provide a ratio of reinforcement area togross concrete area at least equal to 0.01, divided equallybetween the intrados and the extrados. The longitudinalreinforcement shall be enclosed by lateral ties in accor-dance with Article 8.18.2. In arch barrels, upper and lowerlevels of transverse reinforcement shall be provided thatare designed for transverse bending due to loads fromcolumns and spandrel walls and for shrinkage and tem-perature stresses.

8.14.3.5 If transverse expansion joints are not pro-vided in the deck slab, the effects of the combined actionof the arch rib, columns and deck slab shall be considered.Expansion joints shall be provided in spandrel walls.

TABLE 8.14.3 Effective Length Factors, k

Rise-to-Span 3-Hinged 2-Hinged FixedRatio Arch Arch Arch

0.1—0.2 1.16 1.04 0.700.2—0.3 1.13 1.10 0.700.3—0.4 1.16 1.16 0.72

8.14.3.6 DIVISION I—DESIGN 197

8.14.3.6 Walls exceeding 8 feet in height on filledspandrel arches shall be laterally supported by transversediaphragms or counterforts with a slope greater than 45degrees with the vertical to reduce transverse stresses inthe arch barrel. The top of the arch barrel and interiorfaces of the spandrel walls shall be waterproofed and adrainage system provided for the fill.

8.15 SERVICE LOAD DESIGN METHOD(ALLOWABLE STRESS DESIGN)

8.15.1 General Requirements

8.15.1.1 Service load stresses shall not exceed thevalues given in Article 8.15.2.

8.15.1.2 Development and splices of reinforcementshall be as required in Articles 8.24 through 8.32.

8.15.2 Allowable Stresses

8.15.2.1 Concrete

Stresses in concrete shall not exceed the following:

8.15.2.1.1 Flexure

Extreme fiber stress in compression, f ................0.40f,'Extreme fiber stress in tension for plainconcrete, ft........................................................... 0.21f,

Modulus of rupture, f,, from tests, or, if data are notavailable:

Normal weight concrete ..................................7.5"Sand-lightweight" concrete........................... 6.3"All-lightweight" concrete ..............................5.5

8.15.2.1.2 Shear

For detailed summary of allowable shear stress, v., seeArticle 8.15.5.2.

8.15.2.1.3 Bearing Stress

The bearing stress, fb , on loaded area shall not exceed0.30 f,.

When the supporting surface is wider on all sidesthan the loaded area, the allowable bearing stress on theloaded area may be multiplied by AZ/A 1 , but not bymore than 2.

When the supporting surface is sloped or stepped, A 2

may be taken as the area of the lower base of the largestfrustrum of the right pyramid or cone contained wholly

within the support and having for its upper base the loadedarea, and having side slopes of I vertical to 2 horizontal.

When the loaded area is subjected to high-edge stressesdue to deflection or eccentric loading, the allowable bear-ing stress on the loaded area, including any increase dueto the supporting surface being larger than the loaded area,shall be multiplied by a factor of 0.75.

8.15.2.2 Reinforcement

The tensile stress in the reinforcement, fs , shall not ex-ceed the following:

Grade 40 reinforcement ...............................20,000 psiGrade 60 reinforcement ...............................24,000 psi

In straight reinforcement, the range between the max-imum tensile stress and the minimum stress caused by liveload plus impact shall not exceed the value given in Arti-cle 8.16.8.3. Bends in primary reinforcement shall beavoided in regions of high-stress range.

8.15.3 Flexure

8.15.3.1 For the investigation of stresses at serviceloads, the straight-line theory of stress and strain in flex-ure shall be used with the following assumptions.

8.15.3.2 The strain in reinforcement and concrete isdirectly proportional to the distance from the neutral axis,except that for deep flexural members with overall depthto span ratios greater than 2/5 for continuous spans and '/5

for simple spans, a nonlinear distribution of strain shall beconsidered.

8.15.3.3 In reinforced concrete members, concreteresists no tension.

8.15.3.4 The modular ratio, n = E,/E,, may be takenas the nearest whole number (but not less than 6). Exceptin calculations for deflections, the value of n for light-weight concrete shall be assumed to be the same as fornormal weight concrete of the same strength.

8.15.3.5 In doubly reinforced flexural members, aneffective modular ratio of 2E s/Ec shall be used to trans-form the compression reinforcement for stress computa-tions. The compressive stress in such reinforcement shallnot be greater than the allowable tensile stress.

8.15.4 Compression Members

The combined flexural and axial load capacity of com-pression members shall be taken as 35% of that computed


in accordance with the provisions of Article 8.16.4. Slen-derness effects shall be included according to the require-ments of Article 8.16.5. The term P„ in Equation (8-41)shall be replaced by 2.5 times the design axial load. Inusing the provisions of Articles 8.16.4 and 8.16.5, (~ shallbe taken as 1.0.

8.15.5 Shear

8.15.5.1 Shear Stress

8.15.5.1.1 Design shear stress, v, shall be computedby:

V=V

d (8-3)b

w

taken as 0.95 V'. A more detailed calculation of the al-lowable shear stress can be made using:

ve = 0.9 f~ +1,100Pw( 1VV~Id~ 51.6 fc

(8-4)

Note:

(a) M is the design moment occurring simultaneouslywith V at the section being considered.(b) The quantity Vd/M shall not be taken greater than1.0.

8.15.5.2.2 Shear in Compression Members

For members subject to axial compression, the allow-able shear stress carried by the concrete, v,, may be takenas 0.95 V"f—,'. A more detailed calculation can be made

where V is design shear force at section considered, b W is using:

the width of web, and d is the distance from the extreme r 1compression fiber to the centroid of the longitudinal ten- ve = 0.9! 1 + 0.0006A I f

c (8-5)sion reinforcement. Whenever applicable, effects of tor- ` g Jsion* shall be included.

The quantity N/Ag shall be expressed in pounds per square8.15.5.1.2 For a circular section, b w shall be the di- inch.

ameter and d need not be less than the distance from theextreme compression fiber to the centroid of the longitu- 8.15.5.2.3 Shear in Tension Membersdinal reinforcement in the opposite half of the member.

8.15.5.1.3 For tapered webs, bK, shall be the averagewidth or 1.2 times the minimum width, whichever issmaller.

8.15.5.1.4 When the reaction, in the direction of theapplied shear, introduces compression into the end re-gions of a member, sections located less than a distance dfrom the face of support may be designed for the sameshear, V, as that computed at a distance d. An exceptionoccurs when major concentrated loads are imposed be-tween that point and the face of support. In that case sec-tions closer than d to the support shall be designed for Vat distance d plus the major concentrated loads.

8.15.5.2 Shear Stress Carried by Concrete

8.15.5.2.1 Shear in Beams and One-Way Slabs andFootings

For members subject to shear and flexure only, the al-lowable shear stress carried by the concrete, v,, may be

*The design criteria for combined torsion and shear given in "Building Code Re-

quirements for Reinforced Concrete"—American Concrete Institute 318 Bulletinmay be used.

For members subject to axial tension, shear reinforce-ment shall be designed to carry total shear, unless a moredetailed calculation is made using

v e =0.9 1+ 0.004A

f7 (8-6)g

Note:

(a) N is negative for tension.(b) The quantity N/A g shall be expressed in poundsper square inch.

8.15.5.2.4 Shear in Lightweight Concrete

The provisions for shear stress, vc , carried by the con-crete apply to normal weight concrete. When lightweightaggregate concretes are used, one of the following modi-fications shall apply:

(a) When fit is specified, the shear stress, v ,., shall bemodified by substituting f t/6.7 for 'Vf—,', but the valueof fit/6.7 used shall not exceed V 117

.

(b) When fit is not specified, the shear stress, v c , shall bemultiplied by 0.75 for "all-lightweight" concrete, and

8.15.5.2.4 DIVISION I—DESIGN 199

0.85 for "sand-lightweight" concrete. Linear interpola-tion may be used when partial sand replacement is used.

8.15.5.3 Shear Stress Carried by ShearReinforcement

8.15.5.3.1 Where design shear stress v exceeds shearstress carried by concrete, v,, shear reinforcement shallbe provided in accordance with this article. Shear rein-forcement shall also conform to the general requirementsof Article 8.19.

8.15.5.3.2 When shear reinforcement perpendicularto the axis of the member is used:

A =(v–vc)b,s

(8-7)fs

8.15.5.3.3 When inclined stirrups are used:

A =(v – v,)b,s

(8-8)fs (sin a + cos (x)

8.15.5.3.4 When shear reinforcement consists of asingle bar or a single group of parallel bars all bent up atthe same distance from the support:

A =(v–v,)bwd

(8-9)fs sin a

where (v–v.) shall not exceed 1.5 V 7f l.

8.15.5.3.5 When shear reinforcement consists of aseries of parallel bent-up bars or groups of parallel bent-up bars at different distances from the support, the re-quired area shall be computed by Equation (8-8).

8.15.5.3.6 Only the center three-fourths of the in-clined portion of any longitudinal bent bar shall be con-sidered effective for shear reinforcement.

8.15.5.3.7 Where more than one type of shear rein-forcement is used to reinforce the same portion of themember, the required area shall be computed as the sumof the values computed for the various types separately. Insuch computations, vc shall be included only once.

8.15.5.3.8 When (v – vj exceeds 2 T' the maxi-mum spacings given in Article 8.19 shall be reduced byone-half.

8.15.5.3.9 The value of (v – v j shall not exceed4 T,'.

8.15.5.3.10 When flexural reinforcement locatedwithin the width of a member used to compute the shearstrength is terminated in a tension zone, shear reinforce-ment shall be provided in accordance with Article 8.24.1.4.

8.15.5.4 Shear Friction

8.15.5.4.1 Provisions for shear-friction are to be ap-plied where it is appropriate to consider shear transferacross a given plane, such as: an existing or potentialcrack, an interface between dissimilar materials, or an in-terface between two concretes cast at different times.

8.15.5.4.2 A crack shall be assumed to occur alongthe shear plane considered. Required area of shear-fric-tion reinforcement Aq across the shear plane may be de-signed using either Article 8.15.5.4.3 or any other sheartransfer design method that results in prediction ofstrength in substantial agreement with results of com-prehensive tests. Provisions of Articles 8.15.5.4.4through 8.15.5.4.8 shall apply for all calculations ofshear transfer strength.

8.15.5.4.3 Shear friction Design Method

(a) When shear-friction reinforcement is perpendicu-lar to the shear plane, area of shear-friction reinforce-ment Avf shall be computed by:

A, f = V (8-10)fsµ

where µ is the coefficient of friction, in accordance withArticle 8.15.5.4.3(c).(b) When shear-friction reinforcement is inclined tothe shear plane such that the shear force produces ten-sion in shear-friction reinforcement, the area of shear-friction reinforcement A f shall be computed by:

V

A°f _(8-11)

fj Lsina f +cos(x f )

where ofis the angle between the shear-friction rein-

forcement and the shear plane.(c) Coefficient of friction p in Equations (8-10) and(8-11) shall be:

concrete placed monolithically.........................1 AXconcrete placed against hardened concrete withsurface intentionally roughened as specified inArticle 8.15.5.4.7 ..............................................LOX

200 HIGHWAY BRIDGES 8.15.5.4.3

concrete placed against hardened concrete notintentionally roughened....................................0.6Aconcrete anchored to as-rolled structural steel byheaded studs or by reinforcing bars (see Article8.15.5.4.8..........................................................0.7k

where X = 1.0 for normal weight concrete; 0.85 for"sand-lightweight" concrete; and 0.75 for "all light-weight" concrete. Linear interpolation may be appliedwhen partial sand replacement is used.

8.15.5.4.4 Shear stress v shall not exceed 0.09f,' nor360 psi.

8.15.5.4.5 Net tension across the shear plane shall beresisted by additional reinforcement. Permanent net com-pression across the shear plane may be taken as additiveto the force in the shear-friction reinforcement A„ ff,, whencalculating required A,,f.

8.15.5.4.6 Shear-friction reinforcement shall be ap-propriately placed along the shear plane and shall be an-chored to develop the specified yield strength on bothsides by embedment, hooks, or welding to special devices.

8.15.5.4.7 For the purpose of Article 8.15.5.4, whenconcrete is placed against previously hardened concrete,the interface for shear transfer shall be clean and free oflaitance. If µ is assumed equal to LOX, the interface shallbe roughened to a full amplitude of approximately %4 inch.

8.15.5.4.8 When shear is transferred between steelbeams or girders and concrete using headed studs orwelded reinforcing bars, steel shall be clean and free ofpaint.

8.15.5.5 Horizontal Shear Design for CompositeConcrete Flexural Members

8.15.5.5.1 In a composite member, full transfer ofhorizontal shear forces shall be assured at contact surfacesof interconnected elements.

8.15.5.5.2 Design of cross sections subject to hori-zontal shear may be in accordance with provisions ofArticles 8.15.5.5.3 or 8.15.5.5.4 or any other sheartransfer design method that results in prediction ofstrength in substantial agreement with results of compre-hensive tests.

8.15.5.5.3 Design horizontal shear stress Vdh at anycross section may be computed by:

Vvdt, _ b ,d

(8-11A)

where V is the design shear force at the section consideredand d is for the entire composite section. Horizontal shearv

dh shall not exceed permissible horizontal shear v h in ac-cordance with the following:

(a) When the contact surface is clean, free of laitance,and intentionally roughened, shear stress V h shall notexceed 36 psi.(b) When minimum ties are provided in accordancewith Article 8.15.5.5.5, and the contact surface is cleanand free of laitance, but not intentionally roughened,shear stress vh shall not exceed 36 psi.(c) When minimum ties are provided in accordancewith Article 8.15.5.5.5, and the contact surface is clean,free of laitance, and intentionally roughened to a fullmagnitude of approximately %4 inch, shear stress vh

shall not exceed 160 psi.(d) For each percent of tie reinforcement crossing thecontact surface in excess of the minimum requiredby Article 8.15.5.5.5, permissible v,, may be increasedby 72f;,/40,000 psi.

8.15.5.5.4 Horizontal shear may be investigated bycomputing, in any segment not exceeding one-tenth of thespan, the actual change in compressive or tensile force tobe transferred, and provisions made to transfer that forceas horizontal shear between interconnected elements.Horizontal shear shall not exceed the permissible hori-zontal shear stress vh in accordance with Article8.15.5.5.3.

8.15.5.5.5 Ties for Horizontal Shear

(a) When required, a minimum area of tie reinforce-ment shall be provided between interconnected ele-ments. Tie area shall not be less than 50b„ s/fy, and tiespacing s shall not exceed four times the least webwidth of support element, nor 24 inch.(b) Ties for horizontal shear may consist of single barsor wire, multiple leg stirrups, or vertical legs of weldedwire fabric (smooth or deformed). All ties shall be ad-equately anchored into interconnected elements byembedment or hooks.

8.15.5.6 Special Provisions for Slabs andFootings

8.15.5. 61 Shear capacity of slabs and footings in thevicinity of concentrated loads or reactions shall be gov-erned by the more severe of two conditions:


(a) Beam action for the slab or footing, with a criticalsection extending in a plane across the entire width andlocated at a distance d from the face of the concentratedload or reaction area. For this condition, the slab orfooting shall be designed in accordance with Articles8.15.5.1 through 8.15.5.3, except at footings supportedon piles, the shear on the critical section shall be de-termined in accordance with Article 4.4.11.3.(b) Two-way action for the slab or footing, with a crit-ical section perpendicular to the plane of the memberand located so that its perimeter b o is a minimum, butnot closer than d/2 to the perimeter of the concentratedload or reaction area. For this condition, the slab orfooting shall be designed in accordance with Articles8.15.5.6.2 and 8.15.5.6.3.

8.15.5.6.2 Design shear stress, v, shall be computed by:

v= b (8-12)0

where V and bo shall be taken at the critical section de-fined in Article 9.15.5.6.1(b).

8.15.5.63 Design shear stress, v, shall not exceed v,given by Equation (8-13) unless shear reinforcement isprovided in accordance with Article 8.15.5.6.4.

v c _ (0.8 + R)

j- f, 51.8 f~ (8-13)e

P, is the ratio of long side to short side of concentratedload or reaction area.

8.15.5.6.4 Shear reinforcement consisting of bars orwires may be used in slabs and footings in accordancewith the following provisions:

(a) Shear stresses computed by Equation (8-12) shallbe investigated at the critical section defined in Article8.15.5.6.1(b) and at successive sections more distantfrom the support.(b) Shear stress v c at any section shall not exceed 0.9

fC and v shall not exceed 3 -VIT-c'.

(c) Where v exceeds 0.9 N/—fc' , shear reinforcement

shall be provided in accordance with Article 8.15.5.3.

8.15.5.7 Special Provisions for Slabs of BoxCulverts

For slabs of box culverts under 2 feet or more fill, shearstress v, may be computed by:

v c = IV- Vd)+ 2, 200p( M (9-14)

but v, shall not exceed 1.8 f, . For single cell box culvertsonly, v, for slabs monolithic with walls need not be takenless than 1.4 f, , and v, for slabs simply supported neednot be taken less than 1.2 f,' . The quantity Vd/M shall notbe taken greater than 1.0 where M is the moment occurringsimultaneously with V at the section considered. For slabsof box culverts under less than 2 feet of fill, applicable pro-visions of Articles 3.24 and 6.4 should be used.

8.15.5.8 Special Provisions for Brackets andCorbels*

8.15.5.8.1 Provisions of Article 8.15.5.8 shall applyto brackets and corbels with a shear span-to-depth ratioa„/d not greater than unity, and subject to a horizontal ten-sile force N, not larger than V. Distance d shall be mea-sured at the face of support.

8.15.5.8.2 Depth at outside edge of bearing area shallnot be less than 0.5d.

8.15.5.8.3 The section at the face of support shall bedesigned to resist simultaneously a shear V, a moment[Va,, + N, (h — d)], and a horizontal tensile force N~. Dis-tance h shall be measured at the face of support.

(a) Design of shear-friction reinforcement, A„ f, to re-sist shear, V, shall be in accordance with Article8.15.5.4. For normal weight concrete, shear stress vshall not exceed 0.09fc' nor 360 psi. For "all light-weight" or "sand-lightweight" concrete, shear stress vshall not exceed (0.09—0.03av/d)f, nor (360—126av/d)psi.(b) Reinforcement A f to resist moment [Va„ + N,(h —d)] shall be computed in accordance with Articles8.15.2 and 8.15.3.(c) Reinforcement A. to resist tensile force N c shall becomputed by An = N,/fs . Tensile force N, shall not betaken less than 0.2V unless special provisions are madeto avoid tensile forces.(d) Area of primary tension reinforcement, A,, shall bemade equal to the greater of (A f+An), or (2A,,f/3+An).

8.15.5.8.4 Closed stirrups or ties parallel to A,, witha total area Ah not less than 0.5(A,—An), shall be uni-

*These provisions do not apply to beam ledges. The PCA publication,"Notes on ACI 318—83," contains an example design of beam ledges—Part 16, example 16-3.


Framing bar to anchor Jstirrups or ties

FIGURE 8.15.5.8

Ah (closedstirrups or ties)

A, (primaryreinforcement)

formly distributed within two-thirds of the effective depthadjacent to A 5 .

8.15.5.8.5 Ratio p = A,/bd shall not be taken lessthan 0.04(f,'/fy).

8.15.5.8.6 At the front face of a bracket or corbel,primary tension reinforcement, A5 , shall be anchored byone of the following:

(a) a structural weld to a transverse bar of at leastequal size; weld to be designed to develop specifiedyield strength fy of A, bars;(b) bending primary tension bars A, back to form ahorizontal loop; or(c) some other means of positive anchorage.

8.15.5.8.7 Bearing area of load on a bracket or cor-bel shall not project beyond the straight portion of primarytension bars As, nor project beyond the interior face of atransverse anchor bar (if one is provided).

8.16 STRENGTH DESIGN METHOD(LOAD FACTOR DESIGN)

8.16.1 Strength Requirements

8.16.1.1 Required Strength

The required strength of a section is the strength nec-essary to resist the factored loads and forces applied to

the structure in the combinations stipulated in Article3.22. All sections of structures and structural membersshall have design strengths at least equal to the requiredstrength.

8.16.1.2 Design Strength

8.16.1.2.1 The design strength provided by a mem-ber or cross section in terms of load, moment, shear, orstress shall be the nominal strength calculated in accor-dance with the requirements and assumptions of thestrength-design method, multiplied by a strength-reduc-tion factor (~.*

8.16.1.2.2 The strength-reduction factors, 4, shall beas follows:

(a) Flexure................................................... = 0.90(b) Shear.......................................................~ = 0.85(c) Axial compression with

Spirals .................................................... = 0.75Ties..........................................................~ = 0.70

(d) Bearing on concrete............................... = 0.70

The value of 4may be increased linearly from the

value for compression members to the value for flexure asthe design axial load strength, ~)P,,, decreases from 0.1Of,Ag or (~Pb, whichever is smaller, to zero.

8.16.1.2.3 The development and splice lengths of re-inforcement specified in Articles 8.24 through 8.32 do notrequire a strength-reduction factor.

8.16.2 Design Assumptions

8.16.2.1 The strength design of members for flexureand axial loads shall be based on the assumptions given inthis article, and on the satisfaction of the applicable con-ditions of equilibrium of internal stresses and compatibil-ity of strains.

8.16.2.2 The strain in reinforcement and concrete isdirectly proportional to the distance from the neutral axis.

8.16.2.3 The maximum usable strain at the extremeconcrete compression fiber is equal to 0.003.

*The coefficient (~ provides for the possibility that small adverse vari-ations in material strengths, workmanship, and dimensions, while indi-vidually within acceptable tolerances and limits of good practice, maycombine to result in understrength.


8.16.2.4 The stress in reinforcement below its speci-fied yield strength, f y , shall be ES times the steel strain. Forstrains greater than that corresponding to fy, the stress inthe reinforcement shall be considered independent ofstrain and equal to fy .

8.16.2.5 The tensile strength of the concrete is ne-glected in flexural calculations.

8.16.2.6 The concrete compressive stress/strain dis-tribution may be assumed to be a rectangle, trapezoid,parabola, or any other shape that results in prediction ofstrength in substantial agreement with the results of com-prehensive tests.

8.16.2.7 A compressive stress/strain distribution,which assumes a concrete stress of 0.85 f.' uniformly dis-tributed over an equivalent compression zone bounded bythe edges of the cross section and a line parallel to the neu-tral axis at a distance a = (3 1 c from the fiber of maximumcompressive strain, may be considered to satisfy the re-quirements of Article 8.16.2.6. The distance c from thefiber of maximum strain to the neutral axis shall be mea-sured in a direction perpendicular to that axis. The factorRt shall be taken as 0.85 for concrete strengths, f,', up toand including 4,000 psi. For strengths above 4,000 psi, R1shall be reduced continuously at a rate of 0.05 for each1,000 psi of strength in excess of 4,000 psi but

Ri shall notbe taken less than 0.65.

8.16.3 Flexure

8.16.3.1 Maximum Reinforcement of FlexuralMembers

8.163.1.1 The ratio of reinforcement p providedshall not exceed 0.75 of the ratio

Pb that would producebalanced strain conditions for the section. The portion ofPb balanced by compression reinforcement need not be re-duced by the 0.75 factor.

8.163.1.2 Balanced strain conditions exist at acrosssection when the tension reinforcement reaches the straincorresponding to its specified yield strength, fy , just as theconcrete in compression reaches its assumed ultimatestrain of 0.003.

8.16.3.2 Rectangular Sections with TensionReinforcement Only

8.163.2.1 The design moment strength, (~Mn, maybe computed by:

W„ _ 0 l A sfy d~1— 0.6 Pfy )] (8-15)

_ [Asfy Cd 2 J](8-16)

where,

a = Asfy (8-17)0.85 f,b

8.16.3.2.2 The balanced reinforcement ratio, Pb, isgiven by:

_ 0.85 P lfl 87,000 y (8-18Pbfy ~ 87,000+f

8.16.3.3 Flanged Sections with TensionReinforcement Only

8.163.3.1 When the compression flange thickness isequal to or greater than the depth of the equivalent rec-tangular stress block, a, the design moment strength, (~M n,may be computed by Equations (8-15) and (8-16).

8.16.3.3.2 When the compression flange thickness isless than a, the design moment strength may be computedby:

(~M„ = (~L(As —Asf)fy (d—a/2)+ A sffy (d—0.5h f)] (8-19)

where,

Asf =0.85f,' (b—bµ,)hf

(8-20)fy

a (AS—Asf)fy

(8-21)0.85f,'bw

8.16.3.3.3 The balanced reinforcement ratio,Pb,

isgiven by:

Pb = Ib)[~0.85P,f,'1( 87,000 1

+pfJ

(8-22)l fy /

II\ 87,000+fy J

where,

Pf i (8-23)b w d


8.16.3.3.4 For T-girder and box-girder construction, stress and strain compatibility using assumptions given inthe width of the compression face, b, shall be equal to the Article 8.16.2. The requirements of Article 8.16.3.1 shalleffective slab width as defined in Article 8.10. also be satisfied.

8.16.3.4 Rectangular Sections with CompressionReinforcement

8.163.4.1 The design moment strength, (~Mn, maybe computed as follows:

If ( As—As 0.85(31(fd )(87,000

)bd fy d 87, 000 – fy

(8-24)

then,

(~ M n = ~[(A

s — As)fy(d — a/2) + Asfy (d — d ' )](8-25)

where,

(As —A' )fYa = (8-26)0.85f,b

8.16.3.4.2 When the value of (A s — A,)/bd is lessthan the value required by Equation (8-24), so that thestress in the compression reinforcement is less than theyield strength, fy , or when effects of compression rein-forcement is less than the yield strength, fy , or when ef-fects of compression reinforcement are neglected, the de-sign moment strength may be computed by the equationsin Article 8.16.3.2. Alternatively, a general analysis maybe made based on stress and strain compatibility using theassumptions given in Article 8.16.2.

8.16.3.4.3 The balanced reinforcement ratio Pb forrectangular sections with compression reinforcement isgiven by:

Pb = C 0.85R1

fc

87,0000 of )]+P,(s')

f(8-27)

Y Y Y

where,

fs = 87, 0001–(d

')(8787,000

00fy

]:!~fy(8-28)

8.16.3.5 Other Cross Sections

For other cross sections the design moment strength,(~Mn, shall be computed by a general analysis based on


8.16.4.1 General Requirements

8.16.4.1.1 The design of members subject to axialload or to combined flexure and axial load shall be basedon stress and strain compatibility using the assumptionsgiven in Article 8.16.2. Slenderness effects shall be in-cluded according to the requirements of Article 8.16.5.

8.16.4.1.2 Members subject to compressive axialload combined with bending shall be designed for themaximum moment that can accompany the axial load.The factored axial load, Pa, at a given eccentricity shallnot exceed the design axial load strength (~ P

n(max) where:

(a) For members with spiral reinforcement conform-ing to Article 8.18.2.2

Pn~.ax) = 0.85[0.85 fc' (A g —Ast)+fyAsJ (8-29)

(~ = 0.75(b) For members with tie reinforcement conforming toArticle 8.18.2.3

Po(m,x) = 0.80[0.85 f,' (Ag —A, t)+fyA st] (8-30)(~ = 0.70

The maximum factored moment, Mu, shall be magnifiedfor slenderness effects in accordance with Article 8.16.5.

8.16.4.2 Compression Member Strengths

The following provisions may be used as a guide to de-fine the range of the load-moment interaction relationshipfor members subjected to combined flexure and axialload.

8.16.4.2.1 Pure Compression

The design axial load strength at zero eccentricity, (~P n ,may be computed by:

(~Po = (~[0.85f,' (A g — A s p) + A stfy] (8-31)

For design, pure compressive strength is a hypotheticalcondition since Article 8.16.4.1.2 limits the axial loadstrength of compression members to 85 and 80% of theaxial load at zero eccentricity.


8.16.4.2.2 Pure Flexure when the factored axial load,

The assumptions given in Article 8.16.2 or the applic - Pu _ 0.1 f, Ag (8-37)able equations for flexure given in Article 8.16.3 may beused to compute the design moment strength, Wn, in or,pure flexure.

8.16.4.2.3 Balanced Strain Conditions

Balanced strain conditions for a cross section are de-fined in Article 8.16.3.1.2. For a rectangular section withreinforcement in one face, or located in two faces at ap-proximately the same distance from the axis of bending,the balanced load strength, (~ P

b, and balanced momentstrength, Wb, may be computed by:

Ob = 4[0.85fc bab + A,f,' – A,fy] (8-32)

and,

Wb = (~[0.85f,'bab (d – d" – ab/2)+ A,f,(d – d' – d " ) + A,fyd" ]

(8-33)

where,

abC

87,000Rd (8-34)

e 87,000+fyPI

and,

f,' = 87, 000 1– l y < fy (8-35)C

d

d

'

J

87,

87,

000+

000

f

8.16.4.2.4 Combined Flexure and Axial Load

The strength of a cross section is controlled by tensionwhen the nominal axial load strength, P n, is less than thebalanced load strength, P b , and is controlled by compres-sion when P„ is greater than Pb .

The nominal values of axial load strength, P,,, and mo-ment strength, M n, must be multiplied by the strength re-duction factor, (~, for axial compression as given in Arti-cle 8.16.1.2.

8.16.4.3 Biaxial Loading

In lieu of a general section analysis based on stress andstrain compatibility, the design strength of noncircularmembers subjected to biaxial bending may be computedby the following approximate expressions:

1 _ 1 1 1(8-36)

Pnxy Pnx Pny

P.

Max + M ° y <<< 1 (8-38)Wnx Wny

when the factored axial load,

Pu < 0.1 f,' Ag (8-39)

8.16.4.4 Hollow Rectangular CompressionMembers

8.16.4.4.1 The wall slenderness ratio of a hollowrectangular cross section, Xu/t, is defined in Figure8.16.4.4.1. Wall slenderness ratios greater than 35.0 arenot permitted, unless specific analytical and experimentalevidence is provided justifying such values.

8.16.4.4.2 The equivalent rectangular stress blockmethod shall not be employed in the design of hollow rec-tangular compression members with a wall slendernessratio of 15 or greater.

8.16.4.4.3 If the wall slenderness ratio is less than 15,then the maximum usable strain at the extreme concretecompression fiber is equal to 0.003. If the wall slendernessratio is 15 or greater, then the maximum usable strain atthe extreme concrete compression fiber is equal to thecomputed local buckling strain of the widest flange of thecross section, or 0.003, whichever is less.

8.16.4.4.4 The local buckling strain of the widestflange of the cross section may be computed assumingsimply supported boundary conditions on all four edgesof the flange. Nonlinear material behavior shall be con-sidered by incorporating the tangent material moduli ofthe concrete and reinforcing steel in computations of thelocal buckling strain.

8.16.4.4.5 In lieu of the provisions of Articles8.16.4.4.2, 8.16.4.4.3 and 8.16.4.4.4, the following ap-proximate method may be used to account for the strengthreduction due to wall slenderness. The maximum usablestrain at the extreme concrete compression fiber shall betaken as 0.003 for all wall slenderness ratios up to and in-cluding 35.0. A strength reduction factor `)w shall be ap-plied in addition to the usual strength reduction factor, (~,in Article 8.16.1.2. The strength reduction factor Ì w shallbe taken as 1.0 for all wall slenderness ratios up to andincluding 15.0. For wall slenderness ratios greater than


X„ X, + 0 - l/auer of ?r or 2y1

ryPADOi M&WIlAk Plor Sullen TYPICOSOPW10PIN SOCfkn

rNON S/wvnau Rock + X

FIGURE 8.16.4.4.1 Definition of Wall Slenderness Ratio

15.0 and less than or equal to 25.0, the strength reductionfactor

~wshall be reduced continuously at a rate of 0.025

for every unit increase in the wall slenderness ratio above15.0. For wall slenderness ratios greater than 25.0 and lessthan or equal to 35.0, the strength reduction factor (~ W shallbe taken as 0.75.

8.16.4.4.6 Discontinuous, non-post-tensioned rein-forcement in segmentally constructed hollow rectangularcompression members shall be neglected in computationsof member strength.

8.16.5 Slenderness Effects in CompressionMembers


8.16.5.1.1 The design of compression members shallbe based on forces and moments determined from ananalysis of the structure. Such an analysis shall includethe influence of axial loads and variable moment of iner-tia on member stiffness and fixed-end moments, the effectof deflections on the moments and forces, and the effectof the duration of the loads.

8.16.5.1.2 In lieu of the procedure described in Arti-cle 8.16.5.1.1, slenderness effects of compression mem-bers may be evaluated in accordance with the approxi-mate procedure in Article 8.16.5.2.

8.16.5.2 Approximate Evaluation of SlendernessEffects

8.165.2.1 The unsupported length, fu , of a compres-sion member shall be the clear distance between slabs,girders, or other members capable of providing lateral

support for the compression member. Where haunches arepresent, the unsupported length shall be measured to thelower extremity of the haunch in the plane considered.

8.16.5.2.2 The radius of gyration, r, may be assumedequal to 0.30 times the overall dimension in the directionin which stability is being considered for rectangular com-pression members, and 0.25 times the diameter for circu-lar compression members. For other shapes, r may becomputed for the gross concrete section.

8.165.2.3 For compression members braced againstsidesway, the effective length factor, k, shall be taken as 1.0,unless an analysis shows that a lower value may be used. Forcompression members not braced against sidesway, k shallbe determined with due consideration of cracking and rein-forcement on relative stiffness and shall be greater than 1.0.

8.165.2.4 For compression members braced againstsidesway, the effects of slenderness may be neglectedwhen kf u/r is less than 34—(12M, b/Mzb).

8.16.5.2.5 For compression members not bracedagainst sidesway, the effects of slenderness may be ne-glected when kf u /r is less than 22.

8.16.5.2.6 For all compression members where kfu/ris greater than 100, an analysis as defined in Article8.16.5.1 shall be made.

8.16.5.2.7 Compression members shall be designedusing the factored axial load Pu , derived from a conven-tional elastic analysis and a magnified factored moment,M,, defined by

K = Wlb + 8 ,Mzs (8-40)


S6=CP

>_1.0 (8-41)P.OPT

Ss=Y,Pu

>_1.0 (8-41A)1—

01 P,

P_n 2 EI

~(k~u

)z (8-42)

For members braced against sidesway, 8, shall be taken as1.0. For members not braced against sidesway, 8 b shall beevaluated as for a braced member and 8, for an unbracedmember.

In lieu of a more precise calculation, EI may be takeneither as

EJ9+EJ,

El=- 51+(3 d

(8-43)- 43)d

or conservatively as

E,1 9

EI= 2.5 (8-44)1+(3 d

where Rd is the ratio of maximum dead load moment tomaximum total load moment and is always positive. Formembers braced against sidesway and without transverseloads between supports, C m may be taken as

Cm = 0.6 + 0.4 (M, b//M 2b ) (8-45)

but not less than 0.4.For all other cases, C m shall be taken as 1.0.

8.16.5.2.8 If computations show that there is no mo-ment at either end of a compression member braced or un-braced against sidesway or that computed end eccentrici-ties are less than (0.6 + 0.03h) inches, M2b and

M25 inEquation (8-40) shall be based on a minimum eccentric-ity of (0.6 + 0.03h) inches about each principal axis sep-arately. The ratio

Mlb/M2b in Equation (8-45) shall be de-termined by either of the following:

(a) When the computed end eccentricities are less than(0.6 + 0.03h) inches, the computed end moments maybe used to evaluate Mlb/M2b

in Equation (8-45).(b) If computations show that there is essentially nomoment at either end of the member, the ratio Mlb/M2b

shall be equal to one.

8.16.5.2.9 In structures that are not braced againstsidesway, the flexural members framing into the com-pression member shall be designed for the total magnifiedend moments of the compression member at the joint.

8.16.5.2.10 When compression members are subjectto bending about both principal axes, the moment abouteach axis shall be magnified by 6, computed from the cor-responding conditions of restraint about that axis.

8.16.5.2.11 When a group of compression memberson one level comprise a bent, or when they are connectedintegrally to the same superstructure, and collectively re-sist the sidesway of the structure, the value of 8, shall becomputed for the member group with Y.P. and IP, equalto the summations for all columns in the group.

8.16.6 Shear

8.16.6.1 Shear Strength

8.16.6.1.1 Design of cross sections subject to shearshall be based on

V. < 0. (8-46)

where V„ is the factored shear force at the section consid-ered and V„ is the nominal shear strength computed by,

Vn = V, + V, (8-47)

where V, is the nominal shear strength provided by theconcrete in accordance with Article 8.16.6.2, and V, is thenominal shear strength provided by the shear reinforce-ment in accordance with Article 8.16.6.3. Whenever ap-plicable, effects of torsion* shall be included.

8.16.6 1.2 When the reaction, in the direction of ap-plied shear, introduces compression into the end regionsof a member, sections located less than a distance d fromthe face of support may be designed for the same shear,Vu , as that computed at a distance d. An exception occurswhen major concentrated loads are imposed between thatpoint and the face of support. In that case, sections closer

*The design criteria for combined torsion and shear given in `Build-ing Code Requirements for Reinforced Concrete" ACI 318 may be used.

where

and


than d to the support shall be designed for V at a distanced plus the major concentrated loads.

8.16.6.2 Shear Strength Provided by Concrete

8.16.6.2.1 Shear in Beams and One-Way Slabs andFootings

For members subject to shear and flexure only, V, shallbe computed by,

V,=2 1+ 5 00 Ag f,' (b,, d) (8-52)

Note:(a) N„ is negative for tension.(b) The quantity N„/Ag shall be expressed in poundsper square inch.

8.166.2.4 Shear in Lightweight Concrete

v, _ (1.9 f~ + 2,500 p, "A )b v d (8-48) The provisions for shear stress, v., carried by the con-M„ crete apply to normal weight concrete. When lightweight

aggregate concretes are used, one of the following modi-or, fications shall apply:

V, = 2 f,'bWd (8-49)

where b,,, is the width of web and d is the distance from theextreme compression fiber to the centroid of the longitu-dinal tension reinforcement. Whenever applicable, effectsof torsion shall be included. For a circular section, bw, shallbe the diameter and d need not be less than the distancefrom the extreme compression fiber to the centroid of thelongitudinal reinforcement in the opposite half of themember. For tapered webs, b W shall be the average widthor 1.2 times the minimum width, whichever is smaller.

Note:(a) V, shall not exceed 3.5 f-,' b W d when using moredetailed calculations.(b) The quantity V„d/M„ shall not be greater than 1.0where M. is the factored moment occurring simultane-ously with V. at the section being considered.

8.16.6.2.2 Shear in Compression Members

For members subject to axial compression, V, may becomputed by:

V = 2(1 + N°

J

f ' (b d) (8-50)`` 2, 000 A g J

or,

V, = 2 b Wd (8-51)

Note:The quantity N„/Ag shall be expressed in pounds persquare inch.

8.16.6.2.3 Shear in Tension Members

For members subject to axial tension, shear reinforce-ment shall be designed to carry total shear, unless a moredetailed calculation is made using:

(a) When f,, is specified, the shear strength, V G, shallbe modified by substituting f,,16.7 for N/—f,', but thevalue of f,,/6.7 used shall not exceed NIT .

(b) When fit is not specified, V, shall be multiplied by0.75 for "all lightweight" concrete, and 0.85 for "sand-lightweight" concrete. Linear interpolation may beused when partial sand replacement is used.

8.16.6.3 Shear Strength Provided by ShearReinforcement

8.16.6.3.1 Where factored shear force V. exceedsshear strength (~V,, shear reinforcement shall be providedto satisfy Equations (8-46) and (8-47), but not less thanthat required by Article 8.19. Shear strength V, shall becomputed in accordance with Articles 8.16.6.3.2 through8.16.6.3.10.

8.166.3.2 When shear reinforcement perpendicularto the axis of the member is used:

VS = A " fy d(8–53)

where A„ is the area of shear reinforcement within adistance s.

8.16.6.3.3 When inclined stirrups are used:

V =A

Vfy (sin a + cos a)d

(8-54)s

8.16.6.3.4 When a single bar or a single group of par-allel bars all bent up at the same distance from the supportis used:

V S = A„f, sin « <_ 3 fc'bW d (8-55)


8.16.6.3.5 When shear reinforcement consists of aseries of parallel bent-up bars or groups of parallel bent-up bars at different distances from the support, shearstrength V S shall be computed by Equation (8-54).

8.16.63.6 Only the center three-fourths of the in-clined portion of any longitudinal bent bar shall be con-sidered effective for shear reinforcement.

8.166 3.7 Where more than one type of shear rein-forcement is used to reinforce the same portion of themember, shear strength V S shall be computed as the sumof the V S values computed for the various types.

8.16.63.8 When shear strength V S exceeds 4bw d, spacing of shear reinforcement shall not exceed one-half the maximum spacing given in Article 8.19.3.

8.16. 63.9 Shear strength VS shall not be takengreater than 8 Vf,–' b,Nd.

8.1663.10 When flexural reinforcement, locatedwithin the width of a member used to compute the shearstrength, is terminated in a tension zone, shear reinforce-ment shall be provided in accordance with Article 8.24.1.4.

8.16.6.4 Shear Friction

8.16. 64.1 Provisions for shear-friction are to be ap-plied where it is appropriate to consider shear transferacross a given plane, such as: an existing or potentialcrack, an interface between dissimilar materials, or an in-terface between two concretes cast at different times.

8.16.6.4.2 Design of cross sections subject to sheartransfer as described in Article 8.16.6.4.1 shall be basedon Equation (8-46), where shear strength V. is calculatedin accordance with provisions of Article 8.16.6.4.3 or8.16.6.4.4.

8.16.6.4.3 A crack shall be assumed to occur alongthe shear plane considered. Required area of shear-frictionreinforcement A,,f across the shear plane may be designedusing either Article 8.16.6.4.4 or any other shear transferdesign methods that result in prediction of strength in sub-stantial agreement with results of comprehensive tests.Provisions of Articles 8.16.6.4.5 through 8.16.6.4.9 shallapply for all calculations of shear transfer strength.

8.1664.4 Shear-Friction Design Method

(a) When the shear-friction reinforcement is perpen-dicular to the shear plane, shear strength, V,,, shall becomputed by:

V~ = A,ffvµ (8-56)

where p is the coefficient of friction in accordance withArticle (c).(b) When the shear-friction reinforcement is inclinedto the shear plane, such that the shear force producestension in shear-friction reinforcement, shear strengthV n shall be computed by:

V~ = A„ffy (p sin af •+ cos uf) (8-56A)

where o f is the angle between the shear-friction rein-forcement and the shear plane.(c) Coefficient of friction p in Equations (8-56) and(8-56A) shall be:

Concrete placed monolithically .............................1 AXConcrete placed against hardened concrete withsurface intentionally roughened as specified in Ar-ticle 8.16.6.4.8 ....................................................... LOXConcrete placed against hardened concrete not in-tentionally roughened ............................................0.6XConcrete anchored to as-rolled structural steel byheaded studs or by reinforcing bars (see Article8.16.6.4.9) ............................................................. 0.7A

where X = 1.0 for normal weight concrete; 0.85 for"sand lightweight" concrete; and 0.75 for "all light-weight" concrete. Linear interpolation may be appliedwhen partial sand replacement is used.

8.1 66.4.5 Shear strength V„ shall not be takengreater than 0.2f.' A,„ nor 800 A~„ in pounds, where A~„ isthe area of the concrete section resisting shear transfer.

8.16.6.4.6 Net tension across the shear plane shall beresisted by additional reinforcement. Permanent net com-pression across the shear plane may be taken as additiveto the force in the shear-friction reinforcement, A„ffy ,when calculating required A, f .

8.16.6.4.7 Shear-friction reinforcement shall be ap-propriately placed along the shear plane and shall be an-chored to develop the specified yield strength on bothsides by embedment, hooks, or welding to special devices.

8.16.6.4.8 For the purpose of Article 8.16.6.4, whenconcrete is placed against previously hardened concrete,the interface for shear transfer shall be clean and freeof laitance. If p is assumed equal to LOX, the interfaceshall be roughened to a full amplitude of approximately%4 inch.


8.16.64.9 When shear is transferred between as-rolled steel and concrete using headed studs or welded re-inforcing bars, steel shall be clean and free of paint.

8.16.6.5 Horizontal Shear Strength forComposite Concrete Flexural Members

8.16.6.5.1 In a composite member, full transfer ofhorizontal shear forces shall be assured at contact surfacesof interconnected elements.

8.166 5.2 Design of cross sections subject to hori-zontal shear may be in accordance with provisions ofArticle 8.16.6.5.3 or 8.16.6.5.4, or any other shear trans-fer design method that results in prediction of strengthin substantial agreement with results of comprehensivetests.

8.16.6.5.3 Design of cross sections subject to hori-zontal shear may be based on:

V.C

O.h (8-57)

where V. is the factored shear force at the section consid-ered, V„h is the nominal horizontal shear strength in ac-cordance with the following, and where d is for the entirecomposite section.

(a) When contact surface is clean, free of laitance, andintentionally roughened, shear strength V,,h shall not betaken greater than 80b,d, in pounds.(b) When minimum ties are provided in accordancewith Article 8.16.6.5.5, and contact surface is clean andfree of laitance, but not intentionally roughened, shearstrength

Vnh shall not be taken greater than 80 b„d, inpounds.(c) When minimum ties are provided in accordancewith Article 8.16.6.5.5, and contract surface is clean,free of laitance, and intentionally roughened to a fullamplitude of approximately %4 inch, shear strength Vnh

shall not be taken greater than 350b„d, in pounds.(d) For each percent of tie reinforcement crossing thecontact surface in excess of the minimum required byArticle 8.16.6.5.5, shear strength V„ h may be increasedby (160fy /40,000)b,,d, in pounds.

8.16.6.5.4 Horizontal shear may be investigated bycomputing, in any segment not exceeding one-tenth of thespan, the change in compressive or tensile force to betransferred, and provisions made to transfer that force ashorizontal shear between interconnected elements. Thefactored horizontal shear force shall not exceed horizon-

tal shear strength Onh in accordance with Article8.16.6.5.3, except that the length of the segment consid-ered shall be substituted for d.

8.16.6.5.5 Ties for Horizontal Shear

(a) When required, a minimum area of tie reinforce-ment shall be provided between interconnected ele-ments. Tie area shall not be less than 50b vs/f,,, and tiespacing, s, shall not exceed four times the least webwidth of the support element, nor 24 inches.(b) Ties for horizontal shear may consist of single barsor wire, multiple leg stirrups, or vertical legs of weldedwire fabric. All ties shall be adequately anchored intointerconnected elements by embedment or hooks.

8.16.6.6 Special Provisions for Slabs andFootings

8.16.6.6.1 Shear strength of slabs and footings in thevicinity of concentrated loads or reactions shall be gov-erned by the more severe of two conditions:

(a) Beam action for the slab or footing, with a criticalsection extending in a plane across the entire width andlocated at a distance d from the face of the concentratedload or reaction area. For this condition, the slab orfooting shall be designed in accordance with Articles8.16.6.1 through 8.16.6.3 except at footings supportedon piles, the shear on the critical section shall be de-termined in accordance with Article 4.4.11.3.(b) Two-way action for the slab or footing, with acritical section perpendicular to the plane of the mem-ber and located so that its perimeter b o is a minimum,but need not approach closer than d/2 to the perimeterof the concentrated load or reaction area. For this con-dition, the slab or footing shall be designed in accor-dance with Articles 8.16.6.6.2 and 8.16.6.6.3.

8.1666 2 Design of slab or footing for two-wayaction shall be based on Equation (8-46), where shearstrength V„ shall not be taken greater than shear strengthVc given by Equation (8-58), unless shear reinforcementis provided in accordance with Article 8.16.6.6.3.

V~ = 2+ R JfC' b od <_ 4 " b o d (8-58)

C

VC

P c is the ratio of long side to short side of concentratedload or reaction area, and bo is the perimeter of the criti-cal section defined in Article 8.16.6.6.1(b).


8.16.66.3 Shear reinforcement consisting of bars orwires may be used in slabs and footings in accordancewith the following provisions:

(a) Shear strength V„ shall be computed by Equation(8-47), where shear strength V, shall be in accordancewith paragraph (d) and shear strength V, shall be in ac-cordance with paragraph (e).(b) Shear strength shall be investigated at the criticalsection defined in Article 8.16.6.6.1(b), and at succes-sive sections more distant from the support.(c) Shear strength V„ shall not be taken greater than 6N/Tc'bA where b,, is the perimeter of the critical sectiondefined in paragraph (b).(d) Shear strength V, at any section shall not be takengreater than 2 f,' bod, where b u is the perimeter of thecritical section defined in paragraph (b).(e) Where the factored shear force V. exceeds the shearstrength (~Vu as given in paragraph (d), the required areaA„ and shear strength V, of shear reinforcement shall becalculated in accordance with Article 8.16.6.3.

8.16.6.7 Special Provisions for Slabs of BoxCulverts

8.166.7.1 For slabs of box culverts under 2 feet ormore fill, shear strength V, may be computed by:

VC

= (2.14 f~ + 4,600 pMd

)bd (8-59)

u

but V, shall not exceed 4 V "f—,' bd. For single cell box cul-

verts only, V, for slabs monolithic with walls need not betaken less than 3 V—f,' bd, and V, for slabs simply sup-ported need not be taken less than 2.5 Vf,' bd. The quan-tity Vud/M„ shall not be taken greater than 1.0 where M.is the factored moment occurring simultaneously with V.at the section considered. For slabs of box culverts underless than 2 feet of fill, applicable provisions of Articles3.24 and 6.4 should be used.

8.16.6.8 Special Provisions for Brackets andCorbels*

8.16.6.8.1 Provisions of Article 8.16.6.8 shall applyto brackets and corbels with a shear span-to-depth ratioa„/d not greater than unity, and subject to a horizontal ten-sile force N„, not larger than Vu . Distance d shall be mea-sured at the face of support.

8.166.8.2 Depth at the outside edge of bearing areashall not be less than 0.5d.

8.16.6.8.3 The section at the face of the support shallbe designed to resist simultaneously a shear V,,, a moment(Vua,, + Nun (h — d)), and a horizontal tensile force Nu,.Distance h shall be measured at the face of support.

(a) In all design calculations in accordance with Arti-cle 8.16.6.8, the strength reduction factor (~ shall betaken equal to 0.85.(b) Design of shear-friction reinforcement A vf to resistshear V. shall be in accordance with Article 8.16.6.4.For normal weight concrete, shear strength V. shall notbe taken greater than 0.2fc b,,,d nor 800b wd in pounds.For "all lightweight" or "sand-lightweight " concrete,shear strength V„ shall not be taken greater than (0.2 —0.07a„/d)fc'b,,,d nor (800 — 280a„/d)b wd in pounds.(c) Reinforcement Af to resist moment (V„a„ +Nu, (h — d)) shall be computed in accordance with Ar-ticles 8.16.2 and 8.16.3.(d) Reinforcement Au to resist tensile force Nuc

shallbe determined from Nu, < 4Aufy . Tensile force N un

shall not be taken less than 0.2Vu unless special provi-sions are made to avoid tensile forces. Tensile force Nu,shall be regarded as a live load even when tension re-sults from creep, shrinkage, or temperature change.(e) Area of primary tension reinforcement A, shall bemade equal to the greater of (A f + Au) or:

2Avf +An .

3

k (primaryreinforcement)

Ah (closedstirrups or ties)

Framing bar to anchor J

stirrups or ties*These provisions do not apply to beam ledges. The PCA publication,

"Notes on ACI 318-83" contains an example design of beam ledgesPart 16, example 16-3. FIGURE 8.16.6.8


8.1668.4 Closed stirrups or ties parallel to A,, witha total area A,, not less than 0.5(A, — A„), shall be uni-formly distributed within two-thirds of the effective depthadjacent to A,.

8.16.6.8.5 Ratio p = A,/bd shall not be less than0.04(f,'/fy).

8.16.6.8.6 At front face of bracket or corbel, primarytension reinforcement A, shall be anchored by one of thefollowing:

(a) a structural weld to a transverse bar of at leastequal size; weld to be designed to develop specifiedyield strength fy of A, bars,(b) bending primary tension bars A, back to form ahorizontal loop, or(c) some other means of positive anchorage.

8.16.6.8.7 Bearing area of load on bracket or corbelshall not project beyond straight portion of primary ten-sion bars A,, nor project beyond interior face of transverseanchor bar (if one is provided).

8.16.7 Bearing Strength

8.16.7.1 The bearing stress, fb, on concrete shall notexceed 0.85 f, except as provided in Articles 8.16.7.2,8.16.7.3, and 8.16.7.4.

8.16.7.2 When the supporting surface is wider on allsides than the loaded area, the allowable bearing stress onthe loaded area may be multiplied by N/A—

2/A,, but not bymore than 2.

8.16.7.3 When the supporting surface is sloped orstepped, Az may be taken as the area of the lower base ofthe largest frustum of a right pyramid or cone containedwholly within the support and having for its upper basethe loaded area, and having side slopes of 1 vertical to 2horizontal.

8.16.7.4 When the loaded area is subjected tohigh edge stresses due to deflection or eccentric loading,the allowable bearing stress on the loaded area, includingany increase due to the supporting surface being largerthan the loaded area, shall be multiplied by a factorof 0.75.

8.16.8 Serviceability Requirements

8.16.8.1 Application

For flexural members designed with reference to loadfactors and strengths by Strength Design Method, stresses

at service load shall be limited to satisfy the requirementsfor fatigue in Article 8.16.8.3, and for distribution of rein-forcement in Article 8.16.8.4. The requirements for con-trol of deflections in Article 8.9 shall also be satisfied.

8.16.8.2 Service Load Stresses

For investigation of stresses at service loads to satisfythe requirements of Articles 8.16.8.3 and 8.16.8.4, thestraight-line theory of stress and strain in flexure shall beused and the assumptions given in Article 8.15.3 shallapply.

8.16.8.3 Fatigue Stress Limits

The range between a maximum tensile stress and min-imum stress in straight reinforcement caused by live loadplus impact at service load shall not exceed:

ff = 21 — 0.33f, in + 8(r/h) (8-60)

where:

ff = stress range in kips per square inch;

f = algebraic minimum stress level, tension positive,compression negative in kips per square inch;

r/h = ratio of base radius to height of rolled-on trans-verse deformations; when the actual value is notknown, use 0.3.

Bends in primary reinforcement shall be avoided in re-gions of high stress range.

Fatigue stress limits need not be considered for con-crete deck slabs with primary reinforcement perpendicu-lar to traffic and designed in accordance with the approx-imate methods given under Article 3.24.3, Case A.

Fatigue stress limits for welded splices and mechani-cal connections that are subjected to repetitive loads shallconform with the requirements of Article 8.32.2.5.

8.16.8.4 Distribution of Flexural Reinforcement

To control flexural cracking of the concrete, tension rein-forcement shall be well distributed within maximum flexuralzones. When the design yield strength, f y , for tension rein-forcement exceeds 40,000 psi, the bar sizes and spacing atmaximum positive and negative moment sections shall bechosen so that the calculated stress in the reinforcement atservice load f,, in ksi does not exceed the value computed by:

fs=

(dc' / 3

<0.6f, (8-61)A) l

where:


A = effective tension area, in square inches, of con-crete surrounding the flexural tension reinforce-ment and having the same centroid as that re-inforcement, divided by the number of bars orwires. When the flexural reinforcement con-sists of several bar or wire sizes, the numberof bars or wires shall be computed as the totalarea of reinforcement divided by the area of thelargest bar or wire used. For calculation pur-poses, the thickness of clear concrete coverused to compute A shall not be taken greaterthan 2 in.

d, = distance measured from extreme tension fiber tocenter of the closest bar or wire in inches. For

calculation purposes, the thickness of clear con-crete cover used to compute d, shall not be takengreater than 2 inches.

The quantity z in Equation (8-61) shall not exceed170 kips per inch for members in moderate exposureconditions and 130 kips per inch for members in severeexposure conditions. Where members are exposedto very aggressive exposure or corrosive environments,such as deicer chemicals, protection should be providedby increasing the denseness or imperviousness towater or furnishing other protection such as a waterproof-ing protecting system, in addition to satisfying Equa-tion (8-61).

Part DREINFORCEMENT

8.17 REINFORCEMENT OF FLEXURALMEMBERS

8.17.1 Minimum Reinforcement

8.17.1.1 At any section of a flexural member wheretension reinforcement is required by analysis, the rein-forcement provided shall be adequate to develop a mo-ment at least 1.2 times the cracking moment calculated onthe basis of the modulus of rupture for normal weight con-crete specified in Article 8.15.2.1.1.

d~ Mn >_ 1.2 M,r (8-62)

8.17.1.2 The requirements of Article 8.17.1.1 maybewaived if the area of reinforcement provided at a sectionis at least one-third greater than that required by analysisbased on the loading combinations specified in Article 3.22.

8.17.2 Distribution of Reinforcement

8.17.2.1 Flexural Tension Reinforcement inZones of Maximum Tension

8.17.2.1.1 Where flanges of T-girders and box-gird-ers are in tension, tension reinforcement shall be distrib-uted over an effective tension flange width equal to one-tenth the girder span length or a width as defined in Article8.10.1, whichever is smaller. If the actual slab width, cen-ter-to-center of girder webs, exceeds the effective tensionflange width, and for excess portions of the deck slaboverhang, additional longitudinal reinforcement with area

not less than 0.4% of the excess slab area shall be pro-vided in the excess portions of the slab.

8.17.2.1.2 For integral bent caps of T-girder and box-girder construction, tension reinforcement shall be placedwithin a width not to exceed the web width plus an over-hanging slab width on each side of the bent cap web equalto one-fourth the average spacing of the intersectinggirder webs or a width as defined in Article 8.10.1.4 forintegral bent caps, whichever is smaller.

8.17.2.1.3 If the depth of the side face of a memberexceeds 3 feet, longitudinal skin reinforcement shall beuniformly distributed along both side faces of the memberfor a distance d/2 nearest the flexural tension reinforce-ment. The area of skin reinforcement Ask per foot of heighton each side face shall be ? 0.012 (d — 30). The maxi-mum spacing of skin reinforcement shall not exceed thelesser of d/6 and 12 inches. Such reinforcement may beincluded in strength computations if a strain compatibil-ity analysis is made to determine stresses in the individualbars or wires. The total area of longitudinal skin rein-forcement in both faces need not exceed one-half of therequired flexural tensile reinforcement.

8.17.2.2 Transverse Deck Slab Reinforcement inT-Girders and Box Girders

At least one-third of the bottom layer of the transversereinforcement in the deck slab shall extend to the exteriorface of the outside girder web in each group and be an-


chored by a standard 90° hook. If the slab extends beyondthe last girder web, such reinforcement shall extend intothe slab overhang and shall have an anchorage beyond theexterior face of the girder web not less than that providedby a standard hook.

8.17.2.3 Bottom Slab Reinforcement for BoxGirders

8.17.2.3.1 Minimum distributed reinforcement of0.4% of the flange area shall be placed in the bottom slabparallel to the girder span. A single layer of reinforcementmay be provided. The spacing of such reinforcement shallnot exceed 18 inches.

8.17.2.3.2 Minimum distributed reinforcement of0.5% of the cross-sectional area of the slab, based on theleast slab thickness, shall be placed in the bottom slab trans-verse to the girder span. Such reinforcement shall be dis-tributed over both surfaces with a maximum spacing of 18inches. All transverse reinforcement in the bottom slab shallextend to the exterior face of the outside girder web in eachgroup and be anchored by a standard 90° hook.

8.17.3 Lateral Reinforcement of Flexural Members

8.17.3.1 Compression reinforcement used to in-crease the strength of flexural members shall be enclosedby ties or stirrups which shall be at least No. 3 in size forlongitudinal bars that are No. 10 or smaller, and at leastNo. 4 in size for No. 11, No. 14, No. 18, and bundled lon-gitudinal bars. Welded wire fabric of equivalent area maybe used instead of bars. The spacing of ties shall not ex-ceed 16 longitudinal bar diameters. Such stirrups or tiesshall be provided throughout the distance where the com-pression reinforcement is required. This paragraph doesnot apply to reinforcement located in a compression zonewhich has not been considered as compression reinforce-ment in the design of the member.

8.17.3.2 Torsion reinforcement, where required, shallconsist of closed stirrups, closed ties, or spirals, combinedwith longitudinal bars. See Article 8.15.5.1.1 or 8.16.6.1.1.

8.17.3.3 Closed stirrups or ties may be formed in onepiece by overlapping the standard end hooks of ties or stir-rups around a longitudinal bar, or may be formed in one ortwo pieces by splicing with Class C splices (lap of 1.7 f d).

8.17.3.4 In seismic areas, where an earthquake thatcould cause major damage to construction has a highprobability of occurrence, lateral reinforcement shall be

designed and detailed to provide adequate strength andductility to resist expected seismic movements.

8.17.4 Reinforcement for Hollow RectangularCompression Members

8.17.4.1 The area of longitudinal reinforcement inthe cross section shall not be less than 0.01 times the grossarea of concrete in the cross section.

8.17.4.2 Two layers of reinforcement shall be pro-vided in each wall of the cross section, one layer near eachface of the wall. The areas of reinforcement in the two lay-ers shall be approximately equal.

8.17.4.3 The center-to-center lateral spacing of lon-gitudinal reinforcing bars shall be no greater than 1.5times the wall thickness, or 18 inches, whichever is less.

8.17.4.4 The center-to-center longitudinal spacing oflateral reinforcing bars shall be no greater than 1.25 timesthe wall thickness, or 12 inches, whichever is less.

8.17.4.5 Cross ties shall be provided between lay-ers of reinforcement in each wall. The cross ties shall in-clude a standard 135° hook at one end, and a standard90° hook at the other end. Cross ties shall be located atbar grid intersections, and the hooks of all ties shall en-close both lateral and longitudinal bars at the intersec-tions. Each longitudinal reinforcing bar and each lateralreinforcing bar shall. be enclosed by the hook of a crosstie at a spacing not to exceed 24 inches.

8.17.4.6 For segmentally constructed members, ad-ditional cross ties shall be provided along the top andbottom edges of each segment. The cross ties shall beplaced so as to link the ends of each pair of internal andexternal longitudinal reinforcing bars in the walls of thecross section.

8.17.4.7 Lateral reinforcing bars maybe joined at thecorners of the cross section by overlapping 90° bends.Straight lap splices of lateral reinforcing bars are not per-mitted unless the overlapping bars are enclosed over thelength of the splice by the hooks of at least four cross tieslocated at intersections of the lateral bars and longitudinalbars.

8.17.4.8 When details permit, the longitudinal rein-forcing bars in the corners of the cross section shall be en-closed by closed hoops. If closed hoops cannot be pro-vided, then pairs of "U" shaped bars with legs at leasttwice as long as the wall thickness, and orientated 90° toone another, may be substituted.


8.17.4.9 Post-tensioning ducts located in the cor-ners of the cross section shall be anchored into thecorner regions with closed hoops, or by stirrups havinga 90° bend at each end which encloses at least one lon-gitudinal bar near the outer face of the cross section.

8.18 REINFORCEMENT OF COMPRESSIONMEMBERS

8.18.1 Maximum and Minimum LongitudinalReinforcement

8.18.1.1 The area of longitudinal reinforcement forcompression members shall not exceed 0.08 times thegross area, Ag, of the section.

8.18.1.2 The minimum area of longitudinal rein-forcement shall not be less than 0.01 times the gross area,A s, of the section. When the cross section is larger thanthat required by consideration of loading, a reduced ef-fective area may be used. The reduced effective area shallnot be less than that which would require 1% oflongitudinal reinforcement to carry the loading. The min-imum number of longitudinal reinforcing bars shall be sixfor bars in a circular arrangement and four for bars in arectangular arrangement. The minimum size of bars shallbe No. 5.

8.18.2 Lateral Reinforcement

8.18.2.1 General

In a compression member that has a larger cross sec-tion than that required by conditions of loading, the lateralreinforcement requirements may be waived where struc-tural analysis or tests show adequate strength and feasi-bility of construction.

8.18.2.2 Spirals

Spiral reinforcement for compression members shallconform to the following:

8.18.2.2.1 Spirals shall consist of evenly spaced con-tinuous bar or wire, with a minimum diameter of %8 inch.

8.18.2.2.2 The ratio of spiral reinforcement to totalvolume of core, p,, shall not be less than the value givenby:

p, = 045A9

-1 f (8-63)A C fy

where fy is the specified yield strength of spiral reinforce-ment but not more than 60,000 psi.

8.18.2.2.3 The clear spacing between spirals shallnot exceed 3 inches or be less than 1 inch or 1%3 times themaximum size of coarse aggregate used.

8.18.2.2.4 Anchorage of spiral reinforcement shallbe provided by 1% extra turns of spiral bar or wire at eachend of a spiral unit.

8.18.2.2.5 Spirals shall extend from top of footing orother support to the level of the lowest horizontal rein-forcement in members supported above.

8.18.2.2.6 Splices in spiral reinforcement shall be lapsplices of 48 bar or wire diameters but not less than 12inches, or shall be welded.

8.18.2.2.7 Spirals shall be of such size and so as-sembled to permit handling and placing without distortionfrom designed dimensions.

8.18.2.2.8 Spirals shall be held firmly in place by at-tachment to the longitudinal reinforcement and true to lineby vertical spacers.

8.18.2.3 Ties

Tie reinforcement for compression members shall con-form to the following:

8.18.2.3.1 All bars shall be enclosed by lateral tieswhich shall be at least No. 3 in size for longitudinal barsthat are No. 10 or smaller, and at least No. 4 in size for No.11, No. 14, No. 1.8, and bundled longitudinal bars. De-formed wire or welded wire fabric of equivalent area maybe used instead of bars.

8.18.2.3.2 The spacing of ties shall not exceed theleast dimension of the compression member or 12 inches.When two or more bars larger than No. 10 are bundled to-gether, tie spacing shall be one-half that specified above.

8.18.2.3.3 Ties shall be located not more than half atie spacing from the face of a footing or from the nearestlongitudinal reinforcement of a cross-framing member.

8.18.2.3.4 No longitudinal bar shall be more than 2feet, measured along the tie, from a restrained bar on ei-ther side. A restrained bar is one which has lateral supportprovided by the corner of a tie having an included angleof not more than 135°. Where longitudinal bars are lo-


cated around the perimeter of a circle, a complete circulartie may be used.

8.18.2.4 Seismic Requirements

In seismic areas, where an earthquake which couldcause major damage to construction has a high probabil-ity of occurrence, lateral reinforcement for column piersshall be designed and detailed to provide adequatestrength and ductility to resist expected seismic move-ments.

8.19 LIMITS FOR SHEAR REINFORCEMENT

8.19.1 Minimum Shear Reinforcement

8.19.1.1 A minimum area of shear reinforcementshall be provided in all flexural members, except slabs andfootings, where

(a) For design by Strength Design, factored shearforce V„ exceeds one-half the shear strength providedby concrete (~Vc .

(b) For design by Service Load Design, design shearstress v exceeds one-half the permissible shear stresscarried by concrete vc.

8.19.1.2 Where shear reinforcement is required byArticle 8.19.1.1, or by analysis, the area provided shall notbe less than:

A v = 50fWs

(8-64)Y

where b, and s are in inches.

8.19.1.3 Minimum shear reinforcement require-ments may be waived if it is shown by test that the re-quired ultimate flexural and shear capacity can be devel-oped when shear reinforcement is omitted.

8.19.2 Types of Shear Reinforcement

8.19.2.1 Shear reinforcement may consist of:

(a) Stirrups perpendicular to the axis of the member ormaking an angle of 45 1 or more with the longitudinaltension reinforcement.(b) Welded wire fabric with wires located perpendic-ular to the axis of the member.(c) Longitudinal reinforcement with a bent portionmaking an angle of 30° or more with the longitudinaltension reinforcement.

(d) Combinations of stirrups and bent longitudinal re-inforcement.(e) Spirals.

8.19.2.2 Shear reinforcement shall be developed atboth ends in accordance with the requirements of Article8.27.

8.19.3 Spacing of Shear Reinforcement

Spacing of shear reinforcement placed perpendicularto the axis of the member shall not exceed d/2 or 24inches. Inclined stirrups and bent longitudinal reinforce-ment shall be so spaced that every 45° line extending to-ward the reaction from the mid-depth of the member, d/2,to the longitudinal tension reinforcement shall be crossedby at least one line of shear reinforcement.

8.20 SHRINKAGE AND TEMPERATUREREINFORCEMENT

8.20.1 Reinforcement for shrinkage and temperaturestresses shall be provided near exposed surfaces of wallsand slabs not otherwise reinforced. The total area of rein-forcement provided shall be at least A square inch per footin each direction.

8.20.2 The spacing of shrinkage and temperature rein-forcement shall not exceed three times the wall or slabthickness, or 18 inches.

8.21 SPACING LIMITS FOR REINFORCEMENT

8.21.1 For cast-in-place concrete the clear distance be-tween parallel bars in a layer shall not be less than 1.5 bardiameters, 1.5 times the maximum size of the coarse ag-gregate, or 1%2 inches.

8.21.2 For precast concrete (manufactured under plantcontrol conditions) the clear distance between parallelbars in a layer shall be not less than 1 bar diameter, W3

times the maximum size of the coarse aggregate, or 1inch.

8.21.3 Where positive or negative reinforcement isplaced in two or more layers, bars in the upper layers shallbe placed directly above those in the bottom layer with theclear distance between layers not less than 1 inch.

8.21.4 The clear distance limitation between bars shallalso apply to the clear distance between a contact lapsplice and adjacent splices or bars.

8,21.4 DIVISION I—DESIGN 217

8.21.5 Groups of parallel reinforcing bars bundled in con-tact to act as a unit shall be limited to 4 in any one bundle.Bars larger than No. 11 shall be limited to two in any onebundle in beams. Bundled bars shall be located within stir-rups or ties. Individual bars in a bundle cut off within thespan of a member shall terminate at points at least 40-bardiameters apart. Where spacing limitations are based on bardiameter, a unit of bundled bars shall be treated as a singlebar of a diameter derived from the equivalent total area.

8.21.6 In walls and slabs the primary flexural reinforce-ment shall be spaced not farther apart than 1.5 times thewall or slab thickness, or 18 inches.

8.22 PROTECTION AGAINST CORROSION

8.22.1 The following minimum concrete cover shall beprovided for reinforcement:

MinimumCover

(inches)Concrete cast against and permanently

exposed to earth ..................................................3Concrete exposed to earth or weather:

Primary reinforcement........................................2Stirrups, ties, and spirals ....................................1%2

Concrete deck slabs in mild climates:Top reinforcement ..................................Bottom reinforcement............................

Concrete deck slabs which have no positivecorrosion protection and are frequentlyexposed to deicing salts:Top reinforcement............................................. 2%2Bottom reinforcement .........................................1

Concrete not exposed to weather or incontact with ground:Primary reinforcement .......................................1 %2Stirrups, ties, and spirals ........................

Concrete piles cast against and/orpermanently exposed to earth

8.22.2 For bundled bars, the minimum concrete covershall be equal to the equivalent diameter of the bundle, butneed not be greater than 2 inches, except for concrete castagainst and permanently exposed to earth in which casethe minimum cover shall be 3 inches.

8.22.3 In corrosive or marine environments or other se-vere exposure conditions, the amount of concrete protec-tion shall be suitably increased, by increasing the dense-ness and imperviousness to water of the protecting

TABLE 8.23.2.1 Minimum Diameters of Bend

Bar Size Minimum Diameter

Nos. 3 through 8 6 -bar diametersNos. 9, 10, and 11 8-bar diametersNos. 14 and 18 10-bar diameters

concrete or other means. Other means of positive corro-sion protection may consist of, but not be limited to,epoxy-coated bars, special concrete overlays, and imper-vious membranes; or a combination of these means.*

8.22.4 Exposed reinforcement, inserts, and plates in-tended for bonding with future extensions shall be pro-tected from corrosion.

8.23 HOOKS AND BENDS

8.23.1 Standard Hooks

The term "standard hook" as used herein shall meanone of the following:

(1) 180° bend plus 4d b extension, but not less than 2%2inches at free end of bar.(2) 90° bend plus 12db extension at free end of bar.

(3) For stirrup and tie hooks:(a) No. 5 bar and smaller, 90° bend plus 6db exten-sion at free end of bar, or(b) No. 6, No. 7, and No. 8 bar, 90° bend plus 12d b

extension at free end of bar, or(c) No. 8 bar and smaller, 135° bend plus 6db ex-tension at free end of bar.

8.23.2 Minimum Bend Diameters

8.23.2.1 Diameter of bend measured on the inside ofthe bar, other than for stirrups and ties, shall not be lessthan the values given in Table 8.23.2.1.

8.23.2.2 The inside diameter of bend for stirrups andties shall not be less than 4 bar diameters for sizes No. 5and smaller. For bars larger than size No. 5 diameter ofbend shall be in accordance with Table 8.23.2.1.

8.23.2.3 The inside diameter of bend in smooth or de-formed welded wire fabric for stirrups and ties shall not beless than 4-wire diameters for deformed wire larger than D6and 2-wire diameters for all other wires. Bends with inside

*For additional information on corrosion protection methods, refer toNational Cooperative Highway Research Report 297, "Evaluation ofBridge Deck Protective Strategies."


diameters of less than 8-wire diameters shall not be lessthan 4-wire diameters from the nearest welded intersection.

8.24 DEVELOPMENT OF FLEXURALREINFORCEMENT

8.24.1 General

8.24.1.1 The calculated tension or compression inthe reinforcement at each section shall be developed oneach side of that section by embedment length, hook ormechanical device, or a combination thereof. Hooks maybe used in developing bars in tension only.

8.24.1.2 Critical sections for development of rein-forcement in flexural members are at points of maximumstress and at points within the span where adjacent rein-forcement terminates or is bent. The provisions of Article8.24.2.3 must also be satisfied.

8.24.1.2.1 Reinforcement shall extend beyond thepoint at which it is no longer required to resist flexure fora distance equal to the effective depth of the member, 15bar diameters, or %zo of the clear span, whichever isgreater, except at supports of simple spans and at the freeends of cantilevers.

8.24.1.2.2 Continuing reinforcement shall have anembedment length not less than the development length f dbeyond the point where bent or terminated tension rein-forcement is no longer required to resist flexure.

8.24.1.3 Tension reinforcement may be developedby bending across the web in which it lies or by making itcontinuous with the reinforcement on the opposite face ofthe member.

8.24.1.4 Flexural reinforcement within the portion ofthe member used to calculate the shear strength shall notbe terminated in a tension zone unless one of the follow-ing conditions is satisfied:

8.24.1.4.1 The shear at the cutoff point does not ex-ceed two-thirds of that permitted, including the shearstrength of shear reinforcement provided.

8.24.1.4.2 Stirrup area in excess of that required forshear is provided along each terminated bar over a dis-tance from the termination point equal to three-fourths theeffective depth of the member. The excess stirrup area, A.,shall not be less than 60 b,s/f y . Spacing, s, shall notexceed d/(8 Pb) where

Pb is the ratio of the area of rein-forcement cut off to the total area of tension reinforcementat the section.

8.24.1.4.3 For No. 11 bars and smaller, the continu-ing bars provide double the area required for flexure at thecutoff point and the shear does not exceed three-fourthsthat permitted.

8.24.1.5 Adequate end anchorage shall be providedfor tension reinforcement in flexural members where re-inforcement stress is not directly proportional to moment,such as: sloped, stepped, or tapered footings; brackets;deep flexural members; or members in which the tensionreinforcement is not parallel to the compression face.

8.24.2 Positive Moment Reinforcement

8.24.2.1 At least one-third the positive moment rein-forcement in simple members and one-fourth the positivemoment reinforcement in continuous members shall ex-tend along the same face of the member into the support.In beams, such reinforcement shall extend into the supportat least 6 inches.

8.24.2.2 When a flexural member is part of the lateralload resisting system, the positive moment reinforcementrequired to be extended into the support by Article8.24.2.1 shall be anchored to develop the specified yieldstrength, fy , in tension at the face of the support.

8.24.2.3 At simple supports and at points of inflec-tion, positive moment tension reinforcement shall be lim-ited to a diameter such that fd computed for f,, by Article8.25 satisfies Equation (8-65); except Equation (8-65)need not be satisfied for reinforcement terminating beyondcenter line of simple supports by a standard hook, or a me-chanical anchorage at least equivalent to a standard hook.

fd 5 V + fa (8-65)

where M is the computed moment capacity assuming allpositive moment tension reinforcement at the section tobe fully stressed. V is the maximum shear force at thesection. f a at a support shall be the embedment length be-yond the center of the support. At a point of inflection, fa

shall be limited to the effective depth of the member or12 db , whichever is greater. The value MN in the devel-opment length limitation may be increased by 30% whenthe ends of the reinforcement are confined by a compres-sive reaction.

8.24.3 Negative Moment Reinforcement

8.24.3.1 Negative moment reinforcement in a con-tinuous, restrained, or cantilever member, or in any mem-ber of a rigid frame, shall be anchored in or through the


supporting member by embedment length, hooks, or me-chanical anchorage.

8.24.3.2 Negative moment reinforcement shall havean embedment length into the span as required by Article8.24.1.

8.24.3.3 At least one-third of the total tension rein-forcement provided for negative moment at the supportshall have an embedment length beyond the point of in-flection not less than the effective depth of the member, 12-bar diameters or %16 of the clear span, whichever is greater.

8.25 DEVELOPMENT OF DEFORMED BARSAND DEFORMED WIRE IN TENSION

The development length, f d , in inches shall be com-puted as the product of the basic development length de-fined in Article 8.25.1 and the applicable modification fac-tor or factors defined in Article 8.25.2 and 8.25.3, but f d

shall be not less than that specified in Article 8.25.4.

8.25.1 The basic development length shall be:

No. 11 bars and smaller ......................................0.04A bfy

fc

but not less than................................................0.0004dbfy

No. 14 bars............................................................ 0.085fy

f '

No. 18 bars ..............................................................O. l ify

f '

deformed wire...................................................0.03d b fy

f~

8.25.2 The basic development length shall be multipliedby the following applicable factor or factors:

8.25.2.1 Top reinforcement so placedthat more than 12 inches ofconcrete is cast below thereinforcement..........................................1.4

8.25.2.2 Lightweight aggregateconcrete when f, isspecified........................................... 6.7 f~

fct

but not less than 1.0When f,, is not specified

"all lightweight" concrete.................1.33"sand lightweight" concrete ..............1.18

Linear interpolation may beapplied when partial sandreplacement is used.

8.25.2.3 Bars coated with epoxy withcover less than 3db or clearspacing between bars

less than 6db......................................................................1.5All other cases.................................... 1.15The product obtained when combiningthe factor for top reinforcementwith the applicable factor forepoxy coated reinforcement neednot be taken greater than 1.7

8.25.3 The basic development length, modified by theappropriate factors of Article 8.25.2, may be multiplied bythe following factors when:

8.25.3.1 Reinforcement being developed in thelength under consideration is spaced later-ally at least 6 inches on center with at least3 inches clear cover measured in the direc-tion of the spacing.................................. 0.8

8.25.3.2 Anchorage or development for reinforce-ment strength is not specifically required orreinforcement in flexural members is in ex-cess of that required by analysis

(A, required)/(A, provided)

8.25.3.3 Reinforcement is enclosed within a spiral ofnot less than %4 inch in diameter and notmore than 4 inch pitch ..........................0.75

8.25.4 The development length, fd, shall not be less than12 inches except in the computation of lap splices byArticle 8.32.3 and development of shear reinforcement byArticle 8.27.

8.26 DEVELOPMENT OF DEFORMED BARS INCOMPRESSION

The development length, f d, in inches, for deformedbars in compression shall be computed as the product ofthe basic development length of Article 8.26.1 and ap-

220 HIGHWAY BRIDGES 8 . 26

plicable modification factors of 8.26.2, but fd shall not beless than 8 inches.

8.26.1 The basic development length shall be ...............0.02dbfy/but not less than..................................0.0003dbf,

8.26.2 The basic development length may be multipliedby applicable factors when:

8.26.2.1 Anchorage or development for reinforce-ment strength is not specifically required, orreinforcement is in excess of that requiredby analysis............................. (A, required)/(A, provided)

8.26.2.2 Reinforcement is enclosed in a spiral of notless than % inch in diameter and not morethan 4-inch pitch...................................0.75

8.27 DEVELOPMENT OF SHEARREINFORCEMENT

8.27.1 Shear reinforcement shall extend at least to thecentroid of the tension reinforcement, and shall be carriedas close to the compression and tension surfaces of themember as cover requirements and the proximity of otherreinforcement permit. Shear reinforcement shall be an-chored at both ends for its design yield strength. For com-posite flexural members, all beam shear reinforcementshall be extended into the deck slab or otherwise shall beadequately anchored to assure full beam design shearcapacity.

8.27.2 The ends of single leg, single U, or multiple U-stirrups shall be anchored by one of the following means:

8.27.2.1 A standard hook plus an embedment of thestirrup leg length of at least 0.5 f d between the mid-depthof the member d/2 and the point of tangency of the hook.

8.27.2.2 An embedment length of f d above or belowthe mid-depth of the member on the compression side butnot less than 24-bar or wire diameters or, for deformedbars or deformed wire, 12 inches.

8.27.2.3 Bending around the longitudinal reinforce-ment through at least 180°. Hooking or bending stirrupsaround the longitudinal reinforcement shall be consideredeffective anchorage only when the stirrups make an angleof at least 45° with the longitudinal reinforcement.

8.27.2.4 For each leg of welded smooth wire fabricforming single U-stirrups, either:

8.27.2.4.1 Two longitudinal wires at 2-inch spacingalong the member at the top of the U.

8.27.2.4.2 One longitudinal wire located not morethan d/4 from the compression face and a second wirecloser to the compression face and spaced at least 2 inchesfrom the first wire. The second wire may be located on thestirrup leg beyond a bend or on a bend with an inside di-ameter of bend of not less than 8-wire diameters.

8.27.2.5 For each end of a single-leg stirrup ofwelded smooth or welded deformed wire fabric, thereshall be two longitudinal wires at a minimum spacing of2 inches and with the inner wire at least the greater of d/4or 2 inches from mid-depth of member d/2. Outer longi-tudinal wire at the tension face shall not be farther fromthe face than the portion of primary flexural reinforcementclosest to the face.

8.27.3 Pairs of U-stirrups or ties so placed as to form aclosed unit shall be considered properly spliced when thelaps are 1.7 fd .

8.27.4 Between the anchored ends, each bend in thecontinuous portion of a single U- or multiple U-stirrupshall enclose a longitudinal bar.

8.27.5 Longitudinal bars bent to act as shear reinforce-ment, if extended into a region of tension, shall be con-tinuous with the longitudinal reinforcement and, if ex-tended into a region of compression, shall be anchoredbeyond the mid-depth, d/2, as specified for developmentlength in Article 8.25 for that part of the stress in the re-inforcement required to satisfy Equation (8-8) or Equa-tion (8-54).

8.28 DEVELOPMENT OF BUNDLED BARS

The development length of individual bars within abundle, in tension or compression, shall be that for the in-dividual bar, increased by 20% for a three-bar bundle, and33% for a four-bar bundle.

8.29 DEVELOPMENT OF STANDARD HOOKSIN TENSION

8.29.1 Development length fdh in inches, for deformedbars in tension terminating in a standard hook (Article8.23. 1) shall be computed as the product of the basic de-velopment length fhb of Article 8.29.2 and the applicablemodification factor or factors of Article 8.29.3, but fanshall not be less than 8db or 6 inches, whichever is greater.


#3 through #8

#9, #10 and 011

#14 and #18

FIGURE 8.29.1 Hooked-Bar Details for Development ofStandard Hooks

8.29.2 Basic development length f hb for a hookedbar with f,, equal to 60,000 psi shall be.......................................................1,200 db/ fc

8.29.3 Basic development length f hb shall be multipliedby applicable modification factor or factors for:

8.29.3.1 Bar yield strength:Bars with f,, other than 60,000 psi..................................................... fy/60, 000

8.29.3.2 Concrete cover:For No. 11 bar and smaller, side cover (nor-mal to plane of hook) not less than 2% inches,and for 90° hook, cover on bar extension be-yond hook not less than 2 inches............. 0.7

8.29.3.3 Ties or stirrups:For No. 11 bar and smaller, hook enclosedvertically or horizontally within ties or stir-rup-ties spaced along the full developmentlength fdh not greater than 3db , where d b isdiameter of hooked bar ...........................0.8

8.29.3.4 Excess reinforcement:Where anchorage or development for f,, isnot specifically required, reinforcement inexcess of that required by analysis ....(A s

required)/(A, provided)

less than fdh ties or stirrups2'12 in. ,

A-81required

'".'." less than►. 21 /2 in. •

n.J Sects n AAAr~ ♦ 53db

FIGURE 8.29.4 Hooked-Bar Tie Requirements

8.29.3.6 Epoxy-coated reinforcement hooked barswith epoxy coating..................................1.2

8.29.4 For bars being developed by a standard hook atdiscontinuous ends of members with both side cover andtop (or bottom) cover over hook less than 2%2 inches,hooked bar shall be enclosed within ties or stirrups spacedalong the full development length f &„ not greater than 3db,

where db is the diameter of the hooked bar. For this case,the factor of Article 8.29.3.3 shall not apply.

8.29.5 Hooks shall not be considered effective in devel-oping bars in compression.

8.30 DEVELOPMENT OF WELDED WIREFABRIC IN TENSION

8.30.1 Deformed Wire Fabric

8.30.1.1 The development length, fd , in inches ofwelded deformed wire fabric measured from the point ofcritical section to the end of wire shall be computed as theproduct of the basic development length of Article8.30.1.2 or 8.30.1.3 and the applicable modification fac-tor or factors of Articles 8.25.2 and 8.25.3 but f d shall notbe less than 8 inches except in computation of lap splicesby Article 8.32.5 and development of shear reinforcementby Article 8.27.

8.30.1.2 The basic development length of welded de-formed wire fabric, with at least one cross wire within thedevelopment length not less than 2 inches from the pointof critical section, shall be:

0.03db (f,—20,000)/ fc'* (8-66)

8.29.3.5 Lightweight aggregate concrete ..............1.3 *The 20,000 has units of psi.


but not less than,

0.20 A`° • fy (8-67)s u

r"

a bundle. The length of lap, as prescribed in Article 8.32.3or 8.32.4 shall be increased 20% for a three-bar bundleand 33% for a four-bar bundle. Individual bar spliceswithin the bundle shall not overlap.

8.30.1.3 The basic development length of weldeddeformed wire fabric, with no cross wires within the de-velopment length, shall be determined as for deformedwire in accordance with Article 8.25.

8.30.2 Smooth Wire Fabric

The yield strength of welded smooth wire fabric shallbe considered developed by embedment of two crosswires with the closer cross wire not less than 2 inchesfrom the point of critical section. However, developmentlength Ed measured from the point of critical section tooutermost cross wire shall not be less than:

0.27AW . fy (8-68)S, fC

modified by (A s required)/(As provided) for reinforcementin excess of that required by analysis and by factor of Ar-ticle 8.25.2 for lightweight aggregate concrete, but f d shallnot be less than 6 inches except in computation of lapsplices by Article 8.32.6.

8.31 MECHANICAL ANCHORAGE

8.31.1 Any mechanical device shown by tests to be ca-pable of developing the strength of reinforcement withoutdamage to concrete may be used as anchorage.

8.31.2 Development of reinforcement may consist of acombination of mechanical anchorage plus additional em-bedment length of reinforcement between point of maxi-mum bar stress and the mechanical anchorage.

8.32 SPLICES OF REINFORCEMENT

Splices of reinforcement shall be made only as shownon the design drawings or as specified, or as authorized bythe Engineer.

8.32.1 Lap Splices

8.32.1.1 Lap splices shall not be used for bars largerthan No. 11, except as provided in Articles 8.32.4.1 and4.4.11.4.1.

8.32.1.2 Lap splices of bundled bars shall be basedon the lap splice length required for individual bars within

8.32.1.3 Bars spliced by noncontact lap splices inflexural members shall not be spaced transversely fartherapart than one-fifth the required length of lap or 6 inches.

8.32.1.4 The length, fd, shall be the developmentlength for the specified yield strength, fy, as given in Arti-cle 8.25.

8.32.2 Welded Splices and Mechanical Connections

8.32.2.1 Welded splices or other mechanical connec-tions may be used. Except as provided herein, all weldingshall conform to the latest edition of the American Weld-ing Society publication, "Structural Welding Code Rein-forcing Steel."

8.32.2.2 A full welded splice shall develop in tensionat least 125% of the specified yield strength of the bar.

8.32.2.3 A full-mechanical connection shall developin tension or compression, as required, at least 125% ofthe specified yield strength of the bar.

8.32.2.4 Welded splices and mechanical connectionsnot meeting requirements of Articles 8.32.2.2 and 8.32.2.3may be used in accordance with Article 8.32.3.4.

8.32.2.5 For welded or mechanical connections thatare subject to repetitive loads, the range of stress, f f, betweena maximum tensile stress and a minimum stress in a rein-forcing bar caused by live load plus impact at service loadshall not exceed:

ff

for greater thanType of Splice 1,000,000 cycles

Grout-filled sleeve, with or without epoxycoated bar: 18 ksi

Cold-swaged coupling sleeves withoutthreaded ends, and with or withoutepoxy-coated bar;

Integrally-forged coupler with upset NCthreads;

Steel sleeve with a wedge;One-piece taper-threaded coupler; andSingle V-groove direct butt weld: 12 ksiAll other types of splices: 4 ksi


except that, for total cycles of loading, N, Y ,, less than 1

million cycles, f f may be increased by the quantity 24(6 — logN,y,) in ksi to a total not greater than the value offf given by Equation (8-60) in Article 8.16.8.3. Higher val-ues of ff, up to the value given by Equation (8-60), may beused if justified by fatigue test data on splices that are thesame as those which will be placed in service.

8.32.3 Splices of Deformed Bars and DeformedWire in Tension

8.32.3.1 The minimum length of lap for tension lapsplices shall be as required for Class A, B, or C splice, butnot less than 12 inches.

Class A splice .......................................................1.0 fd

Class B splice...................................................... 1.3 fdClass C splice...................................................... 1.7 f

d

8.32.3.2 Lap splices of deformed bars and deformedwire in tension shall conform to Table 8.32.3.2.

8.32.3.3 Welded splices or mechanical connectionsused where the area of reinforcement provided is less thantwice that required by analysis shall meet the require-ments of Article 8.32.2.2 or 8.32.2.3.

8.32.3.4 Welded splices or mechanical connectionsused where the area of reinforcement provided is at leasttwice that required by analysis shall meet the following:

8.32.3.4.1 Splices shall be staggered at least 24inches and in such manner as to develop at every sectionat least twice the calculated tensile force at that section butnot less than 20,000 psi for the total area of reinforcementprovided.

8.32.3.4.2 In computing tensile force developed ateach section, spliced reinforcement may be rated at thespecified splice strength. Unspliced reinforcement shallbe rated at that fraction of fy defined by the ratio of theshorter actual development length to fd required to de-velop the specified yield strength fy .

TABLE 8.32.3.2 Tension Lap Splices

Maximum Percent of A,Spliced within Required

Lap Length

(A, provided)/(A, required)' 50 75 100

Equal to or Greater than 2 Class A Class A Class BLess than 2 Class B Class C Class C

*Ratio of area of reinforcement provided to area of reinforcementrequired by analysis at splice location.

8.32.3.5 Splices in tension tie members shall be madewith a full-welded splice or a full-mechanical connection inaccordance with Article 8.32.2.2 or 8.32.2.3. Splices in ad-jacent bars shall be staggered at least 30 inches.

8.32.4 Splices of Bars in Compression

8.32.4.1 Lap Splices in Compression

The minimum length of lap for compression lap splicesshall be 0.0005fydb in inches, but not less than 12 inches.When the specified concrete strength, f,', is less than3,000 psi, the length of lap shall be increased by one-third.

When bars of different size are lap spliced in compres-sion, splice length shall be the larger of: developmentlength of the larger bar, or splice length of smaller bar. Barsizes No. 14 and No. 18 may be lap spliced to No. 11 andsmaller bars.

In compression members where ties along the splicehave an effective area not less than 0.0015hs, thelap splice length may be multiplied by 0.83, but the laplength shall not be less than 12 inches. The effective areaof the ties shall be the area of the legs perpendicular todimension h.

In compression members when spirals are used for lat-eral restraint along the splice, the lap splice length may bemultiplied by 0.75, but the lap length shall not be less than12 inches.

8.32.4.2 End-Bearing Splices

In bars required for compression only, the compressivestress may be transmitted by bearing of square cut endsheld in concentric contact by a suitable device. Bar endsshall terminate in flat surfaces within 1%2 of a right angleto the axis of the bars and shall be fitted within 3° of fullbearing after assembly. End-bearing splices shall be usedonly in members containing closed ties, closed stirrups, orspirals.

8.32.4.3 Welded Splices or MechanicalConnections

Welded splices or mechanical connections used incompression shall meet the requirements of Article8.32.2.2 or 8.32.2.3.

8.32.5 Splices of Welded Deformed Wire Fabric inTension

8.32.5.1 The minimum length of lap for lap splicesof welded deformed wire fabric measured between theends of each fabric sheet shall not be less than 1.7 Ed or8 inches, and the overlap measured between the outermost


cross wires of each fabric sheet shall not be less than2 inches.

8.32.5.2 Lap splices of welded deformed wire fabric,with no cross wires within the lap splice length, shall bedetermined as for deformed wire in accordance with Arti-cle 8.32.3.1.

8.32.6 Splices of Welded Smooth Wire Fabric inTension

The minimum length of lap for lap splices of weldedsmooth wire fabric shall be in accordance with the fol-lowing:

8.32.6.1 When the area of reinforcement provided isless than twice that required by analysis at the splice lo-cation, the length of overlap measured between the outer-most cross wires of each fabric sheet shall not be less thanone spacing of cross wires plus 2 inches or less than 1.5fd , or 6 inches.

8.32.6.2 When the area of reinforcement provided isat least twice that required by analysis at the splice loca-tion, the length of overlap measured between the outer-most cross wires of each fabric sheet shall not be less than1.5 fd or 2 inches.

Section 9

PRESTRESSED CONCRETE


9.1 APPLICATION

9.1.1 General

The specifications of this section are intended for de-sign of prestressed concrete bridge members. Membersdesigned as reinforced concrete, except for a percentageof tensile steel stressed to improve service behavior, shallconform to the applicable specifications of Section 8.

Exceptionally long span or unusual structures requiredetailed consideration of effects which under this Sectionmay have been assigned arbitrary values.

9.1.2 Notations

AS = area of non-prestressed tension reinforcement(Articles 9.7 and 9.19)

As = area of compression reinforcement (Article9.19)

A* = area of prestressing steel (Article 9.17)A

sf = steel area required to develop the compressivestrength of the overhanging portions of theflange (Article 9.17)

Asr = steel area required to develop the compressivestrength of the web of a flanged section (Arti-cles 9.17-9.19)

A, = area of web reinforcement (Article 9.20)b = width of flange of flanged member or width of

rectangular memberb,, = width of cross section at the contact surface

being investigated for horizontal shear (Arti-cle 9.20).

b ' = width of a web of a flanged memberCRS = loss of prestress due to creep of concrete (Ar-

ticle 9.16)CRS = loss of prestress due to relaxation of pre-

stressing steel (Article 9.16)D = nominal diameter of prestressing steel (Arti-

cles 9.17 and 9.27)

d = distance from extreme compressive fiber tocentroid of the prestressing force, or to cen-troid of negative moment reinforcing for pre-cast girder bridges made continuous

d, = distance from the extreme compressive fiberto the centroid of the non-prestressed tensionreinforcement (Articles 9.7 and 9.17-9.19)

ES = loss of prestress due to elastic shortening (Ar-ticle 9.16)

e = base of Naperian logarithms (Article 9.16)frds = average concrete compressive stress at the c.g.

of the prestressing steel under full dead load(Article 9.16)

= average concrete stress at the c.g. of the pre-stressing steel at time of release (Article 9.16)

f~ = compressive strength of concrete at 28 daysf

~l; = compressive strength of concrete at time ofinitial prestress (Article 9.15)

fit = average splitting tensile strength of light-weight aggregate concrete, psi

fd = stress due to unfactored dead load, at extremefiber of section where tensile stress is causedby externally applied loads (Article 9.20)

fp, = compressive stress in concrete (after al-lowance for all prestress losses) at centroid ofcross section resisting externally appliedloads or at junction of web and flange whenthe centroid lies within the flange (In a com-posite member, fps is resultant compressivestress at centroid of composite section, or atjunction of web and flange when the centroidlies within the flange, due to both prestressand moments resisted by precast member act-ing alone.)(Article 9.20)

f, = compressive stress in concrete due to effectiveprestress forces only (after allowance for allprestress losses) at extreme fiber of sectionwhere tensile stress is caused by externallyapplied loads (Article 9.20)

225


fps = guaranteed ultimate tensile strength of theprestressing steel, A*,f,'

fr = the modulus of rupture of concrete, as definedin Article 9.15.2.3 (Article 9.18)

Afs = total prestress loss, excluding friction (Article9.16)

fse = effective steel prestress after lossesfu = average stress in prestressing steel at ultimate

loadfs = ultimate stress of prestressing steel (Articles

9.15 and 9.17)f, = yield stress of non-prestressed conventional

reinforcement in tension (Articles 9.19 and9.20)

fy = yield stress of non-prestressed conven-tional reinforcement in compression (Article9.19)

fy = yield stress of prestressing steel (Article 9.15)= 0.90 fs for low-relaxation wire or strand= 0.85 fs for stress-relieved wire or strand= 0.85 fs for Type I (smooth) high-strength bar= 0.80 fs for Type II (deformed) high-strength

barh = overall depth of member (Article 9.20)I = moment of inertia about the centroid of the

cross section (Article 9.20)K = friction wobble coefficient per foot of pre-

stressing steel (Article 9.16)L = length of prestressing steel element from jack

end to point x (Article 9.16)M er = moment causing flexural cracking at sec-

tion due to externally applied loads (Article9.20)

M* = cracking moment (Article 9.18)Mdk = composite dead load moment at the section

(Commentary to Article 9.18)Mdine = noncomposite dead load moment at the sec-

tion (Article 9.18)M

max = maximum factored moment at section due toexternally applied loads (Article 9.20)

M, = nominal moment strength of a sectionMn = factored moment at section < (~M n (Articles

9.17 and 9.18)p = Aa /bd, ratio of non-prestressed tension rein-

forcement (Articles 9.7 and 9.17-9.19)p* = A*/bd, ratio of prestressing steel (Articles

9.17 and 9.19)p '

=A' /bd, ratio of compression reinforcement(Article 9.19)

P. = factored tendon forceQ = statical moment of cross-sectional area, above

or below the level being investigated for shear,about the centroid (Article 9.20)

SH = loss of prestress due to concrete shrinkage(Article 9.16)

s = longitudinal spacing of the web reinforcement(Article 9.20)

Se = noncomposite section modulus for the ex-treme fiber of section where the tensile stressis caused by externally applied loads (Article9.18)

Sc = composite section modulus for the extremefiber of section where the tensile stress iscaused by externally applied loads (Article9.18)

t = average thickness of the flange of a flangedmember (Articles 9.17 and 9.18)

T,, = steel stress at jacking end (Article 9.16)Tx = steel stress at any point x (Article 9.16)v = permissible horizontal shear stress (Article

9.20)Ve = nominal shear strength provided by concrete

(Article 9.20)VC1 = nominal shear strength provided by concrete

when diagonal cracking results from com-bined shear and moment (Article 9.20)

V eW = nominal shear strength provided by concretewhen diagonal cracking results from exces-sive principal tensile stress in web (Article9.20)

Vd = shear force at section due to unfactored deadload (Article 9.20)

V; = factored shear force at section due to exter-nally applied loads occurring simultaneouslywith Mmax (Article 9.20)

Vn,, = nominal horizontal shear strength (Article9.20)

VP

= vertical component of effective prestress forceat section (Article 9.20)

VS = nominal shear strength provided by shear re-inforcement (Article 9.20)

V n = factored shear force at section (Article 9.20)Y, = distance from centroidal axis of gross section,

neglecting reinforcement, to extreme fiber intension (Article 9.20)

µ = friction curvature coefficient (Article 9.16)a = total angular change of prestressing steel pro-

file in radians from jacking end to point x (Ar-ticle 9.16)

(3, = factor for concrete strength, as defined in Ar-ticle 8.16.2.7 (Articles 9.17, 9.18 and 9.1.9)

y* = factor for type of prestressing steel (Article9.17)

= 0.28 for low-relaxation steel= 0.40 for stress-relieved steel= 0.55 for bars


9.1.3 Definitions

The following terms are defined for generaluse. Specialized definitions appear in individual articles.

Anchorage Device—The hardware assembly used fortransferring a post-tensioning force from the tendonwires, strands or bars to the concrete.

Anchorage _ Seating—Deformation of anchorageor seating of tendons in anchorage device when pre-stressing force is transferred from jack to anchoragedevice.

Anchorage Spacing—Center-to-center spacing of an-chorage devices.

Anchorage Zone—The portion of the structure inwhich the concentrated prestressing force is transferredfrom the anchorage device into the concrete (Local Zone),and then distributed more widely into the structure (Gen-eral Zone) (Article 9.21.1).

Basic Anchorage Device—Anchorage devicemeeting the restricted bearing stress and minimum platestiffness requirements of Articles 9.21.7.2.2 through9.21.7.2.4; no acceptance test is required for BasicAnchorage Devices.

Bonded Tendon—Prestressing tendon that is bonded toconcrete either directly or through grouting.

Coating—Material used to protect prestressing ten-dons against corrosion, to reduce friction between tendonand duct, or to debond prestressing tendons.

Couplers (Couplings)—Means by which prestressingforce is transmitted from one partial-length prestressingtendon to another.

Creep of Concrete—Time-dependent deformation ofconcrete under sustained load.

Curvature Friction—Friction resulting from bendsor curves in the specified prestressing tendon profile.

Debonding (blanketing)—Wrapping, sheathing, orcoating prestressing strand to prevent bond betweenstrand and surrounding concrete.

Diaphragm—Transverse stiffener in girders to main-tain section geometry.

Duct—Hole or void formed in prestressed member toaccommodate tendon for post-tensioning.

Edge Distance—Distance from the center of theanchorage device to the edge of the concretemember.

Effective Prestress—Stress remaining in concrete dueto prestressing after all calculated losses have been de-ducted, excluding effects of superimposed loads andweight of member; stress remaining in prestressing ten-dons after all losses have occurred excluding effects ofdead load and superimposed load.

Elastic Shortening of Concrete—Shortening ofmember caused by application of forces induced by pre-

stressing.End Anchorage—Length of reinforcement, or me-

chanical anchor, or hook, or combination thereof, beyondpoint of zero stress in reinforcement.

End Block—Enlarged end section of member designedto reduce anchorage stresses.

Friction (post-tensioning)—Surface resistance be-tween tendon and duct in contact during stressing.

General Zone—Region within which the concentratedprestressing force spreads out to a more linear stress dis-tribution over the cross section of the member (SaintVenant Region) (Article 9.21.2.1)

Grout Opening or Vent—Inlet, outlet, vent, or drain inpost-tensioning duct for grout, water, or air

Intermediate Anchorage—Anchorage not located atthe end surface of a member or segment; usually in theform of embedded anchors, blisters, ribs, or recesspockets

Jacking Force—Temporary force exerted by devicethat introduces tension into prestressing tendons.

Local Zone—The volume of concrete surrounding andimmediately ahead of the anchorage device, subjected tohigh local bearing stresses (Article 9.21.2.2)

Loss of Prestress—Reduction in prestressing forceresulting from combined effects of strains in concreteand steel, including effects of elastic shortening, creepand shrinkage of concrete, relaxation of steel stress, andfor post-tensioned members, friction and anchorageseating.

Post-Tensioning—Method of prestressing in whichtendons are tensioned after concrete has hardened.

Precompressed Zone—Portion of flexural membercross section compressed by prestressing force.

Prestressed Concrete—Reinforced concrete inwhich internal stresses have been introduced to reducepotential tensile stresses in concrete resulting fromloads.

Pretensioning—Method of prestressing in which ten-dons are tensioned before concrete is placed.

Relaxation of Tendon Stress—Time-dependent reduc-tion of stress in prestressing tendon at constant strain.

ShearLag—Nonuniform distribution of bending stressover the cross section.

Shrinkage of Concrete—Time-dependent deformationof concrete caused by drying and chemical changes (hy-dration process).

Special Anchorage Device—Anchorage devicewhose adequacy must be proven experimentally in thestandardized acceptance tests of Division II, Article10.3.2.3.


Tendon—Wire, strand, or bar, or bundle of such ele-ments, used to impart prestress to concrete.

TransferAct of transferring stress in prestressingtendons from jacks or pretensioning bed to concretemember.

Transfer Length—Length over which prestressingforce is transferred to concrete by bond in pretensionedmembers.

Wobble Friction—Friction caused by unintended devi-ation of prestressing sheath or duct from its specified pro-file or alignment.

Wrapping or Sheathing—Enclosure around a pre-stressing tendon to avoid temporary or permanentbond between prestressing tendon and surroundingconcrete.

9.2 CONCRETE

The specified compressive strength, f,' , of the concretefor each part of the structure shall be shown on the plans.The requirements for f.' shall be based on tests of cylin-ders made and tested in accordance with Division II, Sec-tion 8, "Concrete Structures."

9.3 REINFORCEMENT

9.3.1 Prestressing Steel

Wire, strands, or bars shall conform to one of the fol-lowing specifications.

"Uncoated Stress-Relieved Wire for Prestressed Con-crete," AASHTO M 204."Uncoated Seven-Wire Stress-Relieved Strand for Pre-stressed Concrete," AASHTO M 203."Uncoated High-Strength Steel Bar for PrestressingConcrete," ASTM A 722.

Wire, strands, and bars not specifically listed in AASHTOM 204, AASHTO M 203, or ASTM A 722 may be usedprovided they conform to the minimum requirements ofthese specifications.

9.3.2 Non-Prestressed Reinforcement

Non-prestressed reinforcement shall conform to the re-quirements in Article 8.3.

Part BANALYSIS

9.4 GENERAL

Members shall be proportioned for adequate strengthusing these specifications as minimum guidelines. Con-tinuous beams and other statically indeterminate struc-tures shall be designed for adequate strength and satisfac-tory behavior. Behavior shall be determined by elasticanalysis, taking into account the reactions, moments,shear, and axial forces produced by prestressing, the ef-fects of temperature, creep, shrinkage, axial deformation,restraint of attached structural elements, and foundationsettlement.


9.5.1 In all bridges, provisions shall be made in thedesign to resist thermal stresses induced, or means shallbe provided for movement caused by temperaturechanges.

9.5.2 Movements not otherwise provided for, includingshortening during stressing, shall be provided for bymeans of hinged columns, rockers, sliding plates, elas-tomeric pads, or other devices.

9.6 SPAN LENGTH

The effective span lengths of simply supported beamsshall not exceed the clear span plus the depth of the beam.The span length of continuous or restrained floor slabs andbeams shall be the clear distance between faces of sup-port. Where fillets making an angle of 45° or more withthe axis of a continuous or restrained slab are built mono-lithic with the slab and support, the span shall be mea-sured from the section where the combined depth of theslab and the fillet is at least one and one-half times thethickness of the slab. Maximum negative moments are tobe considered as existing at the ends of the span, as abovedefined. No portion of the fillet shall be considered asadding to the effective depth.

9.7 FRAMES AND CONTINUOUSCONSTRUCTION

9.7.1 Cast-in-Place Post-Tensioned Bridges

The effect of secondary moments due to prestressingshall be included in stress calculations at working load. Incalculating ultimate strength moment and shear require-ments, the secondary moments or shears induced by pre-


stressing (with a load factor of 1.0) shall be added alge-braically to the moments and shears due to factored or ul-timate dead and live loads.

9.7.2 Bridges Composed of Simple-Span PrecastPrestressed Girders Made Continuous

9.7.2.1 General

When structural continuity is assumed in calculatinglive loads plus impact and composite dead load moments,the effects of creep and shrinkage shall be considered inthe design of bridges incorporating simple span precast,prestressed girders and deck slabs continuous over two ormore spans.

9.7.2.2 Positive Moment Connection at Piers

9.7.2.2.1 Provision shall be made in the design forthe positive moments that may develop in the negativemoment region due to the combined effects of creep andshrinkage in the girders and deck slab, and due to the ef-fects of live load plus impact in remote spans. Shrinkageand elastic shortening of the pier shall be considered whensignificant.

9.7.2.2.2 Non-prestressed positive moment con-nection reinforcement at piers may be designed at a work-ing stress of 0.6 times the yield strength but not to exceed36 ksi.

9.7.2.3 Negative Moments

9.7.2.3.1 Negative moment reinforcement shall beproportioned by strength design with load factors in ac-cordance with Article 9.14.

9.7.2.3.2 The ultimate negative resisting momentshall be calculated using the compressive strength of thegirder concrete regardless of the strength of the diaphragmconcrete.

9.7.3 Segmental Box Girders

9.7.3.1 General

9.7.3.1.1 Elastic analysis and beam theory may beused in the design of segmental box girder structures.

9.7.3.1.2 In the analysis of precast segmental boxgirder bridges, no tension shall be permitted across anyjoint between segments during any stage of erection orservice loading.

9.7.3.1.3 In addition to the usual substructure designconsiderations, unbalanced cantilever moments due to

segment weights and erection loads shall be accommo-dated in pier design or with auxiliary struts. Erectionequipment which can eliminate these unbalanced mo-ments may be used.

9.7.3.2 Flexure

The transverse design of segmental box girders forflexure shall consider the segments as rigid box frames.Top slabs shall be analyzed as variable depth sections con-sidering the fillets between top slab and webs. Wheelloads shall be positioned to provide maximum moments,and elastic analysis shall be used to determine the effec-tive longitudinal distribution of wheel loads for each loadlocation. (See Article 3. 11.) Transverse prestressing of topslabs is generally recommended.

9.7.3.3 Torsion

In the design of the cross section, consideration shallbe given to the increase in web shear resulting from ec-centric loading or geometry of structure.

9.8 EFFECTIVE FLANGE WIDTH

9.8.1 T-Beams

9.8.1.1 For composite prestressed constructionwhere slabs or flanges are assumed to act integrally withthe beam, the effective flange width shall conform to theprovisions for T-girder flanges in Article 8.10.1.

9.8.1.2 For monolithic prestressed construction, withnormal slab span and girder spacing, the effective flangewidth shall be the distance center-to-center of beams. Forvery short spans, or where girder spacing is excessive, an-alytical investigations shall be made to determine the an-ticipated width of flange acting with the beam.

9.8.1.3 For monolithic prestressed design of isolatedbeams, the flange width shall not exceed 15 times the webwidth and shall be adequate for all design loads.

9.8.2 Box Girders

9.8.2.1 For cast-in-place box girders with normalslab span and girder spacing, where the slabs are consid-ered an integral part of the girder, the entire slab widthshall be assumed to be effective in compression.

9.8.2.2 For box girders of unusual proportions, in-cluding segmental box girders, methods of analysis which


consider shear lag shall be used to determine stresses inthe cross section due to longitudinal bending.

9.8.2.3 Adequate fillets shall be provided at the in-tersections of all surfaces within the cell of a box girder,except at the junction of web and bottom flange wherenone are required.

9.8.3 Precast/Prestressed Concrete Beams withWide Top Flanges

9.8.3.1 For composite prestressed concrete whereslabs or flanges are assumed to act integrally with the pre-cast beam, the effective web width of the precast beamshall be the lesser of (1) six times the maximum thicknessof the flange (excluding fillets) on either side of the webplus the web and fillets, and (2) the total width of the topflange.

9.8.3.2 The effective flange width of the com-posite section shall be the lesser of (1) one-fourth ofthe span length of the girder, (2) six (6) times thethickness of the slab on each side of the effective webwidth as determined by Article 9.8.3.1 plus the effec-tive web width, and (3) one-half the clear distance oneach side of the effective web width plus the effective webwidth.

9.9 FLANGE AND WEB THICKNESS—BOXGIRDERS

9.9.1 Top Flange

The minimum top flange thickness shall be %3oth of theclear distance between fillets or webs but not less than 6inches, except the minimum thickness may be reduced forfactory produced precast, pretensioned elements to5%2 inches.

9.9.2 Bottom Flange

The minimum bottom flange thickness shall be %3oth ofthe clear distance between fillets or webs but not less than5%2 inches, except the minimum thickness may be reducedfor factory produced precast, pretensioned elements to5 inches.

9.9.3 Web

Changes in girder stem thickness shall be tapered fora minimum distance of 12 times the difference in webthickness.

9.10 DIAPHRAGMS

9.10.1 General

Diaphragms shall be provided in accordance with Ar-ticles 9.10.2 and 9.10.3 except that diaphragms may beomitted where tests or structural analysis show adequatestrength.

9.10.2 T-Beams

Diaphragms or other means shall be used at span endsto strengthen the free edge of the slab and to transmit lat-eral forces to the substructure. Intermediate diaphragmsshall be placed between the beams at the points of maxi-mum moment for spans over 40 feet.

9.10.3 Box Girders

9.10.3.1 For spread box beams, diaphragms shallbe placed within the box and between boxes at span endsand at the points of maximum moment for spans over80 feet.

9.10.3.2 For precast box multi-beam bridges, di-aphragms are required only if necessary for slab-endsupport or to contain or resist transverse tension ties.

9.10.3.3 For cast-in-place box girders, diaphragms orother means shall be used at span ends to resist lateralforces and maintain section geometry. Intermediate di-aphragms are not required for bridges with inside radiusof curvature of 800 feet or greater.

9.10.3.4 For segmental box girders, diaphragms shallbe placed within the box at span ends. Intermediate di-aphragms are not required for bridges with inside radiusof curvature of 800 feet or greater.

9.10.3.5 For all types of prestressed boxes in bridgeswith inside radius of curvature less than 800 feet, inter-mediate diaphragms may be required and the spacing andstrength of diaphragms shall be given special considera-tion in the design of the structure.

9.11 DEFLECTIONS

9.11.1 General

Deflection calculations shall consider dead load, liveload, prestressing, erection loads, concrete creep andshrinkage, and steel relaxation.


9.11.2 Segmental Box Girders

Deflections shall be calculated prior to casting of seg-ments and they shall be based on the anticipated castingand erection schedules. Calculated deflections shall beused as a guide against which actual deflection measure-ments are checked.

9.11.3 Superstructure Deflection Limitations

When making deflection computations, the followingcriteria are recommended.

9.11.3.1 Members having simple or continuousspans preferably should be designed so that the deflectiondue to service live load plus impact shall not exceed %800

of the span, except on bridges in urban areas used in partby pedestrians whereon the ratio preferably shall notexceed %i000.

9.11.3.2 The deflection of cantilever arms due to ser-vice live load plus impact preferably should be limited to%00 of the cantilever arm except for the case includingpedestrian use, where the ratio preferably should be %375.

9.12 DECK PANELS

9.12.1 General

9.12.1.1 Precast prestressed deck panels used as per-manent forms spanning between stringers may be de-signed compositely with the cast-in-place portion of theslabs to support additional dead loads and live loads.

9.12.1.2 The panels shall be analyzed assuming theysupport their self-weight, any construction loads, and theweight of the cast-in-place concrete, and shall be analyzedassuming they act compositely with the cast-in-place con-crete to support moments due to additional dead loads andlive loads.

912.2 Bending Moment

9.12.2.1 Live load moments shall be computed in ac-cordance with Article 3.24.3.

9.12.2.2 In calculating stresses in the deck panel dueto negative moment near the stringer, no compression dueto prestressing shall be assumed to exist.

Part CDESIGN

9.13 GENERAL

9.13.1 Design Theory and General Considerations

9.13.1.1 Members shall meet the strength require-ments specified herein.

9.13.1.2 Design shall be based on strength (LoadFactor Design) and on behavior at service conditions (Al-lowable Stress Design) at all load stages that may be crit-ical during the life of the structure from the time pre-stressing is first applied.

9.13.1.3 Stress concentrations due to the prestressingshall be considered in the design.

9.13.1.4 The effects of temperature and shrinkageshall be considered.

9.13.2 Basic Assumptions

The following assumptions are made for design pur-poses for monolithic members.

9.13.2.1 Strains vary linearly over the depth of themember throughout the entire load range.

9.13.2.2 Before cracking, stress is linearly propor-tional to strain.

9.13.2.3 After cracking, tension in the concrete is ne-glected.

9.13.3 Composite Flexural Members

Composite flexural members consisting of precastand/or cast-in-place concrete elements constructed in sep-arate placements but so interconnected that all elementsrespond to superimposed loads as a unit shall conform tothe provisions of Articles 8.14.2.1 through 8.14.2.4,Article 8.14.2.6, and the following.

9.13.3.1 Where an entire member is assumed to re-sist the vertical shear, the design shall be in accordancewith the requirements of Articles 9.20.1 through 9.20.3.

9.13.3.2 The design shall provide for full transferof horizontal shear forces at contact surfaces of inter-connected elements. Design for horizontal shear shallbe in accordance with the requirements of Article9.20.4.


9.13.3.3 In structures with a cast-in-place slab onprecast beams, the differential shrinkage tends to causetensile stresses in the slab and in the bottom of the beams.Because the tensile shrinkage develops over an extendedtime period, the effect on the beams is reduced by creep.Differential shrinkage may influence the cracking loadand the beam deflection profile. When these factors areparticularly significant, the effect of differential shrinkageshould be added to the effect of loads.

9.14 LOAD FACTORS

The computed strength capacity shall not be less thanthe largest value from load factor design in Article 3.22.For the design of post-tensioned anchorage zones a loadfactor of 1.2 shall be applied to the maximum tendon j ack-ing force.

The following strength capacity reduction factors shallbe used:

For factory produced precast prestressed concretemembers (~ = 1.0For post-tensioned cast-in-place concrete members= 0.95For shear = 0.90For anchorage zones 4) = 0.85 for normal weight con-crete and (~ = 0.70 for lightweight concrete.

9.15 ALLOWABLE STRESSES

The design of precast prestressed members ordinarilyshall be based on f,' = 5,000 psi. An increase to 6,000 psiis permissible where, in the Engineer's judgment,it is reasonable to expect that this strength will be ob-tained consistently. Still higher concrete strengths may beconsidered on an individual area basis. In such cases,the Engineer shall satisfy himself completely that thecontrols over materials and fabrication procedures willprovide the required strengths. The provisions of thisSection are equally applicable to prestressed concretestructures and components designed with lower concretestrengths.

9.15.1 Prestressing Steel

Pretensioned members:Stress immediately prior to transferLow-relaxation strands..................................0.75 f,'Stress-relieved strands ...................................0.70 f,'

Post-tensioned members:Stress immediately after seatingAt anchorage................................................. 0.70 f,'

At the end of the seating loss zone...............0.83 fyTensioning to 0.90 fy for short periods oftime prior to seating may be permitted tooffset seating and friction losses providedthe stress at the anchorage does not exceedthe above value.

Stress at service load' after losses....................0.80 fy

9.15.2 Concrete

9.15.2.1 Temporary Stresses Before Losses Dueto Creep and Shrinkage

Compression:Pretensioned members..................................0.60 f~'iPost-tensioned members...............................0.55 f~'

i

Tension:Precompressed tensile zone...............No temporaryallowable stresses are specified. See Article9.15.2.2 for allowable stresses after losses.Other AreasIn tension areas withno bonded reinforcement ...............200 psi or 3NAZ,Where the calculated tensile stress exceeds

this value, bonded reinforcement shall beprovided to resist the total tension force inthe concrete computed on the assumptionof an uncracked section. The maximumtensile stress shall not exceed .................. 7.5 fli

9.15.2.2 Stress at Service Load After LossesHave Occurred

Compression:(a) The compressive stresses under all load combina-tions, except as stated in (b) and (c), shall not exceed0.60f, .(b) The compressive stresses due to effective prestressplus permanent (dead) loads shall not exceed 0.40f,.(c) The compressive stress due to live loads plus one-half of the sum of compressive stresses due to prestressand permanent (dead) loads shall not exceed 0.40f,.

Tension in the precompressed tensile zone:(a) For members with bonded reinforce-ment*...................................................................6For severe corrosive exposure conditions,such as coastal areas............................................3

*Includes bonded prestressed strands,tService load consists of all loads contained in Article 3.2 but does not

include overload provisions.


(b) For members without bonded reinforce-ment............................................................................0

Tension in other areas is limited by allowable temporarystresses specified in Article 9.15.2.1.

9.15.2.3 Cracking Stress*

Modulus of rupture from tests or if not available.For normal weight concrete ............................. 7.5 fTFor sand-lightweight concrete ..........................6.3 f'For all other lightweight concrete .................... 5.5 f~

9.15.2.4 Anchorage Bearing Stress

Post-tensioned anchorage at service load ...3,000 psi(but not to exceed 0.9 f,')

9.16 LOSS OF PRESTRESS

9.16.1 Friction Losses

Friction losses in post-tensioned steel shall be based onexperimentally determined wobble and curvature coeffi-cients, and shall be verified during stressing operations.The values of coefficients assumed for design, and the ac-ceptable ranges of jacking forces and steel elongationsshall be shown on the plans. These friction losses shall becalculated as follows:

To = TXe(KL +pa) (9-1)

When (KL + pa) is not greater than 0.3, the followingequation may be used:

To = TX (1 + KL + pot) (9-2)

The following values for K and µ may be used whenexperimental data for the materials used are not available:

Type of Steel Type of Duct K/ft µ

Wire or strand Rigid and semi-rigidgalvanized metal 0.0002 0.15—0.25,

sheathingPolyethylene 0.0002 0.23Rigid steel pipe 0.0002 0.256

High Strengthbars Galvanized metal sheathing 0.0002 0.15

aA friction coefficient of 0.25 is appropriate for 12 strand tendons. Alower coefficient may be used for larger tendon and duct sizes.6Lubrication will probably be required.

Friction losses occur prior to anchoring but should beestimated for design and checked during stressing opera-

*Refer to Article 9.18.

tions. Rigid ducts shall have sufficient strength to main-tain their correct alignment without visible wobble duringplacement of concrete. Rigid ducts may be fabricated witheither welded or interlocked seams. Galvanizing of thewelded seam will not be required.

9.16.2 Prestress Losses

9.16.2.1 General

Loss of prestress due to all causes, excluding friction,may be determined by the following method.** Themethod is based on normal weight concrete and one of thefollowing types of prestressing steel: 250 or 270 ksi,seven-wire, stress-relieved or low-relaxation strand; 240ksi stress-relieved wires; or 145 to 160 ksi smooth or de-formed bars. Refer to documented tests for data regardingthe properties and the effects of lightweight aggregateconcrete on prestress losses.

TOTAL LOSS

Afs = SH + ES + CRS + CRS (9-3)

where:

Af, = total loss excluding friction in pounds persquare inch;

SH = loss due to concrete shrinkage in pounds persquare inch;

ES = loss due to elastic shortening in pounds persquareinch;

CR, = loss due to creep of concrete in pounds persquareinch;

CR S = loss due to relaxation of prestressing steel inpounds per square inch.

9.16.2.1.1 Shrinkage

Pretensioned Members:

SH = 17,000 — 150 RH (9-4)

Post-tensioned Members:

SH = 0.80 (17,000 — 150 RH) (9-5)

**Should more exact prestress losses be desired, data representing thematerials to be used, the methods of curing, the ambient service condi-tion and any pertinent structural details should be determined for use inaccordance with a method of calculating prestress losses that is sup-ported by appropriate research data. See also FHWA Report FHWA/RD85/045, Criteria for Designing Lightweight Concrete Bridges.


where RH = mean annual ambient relative humidity in 9.16.2.1.3 Creep of Concrete

percent. (See Figure 9.16.2.1.1.) Pretensioned and post-tensioned members

9.16.2.1.2 Elastic ShorteningCR S =12 fair — 7

fca5 (9-9)Pretensioned Members

where

E fads = concrete stress at the center of gravity of the

ES = s fair (9-6) prestressing steel due to all dead loads exceptE°' the dead load present at the time the pre-

Post-tensioned Members*stressing force is applied.

9.16.2.1.4 Relaxation of Prestressing Steel **

ES = 0.5ES

fair (9-7) Pretensioned MembersE c ,

where

ES = modulus of elasticity of prestressing steelstrand, which can be assumed to be 28 X 10 6

psi;Eci = modulus of elasticity of concrete in psi at

transfer of stress, which can be calculatedfrom:

E ci = 33w3/2

'Ci (9-8)

in which w is the concrete unit weight inpounds per cubic foot and f c'i is in pounds persquare inch;

fair = concrete stress at the center of gravity of theprestressing steel due to prestressing force anddead load of beam immediately after transfer;f ir shall be computed at the section or sectionsof maximum moment. (At this stage, the ini-tial stress in the tendon has been reduced byelastic shortening of the concrete and tendonrelaxation during placing and curing the con-crete for pretensioned members, or by elasticshortening of the concrete and tendon frictionfor post-tensioned members. The reductionsto initial tendon stress due to these factors canbe estimated, or the reduced tendon stress canbe taken as 0.63 fs for stress relieved strand or0.69 fs for low relaxation strand in typical pre-tensioned members.)

250 to 270 ksi StrandCR S = 20,000 — 0.4 ES — 0.2 (SH + CRS)

for stress relieved strand (9-10)

CR S 5,000 — 0.10 ES — 0.05 (SH + CR,)for low relaxation strand (9-10A)

Post-tensioned Members

250 to 270 ksi StrandCRS = 20,000 — 0.3 FR — 0.4 ES — 0.2 (SH + CR S)

for stress relieved strand (9-11)

CR S = 5,000 — 0.07 FR — 0.1 ES — 0.05 (SH + CR S)for low relaxation strand (9-11A)

240 ksi WireCR S = 18,000 — 0.3 FR — 0.4 ES — 0.2 (SH + CR S)

(9-12)

145- to 160-ksi BarsCRS = 3,000

FR = friction loss stress reduction in psi belowthe level of 0.70 fs at the point underconsideration, computed according toArticle 9.16.1,

ES, SH, = appropriate values as determined forand CR, either pretensioned or post-tensioned

members.

where

*Certain tensioning procedures may alter the elastic shortening losses.**The relaxation losses are based on an initial stress equal to the stress

at anchorages allowed by Article 9.15.1.

MEAN ANNUAL RELATIVE HUMIDITY(%)70

A

60

0 60

Tf

70CA

.04.

400c O—n

.10

'per77 Based on 1:30 a.m. & p.m-70

AA.h-

ICS P"~

70 and 7:30 a.m. & p.m., e.s.t.observations for 20 yearsor more through 1964.

8H.J-D 6 a I IFM c

ALASKAHAWAII

z

FIGURE 9.16.2.1.1 Mean Annual Relative Humidity


9.16.2.2 Estimated Losses

In lieu of the preceding method, the followingestimates of total losses may be used for prestressedmembers or structures of usual design. These loss valuesare based on use of normal weight concrete, normalprestress levels, and average exposure conditions. Forexceptionally long spans, or for unusual designs, themethod in Article 9.16.2.1 or a more exact method shallbe used.

TABLE 9.16.2.2 Estimate of Prestress Losses

Type of Total Loss

Prestressing Steel f,' = 4,000 psi fe = 5,000 psi

Pretensioning Strand — 45,000 psiPost-Tensioning'

Wire or Strand 32,000 psi 33,000 psiBars 22,000 psi 23,000 psi

'Losses due to friction are excluded. Friction losses should be com-puted according to Article 9.16.1.

9.17 FLEXURAL STRENGTH

9.17.1 General

Prestressed concrete members may be assumed to actas uncracked members subjected to combined axial andbending stresses within specified service loads. In calcu-lations of section properties, the transformed area ofbonded reinforcement may be included in pretensionedmembers and in post-tensioned members after grouting;prior to bonding of tendons, areas of the open ducts shallbe deducted.

9.17.2 Rectangular Sections

For rectangular or flanged sections having prestressingsteel only, which the depth of the equivalent rectangularstress block, defined as (A* f *,)/(0.85 fib), is not greaterthan the compression flange thickness "t", and which sat-isfy Equation (9-20), the design flexural strength shall beassumed as:

*OM„=0 Asf, d 1—0.0-

*fsu(9-13)

c

For rectangular or flanged sections with non-prestressed tension reinforcement included, in whichthe depth of the equivalent rectangular stress block,defined as (A* f

s+ Asf,,,)/(0.85 f,b), is not greater

than the compression flange thickness "t," and which

satisfy Equation (9-24), the design flexural strength shallbe assumed as:

O Mn =0j SfS dl

1-0.6

\ pf~~ + dt pf,' y

JJlrrL

c'

+AsfsydtL1—0.61dcpffSu+pfV

JJ~

(9 -13a)

9.17.3 Flanged Sections

For sections having prestressing steel only, in whichthe depth of the equivalent rectangular stress block,defined as (A,,f*,)/(0.85f'b') is greater than thecompression flange thickness "t," and which satisfyEquation (9-21), the design flexural strength shall be as-sumed as:

OMn - 0 A sr fs d 1— 0.6srf~

c

+ 0.85 fc (b — b')(t)(d — 0.5t) (9-14)

For sections with non-prestressed tension reinforce-ment included, in which the depth of the equivalent rec-tangular stress block, defined as (Asrf*„)/(0.85 f c'b') isgreater than the compression flange thickness "t," andwhich satisfy Equation (9-25), the design flexural strengthshall be assumed as:

O M n = 0 Asr fs d 1— 0.6A

sr fsub,df, + A, fsy (d t — d)

c

+ 0.85 f, (b — b ')(t)(d — 0.5t) (9 -14a)

where:

A sr = A*S — A,f in Equation (9-14); (9-15)

Asr = A* + (Asfsy/f *) — Asf,in Equation (9-14a) (9-15a)

Asf = 0.85 f,' (b — b ' )t/fu; (9-16)

Asf = the steel area required to develop the ultimatecompressive strength of the overhanging por-tions of the flange.


9.17.4 Steel Stress

9.17.4.1 Unless the value of f*,, can be more accu-rately known from detailed analysis, the following valuesmay be used:

Bonded Members ...with prestressing only (as defined);

Q. =fs[1—(7*/Ri)(p*fs/f,')] (9-17)

with non-prestressed tension reinforcement included;

fU=f; ~ l—

1*Ipf , +dl(p`-yb(9-17a)

Unbonded members ... ft = to + 900((d — y„)/le) (9-18)

but shall not exceed Q.

Where

y„ = distance from extreme compression fiber tothe neutral axis assuming the tendon pre-stressing steel has yielded.

1 e = 1;1(1 + 0.5N5); effective tendon length.1; = tendon length between anchorages (inch).N, = number of support hinges crossed by the ten-

don between anchorages or discretely bondedpoints.

provided that

(1) The stress-strain properties of the prestressingsteel approximate those specified in Division II, Arti-cle 10.3.1.1.(2) The effective prestress after losses is not less than0.5 fs.

9.17.4.2 At ultimate load, the stress in the pre-stressing steel of precast deck panels shall be limited to

su D 3 se

but shall not be greater than f*u as given by the equationsin Article 9.17.4.1. In the above equation:

D = nominal diameter of strand in inches;f5e = effective stress in prestressing strand after losses

in kips per square inch;f X = distance from end of prestressing strand to center

of panel in inches.

9.18 DUCTILITY LIMITS

9.18.1 Maximum Prestressing Steel

Prestressed concrete members shall be designed so thatthe steel is yielding as ultimate capacity is approached. Ingeneral, the reinforcement index shall be such that

(p*fu

)/f,' for rectangular sections (9-20)

and

A srf u/(b ' df,' ) for flanged sections (9-21)

does not exceed 0.36(3 1 . (See Article 9.19 for rein-forcement indices of sections with non-prestressedreinforcement.).

For members with reinforcement indices greater than0.36(3 1 , the design flexural strength shall be assumed notgreater than:

For rectangular sections

Wn = ~) [(0.36 Rl — 0.08 (3;) f,bd2] (9-22)

For flanged sections

(~M~ _ (K(0 -36p , — 0.08 (3;) f,b ' d

2+

0.85 f,' (b — b') t (d — 0.5t)] (9-23)

9.18.2 Minimum Steel

9.18.2.1 The total amount of prestressed and non-prestressed reinforcement shall be adequate to develop anultimate moment at the critical section at least 1.2 timesthe cracking moment M*

(~Mn ? 1.2 M*

where

Mor = Sovfr + f

pe) — Mame (S

c/Sb —

1 )

Appropriate values for M d/ne and S b shall be used for anyintermediate composite sections. Where beams are de-signed to be noncomposite, substitute Sb for S e in theabove equation for the calculation of M*.

9.18.2.2 The requirements of Article 9.18.2.1 may bewaived if the area of prestressed and non-prestressed re-inforcement provided at a section is at least one-third


greater than that required by analysis based on the load-ing combinations specified in Article 3.22.

9.18.2.3 The requirements of Article 9.18.2.1 may bewaived if the area of prestressed and non-prestressed re-inforcement provided at a section is at least one-thirdgreater than that required by analysis based on the load-ing combinations specified in Article 3.22.

9.18.2.4 The minimum amount of non-prestressedlongitudinal reinforcement provided in the cast-in-placeportion of slabs utilizing precast prestressed deck panel'sshall be 0.25 square inch per foot of slab width.

9.19 NON-PRESTRESSED REINFORCEMENT

Non-prestressed reinforcement may be considered ascontributing to the tensile strength of the beam at ultimatestrength in an amount equal to its area times its yieldpoint, provided that

For rectangular sections

C pfcy1d

+ Pffs

" —(pf

fs')50.36p, (9-24)

For flanged sections

(Asf,)/(b'df~) + (A

u f U)/(b'df,')— (Asfy)/(b'dfG) <_ 0.360 1 (9-25)

Design flexural strength shall be calculated based onEquation (9-13a) or Equation (9-14a) if these values aremet, and on Equation (9-22) or Equation (9-23) if thesevalues are exceeded.

9.20 SHEAR*

9.20.1 General

9.20.1.1 Prestressed concrete flexural members, ex-cept solid slabs and footings, shall be reinforced for shearand diagonal tension stresses. Voided slabs shall be inves-tigated for shear, but shear reinforcement may be omittedif the factored shear force, V,,, is less than half the shearstrength provided by the concrete

4 V,.

9.20.1.2 Web reinforcement shall consist of stirrupsperpendicular to the axis of the member or welded

*The method for design of web reinforcement presented in the 1979Interim AASHTO Standard Specifications for Highway Bridges is anacceptable alternate.

wire fabric with wires located perpendicular to the axisof the member. Web reinforcement shall extend to adistance d from the extreme compression fiber and shallbe carried as close to the compression and tension sur-faces of the member as cover requirements and theproximity of other reinforcement permit. Web rein-forcement shall be anchored at both ends for its designyield strength in accordance with the provisions ofArticle 8.27.

9.20.1.3 Members subject to shear shall be designedso that

V u <_ (~ (V~ + V s) (9-26)

where V. is the factored shear force at the section consid-ered, V, is the nominal shear strength provided by con-crete and V, is the nominal shear strength provided by webreinforcement.

9.20.1.4 When the reaction to the applied loads in-troduces compression into the end regions of the member,sections located at a distance less than h/2 from the faceof the support may be designed for the same shear V. as.that computed at a distance h/2.

9.20.1.5 Reinforced keys shall be provided in thewebs of precast segmental box girders to transfer erectionshear. Possible reverse shearing stresses in the shear keysshall be investigated, particularly in segments near a pier.At time of erection, the shear stress carried by the shearkey shall not exceed 2 VfTl ~

.

9.20.2 Shear-Strength Provided by Concrete

9.20.2.1 The shear strength provided by concrete, V,,shall be taken as the lesser of the values V, i or V,,.

9.20.2.2 The shear strength, V ii , shall be computedby

Vii = 0.6 f, b 'd + Vd +V1Mcr

(9-27)M

max

but need not be less than 1.7 f,' b' d and d need not betaken less than 0.8h.

The moment causing flexural cracking at the sectiondue to externally applied loads, M,, shall be computed by:

M ir = 1 (6 f~ + fpe — fd ) (9-28)Y,

The maximum factored moment and factored shear atthe section due to externally applied loads, M.. and V i ,


shall be computed from the load combination causingmaximum moment at the section.

9.20.3.3 The minimum area of web reinforcementshall be

9.20.2.3 The shear strength, V,,, shall be computedAV _ 50 b's

(9-31)f

syby

V,, _ (3.5 f~ + 0.3 fp,) b'd + Vp (9-29)

but d need not be taken less than 0.8h.

9.20.2.4 For a pretensioned member in whichthe section at a distance h/2 from the face of supportis closer to the end of the member than the transfer lengthof the prestressing tendons, the reduced prestress shallbe considered when computing V i ,. The prestressforce may be assumed to vary linearly from zero at theend of the tendon to a maximum at a distance fromthe end of the tendon equal to the transfer length, as-sumed to be 50 diameters for strand and 100 diametersfor single wire.

9.20.2.5 The provisions for computing the shearstrength provided by concrete, V, i and V, µ , apply to nor-mal weight concrete. When lightweight aggregate con-cretes are used (see definition, concrete, structural light-weight, Article 8.1.3), one of the following modificationsshall apply:

(a) When f,, is specified, the shear strength, V,, andV,W, shall be modified by substituting f,,/6.7 for Tc;,

but the value of f it/6.7 used shall not exceed VTT.

(b) When f,, is not specified, V,; and V FW shall be mod-ified by multiplying each term containing N/ /-f—c' by 0.75for "all lightweight" concrete, and 0.85 for "sand-light-weight" concrete. Linear interpolation may be usedwhen partial sand replacement is used.

9.20.3 Shear Strength Provided by WebReinforcement

9.20.3.1 The shear strength provided by web rein-forcement shall be taken as:

VS = AVfSyd (9-30)s

where A V is the area of web reinforcement within a dis-tance s. V S shall not be taken greater than 8 V'f,' b ' d andd need not be taken less than 0.8h.

9.20.3.2 The spacing of web reinforcing shall not ex-ceed 0.75h or 24 inches. When V S exceeds 4 f, b' d, thismaximum spacing shall be reduced by one-half.

where b ' and s are in inches and f sy is in psi.

9.20.3.4 The design yield strength of web reinforce-ment, fsy, shall not exceed 60,000 psi.

9.20.4 Horizontal Shear Design—CompositeFlexural Members

9.20.4.1 In a composite member, full transfer of hor-izontal shear forces shall be assured at contact surfaces ofinterconnected elements.

9.20.4.2 Design of cross sections subject to horizon-tal shear may be in accordance with provisions of Article9.20.4.3 or 9.20.4.4, or any other shear transfer designmethod that results in prediction of strength in substantialagreement with results of comprehensive tests.

9.20.4.3 Design of cross sections subject to horizon-tal shear may be based on:

V. < (W.h (9-31a)

where V„ is factored shear force at section considered, Vnh

is nominal horizontal shear strength in accordance withthe following, and where d is for the entire composite sec-tion.

(a) When contact surface is clean, free of laitance, andintentionally roughened, shear strength V nh shall not betaken greater than 80b„d, in pounds.(b) When minimum ties are provided in accordancewith Article 9.20.4.5, and contact surface is clean andfree of laitance, but not intentionally roughened, shearstrength V nh shall not be taken greater than 80b„d, inpounds.(c) When minimum ties are provided in accordancewith Article 9.20.4.5, and contact surface is clean, freeof laitance, and intentionally roughened to a full am-plitude of approximately %4 inch, shear strength Vnh

shall not be taken greater than 350b,d, in pounds.(d) For each percent of tie reinforcement crossing thecontact surface in excess of the minimum required byArticle 9,20.4.5, shear strength V nh may be increasedby (160f,,/40,000)b,,d, in pounds.

9.20.4.4 Horizontal shear may be investigated bycomputing, in any segment not exceeding one-tenth of the


span, the change in compressive or tensile force to betransferred, and provisions made to transfer that force ashorizontal shear between interconnected elements. Thefactored horizontal shear force shall not exceed horizon-tal shear strength (~ V

nh in accordance with Article9.20.4.3, except that length of segment considered shall besubstituted for d.

9.20.4.5 Ties for Horizontal Shear

(a) When required, a minimum area of tie reinforce-ment shall be provided between interconnected ele-ments. Tie area shall not be less than 50 b,s/f,, and tiespacing "s" shall not exceed four times the least webwidth of support element, nor 24 inches.(b) Ties for horizontal shear may consist of single barsor wire, multiple leg stirrups, or vertical legs of weldedwire fabric. All ties shall be adequately anchored intointerconnected elements by embedment or hooks.

9.21 POST-TENSIONED ANCHORAGE ZONES

9.21.1 Geometry of the Anchorage Zone

9.21.1.1 The anchorage zone is geometrically de-fined as the volume of concrete through which the con-centrated prestressing force at the anchorage devicespreads transversely to a linear stress distribution acrossthe entire cross section.

9.21.1.2 For anchorage zones at the end of a memberor segment, the transverse dimensions may be taken as thedepth and width of the section. The longitudinal extent ofthe anchorage zone in the direction of the tendon (aheadof the anchorage) shall be taken as not less than the largertransverse dimension but not more than 1%2 times thatdimension.

9.21.1.3 For intermediate anchorages in addition tothe length of Article 9.21.1.2 the anchorage zone shall beconsidered to also extend in the opposite direction for adistance not less than the larger transverse dimension.

9.21.1.4 For multiple slab anchorages, both widthand length of the anchorage zone shall be taken as equalto the center-to-center spacing between stressed tendons,but not more than the length of the slab in the direction ofthe tendon axis. The thickness of the anchorage zone shallbe taken equal to the thickness of the slab.

9.21.1.5 For design purposes, the anchorage zoneshall be considered as comprised of two regions; the gen-eral zone as defined in Article 9.21.2.1 and the local zoneas defined in Article 9.21.2.2.

9.21.2 General Zone and Local Zone

9.21.2.1 General Zone

9.21.2.1.1 The geometric extent of the general zoneis identical to that of the overall anchorage zone as definedin Article 9.2 and includes the local zone.

9.21.2.1.2 Design of general zones shall meet the re-quirements of Articles 9.14 and 9.21.3.

9.21.2.2 Local Zone

9.21.2.2.1 The local zone is defined as the rectangu-lar prism (or equivalent rectangular prism for circular oroval anchorages) of concrete surrounding and immedi-ately ahead of the anchorage device and any integral con-fining reinforcement. The dimensions of the local zone aredefined in Article 9.21.7.

9.21.2.2.2 Design of local zones shall meet the re-quirements of Articles 9.14 and 9.21.7 or shall be basedon the results of experimental tests required in Article9.21.7.3 and described in Article 10.3.2.3 of Division 1I.Anchorage devices based on the acceptance test of Divi-sion 11, Article 10.3.2.3, are referred to as special anchor-age devices.

9.21.2.3 Responsibilities

9.21.2.3.1 The engineer of record is responsible forthe overall design and approval of working drawings forthe general zone, including the specific location of the ten-dons and anchorage devices, general zone reinforcement,and the specific stressing sequence. The engineer ofrecord is also responsible for the design of local zonesbased on Article 9.21.7.2 and for the approval of specialanchorage devices used under the provisions of Article9.21.7.3. All working drawings for the local zone must beapproved by the engineer of record.

9.21.2.3.2 Anchorage device suppliers are responsi-ble for furnishing anchorage devices which satisfy the an-chor efficiency requirements of Division 11, Article 10.3.2.In addition, if special anchorage devices are used, the an-chorage device supplier is responsible for furnishing an-chorage devices that satisfy the acceptance test require-ments of Article 9.21.7.3 and of Division 1I, Article10.3.23. This acceptance test and the anchor efficiencytest shall be conducted by an independent testing agencyacceptable to the engineer of record. The anchorage de-vice supplier shall provide records of the acceptance testin conformance with Division II, Article 10.3.2.3.12 to the


engineer of record and to the constructor and shall spec-ify auxiliary and confining reinforcement, minimum edgedistance, minimum anchor spacing, and minimumconcrete strength at time of stressing required for properperformance of the local zone.

9.21.2.3.3 The responsibilities of the constructor arespecified in Division Il, Article 10.4.

9.21.3 Design of the General Zone

9.21.3.1 Design Methods

The following methods may be used for the design ofgeneral zones:

(1) Equilibrium based plasticity models (strut-and-tiemodels) (see Article 9.21.4)(2) Elastic stress analysis (finite element analysis orequivalent) (see Article 9.21.5)(3) Approximate methods for determining the com-pression and tension forces, where applicable. (SeeArticle 9.21.6.)

Regardless of the design method used, all designs shallconform to the requirements of Article 9.21.3.4.

The effects of stressing sequence and three-dimen-sional effects shall be considered in the design. Whenthese three dimensional effects appear significant, theymay be analyzed using three-dimensional analysis proce-dures or may be approximated by considering two or moreplanes. However, in these approximations the interactionof the planes' models must be considered, and the modelloadings and results must be consistent.

9.21.3.2 Nominal Material Strengths

9.21.3.2.1 The nominal tensile strength of bonded re-inforcement is limited to f, for non-prestressed reinforce-ment and to fy for prestressed reinforcement. The nominaltensile strength of unbonded prestressed reinforcement islimited to f5e + 15,000 psi.

9.21.3.2.2 The effective nominal compressivestrength of the concrete of the general zone, exclusive ofconfined concrete, is limited to 0.7 f,'. The tensile strengthof the concrete shall be neglected.

9.21.3.2.3 The compressive strength of concrete attransfer of prestressing shall be specified on the construc-tion drawings. If not otherwise specified, stress shall notbe transferred to concrete until the compressive strengthof the concrete as indicated by test cylinders, cured by

methods identical with the curing of the member, is atleast 4,000 psi.

9.21.3.3 Use of Special Anchorage Devices

Whenever special anchorage devices which do notmeet the requirements of Article 9.21.7.2 are to be used,reinforcement similar in configuration and at least equiv-alent in volumetric ratio to the supplementary skin rein-forcement permitted under the provisions of Division II,Article 10.3.2.3.4 shall be furnished in the correspondingregions of the anchorage zone.

9.21.3.4 General Design Principles and DetailingRequirements

Good detailing and quality workmanship are essentialfor the satisfactory performance of anchorage zones.Sizes and details for anchorage zones should respect theneed for tolerances on the bending, fabrication and place-ment of reinforcement, the size of aggregate and the needfor placement and sound consolidation of the concrete.

9.21.3.4.1 Compressive stresses in the concreteahead of basic anchorage devices shall meet the require-ments of Article 9.21.7.2.

9.21.3.4.2 Compressive stresses in the concreteahead of special anchorage devices shall be checked at adistance measured from the concrete-bearing surfaceequal to the smaller of.

(1) The depth to the end of the local confinement re-inforcement.(2) The smaller lateral dimension of the anchorage de-vice.

These compressive stresses may be determined accordingto the strut-and-tie model procedures of Article 9.21.4,from an elastic stress analysis according to Article9.21.5.2, or by the approximate method outlined in Arti-cle 9.21.6.2. These compressive stresses shall not exceed0.7 f,';.

9.21.3.4.3 Compressive stresses shall also bechecked where geometry or loading discontinuities withinor ahead of the anchorage zone may cause stress concen-trations.

9.21.3.4.4 The bursting force is the tensile force inthe anchorage zone acting ahead of the anchorage deviceand transverse to the tendon axis. The magnitude of thebursting force, Tbw,t, and its corresponding distance from


the loaded surface, db~..1, can be determined using thestrut-and-tie model procedures of Article 9.21.4, from anelastic stress analysis according to Article 9.21.5.3, or bythe approximate method outlined in Article 9.21.6.3.Three-dimensional effects shall be considered for the de-termination of the bursting reinforcement requirements.

9.21.3.4.5 Resistance to bursting forces, (~Aj,,and/or (~A*f

Y, shall be provided by non-prestressed or

prestressed reinforcement, in the form of spirals, closedhoops, or well-anchored transverse ties. This reinforce-ment is to be proportioned to resist the total factored burst-ing force. Arrangement and anchorage of bursting rein-forcement shall satisfy the following:

(1) Bursting reinforcement shall extend over the fullwidth of the member and must be anchored as close tothe outer faces of the member as cover permits.(2) Bursting reinforcement shall be distributed aheadof the loaded surface along both sides of the tendonthroughout a distance of 2.5 dburet for the plane consid-ered, but not to exceed 1.5 times the corresponding lat-eral dimension of the section. The centroid of the burst-ing reinforcement shall coincide with the distance db,,,,used for the design.(3) Spacing of bursting reinforcement shall exceedneither 24-bar diameters nor 12 inches.

9.21.3.4.6 Edge tension forces are tensile forcesin the anchorage zone acting parallel and close tothe transverse edge and longitudinal edges of the mem-ber. The transverse edge is the surface loaded by theanchors. The tensile force along the transverse edge isreferred to as spalling force. The tensile force along thelongitudinal edge is referred to as longitudinal edgetension force.

9.21.3.4.7 Spalling forces are induced in con-centrically loaded anchorage zones, eccentrically loadedanchorage zones, and anchorage zones for multipleanchors. Longitudinal edge tension forces are inducedwhen the resultant of the anchorage forces consideredcauses eccentric loading of the anchorage zone. Theedge tension forces can be determined from anelastic stress analysis, strut-and-tie models, or inaccordance with the approximate methods of Article9.21.6.4.

9.21.3.4.8 In no case shall the spalling force betaken as less than 2% of the total factored tendon force.

9.21.3.4.9 Resistance to edge tension forces, (¢A,f S,,and/or ~)A*f,*„ shall be provided in the form of non-pre-

stressed or prestressed reinforcement located close to thelongitudinal and transverse edge of the concrete. Arrange-ment and anchorage of the edge tension reinforcementshall satisfy the following:

(1) Minimum spalling reinforcement satisfying Arti-cle 9.21.3.4.8 shall extend over the full width of themember.(2) Spalling reinforcement between multiple anchor-age devices shall effectively tie these anchorage de-vices together.(3) Longitudinal edge tension reinforcement andspalling reinforcement for eccentric anchorage devicesshall be continuous. The reinforcement shall extendalong the tension face over the full length of the an-chorage zone and shall extend along the loaded facefrom the longitudinal edge to the other side of the ec-centric anchorage device or group of anchorage devices.

9.21.3.5 Intermediate Anchorages

9.21.3.5.1 Intermediate anchorages shall not be usedin regions where significant tension is generated behindthe anchor from other loads. Whenever practical, blistersshall be located in the corner between flange and webs, orshall be extended over the full flange width or web heightto form a continuous rib. If isolated blisters must be usedon a flange or web, local shear, bending and direct forceeffects shall be considered in the design.

9.21.3.5.2 Bonded reinforcement shall be providedto tie back at least 25% of the intermediate anchorage un-factored stressing force into the concrete section behindthe anchor. Stresses in this bonded reinforcement are lim-ited to a maximum of 0.6f s,, or 36 ksi. The amount oftie back reinforcement may be reduced using Equation(9-32), if permanent compressive stresses are generatedbehind the anchor from other loads.

Ti. = 0.25P s — fbA cb (9-32)

where, Ti , = the tie back tension force at the interme-diate anchorage;

PS = the maximum unfactored anchoragestressing force;

f1b = the compressive stress in the region be-

hind the anchor;Alb = the area of the continuing cross section

within the extensions of the sides of theanchor plate or blister. The area of theblister or rib shall not be taken as part ofthe cross section.


9.21.3.5.3 Tie back reinforcement satisfying Article9.21.3.5.2 shall be placed no further than one plate widthfrom the tendon axis. It shall be fully anchored so that theyield strength can be developed at a distance of one platewidth or half the length of the blister or rib ahead of theanchor as well as at the same distance behind the anchor.The centroid of this reinforcement shall coincide with thetendon axis, where possible. For blisters and ribs, the re-inforcement shall be placed in the continuing section nearthat face of the flange or web from which the blister or ribis projecting.

9.21.3.5.4 Reinforcement shall be provided through-out blisters or ribs are required for shear friction, corbel ac-tion, bursting forces, and deviation forces due to tendoncurvature. This reinforcement shall be in the form of tiesor U-stirrups which encase the anchorage and tie it effec-tively into the adjacent web and flange. This reinforcementshall extend as far as possible into the flange or web andbe developed by standard hooks bent around transversebars or equivalent. Spacing shall not exceed the smallest ofblister or rib height at anchor, blister width, or 6 inches.

9.21.3.5.5 Reinforcement shall be provided to resistlocal bending in blisters and ribs due to eccentricity of thetendon force and to resist lateral bending in ribs due totendon deviation forces.

9.21.3.5.6 Reinforcement required by Articles9.21.3.4.4 through 9.21.3.4.9 shall be provided to resisttensile forces due to transfer of the anchorage force fromthe blister or rib into the overall structure.

9.21.3.6 Diaphragms

9.21.3.6.1 For tendons anchored in diaphragms, con-crete compressive stresses shall be limited within the di-aphragm in accordance with Articles 9.21.3.4.1 through9.21.3.4.3. Compressive stresses shall also be checked atthe transition from the diaphragm to webs and flanges ofthe member.

9.21.3.62 Reinforcement shall be provided to ensurefull transfer of diaphragm anchor loads into the flangesand webs of the girder. The more general methods of Ar-ticle 9.21.4 or 9.21.5 shall be used to determine this rein-forcement. Reinforcement shall also be provided to tieback deviation forces due to tendon curvature.

9.21.3.7 Multiple Slab Anchorages

9.21.3.7.1 Minimum reinforcement meeting the re-quirements of Articles 9.21.3.7.2 through 9.21.3.7.4 shallbe provided unless a more detailed analysis is made.

9.21.3.7.2 Reinforcement shall be provided for thebursting force in the direction of the thickness of the slaband normal to the tendon axis in accordance with Articles9.21.3.4.4 and 9.21.3.4.5. This reinforcement shall be an-chored close to the faces of the slab with standard hooksbent around horizontal bars, or equivalent. Minimum re-inforcement is two #3 bars per anchor located at a distanceequal to one-half the slab thickness ahead of the anchor.

9.21.3.7.3 Reinforcement in the plane of the slab andnormal to the tendon axis shall be provided to resist edgetension forces, T,, between anchorages (Equation (9-33))and bursting forces, T2, ahead of the anchorages (Equation(9-34)). Edge tension reinforcement shall be placed im-mediately ahead of the anchors and shall effectively tieadjacent anchors together. Bursting reinforcement shall bedistributed over the length of the anchorage zones. (SeeArticle 9.21.1.4.)

T = O. lO p,, I –a)

(9-33)\ s/

T2 = 0.20P„Cl –

a)(9-34)

s

where T l = the edge tension force;T2 =the bursting force;P„ = the factored tendon load on an individual

anchor;= the anchor plate width;= the anchorage spacing.

9.21.3.7.4 For slab anchors with an edge distanceof less than two plate widths or one slab thickness,the edge tension reinforcement shall be proportioned toresist 25% of the factored tendon load. This reinforcementshall preferably be in the form of hairpins and shall be dis-tributed within one plate width ahead of the anchor. Thelegs of the hairpin bars shall extend from the edge of theslab past the adjacent anchor but not less than a distanceequal to five plate widths plus development length.

9.21.4 Application of Strut-and-Tie Models to theDesign of Anchorage Zones

9.21.4.1 General

9.21.4.1.1 The flow of forces in the anchorage zonemay be approximated by a series of straight compressionmembers (struts) and straight-tension members (ties) thatare connected at discrete points (nodes). Compressionforces are carried by concrete compression struts and ten-


sion forces are carried by non-prestressed or prestressedreinforcement,

9.21.4.1.2 The selected strut-and-tie model shall fol-low a load path from the anchorages to the end of the an-chorage zone. Other forces acting on the anchorage zone,such as reaction forces, tendon deviation forces, and ap-plied loads, shall be considered in the selection of thestrut-and-tie model. The forces at the end of the anchor-age zone can be obtained from an axial-flexural beamanalysis.

9.21.4.2 Nodes

Local zones which meet the provisions of Article9.21.7 or Division II, Article 10.3.2.3 are considered asproperly detailed, adequate nodes. The other nodes in theanchorage zone are adequate if the effective concretestresses in the struts meet the requirements of Article9.21.4.3 and the tension ties are properly detailed to de-velop the full-yield strength of the reinforcement.

9.21.4.3 Struts

9.21,4.31 The effective concrete compressivestrength for the general zone shall usually be limited to0.7c f,',, In areas where the concrete may be extensivelycracked at ultimate due to other load effects, or if largeplastic rotations are required, the effective compressivestrength shall be limited to 0.6(~ f

9.21.4.3.2 In anchorage zones the critical section forcompression struts is ordinarily located at the interfacewith the local zone node. If special anchorage devices areused, the critical section of the strut can be taken as thatsection whose extension intersects the axis of the tendonat a depth equal to the smaller of the depth of the localconfinement reinforcement or the lateral dimension of theanchorage device.

9.21.4.3.3 For thin members with a ratio of memberthickness to anchorage width of no more than three, thedimension of the strut in the direction of the thickness ofthe member can be approximated by assuming that thethickness of the compression strut varies linearly from thetransverse lateral dimension of the anchor at the surfaceof the concrete to the total thickness of the section at adepth equal to the thickness of the section.

9.21.4.3.4 The compression stresses can be assumedas acting parallel to the axis of the strut and as uniformlydistributed over its cross section.

9.21.4.4 Ties

9.21.4.4.1 Tension forces in the strut-and-tie modelshall be assumed to be carried completely by non-pre-stressed or prestressed reinforcement. Tensile strength ofthe concrete shall be neglected.

9.21.4.4.2 Tension ties shall be properly detailed andshall extend beyond the nodes to develop the full tensiontie force at the node. The reinforcement layout mustclosely follow the directions of the ties in the strut-and-tiemodel.

9.21.5 Elastic Stress Analysis

9.21.5.1 Analyses based on assumed elastic materialproperties, equilibrium, and compatibility of strains areacceptable for analysis and design of anchorage zones.

9.21.5.2 If the compressive stresses in the concreteahead of the anchorage device are determined from a lin-ear-elastic stress analysis, local stress maxima may be av-eraged over an area equal to the bearing area of the an-chorage device.

9.21.5.3 Location and magnitude of the burstingforce may be obtained by integration of the correspondingtensile bursting stresses along the tendon path.

9.21.6 Approximate Methods

9.21.6.1 Limitations

In the absence of a more accurate analysis, concretecompressive stresses ahead of the anchorage device, loca-tion and magnitude of the bursting force, and edge tensionforces may be estimated by Equations (9-35) through(9-38), provided that:

(1) The member has a rectangular cross section and itslongitudinal extent is at least equal to the largest trans-verse dimension of the cross section.(2) The member has no discontinuities within or aheadof the anchorage zone.(3) The minimum edge distance of the anchorage inthe main plane of the member is at least 1 %2 times thecorresponding lateral dimension, a, of the anchoragedevice.(4) Only one anchorage device or one group of closelyspaced anchorage devices is located in the anchoragezone. Anchorage devices can be treated as closelyspaced if their center-to-center spacing does not exceed1%2 times the width of the anchorage devices in thedirection considered.


(5) The angle of inclination of the tendon with respectto the center line of the member is not larger than 20°if the anchor force points toward the centroid of thesection and for concentric anchors, and is not largerthan 5° if the anchor force points away from the cen-troid of the section.

9.21.6.2 Compressive Stresses

9.21.62.1 No additional check of concrete compres-sive stresses is necessary for basic anchorage devices sat-isfying Article 9.21.7.2.

9.21.6.2.2 The concrete compressive stresses aheadof special anchorage devices at the interface between localzone and general zone shall be approximated by Equa-tions (9-35) and (9-36).

fca= K 0.6P„ 1

(9-35)

Ab 1+f, II

( beff t

)

K =1 + 2---s

— C0.3 + n)fors<2a,, (9-36)aeff 15

K = 1 for s ? 2aeff

where:

f a = the concrete compressive stress ahead of the an-chorage device;

K = a correction factor for closely spaced anchor-ages;

Ab = an effective bearing area as defined in Article9.21.6.2.3;

aeff =the lateral dimension of the effective bearingarea measured parallel to the larger dimension ofthe cross section or in the direction of closelyspaced anchors;

beff = the lateral dimension of the effective bearingarea measured parallel to the smaller dimensionof the cross section;

f~ = the longitudinal extent of confining reinforce-ment for the local zone, but not more than thelarger of 1.15 aeff or 1.15 b efF ;

P„ = the factored tendon load;t = the thickness of the section;s = the center-to-center spacing of multiple anchor-

ages;n = the number of anchorages in a row.

If a group of anchorages is closely spaced in two direc-tions, the product of the correction factors, K, for each di-

rection is used in Equation (9-36).

9.21. 62.3 Effective bearing area, A b , in Equation(9-35) shall be taken as the larger of the anchor bearingplate area, Aplate, or the bearing area of the confinedconcrete in the local zone, A,onf, with the following limi-tations:

(1) IfAp,ate

controls, Apure shall not be taken larger than

4/iT Acanf .

(2) If A,nnfcontrols, the maximum dimension of A,onf

shall not be more than twice the maximum dimensionof

Ap,ateor three times the minimum dimension of A,,,,,.

If any of these limits is violated the effective-bearingarea, Ab, shall be based on A

p,ae•(3) Deductions shall be made for the area of the ductin the determination of Ab .

9.21.6.3 Bursting Forces

Values for the magnitude of the bursting force, Tb.,t,and for its distance from the loaded surface, dbnr,t,

shall beestimated by Equations (9-37) and (9-38), respectively. Inthe application of Equations (9-37) and (9-38) the speci-fied stressing sequence shall be considered if more thanone tendon is present.

Tbunt = 0.25EP„ f 1 — h I + 0.5P„ sin a (9 - 37)

db,,, = 0.5(h — 2e) + 5e since (9-38)

where, YPn = the sum of the total factored tendonloads for the stressing arrangementconsidered;

a = the lateral dimension of the anchoragedevice or group of devices in the direc-tion considered;

e = the eccentricity (always taken as posi-tive) of the anchorage device or groupof devices with respect to the centroidof the cross section;

h = the lateral dimension of the cross sec-tion in the direction considered;

at = the angle of inclination of the resultantof the tendon forces with respect to thecenter line of the member.

9.21.6.4 Edge-Tension Forces

9.21.6.4.1 For multiple anchorages with a center-to-center spacing of less than 0.4 times the depth of the sec-tion, the spalling forces shall be given by Article


9.21.3.4.8. For larger spacings, the spalling forces shall bedetermined from a more detailed analysis, such as strut-and-tie models or other analytical procedures.

9.21.6.4.2 If the centroid of all tendons considered islocated outside of the kern of the section both spallingforces and longitudinal edge tension forces are induced.The longitudinal edge-tension force shall be determinedfrom an axial-flexural beam analysis at a section locatedat one-half the depth of the section away from the loadedsurface. The spalling force shall be taken as equal to thelongitudinal edge-tension force but not less than specifiedin Article 9.21.3.4.8.

9.21.7 Design of the Local Zone

9.21.7.1 Dimensions of the Local Zone

9.21.7.1.1 When no independently verified manufac-turer's edge-distance recommendations for a particularanchorage device are available, the transverse dimensionsof the local zone in each direction shall be taken as thelarger of:

(1) The corresponding bearing plate size plus twicethe minimum concrete cover required for the particu-lar application and environment.(2) The outer dimension of any required confining re-inforcement plus the required concrete cover over theconfining reinforcing steel for the particular applica-tion and environment.

9.21.7.1.2 When independently verified manufac-turer's recommendations for minimum cover, spacing andedge distances for a particular anchorage device are avail-able, the transverse dimensions of the local zone in eachdirection shall be taken as the smaller of:

(1) Twice the edge distance specified by the anchoragedevice supplier.(2) The center-to-center spacing specified by the an-chorage device supplier.

The manufacturer's recommendations for spacing andedge distance of anchorages shall be considered minimumvalues.

9.21.7.1.3 The length of the local zone along the ten-don axis shall be taken as the greater of:

(1) The maximum width of the local zone.(2) The length of the anchorage device confining rein-forcement.(3) For anchorage devices with multiple-bearing sur-faces, the distance from the loaded concrete surface to

the bottom of each bearing surface plus the maximumdimension of that bearing surface.

In no case shall the length of the local zone be taken asgreater than 1%2 times the width of the local zone.

9.21.7.1.4 For closely spaced anchorages an en-larged local zone enclosing all individual anchorages shallalso be considered.

9.21.7.2 Bearing Strength

9.21.7.2.1 Anchorage devices may be either basicanchorage devices meeting the bearing compressivestrength limits of Articles 9.21.7.2.2 through 9.21.7.2.4 orspecial anchorage devices meeting the requirements ofArticle 9.21.7.3.

9.21.7.2.2 The effective concrete bearing compres-sive strength fb used for design shall not exceed that ofEquations (9-39) or (9-40).

fb <_0.7 Of,', A/A, (9-39)

but, fb < 2.25 -~ f~' j (9-40)

where:

fb = the maximum factored tendon load, P,,, dividedby the effective bearing area A b ;

fl, = the concrete compressive strength at stressing;A = the maximum area of the portion of the support-

ing surface that is geometrically similar to theloaded area and concentric with it;

Ag = the gross area of the bearing plate if the require-ments of Article 9.21.7.2.3 are met, or is the areacalculated in accordance with Article 9.21.7.2.4;

A b = the effective net area of the bearing plate calcu-lated as the area Ag minus the area of openings inthe bearing plate.

Equations (9-39) and (9-40) are only valid if general zonereinforcement satisfying Article 9.21.3.4 is provided andif the extent of the concrete along the tendon axis aheadof the anchorage device is at least twice the length of thelocal zone as defined in Article 9.21.7.1.3.

9.21.7.2.3 The full bearing plate area may be usedfor A g and the calculation of Ab if the anchorage device issufficiently rigid. To be considered sufficiently rigid, theslenderness of the bearing plate (n/t) must not exceed thevalue given in Equation (9-41). The plate must also bechecked to ensure that the plate material does not yield.


n/t <_ 0.08 3 E6 / fb (9–41)

where:

n = the largest distance from the outer edge of thewedge plate to the outer edge of the bearingplate. For rectangular-bearing plates this dis-tance is measured parallel to the edges of thebearing plate. If the anchorage has no separatewedge plate, the size of the wedge plate shall betaken as the distance between the extreme wedgeholes in the corresponding direction.

t = the average thickness of the bearing plate.Eb = the modulus of elasticity of the bearing-plate

material.

9.21.7.2.4 For bearing plates that do not meet thestiffness requirements of Article 9.21.7.2.3, the effectivegross-bearing area, Ag , shall be taken as the area geomet-rically similar to the wedge plate (or to the outer perime-ter of the wedge-hole pattern for plates without separatewedge plate) with dimensions increased by assuming loadspreading at a 45° angle. A larger effective-bearing areamay be calculated by assuming an effective area andchecking the new fb and n/t values for conformance withArticles 9.21.7.2.2 and 9.21.7.2.3.

9.21.7.3 Special Anchorage Devices

Special anchorage devices that do not meet the require-ments of Article 9.21.7.2 as well as other devices that domeet the requirements of Article 9.21.7.2 but which the en-gineer of record requires to have tested may be used pro-vided that they have been tested by an independent testingagency acceptable to the engineer of record according tothe procedures described in Division II, Article 10.3.2 (orequivalent) and meet the acceptance criteria specified in Di-vision II, Article 10.3.2.3. 10. For a series of similar specialanchorage devices, tests are only required for representativesamples unless tests for each capacity of the anchorages inthe series are required by the engineer of record.

9.22 PRETENSIONED ANCHORAGE ZONES

9.22.1 In pretensioned beams, vertical stirrups acting ata unit stress of 20,000 psi to resist at least 4% of the totalprestressing force shall be placed within the distance ofd/4 of the end of the beam.

9.22.2 For at least the distance d from the end of thebeam, nominal reinforcement shall be placed to enclosethe prestressing steel in the bottom flange.

9.22.3 For box girders, transverse reinforcement shallbe provided and anchored by extending the leg into theweb of the girder.

9.22.4 Unless otherwise specified, stress shall not betransferred to concrete until the compressive strength ofthe concrete as indicated by test cylinders, cured by meth-ods identical with the curing of the member, is at least4,000 psi.

9.23 CONCRETE STRENGTH ATSTRESS TRANSFER

Unless otherwise specified, stress shall not be trans-ferred to concrete until the compressive strength of theconcrete as indicated by test cylinders, cured by methodsidentical with the curing of the members, is at least 4,000psi for pretensioned members (other than piles) and 3,500psi for post-tensioned members and pretensioned piles.

9.24 DECK PANELS

9.24.1 Deck panels shall be prestressed with pre-tensioned strands. The strands shall be in a directiontransverse to the stringers when the panels are placed onthe supporting stringers. The top surface of the panels shallbe roughened in such a manner as to ensure composite ac-tion between the precast and cast-in-place concrete.

9.24.2 Reinforcing bars, or equivalent mesh, shall beplaced in the panel transverse to the strands to provide atleast 0.11 square inches per foot of panel.

Part DDETAILING

9.25 FLANGE REINFORCEMENT

Bar reinforcement for cast-in-place T-beam and boxgirder flanges shall conform to the provisions in Articles8.17.2.2 and 8.17.2.3 except that the minimum reinforcementin bottom flanges shall be 0.3% of the flange section.

9.26 COVER AND SPACING OF STEEL

9.26.1 Minimum Cover

The following minimum concrete cover shall be pro-vided for prestressing and conventional steel:


9.26.1.1 Prestressing Steel and MainReinforcement ...................................................... 1 %2 inch

9.26.1.2 Slab Reinforcement

9.26.1.2.1 Top of Slab...................................1 %2 inchWhen deicers are used....................2 inch

9.26.1.2.2 Bottom of Slab................................1 inch

9.26.1.3 Stirrups and Ties............................. l inch

9.26.1.4 When deicer chemicals are used, drainagedetails shall dispose of deicer solutions without constantcontact with the prestressed girders. Where such contactcannot be avoided, or in locations where members are ex-posed to salt water, salt spray, or chemical vapor, addi-tional cover should be provided.

9.26.2 Minimum Spacing

9.26.2.1 The minimum clear spacing of prestressingsteel at the ends of beams shall be as follows:

Pretensioning steel: The clear distance betweenstrands shall not be less than 1 1/3 times the maximumsize of the concrete aggregate. Also, the minimumspacing center-to-center of strand shall be as follows:

Strand Size Spacing1/2 inch special, 9

/16 inch, 9/16 inch 2 inches

special, and 6/o inch'116 inch and 1/2 inch 1 3

/4 inches3/8 inch 1 1/2 inches

Post-tensioning steel: 1%2 inches or 1%2 times the maxi-mum size of the concrete aggregate, whichever is greater.

9.26.2.2 Prestressing strands in deck panels shall bespaced symmetrically and uniformly across the width ofthe panel. They shall not be spaced farther apart than 1%2times the total composite slab thickness or more than 18inches.

9.26.3 Bundling

9.26.3.1 When post-tensioning steel is draped or de-flected, post-tensioning ducts may be bundled in groupsof three maximum, provided that the spacing specified inArticle 9.26.2 is maintained in the end 3 feet of themember.

9.26.3.2 Where pretensioning steel is bundled, allbundling shall be done in the middle third of the beamlength and the deflection points shall be investigated forsecondary stresses.

9.26.4 Size of Ducts

9.26.4.1 For tendons made up of a number of wires,bars, or strands, duct area shall be at least twice the netarea of the prestressing steel.

9.26.4.2 For tendons made up of a single wire, bar,or strand, the duct diameter shall be at least %4 inchlarger than the nominal diameter of the wire, bar, or strand.

9.27 POST-TENSIONING ANCHORAGES ANDCOUPLERS

9.27.1 Anchorages, couplers, and splices for bondedpost-tensioned reinforcement shall develop at least 95% ofthe minimum specified ultimate strength of the prestress-ing steel, tested in an unbonded state without exceedinganticipated set. Bond transfer lengths between anchoragesand the zone where full prestressing force is requiredunder service and ultimate loads shall normally be suffi-cient to develop the minimum specified ultimate strengthof the prestressing steel. Couplers and splices shall beplaced in areas approved by the Engineer and enclosed ina housing long enough to permit the necessary move-ments. When anchorages or couplers are located at criti-cal sections under ultimate load, the ultimate strength re-quired of the bonded tendons shall not exceed the ultimatecapacity of the tendon assembly, including the anchorageor coupler, tested in an unbonded state.

9.27.2 The anchorages of unbonded tendons shall de-velop at least 95% of the minimum specified ultimatestrength of the prestressing steel without exceeding antic-ipated set. The total elongation under ultimate load of thetendon shall not be less than 2% measured in a minimumgauge length of 10 feet.

9.27.3 For unbonded tendons, a dynamic test shall beperformed on a representative specimen and the tendonshall withstand, without failure, 500,000 cycles from 60%to 66% of its minimum specified ultimate strength, andalso 50 cycles from 40% to 80% of its minimum specifiedultimate strength. The period of each cycle involves thechange from the lower stress level to the upper stress leveland back to the lower. The specimen used for the seconddynamic test need not be the same used for the first dy-namic test. Systems utilizing multiple strands, wires, orbars may be tested utilizing a test tendon of smaller capac-ity than the full size tendon. The test tendon shall duplicatethe behavior of the full size tendon and generally shall nothave less than 10% of the capacity of the full size tendon.Dynamic tests are not required on bonded tendons, unlessthe anchorage is located or used in such manner that re-peated load applications can be expected on the anchorage.


9.27.4 Couplings of unbonded tendons shall be usedonly at locations specifically indicated and/or approved bythe Engineer. Couplings shall not be used at points of sharptendon curvature. All couplings shall develop at least 95%of the minimum specified ultimate strength of the pre-stressing steel without exceeding anticipated set. The cou-pling of tendons shall not reduce the elongation at rupturebelow the requirements of the tendon itself. Couplingsand/or coupling components shall be enclosed in housingslong enough to permit the necessary movements. All thecoupling components shall be completely protected with acoating material prior to final encasement in concrete.

9.27.5 Anchorages, end fittings, couplers, and exposedtendons shall be permanently protected against corrosion.

9.28 EMBEDMENT OF PRESTRESSEDSTRAND

9.28.1 Three- or seven-wire pretensioning strand shallbe bonded beyond the critical section for a developmentlength in inches not less than

ft — 2 fSe)D (9-42)

where D is the nominal diameter in inches, f* and f Se arein kips per square inch, and the parenthetical expressionis considered to be without units.

9.28.2 Investigations may be limited to those cross sec-tions nearest each end of the member which are requiredto develop their full ultimate capacity.

9.28.3 Where strand is debonded at the end of a mem-ber and tension at service load is allowed in the precom-pressed tensile zone, the development length requiredabove shall be doubled.

9.29 BEARINGS

Bearing devices for prestressed concrete structuresshall be designed in accordance with Article 10.29 andSection 14.

Section 10

STRUCTURAL STEEL


10.1 APPLICATION

10.1.1 Notations

A = area of cross section (Articles 10.37.1.1,10.34.4, 10.48.1.1, 10.482.1, 10.48.4.2,10.48.5.3, and 10.55.1)

A = bending moment coefficient (Article10.50.1.1.2)

Ae = effective area of a flange or splice platewith holes or a tension member with holes( Articles 10.12, 10.18.2.2.1, 10.18.2.2.3,10.18.2.2.4, and 10.18.4.1)

AF = amplification factor (Articles 10.37.1.1 and10.55.1)

(AF,) bf = product of area and yield point for bottomflange of steel section (Article 10.50.1.1.1)

(AF,,), = product of area and yield point of that part ofreinforcing which lies in the compressionzone of the slab (Article 10.50.1.1.1)

(AF Y ) tf = product of area and yield point for top flangeof steel section (Article 10.50.1.1.1)

(AF,),,. = product of area and yield point for web ofsteel section (Article 10.50.1.1.1)

Af = area of flange (Articles 10.39.4.4.2,10.48.2.1, 10.53.1.2, and 10.56.3)

Af = the sum of the area of filler plates on the topand bottom of the connected plate (Article10.18.1.2.1)

A, = area of compression flange (Articles10.48.4.1 and 10.50.1.2.1)

A g = gross area of a flange, splice plate or tensionmember (Articles 10.18.2.2.2, 10.18.2.2.4,and 10.18.4.1)

A„ = net section of a tension member (Article10.18.4.1)

A F = the smaller of either the connected plate areaor the sum of the splice plate areas on the topand bottom of the connected plate (Article10.18.1.2.1)

As = total area of longitudinal reinforcing steel atthe interior support within the effectiveflange width (Article 10.38.5.1.2)

A s, = total area of longitudinal slab reinforcementsteel for each beam over interior support (Ar-ticle 10.38.5.1.3)

AS = area of steel section (Articles 10.38.5.1.2,10.54.1.1, and 10.54.2.1)

Asc = cross-sectional area of a stud shear connector(Article 10.38.5.1.2)

AW = area of web of beam (Article 10.53.1.2)a = distance from center of bolt under con-

sideration to edge of plate, in. (Articles10.32.3.3.2 and 10.56.2)

a = spacing of transverse stiffeners (Article10.39.4.4.2)

a = depth of stress block (Figure 10.50A)a = ratio of numerically smaller to the larger end

moment (Article 10.54.2.2)B = constant based on the number of stress cycles

(Article 10.38.5.1.1)B = constant for stiffeners (Articles 10.34.4.7

and 10.48.5.3)b = compression flange width (Table 10.32.1A

and Articles 10.34.2.1, 10.48, 10.48.1.1,10.48.2, 10.48.2.1, and 10.61.4)

b = distance from center of bolt under consider-ation to toe of fillet of connected part, in. (Ar-ticles 10.32.3.3.2 and 10.56.2)

b = effective width of slab (Article 10.50.1.1.1)b = effective flange width (Articles 10.38.3 and

10.38.5.1.2)b = widest flange width (Article 10.15.2.1)b = distance from edge of plate or edge of perfo-

ration to the point of support (Article10.35.2.3)

b = unsupported distance between points of sup-port (Article 10.35.2.7)

b = flange width between webs (Articles10.37.3.1, 10.39.4.2, 10.51.5.1, and 10.55.3)

251


b ' = width of stiffeners (Articles 10.34.5.2,10.34.6, 10.37.2.4, 10.39.4.5.1, and 10.55.2)

b ' = width of a projecting flange element, angle,or stiffener (Articles 10.34.2.2, 10.34.4.7,10.37.3.2, 10.39.4.5.1, 10.48.5.3, 10.51.5.5,and 10.55.3)

C = web buckling coefficient (Articles 10.34.4,10.38.1.7, 10.48.5.3, and 10.48.8)

C = compressive force in the slab (Article10.50.1.1.1)

C = equivalent moment factor (Article 10.54.2.1)C ' = compressive force in top portion of steel sec-

tion (Article 10.50.1.1.1)Cb = bending coefficient (Table 10.32.1A and Ar-

ticles 10.48.4.1 and 10.50.2.2)C, = column slenderness ratio dividing elastic and

inelastic buckling (Table 10.32.1A)C,,,X = coefficient about X axis (Article 10.36)C,,,,, = coefficient about the Y axis (Article 10.36)c = buckling stress coefficient (Article

d = depth of beam or girder, in. (Table 10.32.1Aand Articles 10.13, 10.48.2, 10.48.4.1, and10.50.1.1.2)

d = diameter of rocker or roller, in. (Article10.32.4.2)

db = beam depth (Article 10.56.3)d, = column depth (Article 10.56.3)do = spacing of intermediate stiffener (Articles

10.34.4, 10.34.5, 10.48.5.3, 10.48.6.3, and10.48.8)

d, = distance from the centerline of a plate longi-tudinal stiffener or the gage line of an anglelongitudinal stiffener to the inner surface orthe leg of the compression flange component(Articles 10.34.3.2.1, 10.34.5.1, 10.48.4.1,10.49.3.2(a), and 10.61.1)

E = modulus of elasticity of steel, psi (Table10.32.1A and Articles 10.15.3, 10.36, 10.37,10.39.4.4.2, 10.54.1, and 10.55.1)

E, = modulus of elasticity of concrete, psi (Article10.38.5.1.2)

C = distance from the centerline of a splice to thecentroid of the connection on the side of thejoint under consideration (Articles 10. 18.2.3.3,10.18.2.3.5, and 10.18.2.3.7)

F = maximum induced stress in the bottomflange (Article 10.20.2.1)

10.51.5.2)D = clear distance between flanges, in. (Article

10.15.2)D = clear unsupported distance between flange

components (Articles 10. 18.2.3.4, 10.18.2.3.7,10.18.2.3.8, 10.18.2.3.9, 10.34.3, 10.34.4,10.34.5, 10.37.2, 10.48.1, 10.48.2, 10.48.4,10.48.5, 10.48.6, 10.48.8, 10.49.2, 10.49.3.2,10.50.1.1.2, 10.50.2.1, 10.55.2, and 10.61.1)

D' = distance from the top of the slab to the neu-tral axis at which a composite section in pos-itive bending theoretically reaches its plastic-moment capacity when the maximum strainin the slab is at 0.003 (Article 10.50.1.1.2)

D, = clear distance between the neutral axis and thecompression flange (Articles 10.34.3.2.1110.34.5.1, 10.48.4.1, 10.49.2, 10.49.3,10.50(b), 10.57, and 10.61.1)

D, = moments caused by dead load acting on com-posite girder (Article 10.50.1.2.2)

D,P = depth of the web in compression at the plas-tic moment (Articles 10.50(b), 10.50.1.1.2,and 10.50.2.1)

Des = depth of the web in compression of the non-composite steel beam or girder (Articles10.34.5.1 and 10.49.3.2(a))

DP = distance from the top of the slab to the plas-tic neutral axis, in. (Article 10.50.1.1.2)

D, = moments caused by dead load acting on steelgirder (Article 10.50.1.2.2)

d = bolt diameter (Table 10.32.3B)d = diameter of stud, in. (Article 10.38.5.1)

F = maximum compressive stress, psi (Article10.41.4.6)

F a = allowable axial unit stress (Table 10.32.1Aand Articles 10.36, 10.37.1.2, and 10.55. 1)

Fb = allowable bending unit stress (Table 10.32.1Aand Articles 10.18.2.2.3, 10.37.1.2, and10.55.1)

Fb- = compressive bending stress permitted aboutthe X axis (Article 10.36)

Fby = compressive bending stress permitted aboutthe Y axis (Article 10.36)

Fir = buckling stress of the compression flangeplate or column (Articles 10.48.2, 10.50.2.2,10.51.1, 10.51.5, 10.54.1.1, and 10.54.2.1)

F,r = local buckling stress of a stiffener (Articles10.34.4.7 and 10.48.5.3)

F,~f = design stress for the controlling flange at apoint of splice (Articles 10. 18.2.2.3 and10.18.2.3.8)

F e„ = design stress for the controlling flange at apoint of splice (Articles 10.18.2.2.1 and10.18.2.3.4)

FD = maximum horizontal force (Article10.20.2.2)

F e = Euler buckling stress (Articles 10.37.1,10.54.2.1, and 10.55.1)


Fe = Euler stress divided by a factor of safety (Ar- fa= computed axial compression stress (Articles

ticle 10.36) 10.35.2.10, 10.36, 10.37, 10.55.2, and

F ief = design stress for the noncontrolling flange at 10.55.3)

a point of splice (Article 10. 18.2.2.3) fb = computed compressive bending stress (Arti-

F1eU = design stress for the noncontrolling flange at cles 10.34.2, 10.34.3, 10.34.5.2, 10.37,

a point of splice (Article 10.18.2.2.1) 10.39, and 10.55)

Fp = computed bearing stress due to design load fb= factored bending stress in the compression

(Table 10.32.313) flange (Articles 10.48, 10.48.2.1(b),

F, = limiting bending stress (Article 10.34.4) 10.48.4.1, 10.50.1.2.1, 10.50.2.2, 10.53, and

F sr = allowable range of stress (Table 10.3.1A) 10.53.1.2)

F; = reduced allowable tensile stress on rivet orf

b = maximum factored noncomposite dead load

bolt due to the applied shear stress, ksi (Ar- compressive bending stress in the web (Arti-

ticles 10.32.3.3.4 and 10.56.1.3.3) cle 10.61.1)

FY

= specified minimum yield point of the rein- f~ = unit ultimate compressive strength of con-

forcing steel (Article 10.38.5.1.2) crete as determined by cylinder tests at age of

F.S. = factor of safety (Table 10.32. IA and Articles 28 days, psi (Articles 10.38.1, 10.38.5.1.2,

10.32.1 and 10.36)10.45.3, and 10.50.1.1.1)

F„ = specified minimum tensile strength (Tablesfef = maximum flexural stress at the mid-thickness

10.2A, 10.32.1A and 10.32.313 and Articleof the flange under consideration at a point of

10.18.4)splice (Articles 10. 18.2.2.3 and 10. 18.2.3.8)

F„ = tensile strength of electrode classification fey = maximum flexural stress due to the factored

(Table 10.56A and Article 10.32.2)loads at the mid-thickness of the controlling

F,, = maximum bending strength of the flangeflange at a point of splice (Articles 10. 18.2.2.1

(Articles 10.48.8.2, 10.50.1.2.1, andf.,,

and 10.18.2.3.4)= noncomposite dead load stress in the com-

F,10.50.2.2)

=allowable shear stress (Table 10.32.1A and pression flange (Articles 10.34.5.1 and

10.32.3B and Articles 10.18.2.3.6, 10.32.2,f",

10.49,3.2(a))= top flange compressive stress due to the fac-

F,10.32.3, 10.34.4, 10.38.17, and 10.40.2.2)

= shear strength of a fastener (Article 10.56.1.3) tored noncomposite dead load divided by the

F Ye = combined tension and shear in bearing-type factor Rb (Article 10.61.4)

connections (Article 10.56.1.3) fDL+ = total noncomposite and composite dead-load

FW = design shear stress in the web at a point of plus composite live-load stress in the com-

splice (Articles 10. 18.2.3.6, 10.18.2.3.7, and pression flange at the most highly stressed

10.18.2.3.9) section of the web (Articles 10.34.5.1 and

Fy

= specified minimum yield point of steel (Arti- 10.49.3.2(a))

cles 10.15.2.1, 10.15.3, 10.16.11, 10.32.1, fael = top flange compressive stress due to non-

10.32.4, 10.34, 10.35, 10.37.1.3, 10.38.1.7, composite dead load (Articles 10.34.2.1 and

10.38.5, 10.39.4, 10.40.2.2, 10.41.4.6, 10.46, 10.34.2.2)

10.48, 10.49, 10.50, 10.51.5, 10.54, and faef = flexural stress at the mid-thickness of the non-

10.61.4) controlling flange concurrent with f~f (ArticlesF

yf = specified minimum yield strength of the flange 10.18.2.2.3 and 10.18.2.3.8)

(Articles 10.18.2.2.1, 10.48.1.1, 10.53.1, f. = flexural stress due to the factored loads at the

10.57.1, and 10.57.2) mid-thickness of the noncontrolling flange at

Fy sriff,,, = specified minimum yield strength of a a point of splice concurrent with feu (Articles

transverse stiffener (Articles 10.34.4.7 and 10.18.2.2.1 and 10.18.2.3.4)

10.48.5.3) fo = maximum flexural stress due to D + PL (L + I)

Fyw, = specified minimum yield strength of the web at the mid-thickness of the flange under

(Articles 10. 18.2.2.1, 10.18.2.2.2, 10.18.2.3.4, consideration at a point of splice (Articles

10.53.1, and 10.61.1) 10.18.2.2.2 and 10.18.2.3.5)

Fy Web = specified mimimum yield strength of the web fof = flexural stress due to D + PL (L + 1) at the mid-

(Articles 10.34.4.7 and 10.48.5.3) thickness of the other flange at a point off = the lesser of (fb/Rb) or Fy (Articles splice concurrent with fo in the flange under

10.48.2.1(b), 10.48.2.2, and 10.53) consideration (Article 10.18.2.3.5)


fr = range of stress due to live load plus impact,in the slab reinforcement over the support(Article 10.38.5.1.3)

fr = modulus of rupture of concrete specified inArticle 8.15.2.1.1 (Article 10.50.2.3)

f5 = maximum longitudinal bending stress in theflange of the panels on either side of thetransverse stiffener (Article 10.39.4.4)

L = factored bending stress in either the top orbottom flange, whichever flange has thelarger ratio of (fRu ) (Article 10.48.8.2)

ft = tensile stress due to applied loads (Articles10.32.3.3.3 and 10.56.1.3.2)

ft = allowable tensile stress in the concrete spec-ified in Article 8.15.2. 1.1 (Article 10.3 8.4.3)

f,, = unit shear stress (Articles 10.32.3.2.3,10.34.4.4, and 10.34.4.7)

f~ = maximum shear stress in the web at a point ofsplice (Article 10.18.2.3.6)

fb . = computed compressive bending stress aboutthe x axis (Article 10.36)

fbl = computed compressive bending stress aboutthe y axis (Article 10.36)

g = gage between fasteners, in. (Articles10.16.14, 10.24.5, and 10.24.6)

H = height of stud, in. (Article 10.38.5.1.1)H, = horizontal design force resultant in the web

at a point of splice (Articles 10. 18.2.3.8 and10.18.2.3.9)

HWo = overload horizontal design force resultantin the web at a point of splice (Article10.18.2.3.5)

HW„ = horizontal design force resultant in the webat a point of splice (Articles 10.18.2.3.4and 10.18.2.3.5)

h = average flange thickness of the channelflange, in. (Article 10.38.5.1.2)

I = moment of inertia, in. 4 (Articles 10.34.4,10.34.5, 10.38.5.1.1, 10.48.5.3, and10.48.6.3)

I, = moment of inertia of stiffener (Articles10.37.2, 10.39.4.4.1, and 10.51.5.4)

It = moment of inertia of transverse stiffeners(Article 10.39.4.4.2)

I1 = moment of inertia of member about the ver-tical axis in the plane of the web, in 4 (Article10.48.4.1)

IyC = moment of inertia of compression flangeabout the vertical axis in the plane of the web,in4 (Table 10.32. IA and Article 10.48.4.1)

J = required ratio of rigidity of one transversestiffener to that of the web plate (Articles10.34.4.7 and 10.48.5.3)

J = St. Venant torsional constant, in 4 (Table10.32.1A and Article 10.48.4.1)

K = effective length factor in plane of buckling(Table 10.32. IA and Articles 10.37, 10.54.1,and 10.54.2)

K b = effective length factor in the plane of bend-ing (Article 10.36)

k = constant: 0.75 for rivets; 0.6 for high-strength bolts with thread excluded fromshear plane (Article 10.32.3.3.4)

k = buckling coefficient (Articles 10.34.3.2.1,10.34.4, 10.39.4.3, 10.48.4.1, 10.48.8,10.51.5.4, and 10.61.1)

k = distance from outer face of flange to toe ofweb fillet of member to be stiffened (Article10.56.3)

k, = buckling coefficient (Article 10.39.4.4)L = distance between bolts in the direction of the

applied force (Table 10.32.38)L = actual unbraced length (Table 10.32.1A and

Articles 10.7.4, 10.15.3, and 10.55.1)L = 1/2 of the length of the arch rib (Article

10.37.1)L = distance between transverse beams (Article

10.41.4.6)L b = unbraced length (Table 10.48.2. LA and Arti-

cles 10.36, 10.48.1.1, 10.48.2.1, 10.48.4.1,and 10.53.1.3)

L, = length of member between points of support,in. (Article 10.54.1.1)

L, = clear distance between the holes, or betweenthe hole and the edge of the material in the di-rection of the applied bearing force, in. (Table10.32.38 and Article 10.56.1.3.2)

L P = limiting unbraced length (Article 10.48.4.1)Lt = limiting unbraced length (Article 10.48.4.1)f = member length (Table 10.32. and Article

10.35.1)M = maximum bending moment (Articles

10.48.8, 10.54.2.1, and 10.50.1.1.2)M, = smaller moment at the end of the unbraced

length of the member (Article 10.48.1.1(c))Ml & M2 = moments at two adjacent braced points (Ta-

bles 10.32.1A and 10.36A and Articles10.48.4.1 and 10.50.2.2)

M, = column moment (Article 10.56.3.2)MP = full plastic moment of the section (Articles

10.50.1.1.2 and 10.54.2.1)Mr = lateral torsional buckling moment or yield

moment (Articles 10.48.2, 10.48.4.1,10.50.1.2.1, 10.50.2.2, and 10.53.1.3)

M, = elastic pier moment for loading producingmaximum positive moment in adjacent span(Article 10.50.1.1.2)

M„ = maximum bending strength ( Articles10.18.2.2.1, 10.48, 10.49, 10,50.1, 10.50.2,10.51.1, 10.53.1, 10.54.2.1, and 10.61.3)


M,, = design moment due to the eccentricity of thedesign shear at a point of splice (Articles10.18.2.3.7 and 10.18.23.9)

M,,O = overload design moment due to the eccentric-ity of the overload design shear at a point ofsplice (Article 10.18.2.3.5)

M v„ = design moment due to the eccentricity of thedesign shear at a point of splice (Articles10.18.2.3.3 and 10.18.2.3.5)

Mw, = design moment at a point of splice represent-ing the portion of the flexural moment as-sumed to be resisted by the web (Articles10. 18.2.3.8 and 10. 18.2.3.9)

M WO = overload design moment at a point of splicerepresenting the portion of the flexural mo-ment assumed to be resisted by the web (Ar-ticle 10. 18.2.3.5)

MW„ = design moment at a point of splice represent-ing the portion of the flexural moment as-sumed to be resisted by the web (Articles10.18.2.3.4 and 10.18.2.3.5)

MY = moment capacity at first yield (Articles10.18.2.2.1, 10.50.1.1.2, and 10.61.3)

N I & N 2 = number of shear connectors (Article10.38.5.1.2)

N~ = number of additional connectors for eachbeam at point of contraflexure (Article10.38.5.1.3)

NS = number of slip planes in a slip-critical con-nection (Articles 10.32.3.2.1 and 10.57.3.1)

NW = number of roadway design lanes (Article10.39.2)

n = ratio of modulus of elasticity of steel to thatof concrete (Article 10.38.1)

n = number of longitudinal stiffeners (Articles10.39.4.3, 10.39.4.4, and 10.51.5.4)

P = allowable compressive axial load on mem-bers (Article 10.35.1)

P = axial compression on the member (Articles10.48.1.1, 10.48.2.1, and 10.54.2.1)

P, P l , P2, = force in the slab (Article 10.38.5.1.2)& P 3

Pa = design force in the controlling flange at a pointof splice (Article 10. 18.2.2.3)

P"„ = design force for the controlling flange at apoint of splice (Article 10.18.2.2.1)

PfO = overload design force in the flange at a point of

splice (Article 10.18.2.2.2)P„.f = design force for the noncontrolling flange at a

point of splice (Article 10. 18.2.2.3)

P.C. = design force in the noncontrolling flange at apoint of splice (Article 10.18.2.2.1)

P. = design force for checking slip of a bolted splicein a tension member (Article 10.18.4.2)

P S = allowable slip resistance (Article 10.32.3.2.1)P„ = maximum axial compression capacity (Arti-

cle 10.54.1.1)Pu = design force for checking the strength of a

bolted splice in a tension member (Article10.18.4.1)

p = allowable bearing (Article 10.32.4.2)Q = prying tension per bolt (Articles 10.32.3.3.2

and 10.56.2)Q = statical moment about the neutral axis (Arti-

cle 10.38.5.1.1)R = radius (Article 10.15.2.1)R = number of design lanes per box girder (Arti-

cle 10.39.2.1)R = reduction factor for hybrid girders (Articles

10.18.2.2.1, 10.18.2.2.2, 10.18.2.2.3,10.18.2.3.4, 10.18.2.3.8, 10.40.2.1.1,10.53.1.2, and 10.53.1.3)

R = reduction factor applied to the design shearstrength of fasteners passing through fillers(Article 10.18.1.2.1)

Rb = bending capacity reduction factor (Articles10.48.2, 10.48.4.1, 10.50.1.2.1, 10.50.2.2,10.53.1.2, 10.53.1.3, and 10.61.4)

&f = absolute value of the ratio of F~f to f~ f for thecontrolling flange at a point of splice (Articles10.18.2.2.3 and 10.18.2.3.8)

R c„ = the absolute value of the ratio of Fc „ to f,O forthe controlling flange at a point of splice(Articles 10.18.2.2.1 and 10.18.2.3.4)

Rev = a range of stress involving both tension andcompression during a stress cycle (Table10.3.113)

RS = vertical force at connections of vertical stiff-eners to longitudinal stiffeners (Article10.39.4.4.8)

RW = vertical web force (Article 10.39.4.4.7)r =radius of gyration, in (Articles 10.35.1,

10.37.1, 10.41.4.6, 10.48.6.3, 10.54.1.1,10.54.2.1, and 10.55.1)

rb = radius of gyration in plane of bending, in.(Article 10.36)

rY = radius of gyration with respect to the Y-Yaxis, in. (Article 10.48.1.1)

r' = radius of gyration of the compression flangeabout the axis in the plane of the web, in.(Table 10.32. and Article 10.48.4.1)

S = allowable rivet or bolt unit stress in shear(Article 10.32.3.3.4)

S = section modulus, in. 3 (Articles 10.48.2,10.51.1, 10.53.1.2, and 10.53.1.3)

S = pitch of any two successive holes in the chain(Article 10.16.14.2)

S r = range of horizontal shear (Article10.38.5.1.1)


S, = section modulus of transverse stiffener, in. '

(Articles 10.39.4.4 and 10.48.6.3)S t = section modulus of longitudinal or transverse

stiffener, in.3

(Article 10.48.6.3)S„ = ultimate strength of the shear connector (Ar-

ticle 10.38.5.1.2)S XO = section modulus with respect to the com-

pression flange, in. ' (Table 10.32.1A andArticles 10.48.2, 10.48.4.1, 10.50.1.2.1,10.50.2.2 and 10.53.1.2)

S xt = section modulus with respect to the tensionflange, in. 3 (Articles 10.48.2 and 10.53.1.2)

s = computed rivet or bolt unit stress in shear(Article 10.32.3.3.4)

T = range in tensile stress (Table 10.3.113)T = direct tension per bolt due to external load

(Articles 10.32.3 and 10.56.2)T = arch rib thrust at the quarter point from

dead+live+impact loading (Articles10.37.1 and 10.55.1)

t = thickness of the thinner outside plate orshape (Article 10.35.2)

t = thickness of members in compression (Arti-cle 10.35.2)

t = thickness of thinnest part connected, in (Ar-ticles 10.32.3.3.2 and 10.56.2)

t = computed rivet or bolt unit stress in tension,including any stress due to prying action (Ar-ticle 10.32.3.3.4)

t = thickness of the wearing surface, in. (Article10.41.2)

t = flange thickness, in. (Articles 10.18.2.2.4,10.34.2.1, 10.34.2.2, 10.39.4.2, 10.48,10.48.1.1, 10.48.2, 10.48.2.1, 10.51.5.1, and10.61.4)

t = thickness of a flange angle (Article 10.34.2.2)t = thickness of the web of a channel, in. (Arti-

cle 10.38.5.1.2)t = thickness of stiffener (Articles 10.34.4.7 and

10.48.5.3)tb = thickness of flange delivering concentrated

force (Article 10.56.3.2)t, = thickness of flange of member to be stiffened

(Article 10.56.3.2)t f = thickness of the flange (Articles 10.37.3,

10.55.3, and 10.39.4.3)th = thickness of the concrete haunch above the

beam or girder top flange (Article 10.50.1.1.2)t$ = thickness of stiffener (Article 10.37.2 and

10.55.2)is = slab thickness (Articles 10.38.5.1.2,

10.50.1.1.1, and 10.50.1.1.2)tW = web thickness, in. (Articles 10.15.2.1,

10.18.2.3.4, 10.18.2.3.7, 10.18.2.3.8,10.18.2.3.9, 10.34.3, 10.34.4, 10.34.5,

10.37.2, 10.48, 10.49.2, 10.49.3, 10.55.2,10.56.3, and 10.61.1)

ttf = thickness of top flange (Article 10.50.1.1.1)

t ' = thickness of outstanding stiffener element(Articles 10.39.4.5.1 and 10.51.5.5)

V = shearing force (Articles 10.35.1, 10.48.5.3,10.48.8, and 10.51.3)

V = maximum shear in the web at a point ofsplice due to the factored loads (Article10.18.2.3.2)

VO = maximum shear in the web at the point of splicedue to D + PL (L + 1) (Article 10. 18.2.3.5)

VP = shear yielding strength of the web (Articles10.48.8 and 10.53.14)

Vr = range of shear due to live loads and impact,kips (Article 10.38.5.1.1)

V„ = maximum shear force (Articles 10.18.2.3.2,10.34.4, 10.48.5.3, 10.48.8, and 10.53.1.4)

V,, = vertical shear (Article 10.39.3.1)V W = design shear for a web (Articles 10.39.3.1

and 10.51.3)VW = design shear in the web at a point of splice

(Articles 10.18.2.3.2, 10.18.2.3.3, and10.18.2.3.5)

VWO = overload design shear in the web at a pointof splice (Article 10.18.2.3.5)

VW„ = design shear in the web at a point of splice(Articles 10.18.2.3.2, 10.18.2.3.3, and10.18.2.3.5)

W = length of a channel shear connector, in. (Article 10.38.5.1.2)

W, = roadway width between curbs in feet or bar-riers if curbs are not used (Article 10.39.2.1)

W. = least net width of a flange (Article 10. 18.2.2.4)WL = fraction of a wheel load (Article 10.39.2)w = length of a channel shear connector in inches

measured in a transverse direction on theflange of a girder (Article 10.38.5.1.1)

W = unit weight of concrete, lb per cu ft (Article10.38.5.1.2)

w = width of flange between longitudinal stiffen-ers (Articles 10.39.4.3, 10.39.4.4, and10.51.5.4)

YO = distance from the neutral axis to the extremeouter fiber, in. (Article 10. 15.3)

y = location of steel sections from neutral axis(Article 10.50.1.1.1)

Z = plastic section modulus (Articles 10.48.1,10.53.1.1, and 10.54.2.1)

Zr = allowable range of horizontal shear, inpounds on an individual connector (Article10.38.5.1)

a = constant based on the number of stress cycles(Article 10.38.5.1.1)


a = minimum specified yield strength of the webdivided by the minimum specified yieldstrength of the tension flange (Articles10.40.2 and 10.40.4)

a. = factor for flange splice design equal to 1.0,except that a lower value equal to (M„/M,,)may be used for flanges subject to com-pression at sections where M. does not ex-ceed My (Article 10.18.2.2.1)

U = constant equal to 1.3 for members without alongitudinal stiffener and 1.0 for memberswith a longitudinal stiffener (Article 10.61.1)

R = area of the web divided by the area of the ten-sion flange (Articles 10.40.2 and 10.53.1.2)

R = factor applied to gross area of flange, spliceplate or tension member in computing theeffective area (Articles 10. 18.2.2.4 and10.18.4.1)

y = the ratio of Af to Ap (Article 10.18.1.2.1)y = load factor equal to 1.3 (Article 10.61)

P = F yw/Fyf (Article 10.53.1.2)0 = angle of inclination of the web plate to the

vertical (Articles 10.39.3.1 and 10.51.3)

4 = ratio of total cross-sectional area to the cross-sectional area of both flanges (Article 10. 15,2)

= distance from the outer edge of the tensionflange to the neutral axis divided by the depthof the steel section (Articles 10.40.2 and10.53.1.2)

A = amount of camber, in. (Article 10. 15.3)A

DL = dead load camber in inches at any point (Ar-ticle 10.15.3)

A m = maximum value of A DL, in. (Article 10. 15.3)cp = reduction factor (Articles 10.38.5.1.2,

10.56.1.1, and 10.56.1.3)= longitudinal stiffener coefficient (Articles

10.39.4.3 and 10.51.5.4)µ = slip coefficient in a slip-critical joint (Article

10.57.3)

10.2 MATERIALS

pounds per square inch.) The modulus of elasticity of allgrades of structural steel shall be assumed to be29,000,000 psi and the coefficient of linear expansion0.0000065 per degree Fahrenheit.

10.2.3 Steels for Pins, Rollers, and ExpansionRockers

Steels for pins, rollers, and expansion rockers shallconform to one of the designations listed in Tables 10.2Aand 10.213, or shall be stainless steel conforming to ASTMA 240 or ASTM A 276 HNS 21800.

10.2.4 Fasteners—Rivets and Bolts

Fasteners may be carbon steel bolts (ASTM A 307);power-driven rivets, AASHTO M 228 Grades 1 or 2(ASTM A 502 Grades 1 or 2); or high-strength bolts,AASHTO M 164 (ASTM A 325) or AASHTO M 253(ASTM A 490).

10.2.5 Weld Metal

Weld metal shall conform to the current require-ments of the ANSI/AASHTO/AWS DI.S Bridge WeldingCode.

10.2.6 Cast Steel, Ductile Iron Castings, MalleableCastings, and Cast Iron

10.2.6.1 Cast Steel and Ductile Iron

Cast steel shall conform to specifications for SteelCastings for Highway Bridges, AASHTO M 192 (ASTMA 486); Mild-to-Medium-Strength Carbon-Steel Cast-ings for General Application, AASHTO M 103 (ASTMA 27); and Corrosion-Resistant Iron-Chromium,Iron-Chromium-Nickel and Nickel-Based Alloy Castingsfor General Application, AASHTO M 163 (ASTM A743). Ductile iron castings shall conform to ASTM A536.

10.2.1 General10.2.6.2 Malleable Castings

These specifications recognize steels listed in the fol-lowing subparagraphs. Other steels may be used; how-ever, their properties, strengths, allowable stresses, andworkability must be established and specified.

10.2.2 Structural Steels

Structural steels shall conform to the material desig-nated in Table 10.2A. (The stresses in this table are in

Malleable castings shall conform to specifications forMalleable Iron Castings, ASTM A 47, Grade 35018 (min-imum yield point 35,000 psi).

10.2.6.3 Cast Iron

Cast iron castings shall conform to specifications forGray Iron Castings, AASHTO M 105, Class 30.

258 HIGHWAY BRIDGES 10.2

TABLE 10.2A

Minimum Material PropertiesStructural Steel

AASHTO Designation" M 270 M 270 M 270 M 270 M 270Grade 36 Grade 50 Grade 50W Grade HPS70W O Grades 100/10OW

Equivalent ASTMDesignation° A 709 A 709 A 709 A 709 A 709

Grade 36 Grade 50 Grade 50W Grade HPS70W Grades 100/100W°

Thickness of PIates Up to 4 in. Up to 4 in. Up to 4 in. Up to 4 in. Up to 21/2 in. Over 2~/2 in. toincl. , incl. incl. incl. incl. 4 in, incl.

Shapes fAll groups , All groups All groups Not applicable Not applicable Not applicable

Minimum TensileStrength, F„ 58,000 65,000 70,000 90,000 110,000 100,000

Minimum Yield Pointor Minimum YieldStrength,Fy 36,000 50,000 50,000 70,000 100,000 90,000

'Except for the mandatory notch toughness and weldability requirements, the ASTM designations are similar to the AASHTO designations. Steelsmeeting the AASHTO requirements are prequalified for use in welded bridges.

b M 270 Gr. 36 and A 709 Gr. 36 are equivalent to M 183 and A 36.M 270 Gr. 50 and A 709 Gr. 50 are equivalent to M 223 Gr. 50 and A 572 Gr. 50.M 270 Gr. 50W and A 709 Gr. 50W are equivalent to M 222 and A 588.M 270 Gr. 70W and A 709 Gr. 70W are equivalent to A 852.M 270 Gr. 100/10OW and A 709 Gr. 100/10OW are equivalent to M 244 and A 514.

ÀASHTOM 270 Grade HPS70W replaces AASHTO M 270 Grade70W. The intent of this replacement is to encourage the use of high-performancesteel (HPS) over conventional bridge steels due to its enhanced properties. AASHTO M 270 Grade 70W steel is still available, but should be usedonly with the owners approval.

d Quenched and tempered alloy steel structural shapes and seamless mechanical tubing meeting all mechanical and chemical requirements of A 709Grades 100/ 100W, except that the specified maximum tensile strength may be 140,000 psi for structural shapes and 145,000 psi for seamless mechan-ical tubing, shall be considered as A 709 Grades 100/100W.

`For nonstructural applications or bearing assembly components over 4" thick, use AASHTO M 270 Gr. 36 (ASTM A 709 Gr. 36).f Groups 1 and 2 include all shapes except those in Groups 3, 4, and 5. Group 3 includes L-shapes over 3/4 inch in thickness. HP shapes over 102

pounds/foot, and the following W shapes:Designation:W36 x 230 to 300 incl.W33 x 200 to 240 incl.W14 x 142 to 211 incl.W12 x 120 to 190 incl.

Group 4 includes the following W shapes: W14 x 219 to 550 incl.Group 5 includes the following W shapes: W14 x 605 to 730 incl.For breakdown of Groups I and 2, see ASTM A 6.

TABLE 10.213

Minimum Material PropertiesPins, Rollers, and Rockers

Expansion Rollers Shall be Not less Than 4 Inches in Diameter

AASHTO Designation M 169 M 102 M 102 M 102 M 102with Size Limitations 4 in. in dia. or to 20 in. in dia. to 20 in. in dia. to 10 in. in dia. to 20 in, in dia.

less

ASTM Designation A 108 A 668 A 668 A 668 A 668'

Grade or Class Grades 1016 to1030 incl. Class C Class D Class F Class G

Minimum Yield Point, psiFy 36,000 b 33,000 37,500 50,000 50,000

'May substitute rolled material of the same properties.b For design purpose only. Not a part of the A 108 specifications. Supplementary material requirements should provide guarantee that material will

meet these values.

10.3 DIVISION I—DESIGN 259

Part BDESIGN DETAILS

10.3 REPETITIVE LOADING AND TOUGHNESSCONSIDERATIONS

10.3.1 Allowable Fatigue Stress Ranges

Members and fasteners subject to repeated variationsor reversals of stress shall be designed so that the maxi-mum stress does not exceed the basic allowable stressesgiven in Article 10.32 and that the actual range of stressdoes not exceed the allowable fatigue stress range givenin Table 10.3.1A for the appropriate type and locationof material given in Table 10.3.113 and shown in Fig-ure 10.3. C. For members with shear connectors providedthroughout their entire length that also satisfy the provi-sions of Article 10.38.4.3, the range of stress may be com-puted using the composite section assuming the concretedeck to be fully effective for both positive and negativemoment.

For unpainted weathering steel, A709, all grades, thevalues of allowable fatigue stress range, Table 10.3.1A, asmodified by footnote d, are valid only when the designand details are in accordance with the FHWA TechnicalAdvisory on Uncoated Weathering Steel in Structures,dated October 3, 1989.

Main load carrying components subjected to tensilestresses that may be considered nonredundant load pathmembers—that is, where failure of a single element couldcause collapse—shall be designed for the allowable stressranges indicated in Table 10.3.1A for Nonredundam LoadPath Structures. Examples of nonredundant load pathmembers are flange and web plates in one or two girderbridges, main one-element truss members, hanger plates,and caps at single or two-column bents.

10.3.2 Load Cycles

10.3.2.1 The number of cycles of maximum stressrange to be considered in the design shall be selected fromTable 10.3.2A unless traffic and loadometer surveys orother considerations indicate otherwise. The fatigue liveload preferably shall not exceed HS 20 loading.

10.3.2.2 Allowable fatigue stress ranges shall applyto those Group Loadings that include live load or windload.

10.3.2.3 The number of cycles of stress range to beconsidered for wind loads in combination with dead loads,

except for structures where other considerations indicatea substantially different number of cycles, shall be100,000 cycles.

10.3.3 Charpy V-Notch Impact Requirements

10.3.3.1 Main load carrying member componentssubjected to tensile stress require supplemental impactproperties as described in the Material Specifications.*

10.3.3.2 These impact requirements vary dependingon the type of steel, type of construction, welded or me-chanically fastened, and the average minimum servicetemperature to which the structure may be subjected.**Table 10.33A contains the temperature zone designations.

10.3.3.3 Components requiring mandatory impactproperties shall be designated on the drawings and the ap-propriate zone shall be designated in the contract docu-ments.

10.3.4 Shear

10.3.4.1 When longitudinal beam or girder membersin bridges designed for Case I roadways are investigatedfor "over 2 million" stress cycles produced by placing asingle truck on the bridge (see footnote c of Table10.3.2A), the total shear force in the beam or girder underthis single-truck loading shall be limited to 0.58 F,,Dt W C.The constant C, the ratio of the buckling shear stress to theshear yield stress is defined in Article 10.34.4.2 or Article10.48.8.1.

10.4 EFFECTIVE LENGTH OF SPAN

For the calculation of stresses, span lengths shall be as-sumed as the distance between centers of bearings or otherpoints of support.

*AASHTO Standard Specifications for Transportation Materials andMethods of Sampling and Testing.

**The basis and philosophy used to develop these requirements aregiven in a paper entitled "The Development of AASHTO Fracture-Toughness Requirements for Bridge Steels" by John M. Barsom, Feb-ruary 1975, available from the American Iron and Steel Institute, Wash-ington, D.C.


TABLE 10.3.1A Allowable Fatigue Stress Range

Redundant Load Path Structures a

Allowable Range of Stress, F sr (ksi)b

Category For For For For over(See Table 100,000 500,000 2,000,000 2,000,00010,3.1B) Cycles Cycles Cycles Cycles

A 63 (49) e 37 (29) e 24 (18)° 24 (16) e

B 49 29 18 16B ' 39 23 14.5 12C 35.5 21 13 10

12 d

D 28 16 10 7E 22 13 8 4.5E' 16 9.2 5.8 2.6F 15 12 9 8

Nonredundant Load Path Structures

Allowable Range of Stress, F s, (ksi)b

Category For For For For over(See Table 100,000 500,000 2,000,000 2,000,00010.3.113) Cycles Cycles Cycles Cycles

A 50 (39)° 29 (23)° 24 (16)° 24 (16)°B 39 23 16 16B ' 31 18 11 11C 28 16 10 9

12 d ll d

D 22 13 8 5E e 17 10 6 2.3E ' 12 7 4 1.3F 12 9 7 6

' Structure types with multi-load paths where a single fracture in amember cannot lead to the collapse. For example, a simply supportedsingle span multi-beam bridge or a multi-element eye bar truss memberhas redundant load paths.

b The range of stress is defined as the algebraic difference betweenthe maximum stress and the minimum stress. Tension stress is

considered to have the opposite algebraic sign from compressionstress.

` For unpainted weathering steel, A 709, all grades, when used inconformance with the FHWA Technical Advisory on UncoatedWeathering Steel in Structures, dated October 3, 1989.

dFor transverse stiffener welds on girder webs or flanges.'Partial length welded cover plates shall not be used on flanges more

than 0.8 inches thick for nonredundant load path structures.

10.5 DEPTH RATIOS

10.5.1 For beams or girders, the ratio of depth to lengthof span preferably should not be less than %25.

10.5.2 For composite girders, the ratio of the overalldepth of girder (concrete slab plus steel girder) to thelength of span preferably should not be less than %25, andthe ratio of depth of steel girder alone to length of spanpreferably should not be less than %3o.

10.5.3 For trusses the ratio of depth to length of spanpreferably should not be less than %o.

10.5.4 For continuous span depth ratios the span lengthshall be considered as the distance between the dead loadpoints of contraflexure.

10.5.5 The foregoing requirements as they relate tobeam or girder bridges may be exceeded at the discretionof the designer.*

10.6 DEFLECTION

10.6.1 The term "deflection" as used herein shall bethe deflection computed in accordance with the assump-tion made for loading when computing the stress in themember.

10.6.2 Members having simple or continuous spanspreferably should be designed so that the deflection due toservice live load plus impact shall not exceed %oo of thespan, except on bridges in urban areas used in part bypedestrians whereon the ratio preferably shall not exceed%000. For checking deflection, the service live load prefer-ably shall not exceed HS 20 loading.

10.6.3 The deflection of cantilever arms due to servicelive load plus impact preferably should be limited to %3oo

of the cantilever arm except for the case including pedes-trian use, where the ratio preferably should be %375.

10.6.4 When spans have cross-bracing or diaphragmssufficient in depth or strength to ensure lateral distribu-tion of loads, the deflection may be computed for thestandard H or HS loading (M or MS) considering allbeams or stringers as acting together and having equaldeflection.

10.6.5 The moment of inertia of the gross cross-sec-tional area shall be used for computing the deflections ofbeams and girders. When the beam or girder is a part of acomposite member, the service live load may be consid-ered as acting upon the composite section.

10.6.6 The gross area of each truss member shallbe used in computing deflections of trusses. If per-forated plates are used, the effective area shall be the net

*For considerations to be taken into account when exceeding theseli mitations, reference is made to "Bulletin No. 19, Criteria for the De-flection of Steel Bridges," available from the American Iron and SteelInstitute, Washington, D.C.


TABLE 10.3.0

Kind ofGeneral Condition Situation Stress

Plain Member Base metal with rolled or cleaned surface. Flame-cut edges T or Rev a

with ANSI smoothness of 1,000 or less.Built-Up Members Base metal and weld metal in members of built-up plates or T or Rev

shapes (without attachments) connected by continuous fullpenetration groove welds (with backing bars removed) or bycontinuous fillet welds parallel to the direction of appliedstress.

Base metal and weld metal in members of built-up plates or T or Revshapes (without attachments) connected by continuous fullpenetration groove welds with backing bars not removed, orby continuous partial penetration groove welds parallel to thedirection of applied stress.

Calculated flexural stress at the toe of transverse stiffener T or Rev C 6welds on girder webs or flanges.

Base metal at ends of partial length welded coverplates with T or Rev B 22high-strength bolted slip-critical end connections. (See Note b)

Base metal at ends of partial length welded coverplatesnarrower than the flange having square or tapered ends, withor without welds across the ends, or wider than flange withwelds across the ends:

(a) Flange thickness s 0.8 in. T or Rev E 7(b) Flange thickness > 0.8 in. T or Rev E' 7

Base metal at ends of partial length welded coverplates wider T or Rev E ' 7than the flange without welds across the ends.

Groove Welded Base metal and weld metal in or adjacent to full penetration T or Rev B 8,10Connections groove weld splices of rolled or welded sections having similar

profiles when welds are ground flush with grinding in thedirection of applied stress and weld soundness established bynondestructive inspection.Base metal and weld metal in or adjacent to full penetration T or Rev B 13groove weld splices with 2 ft radius transitions in width,when welds are ground flush with grinding in the directionof applied stress and weld soundness established bynondestructive inspection.

Base metal and weld metal in or adjacent to full penetrationgroove weld splices at transitions in width or thickness, withwelds ground to provide slopes no steeper than 1 to 21/2, withgrinding in the direction of the applied stress, and weldsoundness established by nondestructive inspection:(a) AASHTO M 270 Grades 100/ 100W (ASTM A 709) T or Rev B ' 11,12

base metal(b) Other base metals T or Rev B 11,12Base metal and weld metal in or adjacent to full penetration T or Rev C 8,10,11,12groove weld splices, with or without transitions having slopesno greater than 1 to 2 1/2, when the reinforcement is notremoved and weld soundness is established by nondestructiveinspection.

Groove Welded Base metal adjacent to details attached by full or partial T or Rev C 6,15Attachments— penetration groove welds when the detail length, L, in theLongitudinally direction of stress, is less than 2 in.Loaded° Base metal adjacent to details attached by full or partial T or Rev D 15

penetration groove welds when the detail length, L, in thedirection of stress, is between 2 in. and 12 times the platethickness but less than 4 in.

Stress IllustrativeCategory Example(See Table (See Figure10.3.1A) 10.3.1C)

A 1,2

B 3,4,5,7

B' 3,4,5,7


TABLE 10.3.111 (Continued)

General Condition SituationKind ofStress

StressCategory(See Table10.3.IA)

IllustrativeExample

(See Figure10.3.1C)

Base metal adjacent to details attached by full or partialpenetration groove welds when the detail length, L, in thedirection of stress, is greater than 12 times the plate thicknessor greater than 4 in.:

(a) Detail thickness < 1.0 in. T or Rev E 15(b) Detail thickness > 1.0 in. T or Rev E' 15

Base metal adjacent to details attached by full or partialpenetration groove welds with a transition radius, R,regardless of the detail length:

—With the end welds ground smooth T or Rev 16(a) Transition radius ? 24 in. B(b) 24 in. > Transition radius ? 6 in. C(c) 6 in. > Transition radius > 2 in. D(d) 2 in. > Transition radius ? 0 in. E

—For all transition radii without end welds ground smooth. T or Rev E 16

Groove welded Detail base metal attached by full penetration groove weldsAttachments— with a transition radius, R, regardless of the detail length andTransversely with weld soundness transverse to the direction of stressLoaded `,d established by nondestructive inspection:

—With equal plate thickness and reinforcement removed T or Rev 16(a) Transition radius >: 24 in. B(b) 24 in. > Transition radius ? 6 in. C(c) 6 in. > Transition radius 2 in. D(d) 2 in. > Transition radius >_ 0 in. E

—With equal plate thickness and reinforcement not removed T or Rev 16(a) Transition radius ? 6 in. C(b) 6 in. > Transition radius ? 2 in. D(c) 2 in. > Transition radius ? 0 in. E

—With unequal plate thickness and reinforcement removed T or Rev 16(a) Transition radius ? 2 in. D(b) 2 in. > Transition radius ? 0 in. E

—For all transition radii with unequal plate thickness and T or Rev E 16reinforcement not removed.

Fillet Welded Base metal at details connected with transversely loadedConnections welds, with the welds perpendicular to the direction of stress:

(a) Detail thickness <— 0.5 in. T or Rev C 14(b) Detail thickness > 0.5 in. T or Rev See Note'

Base metal at intermittent fillet welds. T or Rev E —

Shear stress on throat of fillet welds. Shear F 9

Fillet Welded Base metal adjacent to details attached by fillet welds with T or Rev C 15,17,18,20Attachments— length, L, in the direction of stress, is less than 2 in. andLongitudinally stud-type shear connectors.Loaded 1,d

Base metal adjacent to details attached by fillet welds with T or Rev D 15,17length, L, in the direction of stress, between 2 in. and 12times the plate thickness but less than 4 in.

Base metal adjacent to details attached by fillet welds withlength, L, in the direction of stress greater than 12 times theplate thickness or greater than 4 in.:

(a) Detail thickness < 1.0 in. T or Rev E 7,9,15,17(b) Detail thickness ? 1.0 in. T or Rev E' 7,9,15


TABLE 10.3.1B (Continued)

Stress IllustrativeCategory Example

Kind of (See Table (See FigureGeneral Condition Situation Stress 10.3.1A) 10.3.1C)

Base metal adjacent to details attached by fillet welds with atransition radius, R, regardless of the detail length:

—With the end welds ground smooth T or Rev 16(a) Transition radius at 2 in. D(b) 2 in. > Transition radius ? 0 in. E

—For all transition radii without the end welds T or Rev E 16ground smooth.

Fillet Welded Detail base metal attached by fillet welds with a transitionAttachments— radius, R, regardless of the detail length (shear stress on theTransversely Loaded throat of fillet welds governed by Category F):with the Weld in —With the end welds ground smooth T or Revthe Direction of 16

(a) Transition radius _ 2 in.Principal Stress° f (b)

D2 in. > Transition radius ? 0 in. E

—For all transition radii without the end welds T or Rev E 16ground smooth.

Mechanically Base metal at gross section of high-strength bolted slip T or Rev B 21Fastened resistant connections, except axially loaded joints whichConnections induce out-of-plane bending in connecting materials.

Base metal at net section of high-strength bolted T or Rev B 21bearing-type connections.

Base metal at net section of riveted connections. T or Rev D 21

Eyebar or Pin Plates Base metal at the net section of eyebar head, or pin T E 23,24plateBase metal in the shank of eyebars, or through the grosssection of pin plates with:(a) rolled or smoothly ground surfaces T A 23,24(b) flame-cut edges T B 23,24

a"T" signifies range in tensile stress only, "Rev" signifies a range of stress involving both tension and compression during a stress cycle.

b See Wattar, Albrecht and Sahli, Journal of Structural Engineering, ASCE, Vol. III, No. 6, June 1985, pp. 1235—1249.

"'Longitudinally Loaded" signifies direction of applied stress is parallel to the longitudinal axis of the weld. "Transversely Loaded" signifiesdirection of applied stress is perpendicular to the longitudinal axis of the weld.

°Transversely loaded partial penetration groove welds are prohibited.Àllowable fatigue stress range on throat of fillet welds transversely loaded is a function of the effective throat and plate thickness. (See Frank and

Fisher, Journal of the Structural Division, ASCE, Vol. 105, No. ST9, Sept. 1979.)tp

_ 0.06+0.79H/tp.Sr - sr

~X

1.1t,,116

where Sc is equal to the allowable stress range for Category C given in Table 10.3.IA. This assumes no penetration at the weld root.I Gusset plates attached to girder flange surfaces with only transverse fillet welds are prohibited.

volume divided by the length from center to center of 10.7 LIMITING LENGTHS OF MEMBERSperforations.

10.6.7 The foregoing requirements as they relate tobeam or girder bridges may be exceeded at the discretionof the designer.*

*For considerations to be taken into account when exceeding theselimitations, reference is made to "Bulletin No. 19, Criteria for the De-flection of Steel Bridges," available from the American Iron and SteelInstitute, Washington, D.C.

10.7.1 For compression members, the slendernessratio, KL/r, shall not exceed 120 for main members, orthose in which the major stresses result from dead or liveload, or both; and shall not exceed 140 for secondarymembers, or those whose primary purpose is to brace thestructure against lateral or longitudinal force, or to braceor reduce the unbraced length of other members, main orsecondary.


C:)

Diaph. Gusset 8Squared End, Tapered

Catege-y s or Wider than FlangeCat

egory E ta

CCate o D

to o . BCat

egory E*

8

Category Ea(in base Category F (in weld

metal) Category E*

m etal)w (in base m

etal)~yf~

9-9 At End of Weld, Has No Length

12

X Rad.

y

13

Unpusl Thickness - Reml. in PlscsG-Pay C** Unpusl Thickness - RsiM. Rsmowd

Equal Thickness - RsiM. in P4ca~ Epusl Thickness - Reinl. INmowd InNror

*Fa IransWres loading - ehsek transition1 radius for Pons" lower category

16

^ > R > !" D C[248^> R>r D Dr > R E E

" N\ ♦ 4 Ab0 applies to tranawraeboding

v

17

End of Weld Category e(one bon space)

C22

FIGURE 10.3.11C Illustrative Examples


TABLE 10.3.2A Stress CyclesMain (Longitudinal) Load Carrying Members

Truck LaneType of Road Case ADTT' Loading Loading'

Freeways, Expressways, I 2,500 or 2,000,000° 500,000Major Highways, and moreStreets

Freeways, Expressways, II less than 500,000 100,000Major Highways, and 2,500Streets

Other Highways and III 100,000 100,000Streets not included inCase I or II

Transverse Members and Details Subjected to Wheel Loads

TruckType of Road Case ADTT' Loading

Freeways, Expressways, I 2,500 or overMajor Highways, and more 2,000,000Streets

Freeways, Expressways, II less than 2,000,000Major Highways, and 2,500Streets

Other Highways and III — 500,000Streets

'Average Daily Truck Traffic (one direction).'Longitudinal members should also be checked for truck loading.'Members shall also be investigated for "over 2 million" stress

cycles produced by placing a single truck: on the bridge distributed tothe girders as designated in Article 3.23.2 for one traffic lane loading.The shear in steel girder webs shall not exceed 0.58 FYDt„C for thissingle truck loading.

10.7.2 In determining the radius of gyration, r, for thepurpose of applying the limitations of the KLIr ratio, thearea of any portion of a member may be neglected pro-vided that the strength of the member as calculated with-out using the area thus neglected and the strength of themember as computed for the entire section with the KL/rratio applicable thereto, both equal or exceed the com-puted total force that the member must sustain.

10.7.3 The radius of gyration and the effective area forcarrying stress of a member containing perforated coverplates shall be computed for a transverse section throughthe maximum width of perforation. When perforations arestaggered in opposite cover plates, the cross-sectionalarea of the member shall be considered the same as for asection having perforations in the same transverse plane.

10.7.4 Actual unbraced length, L, shall be assumed asfollows:

For the top chords of half-through trusses, the lengthbetween panel points laterally supported as indicatedunder Article 10.16.12; for other main members, the

TABLE 10.3.3A Temperature Zone Designations forCharpy V-Notch Impact Requirements

Minimum TemperatureService Temperature Zone Designation

0°F and above 1-1 IF to – 30°F 2

– 31 °F to – 60°F 3

length between panel point intersections or centers ofbraced points or centers of end connections; for sec-ondary members, the length between the centers of theend connections of such members or centers of bracedpoints.

10.7.5 For tension members, except rods, eyebars, ca-bles, and plates, the ratio of unbraced length to radius ofgyration shall not exceed 200 for main members, shall notexceed 240 for bracing members, and shall not exceed140 for main members subject to a reversal of stress.

10.8 MINIMUM THICKNESS OF METAL

10.8.1 Structural steel (including bracing, cross frames,and all types of gusset plates), except for webs of certainrolled shapes, closed ribs in orthotropic decks, fillers, andin railings, shall be not less than %16 inch in thickness. Theweb thickness of rolled beams or channels shall not beless than 0.23 inches. The thickness of closed ribs in or-thotropic decks shall not be less than %16 inch.

10.8.2 Where the metal will be exposed to marked cor-rosive influences, it shall be increased in thickness or spe-cially protected against corrosion.

10.8.3 It should be noted that there are other provisionsin this section pertaining to thickness for fillers, segmentsof compression members, gusset plates, etc. As statedabove, fillers need not be %16 inch minimum.

10.8.4 For compression members, refer to "Trusses"

(Article 10.16).

10.8.5 For stiffeners and other plates, refer to "PlateGirders" (Article 10.34).

10.8.6 For stiffeners and outstanding legs of angles, etc.,refer to Article 10.10.

10.9 EFFECTIVE AREA OF ANGLES ANDTEE SECTIONS IN TENSION

10.9.1 The effective area of a single angle tension mem-ber, a tee section tension member, or each angle of a dou-


ble angle tension member in which the shapes are con-nected back to back on the same side of a gusset plate shallbe assumed as the net area of the connected leg or flangeplus one-half of the area of the outstanding leg.

10.9.2 If a double angle or tee section tension memberis connected with the angles or flanges back to back on op-posite sides of a gusset plate, the full net area of the shapesshall be considered effective.

10.9.3 When angles connect to separate gusset plates, asin the case of a double-webbed truss, and the angles areconnected by stay plates located as near the gusset as prac-ticable, or by other adequate means, the full net area of theangles shall be considered effective. If the angles are notso connected, only 80% of the net areas shall be consid-ered effective.

10.9.4 Lug angles may be considered as effective intransmitting stress, provided they are connected with atleast one-third more fasteners than required by the stressto be carried by the lug angle.

10.10 OUTSTANDING LEGS OF ANGLES

The widths of outstanding legs of angles in compres-sion (except where reinforced by plates) shall not exceedthe following:

In main members carrying axial stress, 12 times thethickness.In bracing and other secondary members, 16 times thethickness.

For other limitations, see Article 10.35.2.


In all bridges, provisions shall be made in the design toresist thermal stresses induced, or means shall be providedfor movement caused by temperature changes. Provisionsshall be made for changes in length of span resulting fromlive load stresses. In spans more than 300 feet long, al-lowance shall be made for expansion and contraction inthe floor. The expansion end shall be secured against lat-eral movement.

10.12 FLEXURAL MEMBERS

Flexural members shall be designed using the elasticsection modulus except when utilizing compact sections

under Strength Design as specified in Articles 10.48.1,10.50.1.1, and 10.50.2.1. When computing the strength ofa flexural member at a section with holes in the tensionflange, an effective flange area, A e , specified by Equation(10-4g) shall be used for that flange in computing the elas-tic section properties. The diameter of the holes shall betaken as specified in Article 10. 16,14.6. In the case of thestrength design method, the strength of compact sectionswith holes in the tension flange shall not be taken greaterthan the moment capacity at first yield.

10.13 COVER PLATES

10.13.1 The length of any cover plate added to a rolledbeam shall be not less than (2d+3) feet, where (d) is thedepth of the beam in feet.

10.13.2 Partial length welded cover plates shall not beused on flanges more than 0.8 inches thick for nonredun-dant load path structures subjected to repetitive loadingsthat produce tension or reversal of stress in the member.

10.13.3 The maximum thickness of a single cover plateon a flange shall not be greater than two times the thick-ness of the flange to which the cover plate is attached. Thetotal thickness of all cover plates should not be greaterthan 2% times the flange thickness.

10.13.4 Any partial length welded cover plate shall ex-tend beyond the theoretical end by the terminal distance,and it shall extend to a section where the stress range inthe beam flange is equal to the allowable fatigue stressrange for base metal adjacent to or connected by filletwelds. The theoretical end of the cover plate, when usingservice load design methods, is the section at which thestress in the flange without that cover plate equals the al-lowable service load stress, exclusive of fatigue consider-ations. When using strength design methods, the theoret-ical end of the cover plate is the section at which the flangestrength without that cover plate equals the requiredstrength for the design loads, exclusive of fatigue require-ments. The terminal distance is two times the nominalcover plate width for cover plates not welded across theirends, and 1% times for cover plates welded across theirends. The width at ends of tapered cover plates shall benot less than 3 inches. The weld connecting the coverplate to the flange in its terminal distance shall be contin-uous and of sufficient size to develop a total stress of notless than the computed stress in the cover plate at its the-oretical end. All welds connecting cover plates to beamflanges shall be continuous and shall not be smaller thanthe minimum size permitted by Article 10.23.2.


10.13.5 Any partial length end-bolted cover plate shallextend beyond the theoretical end by a terminal distanceequal to the length of the end-bolted portion, and the coverplate shall extend to a section where the stress range in thebeam flange is equal to the allowable fatigue stress rangefor base metal at ends of partial length welded cover plateswith high-strength bolted, slip-critical end connections(Table 10.3.1B). Beams with end-bolted cover plates shallbe fabricated in the following sequence: drill holes; cleanfaying surfaces; install bolts; weld. The theoretical end ofthe end-bolted cover plate is determined in the same man-ner as that of a welded cover plate, as is specified in Arti-cle 10.13.4. The bolts in the slip-critical connections ofthe cover plate ends to the flange, shall be of sufficientnumbers to develop a total force of not less than the com-puted force in the cover plate at the theoretical end. Theslip resistance of the end-bolted connection shall be de-termined in accordance with Article 10.32.3.2 for serviceload design, and Article 10.56.1.4 for load factor design.The longitudinal welds connecting the cover plate to thebeam flange shall be continuous and stop a distance equalto one bolt spacing before the first row of bolts in the end-bolted portion.

10.14 CAMBER

Girders should be cambered to compensate for deadload deflections and vertical curvature required by profilegrade.

10.15 HEAT-CURVED ROLLED BEAMS ANDWELDED PLATE GIRDERS

10.15.1 Scope

This section pertains to rolled beams and welded I-sec-tion plate girders heat-curved to obtain a horizontal cur-vature. Steels that are manufactured to a specified mini-mum yield point greater than 50,000 psi, except for GradeHPS70W steel, shall not be heat-curved.

10.15.2 Minimum Radius of Curvature

10.15.2.1 For heat-curved beams and girders, thehorizontal radius of curvature measured to the center lineof the girder web shall not be less than 150 feet and shallnot be less than the larger of the values calculated (at anyand all cross sections throughout the length of the girder)from the following two equations:

R–14bD

(10-1)FY Vtw

R – 7,500b(10-2)

FY W

In these equations, F, is the specified minimum yieldpoint in kips per square inch of steel in the girder web, ~is the ratio of the total cross-sectional area to the cross-sectional area of both flanges, b is the widest flange widthin inches, D is the clear distance between flanges ininches, tW is the web thickness in inches, and R is the ra-dius in inches.

10.15.2.2 In addition to the above requirements, theradius shall not be less than 1,000 feet when the flangethickness exceeds 3 inches or the flange width exceeds30 inches.

10.15.3 Camber

To compensate for possible loss of camber of heat-curved girders in service as residual stresses dissipate, theamount of camber in inches, A at any section along thelength L of the girder shall be equal to:

A= AFL

(4M+4R) (10-3)M

0.02 L2F 1,000–ROR

EYo ( 850

AR = 0 for radii greater than 1, 000

where ADL is the camber in inches at any point along thelength L calculated by usual procedures to compensate fordeflection due to dead loads or any other specified loads;A M is the maximum value of ADL in inches within thelength L; E is the modulus of elasticity in ksi; F y is thespecified minimum yield point in ksi of the girder flange;Y,, is the distance from the neutral axis to the extremeouter fiber in inches (maximum distance for nonsymmet-rical sections); R is the radius of curvature in feet; and Lis the span length for simple spans or for continuousspans, the distance between a simple end support and thedead load contraflexure point, or the distance betweenpoints of dead load contraflexure. (L is measured ininches.) Camber loss between dead load contraflexurepoints adjacent to piers is small and may be neglected.

Note: Part of the camber loss is attributable to construc-tion loads and will occur during construction of the


bridge; total camber loss will be complete afterseveral months of in-service loads. Therefore, aportion of the camber increase (approximately50%) should be included in the bridge profile.Camber losses of this nature (but generally smallerin magnitude) are also known to occur in straightbeams and girders.

10.16 TRUSSES

10.16.1 General

10.16.1.1 Component parts of individual truss mem-bers may be connected by welds, rivets, or high-strengthbolts.

10.16.1.2 Preference should be given to trusses withsingle intersection web systems. Members shall be sym-metrical about the central plane of the truss.

10.16.1.3 Trusses preferably shall have inclined endposts. Laterally unsupported hip joints shall be avoided.

10.16.1.4 Main trusses shall be spaced a sufficientdistance apart, center to center, to be secure against over-turning by the assumed lateral forces.

10.16.1.5 For the calculation of stresses, effectivedepths shall be assumed as follows:

Riveted and bolted trusses, distance between centers ofgravity of the chords.Pin-connected trusses, distance between centers ofchord pins.

10.16.2 Truss Members

10.16.2.1 Chord and web truss members shall usu-ally be made in the following shapes:

"H" sections, made with two side segments (composedof angles or plates) with solid web, perforated web, orweb of stay plates and lacing.Channel sections, made with two angle segments, withsolid web, perforated web, or web of stay plates andlacing.Single Box sections, made with side channels, beams,angles, and plates or side segments of plates only, con-nected top and bottom with perforated plates or stayplates and lacing.

Single Box sections, made with side channels, beams,angles and plates only, connected at top with solid

cover plates and at the bottom with perforated plates orstay plates and lacing.Double Box sections, made with side channels, beams,angles and plates or side segments of plates only, con-nected with a conventional solid web, together with topand bottom perforated cover plates or stay plates andlacing.

10.16.2.2 If the shape of the truss permits, compres-sion chords shall be continuous.

10.16.2.3 In chords composed of angles in channel-shaped members, the vertical legs of the angles preferablyshall extend downward.

10.16.2.4 If web members are subject to reversal ofstress, their end connections shall not be pinned. Counterspreferably shall be rigid. Adjustable counters, if used,shall have open turnbuckles, and in the design of thesemembers an allowance of 10,000 pounds per square inchshall be made for initial stress. Only one set of diagonalsin any panel shall be adjustable. Sleeve nuts and loop barsshall not be used.

10.16.3 Secondary Stresses

The design and details shall be such that secondarystresses will be as small as practicable. Secondary stressesdue to truss distortion or floor beam deflection usuallyneed not be considered in any member, the width ofwhich, measured parallel to the plane of distortion, is lessthan one-tenth of its length. If the secondary stress ex-ceeds 4,000 pounds per square inch for tension membersand 3,000 for compression members, the excess shall betreated as a primary stress. Stresses due to the flexuraldead load moment of the member shall be considered asadditional secondary stress.

10.16.4 Diaphragms

10.16.4.1 There shall be diaphragms in the trusses atthe end connections of floor beams.

10.16.4.2 The gusset plates engaging the pedestal pinat the end of the truss shall be connected by a diaphragm.Similarly, the webs of the pedestal shall, if practicable, beconnected by a diaphragm.

10.16.4.3 There shall be a diaphragm between gussetplates engaging main members if the end tie plate is 4 feetor more from the point of intersection of the members.


10.16.5 Camber

The length of the truss members shall be such that thecamber will be equal to or greater than the deflection pro-duced by the dead load.

10.16.6 Working Lines and Gravity Axes

10.16.6.1 Main members shall be proportioned sothat their gravity axes will be as nearly as practicable inthe center of the section.

10.16.6.2 In compression members of unsymmetri-cal section, such as chord sections formed of side seg-ments and a cover plate, the gravity axis of the sectionshall coincide as nearly as practicable with the workingline, except that eccentricity may be introduced to coun-teract dead load bending. In two-angle bottom chord or di-agonal members, the working line may be taken as thegage line nearest the back of the angle or at the center ofgravity for welded trusses.

10.16.7 Portal and Sway Bracing

10.16.7.1 Through truss spans shall have portal brac-ing, preferably, of the two-plane or box type, rigidly con-nected to the end post and the top chord flanges, and asdeep as the clearance will allow. If a single plane portal isused, it shall be located, preferably, in the central trans-verse plane of the end posts, with diaphragms between thewebs of the posts to provide for a distribution of the por-tal stresses. The portal bracing shall be designed to takethe full end reaction of the top chord lateral system, andthe end posts shall be designed to transfer this reaction tothe truss bearings.

10.16.7.2 Through truss spans shall have sway brac-ing 5 feet or more deep at each intermediate panel point.Top lateral struts shall be at least as deep as the top chord.

10.16.7.3 Deck truss spans shall have sway bracingin the plane of the end posts and at all intermediate panelpoints. This bracing shall extend the full depth of thetrusses below the floor system. The end sway bracing shallbe proportioned to carry the entire upper lateral stress tothe supports through the end posts of the truss.

10.16.8 Perforated Cover Plates

When perforated cover plates are used, the followingprovisions shall govern their design.

10.16.8.1 The ratio of length, indirection of stress, towidth of perforation, shall not exceed two.

10.16.8.2 The clear distance between perforations inthe direction of stress shall not be less than the distancebetween points of support.

10.16.8.3 The clear distance between the end perfo-ration and the end of the cover plate shall not be less than1.25 times the distance between points of support.

10.16.8.4 The point of support shall be the inner lineof fasteners or fillet welds connecting the perforated plateto the flanges. For plates butt welded to the flange edge ofrolled segments, the point of support may be taken as theweld whenever the ratio of the outstanding flange widthto flange thickness of the rolled segment is less thanseven. Otherwise, the point of support shall be the root ofthe flange of the rolled segment.

10.16.8.5 The periphery of the perforation at allpoints shall have a minimum radius of 1 %2 inches.

10.16.8.6 For thickness of metal, see Article 10.35.2.

10.16.9 Stay Plates

10.16.9.1 Where the open sides of compressionmembers are not connected by perforated plates, suchmembers shall be provided with lacing bars and shall havestay plates as near each end as practicable. Stay platesshall be provided at intermediate points where the lacingis interrupted. In main members, the length of the end stayplates between end fasteners shall be not less than 1 %4

times the distance between points of support andthe length of intermediate stay plates not less than %4 ofthat distance. In lateral struts and other secondary mem-bers, the overall length of end and intermediate stay platesshall be not less than %4 of the distance between points ofsupport.

10.16.9.2 The point of support shall be the inner lineof fasteners or fillet welds connecting the stay plates tothe flanges. For stay plates butt welded to the flange edgeof rolled segments, the point of support may be taken asthe weld whenever the ratio of outstanding flange widthto flange thickness of the rolled segment is less thanseven. Otherwise, the point of support shall be the root offlange of rolled segment. When stay plates are buttwelded to rolled segments of a member, the allowablestress in the member shall be determined in accordance


with Article 10.3. Terminations of butt welds shall beground smooth.

10.16.9.3 The separate segments of tension memberscomposed of shapes may be connected by perforatedplates or by stay plates or end stay plates and lacing.End stay plates shall have the same minimum length asspecified for end stay plates on main compression mem-bers, and intermediate stay plates shall have a minimumlength of %4 of that specified for intermediate stay plates onmain compression members. The clear distance betweenstay plates on tension members shall not exceed 3 feet.

10.16.9.4 The thickness of stay plates shall be notless than %5o of the distance between points of support formain members, and %6o of that distance for bracing mem-bers. Stay plates shall be connected by not less than threefasteners on each side, and in members having lacing barsthe last fastener in the stay plates preferably shall also passthrough the end of the adjacent bar.

10.16.10 Lacing Bars

When lacing bars are used, the following provisionsshall govern their design.

10.16.10.1 Lacing bars of compression membersshall be so spaced that the slenderness ratio of the portionof the flange included between the lacing bar connectionswill be not more than 40 or more than %3 of the slender-ness ratio of the member.

10.16.10.2 The section of the lacing bars shall be de-termined by the formula for axial compression in whichL is taken as the distance along the bar between its con-nections to the main segments for single lacing, and as70% of that distance for double lacing.

10.16.10.3 If the distance across the member betweenfastener lines in the flanges is more than 15 inches and abar with a single fastener in the connection is used, the lac-ing shall be double and fastened at the intersections.

10.16.10.4 The angle between the lacing bars and theaxis of the member shall be approximately 45° for doublelacing and 60° for single lacing.

10.16.10.5 Lacing bars may be shapes or flat bars.For main members, the minimum thickness of flat barsshall be %4o of the distance along the bar between its con-nections for single lacing and %6o for double lacing. Forbracing members, the limits shall be %5o for single lacingand %75 for double lacing.

10.16.10.6 The diameter of fasteners in lacing barsshall not exceed one-third the width of the bar. There shallbe at least two fasteners in each end of lacing bars con-nected to flanges more than 5 inches in width.

10.16.11 Gusset Plates

10.16.11.1 Gusset or connection plates preferablyshall be used for connecting main members, except whenthe members are pin-connected. The fasteners connectingeach member shall be symmetrical with the axis of themember, so far as practicable, and the full development ofthe elements of the member shall be given consideration.The gusset plates shall be of ample thickness to resistshear, direct stress, and flexure acting on the weakest orcritical section of maximum stress.

10.16.11.2 Re-entrant cuts, except curves made forappearance, shall be avoided as far as practicable.

10.16.11.3 If the length of unsupported edge ofa gusset plate exceeds the value of the expres-sion 11,000NT-y times its thickness, the edge shall bestiffened.

10.16.11.4 Listed below are the values of the expres-sion 11,000/N//-F—, for the following grades of steel:

36,000 psi, Y.P. Min 5850,000 psi, Y.P. Min 4970,000 psi, Y.P. Min 4290,000 psi, Y.P. Min 37

100,000 psi, Y.P. Min 35

10.16.12 Half-Through Truss Spans

10.16.12.1 The vertical truss members and the floorbeams and their connections in half-through truss spansshall be proportioned to resist a lateral force of not lessthan 300 pounds per linear foot applied at the top chordpanel points of each truss.

10.16.12.2 The top chord shall be considered as acolumn with elastic lateral supports at the panel points.The critical buckling force of the column, so determined,shall exceed the maximum force from dead load, live load,and impact in any panel of the top chord by not less than50%.*

*For a discussion of columns with elastic lateral supports, refer to Tim-oshenko & Gere, "Theory of Elastic Stability," McGraw-Hill Book Co.,First Edition, p. 122.


10.16.13 Fastener Pitch in Ends of CompressionMembers

In the ends of compression members, the pitch of fas-teners connecting the component parts of the membershall not exceed four times the diameter of the fastenerfor a length equal to 1 112 times the maximum width of themember. Beyond this point, the pitch shall be increasedgradually for a length equal to 1Y2 times the maximumwidth of the member until the maximum pitch isreached.

10.16.14 Net Section of Riveted or High-StrengthBolted Tension Members

10.16.14.1 The net section of a riveted or high-strength bolted tension member is the sum of the net sec-tions of its component parts. The net section of a part isthe product of the thickness of the part multiplied by itsleast net width.

10.16.14.2 The net width for any chain of holes ex-tending progressively across the part shall be obtained bydeducting from the gross width the sum of the diametersof all the holes in the chain and adding, for each gagespace in the chain, the quantity:

S Z

(10-4)4g

where:

S = pitch of any two successive holes in the chain;= gage of the same holes.

The net section of the part is obtained from the chain thatgives the least net width.

10.16.14.3 For angles, the gross width shall be thesum of the widths of the legs less the thickness. The gagefor holes in opposite legs shall be the sum of gages fromback of angle less the thickness.

10.16.14.4 At a splice, the total stress in the memberbeing spliced is transferred by fasteners to the splicematerial.

10.16.14.5 When determining the unit stress on anyleast net width of either splice material or member beingspliced, the amount of the stress previously transferredby fasteners adjacent to the section being investigated

shall be considered in determining the unit stress on thenet section.

10.16.14.6 The diameter of the hole shall be taken as

%8 inch greater than the nominal diameter of the rivet orhigh-strength bolt, unless larger holes are permitted in ac-cordance with Article 10.24.

10.17 BENTS AND TOWERS

10.17.1 General

Bents preferably shall be composed of two supportingcolumns, and the bents usually shall be united in pairs toform towers. The design of members for bents and towersis governed by applicable articles.

10.17.2 Single Bents

Single bents shall have hinged ends or else shall be de-signed to resist bending.

10.17.3 Batter

Bents preferably shall have a sufficient spread at thebase to prevent uplift under the assumed lateral loadings.In general, the width of a bent at its base shall be not lessthan one-third of its height.

10.17.4 Bracing

10.17.4.1 Towers shall be braced, both transverselyand longitudinally, with stiff members having eitherwelded, high-strength bolted or riveted connections. Thesections of members of longitudinal bracing in each panelshall not be less than those of the members in corre-sponding panels of the transverse bracing.

10.17.4.2 The bracing of long columns shall be de-signed to fix the column about both axes at or near thesame point.

10.17.4.3 Horizontal diagonal bracing shall beplaced in all towers having more than two vertical panels,at alternate intermediate panel points.


10.17.5 Bottom Struts

The bottom struts of towers shall be strong enough toslide the movable shoes with the structure unloaded, thecoefficient of friction being assumed at 0.25. Provision forexpansion of the tower bracing shall be made in the col-umn bearings.

10.18 SPLICES

10.18.1 General

10.18.1.1 Design Strength

Splices may be made by rivets, by high-strength bolts orby the use of welding. In general, splices whether in tension,compression, bending, or shear, shall be designed in the caseof the service load design or strength design methods for acapacity based on not less than the average of the requireddesign strength at the point of splice and the design strengthof the member at the same point but, in any event, not lessthan 75% of the design strength of the member, except asspecified herein. Bolted splices in flexural members shallsatisfy the requirements of Article 10. 18.2. Bolted splices incompression members shall satisfy the requirements of Ar-ticle 10.18.3. Bolted splices in tension members shall sat-isfy the requirements of Article 10.18.4. Welded splicesshall satisfy the requirements of Article 10.18.5. Where asection changes at a splice, the smaller section is to be usedto satisfy the above splice requirements.

10.18.1.2 Fillers

10.18.1.2.1 For fillers % inch and thicker in bolted orriveted axially loaded connections, including girder flangesplices, additional fasteners shall be required to distributethe total stress in the member uniformly over the com-bined section of the member and the filler. The filler shalleither be extended beyond the splice material and securedby additional bolts, or as an alternate to extending thefiller, an equivalent number of bolts may be included inthe connection. Fillers % inch and thicker need not be ex-tended and developed provided that the design shearstrength of the fasteners, specified in Article 10.56.1.3.2in the case of the strength design method and in Table10.32.3B in the case of the service load design method, isreduced by the following factor R:

R=[(1+y)/(1+2y)] (10-4a)

where: 7 = AfA P

Af = sum of the area of the fillers on the top andbottom of the connected plate

AP = smaller of either the connected plate area orthe sum of the splice plate areas on the topand bottom of the connected plate

The design slip force, specified in Article 10.57.3.1 in thecase of the strength design method and in Article10.32.3.2.1 in the case of the service load design method,for slip-critical connections shall not be adjusted for theeffect of the fillers. Fillers % inch or more in thicknessshall consist of not more than two plates, unless specialpermission is given by the Engineer.

10.18.1.2.2 For bolted web splices with thick-ness differences of %6 inch or less, no filler plates arerequired.

10.18.1.2.3 Fillers for welded splices shall conformto the requirements of the ANSI/AASHTO/AWS D1.5Bridge Welding Code.

10.18.1.3 Design Force for Flange Splice Plates

For a flange splice with inner and outer splice plates,the flange design force may be assumed to be dividedequally to the inner and outer plates and their connec-tions when the areas of the inner and outer plates do notdiffer by more than 10%. When the areas of the inner andouter plates differ by more than 10%, the design force ineach splice plate and its connection shall be determinedby multiplying the flange design force by the ratio of thearea of the splice plate under consideration to the totalarea of the inner and outer splice plates. For this case, theshear strength of the connection shall be checked for themaximum calculated splice plate force acting on a sin-gle shear plane. The slip resistance of high-strengthbolted connections for a flange splice with innerand outer splice plates shall always be checked for theflange design force divided equally to the two slipplanes.

10.18.1.4 Truss Chords and Columns

Splices in truss chords and columns shall be locatedas near to the panel points as practicable and usually onthe side where the smaller stress occurs. The arrange-ment of plates, angles, or other splice elements shall besuch as to make proper provision for the stresses, bothaxial and bending, in the component parts of the mem-bers spliced.


10.18.2 Flexural Members

10.18.2.1 General

10.18.2.1.1 In continuous spans, splices shall prefer-ably be made at or near points of dead-load contraflexure.

10.18.2.1.2 In both flange and web splices, thereshall be not less than two rows of bolts on each side of thejoint.

10.18.2.1.3 Oversize or slotted holes shall not be usedin either the member or the splice plates at bolted splices.

10.18.2.1.4 In both flange and web splices, high-strength bolted connections shall be proportioned to pre-vent slip during erection of the steel and during the cast-ing or placing of the deck.

10.18.2.1.5 In the case of the strength designmethod, the strength of compact sections at the point ofsplice shall not be taken greater than the moment capac-ity at first yield, computed by accounting for the holes inthe tension flange as specified in Article 10.12.

10.18.2.1.6 Flange and web splices in areas of stressreversal shall be checked for both positive and negativeflexure.

10.18.2.1.7 Riveted and bolted flange angle splicesshall include two angles, one on each side of the flexuralmember.

10.18.2.2 Flange Splices

10.18.2.2.1 Asa minimum, in the case of the strengthdesign method, the splice plates on the controlling flangeshall be proportioned for a design force, P, u . The control-ling flange shall be taken as the top or bottom flange forthe smaller section at the point of splice, whichever flangehas the maximum ratio of the elastic flexural stress at itsmid-thickness due to the factored loads to its maximumstrength. P,u shall be taken equal to a design stress, Fcu ,times the smaller effective flange area, A,, on either sideof the splice. Ae is defined in Article 10. 18.2.2.4 and F c„ isdefined as follows:

Fcu =

(Jfcu/RJ

2

+aFyf~ >_0.75aFyf (10-4b)

where:

a = 1.0 except that a lower value equal to (M u/M y )may be used for flanges in compression at sec-tions where M. is less than M y .

M„ = maximum bending strength of the section in pos-itive or negative flexure at the point of splice,whichever causes the maximum compressivestress due to the factored loads at the mid-thick-ness of the flange under consideration

m y = moment capacity at first yield for the section atthe point of splice used to compute M,,. For com-posite sections, My shall be calculated in accor-dance with Article 10.50(c). For hybrid sections,My shall be computed in accordance with Article10.53.

fc„ = maximum elastic flexural stress due to the fac-tored loads at the mid-thickness of the control-ling flange at the point of splice.

R = reduction factor for hybrid girders specified inArticle 10.53.1.2. R shall be taken equal to 1.0when fcu is less than or equal to FyW , where F yW isequal to the specified minimum yield strength ofthe web. For homogeneous girders, R shall al-ways be taken equal to 1.0.

Fyf = specified minimum yield strength of the flange

As a minimum, the splice plates for the noncontrollingflange shall be proportioned for a design force, P„ o,,. P„c „shall be taken equal to a design stress, l 7

mu , times thesmaller effective flange area, A,, on either side of thesplice. F„,„ is defined as follows:

Fncu = R cu (Ifncu / RI) ? 0.75u.Fyf (10 - 4c)

where:

R,U = the absolute value of the ratio of Fc„ to f u for thecontrolling flange.

fn, u = flexural stress due to the factored loads at themid-thickness of the noncontrolling flange at thepoint of splice concurrent with f eu

In calculating fc,,, fn, u, M,,, My

and R, holes in the flangesubject to tension shall be accounted for as specified in Ar-ticle 10.12. For a flange splice with inner and outer spliceplates, the flange design force shall be proportioned to theinner and outer plates and their connections as specifiedin Article 10. 18.1.3. The effective area, A,, of each spliceplate shall be sufficient to prevent yielding of the spliceplate under its calculated portion of the design force. A e ofeach splice plate shall be taken as defined in Article10. 18.2.2.4. As a minimum, the connections for both thetop and bottom flange splices shall be proportioned to de-velop the design force in the flange through shear in thebolts and bearing at the bolt holes, as specified in Article10.56.1.3.2. Where filler plates are required, the require-ments of Article 10.18.1.2.1 shall also be satisfied.


10.18.2.2.2 Asa minimum, in the case of the strengthdesign method, high-strength bolted connections for bothtop and bottom flange splices shall be proportioned to pre-vent slip at an overload design force, Pfc. For the flangeunder consideration, P fc shall be computed as follows:

Pfc =ifc /RJA g (10-4d)

where:

fc = maximum flexural stress due to D + (3,(L + I) atthe mid-thickness of the flange under considera-tion for the smaller section at the point of splice,where RL is defined in Article 3.22

R = reduction factor for hybrid girders specified inArticle 10.53.1.2. R shall be taken equal to 1.0when fc is less than or equal to Fyw , where F,,W isequal to the specified minimum yield strength ofthe web. For homogeneous girders, R shall al-ways be taken equal to 1.0.

Ag = smaller gross flange area on either side of thesplice

f, and R shall be computed using the gross section of themember. The slip resistance of the connection shall becomputed from Equation (10-172).

10.18.2.2.3 Asa minimum, in the case of the serviceload design method, the splice plates on the controllingflange shall be proportioned for a design force, Pcf. Thecontrolling flange shall be taken as the top or bottomflange for the smaller section at the point of splice,whichever flange has the maximum ratio of the elasticflexural stress at its mid-thickness to its allowable stress. P

cfshall be taken equal to a design stress, Fcf, times the smallereffective flange area, Ae , on either side of the splice. Ae isdefined in Article 10. 18.2.2.4 and F cf is defined as follows:

Fcf ` (fcf/RI+Fb)>0.75Fb (10-4e)

where:

fcf = maximum elastic flexural stress at the mid-thick-ness of the controlling flange at the point ofsplice.

Fb = allowable flexural stress for the flange under con-sideration at the point of splice

R = reduction factor for hybrid girders specified in Ar-ticle 10.40.2.1. R shall be taken equal to 1.0 whenfcf is less than or equal to the allowable flexuralstress for the web steel. For homogeneous girders,R shall always be taken equal to 1.0.

As a minimum, the splice plates for the noncontrollingflange shall be proportioned for a design force, P,,cf• Pncfshall be taken equal to a design stress, Fncf, times thesmaller effective flange area, A e , on either side of thesplice. Fncf is defined as follows:

Fncf =Rcf (Ifncf/RJ) ? 0.75Fb (10 - 4f)

where:

Rcf = the absolute value of the ratio of Fcf to fcf for thecontrolling flange

fncf = flexural stress at the mid-thickness of the non-controlling flange at the point of splice concur-rent with fcf

In calculating F cf , fncf and R, holes in the flange subject totension shall be accounted for as specified in Article10.12. For a flange splice with inner and outer spliceplates, the flange design force shall be proportioned to theinner and outer plates and their connections as specifiedin Article 10. 18.1.3. The effective area, A e, of each spliceplate shall be sufficient to ensure that the stress in thesplice plate does not exceed the allowable flexural stressunder its calculated portion of the design force. Ae of eachsplice plate shall be taken as defined in Article10, 18.2.2.4. As a minimum, the connections for both thetop and bottom flange splices shall be proportioned to de-velop the design force in the flange through shear in thebolts and bearing at the bolt holes, as specified in Table10.32.3B. Where filler plates are required, the require-ments of Article 10.18.1.2.1 shall also be satisfied. As aminimum, high-strength bolted connections shall also beproportioned to prevent slip at a force equal to the maxi-mum elastic flexural stress due to D + (L + I) at the mid-thickness of the flange under consideration for the smallersection at the point of splice times the smaller value of thegross flange area on either side of the splice. The slip re-sistance of the connection shall be determined as specifiedin Article 10.32.3.2.1.

10.18.2.2.4 For checking the strength of flangesplices, an effective area, A e , shall be used for the flangeand for the individual splice plates as follows:

For flanges and their splice plates subject to tension:

A e =Wn t+PA g SA g (10-4g)

where:

Wn = least net width of the flange or splice plate com-puted as specified in Article 10. 16.14


= flange or splice plate thicknessA g = gross area of the flange or splice plate

R = 0.0 for M 270 Grade 100/10OW steels, or whenholes exceed P/4 inch in diameter.

= 0.15 for all other steels and when holes are lessthan or equal to 1% inch in diameter.

The diameter of the holes shall be taken as specified in Ar-ticle 10.16.14.6.

For the flanges and their splice plates subject tocompression:

A c = A g (10- 4h)

10.18.2.3 Web Splices

10.18.2.3.1 In general, web splice plates and theirconnections shall be proportioned for shear, a momentdue to the eccentricity of the shear at the point of splice,and a portion of the flexural moment that is assumed to beresisted by the web at the point of splice.* Webs shall bespliced symmetrically by plates on each side. The websplice plates shall extend as near as practical for the fulldepth between flanges.

10. 18.2.3.2 As a minimum, in the case of the strengthdesign method, web splice plates and their connectionsshall be proportioned for a design shear in the web at thepoint of splice, V,,,,,, defined as follows:

For V < 0.5Vu :

Vwu =1.5V (10-4i)

For V >_ 0.5Vu :

V[V+Vu

V. –2

(10-4j)

where:

V = maximum shear in the web at the point of splicedue to the factored loads

V„ = shear capacity of the web at the point of splice

*For an alternative approach for compact steel sections, reference ismade to Firas I. Sheikh-Ibrahim and Karl H. Frank, "The UltimateStrength of Symmetric Beam Bolted Splices," AISC Engineering Jour-nal, 3rd Quarter, 1998, and "The Ultimate Strength of UnsymmetricBeam Bolted Splices," AISC Engineering Journal, 2nd Quarter, 2001.

10.18.2.3.3 Asa minimum, in the case of the strengthdesign method, web splice plates and their connectionsshall be proportioned for a design moment, M, due to theeccentricity of the design shear at the point of splice de-fined as follows:

Mvu = Vwu e (10-4k)

where:

Vwu = design shear in the web at the point of splice de-fined in Article 10. 18.2.3.2

e = distance from the centerline of the splice to thecentroid of the connection on the side of thejoint under consideration

10.18.2.3.4 Asa minimum, in the case of the strengthdesign method, web splice plates and their connectionsshall be proportioned for a design moment at the point ofsplice, M w ,, representing the portion of the flexural mo-ment that is assumed to be resisted by the web. M µ,,, shallbe applied at the mid-depth of the web. For sections wherethe neutral axis is not located at mid-depth of the web, ahorizontal design force resultant in the web at the point ofsplice, H wu, shall also be applied at the mid-depth of theweb. Mwu and Hwu may be computed as follows:

2

Mwu = t1D2

JRFcu–Rou.J

(10-41)

Hwu _ twD (RFcu +Rcufncu) (10-4m)

where:

Fc„ = design stress for the controlling flange at thepoint of splice defined in Article 10.18.2.2.1(positive for tension; negative for compression)

R = reduction factor for hybrid girders specified inArticle 10.53.1.2. R shall be taken equal to 1.0when f u is less than or equal to F,,N , where Fyw isequal to the specified minimum yield strength ofthe web. For homogeneous girders, R shall al-ways be taken equal to 1.0.

R,U =the absolute value of the ratio of F, u to f u for thecontrolling flange

fncu= flexural stress due to the factored loads at themid-thickness of the noncontrolling flange at thepoint of splice concurrent with f u (positive fortension; negative for compression)

10.18.2.3.5 Asa minimum, in the case of the strengthdesign method, web splice plates and their connectionsshall be proportioned to develop the most critical combi-


nation of VWU , M„U , M,,,,, and H WU . The connections shall beproportioned as eccentrically loaded connections to de-velop the resultant design force through shear in the boltsand bearing at the bolt holes, as specified in Article10.56.1.3.2. In addition, as a minimum, high-strengthbolted connections for web splices shall be proportionedas eccentrically loaded connections to prevent slip underthe most critical combination of: 1) an overload designshear, VWU, 2) an overload design moment, M ao, due to theeccentricity of the overload design shear, 3) an overloaddesign moment, M w, applied at mid-depth of the web rep-resenting the portion of the flexural moment that is as-sumed to be resisted by the web, and 4) for sections wherethe neutral axis is not located at the mid-depth of the web,an overload horizontal design force resultant, H WU, appliedat mid-depth of the web, as follows:

VIVO = V. (10-4n)

where:

V o = maximum shear in the web due to D + (3, , (L+I)at the point of the splice, where PL is defined inArticle 3.22

MVO = VW, o e (10-4o)

M. and HWU may be computed as follows:

M. = t

W

ifo —fof1 (10-4p)

Hwo

=WD(fo+f.f) (10-4q)

where:

fo = maximum flexural stress due to D + (3,(L+I) atthe mid-thickness of the flange under consider-ation for the smaller section at the pointof splice (positive for tension; negative for com-pression)

fa = flexural stress due to D + P,(L+I) at the mid-thickness of the other flange at the point of spliceconcurrent with f„ in the flange under considera-tion (positive for tension; negative for compres-sion)

fU and fUf shall be computed using the gross section of themember. The maximum resultant force on the eccentri-cally loaded connection shall not exceed the slip resis-tance computed from Equation (10-172) with Ne takenequal to 1.0.

10.18.2.3.6 Asa minimum, in the case of the serviceload design method, web splice plates and their connec-tions shall be proportioned for a design shear stress in theweb at the point of splice, FW , defined as follows:

For f,, < 0.5Fv:

FW, = 1.5fv (10 - 4r)

For f,, >_ 0.5Fv:

F = (f,+Fj

W 2 (10-4s)

where:

f„ = maximum shear stress in the web at the point ofsplice

F,, = allowable shear stress in the web at the point ofsplice

10.18.2.3.7 Asa minimum, in the case of the serviceload design method, web splice plates and their connec-tions shall be proportioned for a design moment, M,,, dueto the eccentricity of the design shear at the point of splicedefined as follows:

M, =FW Dt w e (10-4t)

where:

FW = design shear stress in the web at the point ofsplice defined in Article 10. 18.2.3.6

D = web depthtW = web thickness

1018.2.3.8 As a minimum, in cases of the serviceload design method, web splice plates and their connec-tions shall be proportioned for a design moment at thepoint of splice, M W, representing the portion of the flex-ural moment that is assumed to be resisted by the web. M W

shall be applied at the mid-depth of the web. For sectionswhere the neutral axis is not located at the mid-depth ofthe web, a horizontal design force resultant in the web atthe point of splice, H W , shall also be applied at the mid-depth of the web. MW and HW may be computed as follows:

zMW = t1 J

RFcf –R cffncf1 (10-4u)

Hw = Lw—D(RFcf+Rcffncf)

(10-4v)


where:

F,f = design stress at the point of splice for the con-

trolling flange defined in Article 10.18.2.2.3(positive for tension; negative for compression)

R = reduction factor for hybrid girders specified inArticle 10.40.2.1. R shall be taken equal to 1.0when F,f is less than or equal to the allowableflexural stress for the web steel. For homoge-neous girders, R shall always be taken equal to1.0.

Rif = the absolute value of the ratio of F~ f to f~f for thecontrolling flange

f.Cf = flexural stress at the mid-thickness of the non-controlling flange at the point of splice concur-rent with f~f (positive for tension; negative forcompression)

10.18.2.3.9 As a minimum, in the case of the ser-vice load design method, web splice plates and theirconnections shall be proportioned to develop the mostcritical combination of F,Dt W , M v, M a, and H W . The con-nections shall be proportioned as eccentrically loadedconnections to develop the resultant design forcethrough shear in the bolts and bearing at the bolt holes,as specified in Table 10.32.313. In addition, as a mini-mum, high-strength bolted connections for web splicesshall be proportioned as eccentrically loaded connec-tions to prevent slip under the most critical combina-tion of shear, moment, and horizontal force due to D +(L + I) at the point of splice. The portion of the flexuralmoment that is assumed to be resisted by the web andthe horizontal force resultant shall be computed usingthe gross section of the member. The maximum resul-tant force on the eccentrically loaded connection shallnot exceed the slip resistance computed from Article10.32.3.2.1 with Nb taken to equal 1.0.


Compression members such as columns and chordsshall have ends in close contact at riveted and boltedsplices. Splices of such members which will be fabricatedand erected with close inspection and detailed with milledends in full contact bearing at the splices may be held inplace by means of splice plates and rivets or high-strengthbolts proportioned for not less than 50% of the lower al-lowable design strength of the sections spliced. Thestrength of compression members connected by high-strength bolts or rivets shall be determined using the grosssection.

10.18.4 Tension Members

10.18.4.1. As a minimum, splices in tension mem-bers shall be proportioned for a design force, Pu , equal to

the allowable design strength specified in Article10.18.1.1 times the effective area of the member, A., de-fined as follows:

A e = A. + PA g 5 Ag (10 - 4w)

where:

A„ = net section of the member computed as specifiedin Article 10. 16.14

R = 0.0 for AASHTO M 270 Grade 100/100W(ASTM A 709 Grade 100/100W) steels, or whenholes exceed 1% inch in diameter

= 0.15 for all other steels and when holes are lessthan or equal to 1 % inch in diameter.

Ag = gross area of the member

The diameter of the holes shall be taken as specified in Ar-ticle 10.16.14.6. As a minimum, the connection shall beproportioned to develop the design force through shear inthe bolts and bearing at the bolt holes, as specified in Ar-ticle 10.56.1.3.2 in the case of the strength design methodand in Table 10.32.313 in the case of the service load de-sign method.

10.18.4.2 As a minimum, in the case of the strengthdesign method, high-strength bolted connections forsplices in tension members shall be proportioned to pre-vent slip at an overload design force, Po, equal to the max-imum tensile stress in the member due to D + PL (L + I)times the gross area of the member, where PL is defined inArticle 3.22. The slip resistance of the connection shall becomputed from Equation (10-172). In the case of the ser-vice load design method, high-strength bolted connec-tions shall be proportioned to prevent slip at a force equalto the maximum tensile stress in the member due to D +(L + I) times the gross area of the member. The slip resis-tance of the connection shall be determined as specified inArticle 10.32.3.2.1.

10.18.5 Welded Splices

10.18.5.1 Tension and compression members maybespliced by means of full penetration butt welds, preferablywithout the use of splice plates.

10.18.5.2 Welded field splices preferably should bearranged to minimize overhead welding.


10.18.5.3 Material of different widths spliced by buttwelds shall have transitions conforming to Figure10.18.5A. The type transition selected shall be consistentwith the Fatigue Stress Category from Table 10.3.113 forthe Groove Welded Connection used in the design of themember. At butt-welded splices joining pieces of differentthicknesses, there shall be a uniform slope between the off-set surfaces, including the weld, of not more than 1 in 2%.

10.19 STRENGTH OF CONNECTIONS

10.19.1 General

10.19.1.1 Except as otherwise provided herein, con-nections for main members shall be designed in the caseof service load design for a capacity based on not lessthan the average of the calculated design stress in themember at the point of connection and the allowablestress of the member at the same point, but, in any event,not less than 75% of the allowable stress in the member.Connections for main members in the case of load factor

design shall be designed for not less than the average ofthe required strength at the point of connection and thestrength of the member at the same point, but, in anyevent, not less than 75% of the strength of the member.

10.19.1.2 Connections shall be made symmetricalabout the axis of the members insofar as practicable. Con-nections, except for lacing bars and handrails, shall con-tain not less than two fasteners or equivalent weld.

10.19.1.3 Members, including bracing, preferablyshall be so connected that their gravity axes will intersectin a point. Eccentric connections shall be avoided, if prac-ticable, but if unavoidable the members shall be so pro-portioned that the combined fiber stresses will not exceedthe allowed axial design stress.

10.19.1.4 In the case of connections which transfertotal member shear at the end of the member, the grosssection shall be taken as the gross section of the connectedelements.

DETAIL OF WIDTH TRANSITION

2'/x—~1 m

Butt Joint Width ofNarrower Plate

Width of cIWider Plate

(b) Straight Tapered Transition

(a) 2'-0" Radius Transition

FIGURE 10.18.5A Splice Details


10.19.2 End Connections of Floor Beams andStringers

10.19.2.1 The end connection shall be designed forthe calculated member loads. The end connection anglesof floor beams and stringers shall be not less than %8 inchin finished thickness. Except in cases of special end floorbeam details, each end connection for floor beams andstringers shall be made with two angles. The length ofthese angles shall be as great as the flanges will permit.Bracket or shelf angles which may be used to furnish sup-port during erection shall not be considered in determiningthe number of fasteners required to transmit end shear.

10.19.2.2 End-connection details shall be designedwith special care to provide clearance for making the fieldconnection.

10.19.2.3 End connections of stringers and floorbeams preferably shall be bolted with high-strength bolts;however, they may be riveted or welded. In the case ofwelded end connections, they shall be designed for t~evertical loads and the end-bending moment resulting fromthe deflection of the members.

10.19.2.4 Where timber stringers frame into steelfloor bearns, shelf angles with stiffeners shall be providedto carry the total reaction. Shelf angles shall be not lessthan%6 inch thick.

10.19.3 End Connections of Diaphragms and CrossFrames

10.19.11 The end connections for diaphragms orcross frames in straight rolled-beam and plate-girderbridges shall be designed for the calculated member loads.

10.19.:9.2 Vertical connection plates such as trans-verse stiffeners which connect diaphragms or crossframes to the beam or girder shall be rigidly connected toboth top and bottom flanges.

10.20 DIAPHRAGMS AND CROSS FRAMES

10.20.1 General

Rolled beam and plate girder spans shall be providedwith cross frames or diaphragms at each support andwith intermediate cross frames or diaphragms placed inall bays and spaced at intervals not to exceed 25 feet.Diaphragms for rolled beams shall be at least %3 andpreferably % the beam depth and for plate girders shall

be at least %2 and preferably %4 the girder depth. Crossframes shall be as deep as practicable. Intermediate crossframes shall preferably be of the cross type or vee type.End cross frames or diaphragms shall be proportioned toadequately transmit all the lateral forces to the bearings.Intermediate cross frames shall be normal to the mainmembers when the supports are skewed more than 20°.Cross frames on horizontally curved steel girder bridgesshall be designed as main members with adequate pro-visions for transfer of lateral forces from the girderflanges. Cross frames and diaphragms shall be designedfor horizontal wind forces as described in Article10.21.2.

10.20.2 Stresses Due to Wind Loading When TopFlanges Are Continuously Supported

10.20.2.1 Flanges

The maximum induced stresses, F, in the bottom flangeof each girder in the system can be computed from the fol-lowing:

F = RF~b (10-5)

where:

R = [0.2272L -11] Sae1 s (when no bottom lateral1

l bracing is provided J

(10-6)

R = [0.059L– 0.64] Sal/2 when bottom lateral)(bracing is provided )

(10-7)

Fcb _ 72M2b(psi) (10-8)

t f b f

M eb =.08WSd(ft-lb) (10-9)

W = wind loading along the exterior flange (lb/ft)S d = diaphragm spacing (ft)L = span length (ft)tf = thickness of flange (in.)bf = width of flange (in.)

10.20.2.2 Diaphragms and Cross Frames

The maximum horizontal force (F D) in the transverse di-aphragms and cross frames is obtained from the following:

FD = 1.14WS d with or without bracing (10-10)


10.20.3 Stresses Due to Wind Load When Top 10.22 CLOSED SECTIONS AND POCKETSFlanges Are Not Continuously Supported

The stress shall be computed using the structural sys-tem in the plane of the flanges under consideration.

10.21 LATERAL BRACING

10.21.1 The need for lateral bracing shall be investi-gated. Flanges attached to concrete decks or other decksof comparable rigidity will not require lateral bracing.

10.21.2 A horizontal wind force of 50 pounds persquare foot shall be applied to the area of the super-structure exposed in elevation. Half of this force shall beapplied in the plane of each flange. The stress inducedshall be computed in accordance with Article 10.20.2.1.The allowable stress shall be factored in accordance withArticle 3.22.

10.21.3 When required, lateral bracing preferably shallbe placed in the exterior bays between diaphragms orcross-frames. All required lateral bracing shall be placedin or near the plane of the flange being braced.

10.21.4 Where beams or girders comprise the mainmembers of through spans, such members shall be stiff-ened against lateral deformation by means of gusset platesor knee braces with solid webs which shall be connectedto the stiffeners on the main members and the floor beams.If the unsupported length of the edge of the gusset plate(or solid web) exceeds 60 times its thickness, the plate orweb shall have a stiffening plate or angles connectedalong its unsupported edge.

10.21.5 Through truss spans, deck truss spans, andspandrel braced arches shall have top and bottom lateralbracing.

10.21.6 Bracing shall be composed of angles, othershapes, or welded sections. The smallest angle used inbracing shall be 3 by 2%2 inches. There shall be not lessthan two fasteners or equivalent weld in each end con-nection of the angles.

10.21.7 If a double system of bracing is used, both sys-tems may be considered effective simultaneously if themembers meet the requirements both as tension and com-pression members. The members shall be connected attheir intersections.

10.21.8 The lateral bracing of compression chordspreferably shall be as deep as the chords and effectivelyconnected to both flanges.

10.22.1 Closed sections and pockets or depressions thatwill retain water, shall be avoided where practicable.Pockets shall be provided with effective drain holes or befilled with waterproofing material.

10.22.2 Details shall be so arranged that the destructiveeffects of bird life and the retention of dirt, leaves, andother foreign matter will be reduced to a minimum. Whereangles are used, either singly or in pairs, they preferablyshall be placed with the vertical legs extending down-ward. Structural tees preferably shall have the web ex-tending downward.

10.23 WELDING

10.23.1 General

10.23.1.1 Steel base to be welded, weld metal, andwelding design details shall conform to the requirementsof the ANSUAASHTO/AWS D1.5 Bridge Welding Code.

10.23.1.2 Welding symbols shall conform with thelatest edition of the American Welding Society PublicationAWS A2.4

10.23.1.3 Fabrication shall conform to Article11.4-Division Il.

10.23.2 Effective Size of Fillet Welds

10.23.2.1 Maximum Size of Fillet Welds

The maximum size of a fillet weld that may be assumedin the design of a connection shall be such that the stressesin the adjacent base material do not exceed the values al-lowed in Article 10.32. The maximum size that may beused along edges of connected parts shall be:

(1) Along edges of material less than %4 inch thick, themaximum size may be equal to the thickness of the ma-terial.(2) Along edges of material %4 inch or more in thick-ness, the maximum size shall be %,6 inch less than thethickness of the material, unless the weld is especiallydesignated on the drawings to be built out to obtain fullthroat thickness.

10.23.2.2 Minimum Size of Fillet Welds

The minimum fillet weld size shall be as shown in thefollowing table.


Base Metal Thickness of Minimum SizeThicker Part Jointed (T) of Fillet Weld 4,b

in. mm in. mm

T<_3/4 Ts 20.0 1/4 6 Single-pass3/4<T 20.0<T 5/16 8 welds must

be used

a Except that the weld size need not exceed the thickness of the thin-ner part joined. For this exception, particular care should be taken toprovide sufficient preheat to ensure weld soundness.

b Smaller fillet welds may be approved by the Engineer based uponapplied stress and the use of appropriate preheat.

10.23.3 Minimum Effective Length of FilletWelds

The minimum effective length of a fillet weld shall befour times its size and in no case less than 1%2 inches.

10.23.4 Fillet Weld End Returns

Fillet welds which support a tensile force that is notparallel to the axis of the weld, or which are proportionedto withstand repeated stress, shall not terminate at cornersof parts or members but shall be returned continuously,full size, around the corner for a length equal to twice theweld size where such return can be made in the sameplane. End returns shall be indicated on design and detaildrawings.

10.23.5 Seal Welds

Seal welding shall preferably be accomplished by acontinuous weld combining the functions of sealing andstrength, changing section only as the required strength orthe requirements of minimum size fillet weld, based onmaterial thickness, may necessitate.

10.24 FASTENERS (RIVETS AND BOLTS)

10.24.1 General

10.24.1.1 In proportioning fasteners, for shear andtension the cross-sectional area based upon the nominaldiameter shall be used.

10.24.1.2 High-strength bolts may be substituted forGrade 1 rivets (ASTM A 502) or ASTM A307 bolts. WhenAASHTO M 164 (ASTM A 325) high-strength bolts aresubstituted for ASTM A 307 bolts they need not be in-stalled to the requirements of Article 11.5.6.4, Division 11,

nor inspected to the requirements of Article 11.5.6.4.9, Di-vision II, but shall be tightened to the full effort of a manusing an ordinary spud wrench.

10.24.1.3 All bolts, except high-strength bolts ten-sioned to the requirements of Table 11.5A or Table 11.513,Division II, shall have single self-locking nuts or doublenuts.

10.24.1.4 Joints required to resist shear between theirconnected parts are designated as either slip-critical orbearing-type connections. Slip-critical joints are definedas joints subject to stress reversal, heavy impact loads, se-vere vibration or where stress and strain due to joint slip-page would be detrimental to the serviceability of thestructure. They include:

(1) Joints subject to fatigue loading.(2) Joints with bolts installed in oversized holes.(3) Except where the Engineer intends otherwise andso indicates in the contract documents, joints with boltsinstalled in slotted holes where the force on the joint isin a direction other than normal (between approxi-mately 80 and 100°) to the axis of the slot.(4) Joints subject to significant load reversal.(5) Joints in which welds and bolts share in transmit-ting load at a common faying surface.(6) Joints in which, in the judgment of the Engineer,any slip would be critical to the performance of thejoint or the structure and so designated on the contractplans and specifications.

10.24.1.5 High-strength bolted connections subjectto computed tension or combined shear and computedtension shall be slip-critical connections.

10.24.1.6 Bolted bearing-type connections usinghigh-strength bolts shall be limited to members in com-pression and secondary members.

10.241.7 The effective bearing area of a fastenershall be its diameter multiplied by the thickness of themetal on which it bears. In metal less than %8 inch thick,countersunk fasteners shall not be assumed to carrystress. In metal Y8 inch thick and over, one-half the depthof countersink shall be omitted in calculating the bearingarea.

10.24.1.8 In determining whether the bolt threads areexcluded from the shear planes of the contact surfaces,thread length of bolts shall be calculated as two threadpitches greater than the specified thread length as an al-lowance for thread runout.


10.24.1.9 In bearing-type connections, pull-out shearin a plate should be investigated between the end of theplate and the end row of fasteners. (See Table 10.32.3B,footnote h).

10.24.2 Hole Types

Hole types for high-strength bolted connections arestandard holes, oversize holes, short slotted holes andlong slotted holes. The nominal dimensions for each typehole shall be not greater than those shown in Table10.24.2, except as may be permitted under Division II, Ar-ticle 11.4.8.1.4.

10.24.2.1 In the absence of approval by the Engineerfor use of other hole types, standard holes shall be used inhigh-strength bolted connections.

10.24.2.2 When approved by the Engineer, oversize,short slotted holes or long slotted holes may be used sub-ject to the following joint detail requirements.

10.24.2.2.1 Oversize holes maybe used in all plies ofconnections which satisfy the requirements of Article10.32.3.2.1 or Article 10.57.3, as applicable. Oversizeholes shall not be used in bearing-type connections.

10.24.2.2.2 Short slotted holes maybe used in any orall plies of high-strength bolted connections designed onthe basis of Table 10.32.3B or Table 10.56A, as applica-ble, provided the load is applied approximately normal(between 80 and 100°) to the axis of the slot. Short slot-ted holes may be used without regard for the directionof applied load in any or all plies of connections whichsatisfy the requirements of Article 10.32.3.2.1 or Article10.57.3.1, as applicable.

10.24.2.2.3 Long slotted holes maybe used in one ofthe connected parts at any individual faying surface inhigh-strength bolted connections designed on the basis ofTable 10.32.313 or Table 10.56A, as applicable, provided

TABLE 10.24.2 Nominal Hole Dimension

Hole Dimensions

Bolt Standard Oversize Short Slot Long Slot(Dia.) (Dia.) (Dia.) (Width X Length) (Width X Length)

Y81

161Y16

1116 X 3

/8

116 X 1Y16

Y4 T1615

16 T16 X 1 13/

16 X 1Y8

3/8

1Y16 1 Y16 T16 X V8 T16 X 2 3

/16

1 1 %16 1 %4 1%16 X 15/16 1%16 X 2%2

?Vs d + %16 d + %16 (d + %16) x (d + %) (d + %16) x (2.5 x d)

the load is applied approximately normal (between 80 and100°) to the axis of the slot. Long slotted holes may beused in one of the connected parts at any individual fay-ing surface without regard for the direction of applied loadon connections which satisfy the requirements of Article10.32.3.2.1 or Article 10.57.3.1, as applicable.

10.24.3 Washer Requirements

Design details shall provide for washers in high-strength bolted connections as follows:

10.24.3.1 Where the outer face of the bolted parts hasa slope greater than 1:20 with respect to a plane normal tothe bolt axis, a hardened beveled washer shall be used tocompensate for the lack of parallelism.

10.24.3.2 Hardened washers are not required forconnections using AASHTO M 164 (ASTM A 325) andAASHTO M 253 (ASTM A 490) bolts except as requiredin Articles 10.24.3.3 through 10.24.3.7.

10.24.3.3 Hardened washers shall be used under theelement turned in tightening when the tightening is to beperformed by calibrated wrench method.

10.24.3.4 Irrespective of the tightening method,hardened washers shall be used under both the head andthe nut when AASHTO M 253 (ASTM A 490) bolts are tobe installed in material having a specified yield point lessthan 40 ksi.

10.24.3.5 Where AASHTO M 164 (ASTM A 325)bolts of any diameter or AASHTO M 253 (ASTM A 490)bolts equal to or less than 1 inch in diameter are to be in-stalled in an oversize or short slotted hole in an outer ply, ahardened washer conforming to ASTM F 436 shall be used.

10.24.3.6 When AASHTO M 253 (ASTM A 490)bolts over 1 inch in diameter are to be installed in an over-size or short slotted hole in an outer ply, hardened wash-ers conforming to ASTM F 436 except with %6 inch min-imum thickness shall be used under both the head and thenut in lieu of standard thickness hardened washers. Mul-tiple hardened washers with combined thickness equal toor greater than %16 inch do not satisfy this requirement.

10.24.3.7 Where AASHTO M 164 (ASTM A 325)bolts of any diameter or AASHTO M 253 (ASTM A 490)bolts equal to or less than 1 inch in diameter are to be in-stalled in a long slotted hole in an outer ply, a plate washeror continuous bar of at least %16 inch thickness with stan-dard holes shall be provided. These washers or bars shallhave a size sufficient to completely cover the slot after in-


stallation and shall be of structural grade material, butneed not be hardened except as follows. When AASHTOM 253 (ASTM A 490) bolts over 1 inch in diameter are tobe used in long slotted holes in external plies, a singlehardened washer conforming to ASTM F 436 but with %16

inch minimum thickness shall be used in lieu of washersor bars of structural grade material. Multiple hardenedwashers with combined thickness equal to or greater than%16 inch do not satisfy this requirement.

10.24.4 Size of Fasteners (Rivets or High-Strength Bolts)

10.24.,4.1 Fasteners shall be of the size shown on thedrawings, but generally shall be 3

/4 inch or 1/s inch in di-ameter. Fasteners %8 inch in diameter shall not be used inmembers carrying calculated stress except in 2%2-inch legsof angles and in flanges of sections requiring %-inch fas-teners.

10.24.4.2 The diameter of fasteners in angles carry-ing calculated stress shall not exceed one-fourth the widthof the leg in which they are placed.

10.24.4.3 In angles whose size is not determined bycalculated stress, %8-inch fasteners may be used in 2-inchlegs, %4-inch fasteners in 2%2-inch legs, %8-inch fasteners in3-inch legs, and 1-inch fasteners in 3%2-inch legs.

10.24.4.4 Structural shapes which do not admit theuse of %8-inch diameter fasteners shall not be used exceptin handrails.

10.24.5 Spacing of Fasteners

10.24.5.1 Pitch and Gage of Fasteners

The pitch of fasteners is the distance along the line ofprincipal stress, in inches, between centers of adjacent fas-teners, measured along one or more fastener lines. The gageof fasteners is the distance in inches between adjacent linesof fasteners or the distance from the back of angle or othershape to the first line of fasteners.

10.24.5.2 Minimum Spacing of Fasteners

The minimum distance between centers of fasteners instandard holes shall be three times the diameter ofthe fastener but, preferably, shall not be less than thefollowing:

For 1-inch fasteners, 3%2 inchesFor %8-inch fasteners, 3 inches

For 1/4-inch fasteners, 2%2 inchesFor %8-inch fasteners, 2%4 inches

10.24.5.3 Minimum Clear DistanceBetween Holes

When oversize or slotted holes are used, the minimumclear distance between the edges of adjacent bolt holes inthe direction of the force and transverse to the direction ofthe force shall not be less than twice the diameter of thebolt.

10.24.5.4 Maximum Spacing of Fasteners

The maximum spacing of fasteners shall be inaccordance with the provisions of Article 10.24.6, as ap-plicable.

10.24.6 Maximum Spacing of Sealing and StitchFasteners

10.24.6.1 Sealing Fasteners

For sealing against the penetration of moisture in joints,the fastener spacing along a single line of fasteners adjacentto a free edge of an outside plate or shape shall not exceed4 inches + 4t or 7 inches. If there is a second line of fas-teners uniformly staggered with those in the line adjacentto the free edge, at a gage "g" less than 1%2 inches + 4ttherefrom, the staggered spacing in two such lines, consid-ered together, shall not exceed 4 inches + 4t — 3g/4 or 7inches, but need not be less than one-half the requirementfor a single line, t = the thickness in inches of the thinneroutside plate or shape, and g gage between fasteners ininches.

10.24.6.2 Stitch Fasteners

In built-up members where two or more plates orshapes are in contact, stitch fasteners shall be used to en-sure that the parts act as a unit and, in compression mem-bers, to prevent buckling. In compression members thepitch of stitch fasteners on any single line in the directionof stress shall not exceed 12t, except that, if the fasteners onadjacent lines are staggered and the gage, g, between theline under consideration and the farther adjacent line (ifthere are more than two lines) is less than 24t, the staggeredpitch in the two lines, considered together, shall not exceed12t or 15t — 3g/8. The gage between adjacent lines of fas-teners shall not exceed 24t; t = the thickness, in inches, ofthe thinner outside plate or shape. In tension members thepitch shall not exceed twice that specified for compressionmembers and the gage shall not exceed that specified forcompression members.


The maximum pitch of fasteners in built-up membersshall be governed by the requirements for sealing or stitchfasteners, whichever is the minimum.

For pitch of fasteners in the ends of compression mem-bers, see Article 10. 16.13.

10.24.7 Edge Distance of Fasteners

10.24.7.1 General

The minimum distance from the center of any fastenerin a standard hole to a sheared or thermally cut edge shallbe:

For 1-inch fasteners, 1%4 inchesFor'/8-inch fasteners, 1% inchesFor %4-inch fasteners, 1 %4 inchesFor %s-inch fasteners, 1%s inches

The minimum distance from the center of any fastenerin a standard hole to a rolled or planed edge, except inflanges of beams and channels, shall be:

For 1-inch fasteners, 1%2 inchesFor %a-inch fasteners, 1 %4 inchesFor %4-inch fasteners, 1%8 inchesFor %s-inch fasteners, 1 inch

In the flanges of beams and channels the minimum dis-tance from the center of a standard hole to the edge of theflange shall be:

For 1-inch fasteners, 1%4 inchesFor'/8-inch fasteners, 1%8 inchesFor %4-inch fasteners, 1 inchFor'/8-inch fasteners, %s inch

The maximum distance from the center of any fastenerto any edge shall be eight times the thickness of thethinnest outside plate, but shall not exceed 5 inches.

10.24.7.2 When there is only a single transverse fas-tener in the direction of the line of force in a standard orshort slotted hole, the distance from the center of the holeto the edge of the connected part shall not be less than 1%2

times the diameter of the fastener, unless accounted for bythe bearing provisions of Table 10.32.313 or Article10.56.1.3.2.

10.24.7.3 When oversize or slotted holes are used,the clear distance between edges of holes and edges ofmembers shall not be less than the diameter of the bolt.

10.24.8 Long Rivets

Rivets subjected to calculated stress and having a gripin excess of 4% diameters shall be increased in number atleast 1% for each additional %16 inch of grip. If the gripexceeds six times the diameter of the rivet, speciallydesigned rivets shall be used.

10.25 LINKS AND HANGERS

10.25.1 Net Section

In pin-connected tension members other than eyebars,the net section across the pin hole shall be not less than140%, and the net section back of the pin hole not lessthan 100% of the required net section of the body of themember. The ratio of the net width (through the pin holetransverse to the axis of the member) to the thickness ofthe segment shall not be more than 8. Flanges not bearingon the pin shall not be considered in the net section acrossthe pin.

10.25.2 Location of Pins

Pins shall be so located with respect to the gravity axisof the members as to reduce to a minimum the stresses dueto bending.

10.25.3 Size of Pins

Pins shall be proportioned for the maximum shears andbending moments produced by the stresses in the mem-bers connected. If there are eyebars among the parts con-nected, the diameter of the pin shall be not less than

C

+ (yield point of steel)times the width of

3

400,000 the body of theeyebar ininches (10-11)

10.25.4 Pin Plates

When necessary for the required section or bearingarea, the section at the pin holes shall be increased on eachsegment by plates so arranged as to reduce to a minimumthe eccentricity of the segment. One plate on each sideshall be as wide as the outstanding flanges will allow. Atleast one full-width plate on each segment shall extend tothe far edge of the stay plate and the others not less than 6inches beyond the near edge. These plates shall be con-


nected by enough rivets, bolts, or fillet and plug welds totransmit the bearing pressure, and so arranged as to dis-tribute it uniformly over the full section.

10.25.5 Pins and Pin Nuts

10.25.5.1 Pins shall be of sufficient length to secure afull bearing of all parts connected upon the turned body ofthe pin. They shall be secured in position by hexagonal re-cessed nuts or by hexagonal solid nuts with washers. If thepins are bored, through rods with cap washers may be used.Pin nuts shall be malleable castings or steel. They shall besecured by cotter pins in the screw ends or else the screwends shall be long enough to permit burring the threads.

10.25.5.2 Members shall be restrained against lateralmovement on the pins and against lateral distortion due tothe skew of the bridge.

10.26 UPSET ENDS

Bars and rods with screw ends, where specified, shallbe upset to provide a section at the root of the thread,which will exceed the net section of the body of the mem-ber by at least 15%.

10.27 E'YEBARS

10.27.1 Thickness and Net Section

Eyebars shall be of a uniform thickness without rein-forcement at the pin holes. The thickness of eyebars shallbe not less than %8 of the width, nor less than %a inch, andnot greater than 2 inches. The section of the head throughthe center of the pin hole shall exceed the required sectionof the body of the bar by at least 35%. The net sectionback of the pin hole shall not be less than 75% of the re-quired net section of the body of the member. The radiusof transition between the head and body of the eyebarshall be equal to or greater than the width of the headthrough the center line of the pin hole.

10.27.2 Packing of Eyebars

10.27.2..1 The eyebars of a set shall be symmetricalabout the central plane of the truss and as nearly parallelas practicable. Bars shall be as close together as practica-ble and held against lateral movement, but they shall beso arranged that adjacent bars in the same panel will beseparated by at least %2 inch.

10.27.2.2 Intersecting diagonal bars not far enoughapart to clear each other at all times shall be clamped to-gether at the intersection.

10.27.2.3 Steel filling rings shall be provided, ifneeded, to prevent lateral movement of eyebars or othermembers connected on the pin.

10.28 FORKED ENDS

Forked ends will be permitted only where unavoidable.There shall be enough pin plates on forked ends to makethe section of each jaw equal to that of the member. Thepin plates shall be long enough to develop the pin plate be-yond the near edge of the stay plate, but not less than thelength required by Article 10.25.4.

10.29 FIXED AND EXPANSION BEARINGS

10.29.1 General

10.29.1.1 Fixed ends shall be firmly anchored. Bear-ings for spans less than 50 feet need have no provision fordeflection. Spans of 50 feet or greater shall be providedwith a type of bearing employing a hinge, curved bearingplates, elastomeric pads, or pin arrangement for deflectionpurposes.

10.29.1.2 Spans of less than 50 feet may be arrangedto slide upon metal plates with smooth surfaces and no pro-visions for deflection of the spans need be made. Spans of50 feet and greater shall be provided with rollers, rockers,or sliding plates for expansion purposes and shall also beprovided with a type of bearing employing a hinge, curvedbearing plates, or pin arrangement for deflection purposes.

10.29.1.3 In lieu of the above requirements, elas-tomeric bearings may be used. See Section 14 of thisspecification.

10.29.2 Bronze or Copper-Alloy Sliding ExpansionBearings

Bronze or copper-alloy sliding plates shall be cham-fered at the ends. They shall be held securely in position,usually by being inset into the metal of the pedestals or soleplates. Provisions shall be made against any accumulationof dirt which will obstruct free movement of the span.

10.29.3 Rollers

Expansion rollers shall be connected by substantialside bars and shall be guided by gearing or other effectual


means to prevent lateral movement, skewing, and creep-ing. The rollers and bearing plates shall be protected fromdirt and water as far as practicable, and the design shall besuch that water will not be retained and that the rollernests may be inspected and clean easily.

10.29.4 Sole Plates and Masonry Plates

10.29.4.1 Sole plates and masonry plates shall havea minimum thickness of %4 inch.

10.29.4.2 For spans on inclined grades greater than1% without hinged bearings, the sole plates shall bebeveled so that the bottom of the sole plate is level, unlessthe bottom of the sole plate is radially curved.

10.29.5 Masonry Bearings

Beams, girders, or trusses on masonry shall be so sup-ported that the bottom chords or flanges will be above thebridge seat, preferably not less than 6 inches.

10.29.6 Anchor Bolts

10.29.6.1 Trusses, girders, and rolled beam spanspreferably shall be securely anchored to the substructure.Anchor bolts shall be swedged or threaded to secure a sat-isfactory grip upon the material used to embed them in theholes.

10.29.6.2 The following are the minimum require-ments for each bearing:

For rolled beam spans the outer beams shall be an-chored at each end with 2 bolts, 1 inch in diameter, set10 inches in the masonry.

For trusses and girders:Spans 50 feet in length or less; 2 bolts, 1 inch indiameter, set 10 inches in the masonry.

Spans 51 to 100 feet; 2 bolts, 1%4 inches in diame-ter, set 12 inches in the masonry.

Spans 101 to 150 feet; 2 bolts, 1%2 inches in diame-ter, set 15 inches in the masonry.

Spans greater than 150 feet; 4 bolts, l% inches in di-ameter, set 15 inches in the masonry.

10.29.6.3 Anchor bolts shall be designed to resistuplift as specified in Article 3.17.

10.29.7 Pedestals and Shoes

10.29.7.1 Pedestals and shoes preferably shall bemade of cast steel or structural steel. The difference inwidth between the top and bottom bearing surfaces shallnot exceed twice the distance between them. For hinged

bearings, this distance shall be measured from the centerof the pin. In built-up pedestals and shoes, the web platesand angles connecting them to the base plate shall be notless than %8 inch thick. If the size of the pedestal permits,the webs shall be rigidly connected transversely. The min-imum thickness of the metal in cast steel pedestals shallbe 1 inch. Pedestals and shoes shall be so designed that theload will be distributed uniformly over the entire bearing.

10.29.7.2 Webs and pin holes in the webs shall bearranged to keep any eccentricity to a minimum. The netsection through the hole shall provide 140% of the net sec-tion required for the actual stress transmitted through thepedestal or shoe. Pins shall be of sufficient length to securea full bearing. Pins shall be secured in position by appro-priate nuts with washers. All portions of pedestals andshoes shall be held against lateral movement of the pins.

10.30 FLOOR SYSTEM

10.30.1 Stringers

Stringers preferably shall be framed into floor beams.Stringers supported on the top flanges of floor beamspreferably shall be continuous over two or more panels.

10.30.2 Floor Beams

Floor beams preferably shall be at right angles to thetrusses or main girders and shall be rigidly connectedthereto. Floor beam connections preferably shall be lo-cated so the lateral bracing system will engage both thefloor beam and the main supporting member. In pin-con-nected trusses, if the floor beams are located below thebottom chord pins, the vertical posts shall be extendedsufficiently below the pins to make a rigid connection tothe floor beam.

10.30.3 Cross Frames

In bridges with wooden floors and steel stringers, in-termediate cross frames (or diaphragms) shall be placedbetween stringers more than 20 feet long.

10.30.4 Expansion Joints

10.30.4.1 To provide for expansion and contractionmovement, floor expansion joints shall be provided at allexpansion ends of spans and at other points where theymay be necessary.

10.30.4.2 Apron plates, when used, shall be designedto bridge the joint and to prevent, so far as practicable, theaccumulation of roadway debris upon the bridge seats. Pre-ferably, they shall be connected rigidly to the end floor beam.


10.30.5 End Floor Beams

There shall be end floor beams in all square-endedtrusses and girder spans and preferably in skew spans. Endfloor beams for truss spans preferably shall be designed topermit the use of jacks for lifting the superstructure.For this case, the allowable stresses may be increased 50%.

10.30.6 End Panel of Skewed Bridges

In skew bridges without end floor beams, the end panelstringers shall be secured in correct position by end strutsconnected to the stringers and to the main truss or girder. Theend panel lateral bracing shall be attached to the main trussesor girders and also to the end struts. Adequate provisionsshall be made for the expansion movement of stringers.

10.30.7 Sidewalk Brackets

Sidewalk brackets shall be connected in such a waythat the bending stresses will be transferred directly to thefloor beams.

10.30.8 Stay-in-Place Deck Forms

10.30.8.1 Concrete Deck Panels

When precast prestressed deck panels are used as per-manent forms spanning between beams, stringers, or gird-ers, the requirements of Article 9.12, Deck Panels, and Ar-ticle 9.23, Deck Panels, shall be met.

10.30.8.2 Metal Stay-in-Place Forms

When metal stay-in-place forms are used as permanentforms spanning between beams, stringers, or girders, theforms shall be designed to support, as a minimum, theweight of the concrete (including that in the corrugations,if applicable), a construction load of 50 psf, and the weightof the form. The forms shall be designed to be elastic underconstruction loads. The elastic deformation caused by thedead load of the forms, plastic concrete and reinforcementshall not exceed a deflection of greater than L/180 or%2 inch for form work spans (L) of 10 feet or less, or adeflection of L/240 or %4 inch for form work spans (L)over 10 feet.

Part CSERVICE LOAD DESIGN METHOD

ALLOWABLE STRESS DESIGN

10.31 SCOPE

Allowable stress design is a method for proportioningstructural members using design loads and forces, allow-able stresses, and design limitations for the appropriatematerial under service conditions. See Part D—StrengthDesign Method—Load Factor Design for an alternate de-sign procedure.

10.32 ALLOWABLE STRESSES

10.32.1 Steel

Allowable stresses for steel shall be as specified inTable 10.32.1A.

10.32.2 Weld Metal

Unless otherwise specified, the yield point and ultimatestrength of weld metal shall be equal to or greater than min-imum specified value of the base metal. Allowable stresseson the effective areas of weld metal shall be as follows:

Butt Welds:

The same as the base metal joined, except in the caseof joining metals of different yields when the loweryield material shall govern.

Fillet Welds:

F v = 0.27 F,, (10-12)

where,

F„ = allowable basic shear stress;F„ = tensile strength of the electrode classification

When detailing fillet welds for quenched and temperedsteels—the designer may use electrode classificationswith strengths less than the base metal provided thatthis requirement is clearly specified on the plans.

Plug Welds:

Fv = 12,400 psi for resistance to shear stresses only,where,

F„ = allowable basic shear stress.


TABLE 10.32.1A Allowable Stresses—Structural Steel (In pounds per square inch)

Quenched andStructural Tempered High-Yield Strength

Carbon High-Strength Low Alloy Quenched and TemperedType Steel Low-Alloy Steel Steel Alloy Steel'

M 270 M 270 M 270 M 270 M 270Grade 36 Grade 50 Grade 50W Grade HPS70W& Grades 100/10OW

Grade 70W

A709 A 709 A 709 A 709 A709Grade 36 Grade 50 Grade 50W Grade HPS70W& Grades 100/10OW

Grade 70W

Up to up to Up to Up to Up to Over 2 1/~ in.4 in. incl. 4 in. incl. 4 in. incl. 4 in. incl. 2'/z in. incl. to 4 in. incl.

AASHTO Designationb,e

Equivalent ASTM Designation`

Thickness of Plates

All Groups All Groups All Groups Not Applicable

20,000 27,000 27,000 38,000

Not Applicable

20,000 27,000 27,000 38,000

Not Applicable

Not Applicable

50,600 46,000

Not Applicable

Shapes

Axial tension in members with no 0.55Fyholes

0.46F„

Axial tension in members with holes Grossand tension in extreme fiber of Sectionrolled shapes, girders, and built-up 0.55Fysections with holes subject tobending. Satisfy both Gross and NetSection criterion.

NetSection0.46F„

26,700 29,900 32,200 41,400 50,600 46,000

Axial compression, gross section: 20,000 27,000 27,000 38,000 55,000 49,000stiffeners of plate girders. Compres-sion in splice material, gross section

Compression in extreme fibers ofrolled shapes, girders, and built-up sec-tions subject to bending. Gross sec-tion, when compression flange is:(A) Supported laterally its full length 0.55Fy 20,000 27,000 27,000 38,000 55,000 49,000

by embedment in concrete(B)Partially supported or is unsupported

a,e

2

F b = 50 x 106Cb Iy~

0.772J + 9.87

d)0.55Fy

S' , f ly e f /

C b = 1.75 + 1.05 (Mf /M2) + 0.3 (M 1/M2f 2.3 where Ml is the smaller and M2 the larger end moment in the unbraced segmentof the beam; M 1/M2 is positive when the moments cause reverse curvature and negative when bent in single curvature.

C b = 1.0 for unbraced cantilevers and for members where the moment within a significant portion of the unbraced segment is greaterthan or equal to the larger of the segment end moments.

Compression in concentrically loaded columns f

with C, = (21r 2 E/Fy ) 1/2= 126.1 107.0 107.0 90.4 75.7 79.8

when KL/r C,

Fa = Fy I l – (KL/r)2Fy = 16,980– 23,580– 23,580– 33,020– 47,170– 42,450F.S. L 4,

rr2E 0.53(KL/r) 2 1.03(KL/r)2 1.03(KL/r) 2 2.02(KL/r)2 4.12(KL/r)2 3.33(KL/r) 2

10.32.2 DIVISION I-DESIGN 289

TABLE 10.32.1A Allowable Stresses-Structural Steel (In pounds per square inch) (Continued)

Quenched andStructural Tempered High Yield Strength

Carbon High-Strength Low-Alloy Quenched and TemperedType Steel Low-Alloy Steel Steel Alloy Steel a

when KL/r > C,

IT r-F.

135,000,740

F.S.(KL/r) 2 (KL/r)2

with ES. = 2.12

Shear in girder webs, gross section Fv = 0.33Fy 12,000 17,000 17,000 23,000 33,000 30,000

Bearing on milled stiffeners and other 0.80Fy 29,000 40,000 40,000 56,000 80,000 72,000steel parts in contact (rivets and boltsexcluded)

Stress in extreme fiber of pins 0.80Fy 29,000 40,000 40,000 56,000 80,000 72,000

Shear in pins F, = 0.40Fy 14,000 20,000 20,000 28,000 40,000 36,000

Bearing on pins not subject to rotationh 0.80Fy 29,000 40,000 40,000 56,000 80,000 72,000

Bearing on pins subject to rotation 0.40Fy 14,000 20,000 20,000 28,000 40,000 36,000(such as used in rockers and hinges)

Bearing on connected material at LowCarbon Steel Bolts (ASTM A 307),Ibmed Bolts, Ribbed Bolts, and Rivets(ASTM A 502 Grades 1 and 2)-Governed by Table 10.32.3A

a Quenched and tempered alloy steel structural shapes and seamless mechanical tubing meeting all mechanical and chemical requirements of A709 Grades 100/10OW except that the specified maximum tensile strength may be 140,000 psi for structural shapes and 145,000 psi for seamlessmechanical tubing, shall be considered as A 709 Grades 1001100W steel.

b Except for the mandatory notch toughness and weldability requirements, the ASTM designations are similar to the AASHTO designations. Steelsmeeting the AASHTO requirements are prequalified for use in welded bridges.

` M 270 Gr. 36 and A 709 Gr. 36 are equivalent to M 183 and A 36M 270 Gr. 50 and A 709 Gr. 50 are equivalent to M 223 Gr. 50 and A 572 Gr 50M 270 Gr. 50W and A 709 Gr. 50W are equivalent to M 222 and A 588M 270 Gr. 70W and A 709 Gr. 70W are equivalent to A 852M 270 Gr. 100/10OW and A 709 Gr. 100/10OW are equivalent to M 244 and A 514

d For the use of larger C b values, see Structural Stability Research Council Guide to Stability Design Criteria for Metal Structures, 3rd Ed., p. 135.If cover plates are used, the allowable static stress at the point of theoretical cutoff shall be as determined by the formula.

` f = length in inches, of unsupported flange between lateral connections, knee braces, or other points of support.Iy~ = moment of inertia of compression flange about the vertical axis in the plane of the web in.'d = depth of girder, in.J = [(W), + (bO)t + Dtw ]

µ,here b and t represent the flange width and thickness of the compression and tension flange, respectively (in.').

Sx, = section modulus with respect to compression flange (in.').f E = modulus of elasticity of steelr = governing radius of gyrationL = actual unbraced lengthK = effective length factor (see Appendix C.)F.S. = factor of safety = 2.12

For graphic representation of these formulas, see Appendix C.The formulas do not apply to members with variable moment of inertia. Procedures for designing members with variable moments of inertia can be

found in the following references: "Engineering Journal," American Institute of Steel Construction, January 1969, Volume 6, No. 1, and October1972, Volume 9, No. 4; and "Steel Structures," by William McGuire, 1968, Prentice-Hall, Inc., Englewood Cliffs, New Jersey. For members witheccentric loading, see Article 10.36. Singly symmetric and unsymmetric compression members, such as angles or tees, and doubly symmetriccompression members, such as cruciform or built-up members with very thin walls, may also require consideration of flexural-torsional and torsionalbuckling. Refer to the Manual of Steel Construction, Ninth Edition, 1989, American Institute of Steel Construction.

B See also Article 10.32.4.h This shall apply to pins used primarily in axially loaded members, such as truss members and cable adjusting links. It shall not apply to pins used

in members having rotation caused by expansion or deflection.


TABLE 10.32.3A Allowable Stresses for Low-CarbonSteel Bolts and Power Driven Rivets (in psi)

ShearBearing-Type

Type of Fastener Tension' Bearing b Connection a

(A)Low-Carbon Steel 18,000 20,000 11,000 d

Bolts` Turned Bolts(ASTM A 307)Ribbed Bolts

(B)Power-Driven Rivets(rivets driven bypneumatically orelectrically operatedhammers areconsidered powerdriven)Structural Steel Rivet — 40,000 13,500Grade 1 (ASTM A 502Grade 1)Structural Steel Rivet — 40,000 20,000(high-strength)Grade 2 (ASTM A 502Grade 2)

'Applies to fastener cross-sectional area based upon nominal bodydiameter.

bApplies to nominal diameter of fastener multiplied by the thicknessof the metal.

ÀSTM A 307 bolts shall not be used in connections subject tofatigue.

d In connections transmitting axial force whose length between ex-treme fasteners measured parallel to the line of force exceeds 50 inches, thetabulated value shall be reduced 20 percent.

10.32.3 Fasteners (Rivets and Bolts)

Allowable stresses for fasteners shall be as listed in Ta-bles 10.32.3.A and 10.32.3.B, and the allowable force ona slip-critical connection shall be as provided by Article10.32.3.2.1.

10.32.3.1 General

10.32.3.1.1 In proportioning fasteners for shear ortension, the cross-sectional area based upon the nominaldiameter shall be used except as otherwise noted.

10.32.3.1.2 The effective bearing area of a fastenershall be its diameter multiplied by the thickness of the metalon which it bears. In metal less than 3/8 inch thick, counter-sunk fasteners shall not be assumed to carry stress. In metal3/8 inch thick and over, one-half of the depth of the counter-sink shall be omitted in calculating the bearing area.

10.32.3.1.3 In determining whether the bolt threadsare excluded from the shear planes of the contact surfaces,thread length of bolts shall be calculated as two threadpitches greater than the specified thread length as an al-lowance for thread runout.

10.32.3.1.4 In bearing-type connections, pull-outshear in a plate should be investigated between the end ofthe plate and the end row of fasteners. (See Table10.32.3B, footnote g.)

10.32.3.1.5 All bolts except high-strength bolts,tensioned to the requirements of Division II. Table 11.5Aor Table 11.513, shall have single self-locking nuts ordouble nuts.

10.32.3.1.6 Joints, utilizing high-strength bolts,required to resist shear between their connected parts aredesignated as either slip-critical (See Article 10.24.1.4)or bearing-type connections. Shear connections sub-jected to stress reversal, or where slippage would be un-desirable, shall be slip-critical connections. Potential slip

TABLE 10.32.3B Allowable Stresses on High-StrengthBolts or Connected Material (ksi)

AASHTO AASHTOM 164 M 253

(ASTM (ASTMLoad Condition A 325)' A 490)`

Applied Static Tension' ,' 38d

47Shear, F., on bolt with threads in

shear plane'f 19d

24Bearing, FP , on connected material

in standard, oversize, short-slotted O.SL~F~holes loaded in any direction, or d < F„~"long-slotted holes parallel to theapplied bearing force

Bearing, F., on connected materialin long-slotted holes perpendicular OAF' s 0.8F„ffl l

to the applied bearing force

'AASHTO M 164 (ASTM A 325) and AASHTO M 253 (ASTMA 490) high-strength bolts are available in three types, designated astypes 1, 2, or 3. Type 3 shall be required on the plans when usingunpainted AASHTO M 270 Grade 50W (ASTM A 709 Grade 50W).

b Bolts must be tensioned to requirements of Table 11.5A, Div II.'See Article 10.32.3.4 for bolts subject to tensile fatigue.d The tensile strength of M 164 (A 325) bolts decreases for diameters

greater than 1 inch. The design values listed are for bolts up to 1 inchdiameter. The design values shall be multiplied by 0.875 for diametersgreater than 1 inch.

In connections transmitting axial force whose length between ex-treme fasteners measured parallel to the line of force exceeds 50 inches,tabulated values shall be reduced 20 percent. For flange splices, the50-inch length is to be measured between the extreme bolts on onlyone side of the connection.

'If material thickness or joint details preclude threads in the shearplane, multiply tabulated values by 1.25.

9 1F„ = specified minimum tensile strength of connected material.'Connections using high-strength bolts in slotted holes with the load

applied in a direction other than approximately normal (between 80 and100 degrees) to the axis of the hole and connections with bolts inoversized holes shall be designed for resistance against slip in accord-ance with Article 10.32.3.2.1.

' L, is equal to the clear distance between the holes or between thebole and the edge of the material in the direction of the applied bearingforce, in. and d is the nominal diameter of the bolt, in.

IThe allowable bearing force for the connection is equal to the sumof the allowable bearing forces for the individual bolts in the connec-tion.


of joints should be investigated at intermediate loadstages especially those joints located in compositeregions.

10.32.3.1.7 The percentage of unit stress increaseshown in Article 3.22, Combination of Loads, shall applyto allowable stresses in bolted slip-critical connectionsusing high-strength bolts, except that in no case shall thepercentage of allowable stress exceed 133%, and the re-quirements of Article 10.32.3.3 shall not be exceeded.

10.32.3.1.8 Bolted bearing-type connections shallbe limited to members in compression and secondarymembers.

10.32.3.2 The allowable stress in shear, bearing andtension for AASHTO M 164 (ASTM A 325) and AASHTOM 253 (ASTM A 490) bolts shall be as listed in Table10.32.3B.

10.32.3.2.1 In addition to the allowable stress re-quirements of Article 10.32.3.2 the force on a slip-criticalconnection as defined in Article 10.24.1.4 shall not exceedthe allowable slip force (Ps) of the connection accordingto

P, = F sAbNbNg (10-13)

Where

FS = nominal slip resistance per unit of bolt area fromTable 10.32.3C, ksi.

Ab = area corresponding to the nominal body area ofthe bolt sq in.

Nb = number of bolts in the joint.N, = number of slip planes.

Class A, B, or C surface conditions of the bolted parts asdefined in Table 10.32.3C shall be used in joints desig-nated as slip-critical except as permitted in Article10.32.3.2.2.

10.32.3.2.2 Subject to the approval of the Engineer,coatings providing a slip coefficient less than 0.33 maybeused provided the mean slip coefficient is established bytest in accordance with the requirements of Article10.32.3.2.3, and the slip resistance per unit area are es-tablished. The slip resistance per unit area shall be takenas equal to the slip resistance per unit area from Table10.32.3C for Class A coatings as appropriate for the holetype and bolt type times the slip coefficient determined bytest divided by 0.33.

10.32.3.2.3 Paint, used on the faying surfaces ofconnections specified to be slip-critical, shall be qualifiedby test in accordance with "Test Method to Determine the

TABLE 10.32.3C Nominal Slip Resistance for Slip-Critical Connections (Slip Resistance per Unit of Bolt Area, F s, ksi)

Hole Type and Direction of Load Application

Any Direction Transverse Parallel

Oversized andStandard Short Slot Long Slots Long Slots

AASHTO AASHTO AASHTO AASHTO AASHTO AASHTO AASHTO AASHTOM 164 M 253 M 164 M 253 M 164 M 253 M 164 M 253(ASTM (ASTM (ASTM (ASTM (ASTM (ASTM (ASTM (ASTMA 325)° A 490) A 325)° A 490) A 325)8 A 490) A 325)` A 490)

15 19 13 16 11 13 9 11

23 29 19 24 16 20 14 17

15 19 13 16 11 13 9 11

'The tensile strength of M 164 (A 325) bolts decreases for diameters greater than 1 inch. The design values listed are for bolts up to 1inch diameter. The design values shall be multiplied by 0.875 for diameters greater than 1 inch.

Coatings classified as Class A or Class B include those coatings which provide a mean slip coefficient not less than 0.33 or 0.50,respectively, as determined by Testing Method to Determine the Slip Coefficient for Coatings Used in Bolted Joints. See Article 10.32.3.2.3.

Contact Surface of Bolted Parts

Class A (Slip Coefficient 0.33)Clean mill scale and blast-cleaned surfaces with ClassA coatingsb

Class B (Slip Coefficient 0.50)Blast-cleaned surfaces andblast-cleaned surfaces withClass B coatingsb

Class C (Slip Coefficient 0.33)Hot-dip galvanized surfacesand roughened by wirebrushing after galvanizing

292 HIGHWAY BRIDGES 10,32.3.2.3

Slip Coefficient for Coatings Used in Bolted Joints" asadopted by the Research Council on Structural Connec-tions. See Appendix A of Allowable Stress Design Speci-fication for Structural Joints Using ASTM A 325 or A 490Bolts published by the Research Council on StructuralConnections.

10.32.3.3 Applied Tension, Combined Tension,and Shear

10.32.3.3.1 High-strength bolts preferably shall beused for fasteners subject to tension or combined tensionand shear.

10.32.3.3.2 Bolts required to support applied load bymeans of direct tension shall be so proportioned that theiraverage tensile stress computed on the basis of nominalbolt area will not exceed the appropriate stress in Table10.32.3B. The applied load shall be the sum of the exter-nal load and any tension resulting from prying action. Thetension due to the prying action shall be

Q_[3b – t3]T (10-14)8a 20

where

Q = the prying tension per bolt (taken as zero whennegative);

T = the direct tension per bolt due to external load;a = distance from center of bolt to edge of plate in

inches;b = distance from center of bolt under consideration

to toe of fillet of connected part in inches;t = thickness of thinnest part connected in inches.

10.32.3.3.3 For combined shear and tension inslip-critical joints using high-strength bolts where appliedforces reduce the total clamping force on the fric-tion plane, the slip resistance per unit area of bolt, f,,, shallnot exceed the value obtained from the following equation:

f, = F,(1 – 1.88fr/F„) (10-15)

where:

f = computed tensile stress in the bolt due to appliedloads including any stress due to prying action, ksi;

F, = nominal slip resistance per unit of bolt area fromTable 10.32.3C, ksi;

Fu = 120 ksi for M 164 (A 325) bolts up to 1-inchdiameter;

= 105 ksi for M 164 (A 325) bolts over 1-inchdiameter;

= 150 ksi for M 253 (A 490) bolts.

10.32.3.3.4 Where rivets or high-strength bolts aresubject to both shear and tension, the tensile stress shall notexceed the value obtained from the following equations:

for f„/F„ < 0.33

Fr = Ft (10-16)

for f,,/F„ > 0.33

Fr =Fr 1–(fv /Fv ) 2 (10-17)

where

f„ = computed rivet or bolt shear stress in shear, ksi;F„ = allowable shear stress on rivet or bolt from Table

10.32.3A or Table 10.32.313, ksi;F, = allowable tensile stress on rivet or bolt from

Table 10.32.3A or Table 10.32.3B, ksi;Fr = reduced allowable tensile stress on rivet or bolt

due to the applied shear stress, ksi.

Note: Equation (10-18) has been removed.

10.32.3.4 Fatigue

When subject to tensile fatigue loading, the tensilestress in the bolt due to the service load plus the pry-ing force resulting from application of service loadshall not exceed the following design stresses in kipsper square inch. The nominal diameter of the bolt shallbe used in calculating the bolt stress. The pryingforce shall not exceed 60% of the externally appliedload.

AASHTO AASHTOM 164 M 253(ASTM (ASTM

Number of Cycles A 325) A 490)

Not more than 20,000 38 47From 20,000 to 500,000 35.5 44.0More than 500,000 27.5 34.0

10.32.4 Pins, Rollers, and Expansion Rockers

10.32.4.1 The effective bearing area of a pin shall beits diameter multiplied by the thickness of the material on

29310.32.4.1 DIVISION I—DESIGN

TABLE 10.32.4.3A Allowable Stresses—Steel Bars and Steel Forgings

AASHTO Designation with SizeLimitations

ASTM Designation Grade or Class

Minimum Yield Point, psi

Stress in Extreme Fiber, psi

Shear, psi

Bearing on Pins not Subject to Rotation,psi`

Bearing on Pins Subject to Rotation, psi(such as used in rockers and hinges)

— M 169 4 in. in M 102 To 20 M 102 To 20 M 102 To 10 M 102 To 20dia. or less in. in dia. in. in dia. in. in dia. in. in dia.

— A 108 A 668 A 668 A 668 A 668 3

Grades 1016 Class C Class D Class F Class G1030 incl.

Fy 36 ' 000 b 33,000 37,500 50,000 50,000

0.80Fy 29 ' 000 b 26,000 30,000 40,000 40,000

0.40Fy 14 ' 000 b 13,000 15,000 20,000 20,000

0.80Fy 29,000 b 26,000 30,000 40,000 40,000

0.40Fy 14 ' 000 b 13,000 15,000 20,000 20,000

'May substitute rolled material of the same properties.'For design purposes only. Not a part of the A 108 specifications. Supplementary material requirements should provide guarantee that material will

meet these values.`This shall apply to pins used primarily in axially loaded members, such as truss members and cable adjusting links. It shall not apply to pins used

in members having rotation caused by expansion or deflection.

which it bears. When parts in contact have different yieldpoints, Fy shall be the smaller value.

10.32.4.2 Design stresses for Steel Bars, Carbon ColdFinished Standard Quality, AASHTO M 169 (ASTM A108), and Steel Forgings, Carbon and Alloy, for GeneralIndustrial Use, AASHTO M 102 (ASTM A 668), are givenin Table 10.32.4.3A.

10.32.5 Cast Steel, Ductile Iron Castings, MalleableCastings, and Cast Iron

10.32.5.1 Cast Steel and Ductile Iron

10.32.5.1.1 For cast steel conforming to speci-fications for Steel Castings for Highway Bridges,AASHTO M 192 (ASTM A 486), Mild-to-Medium-Strength Carbon-Steel Castings for General Application,AASHTO M 103 (ASTM A 27), and Corrosion-ResistantIron-Chromium, Iron-Chromium-Nickel and Nickel-Based Alloy Castings for General Application, AASHTOM 163 (ASTM A 743), and for Ductile Iron Cast-ings (ASTM A 536), the allowable stresses in poundsper square inch shall be in accordance with Table10.32.5.1 A.

10.32.5.1.2 When in contact with castings or steel ofa different yield point, the allowable unit bearing stress ofthe material with the lower yield point shall govern. Forriveted or bolted connections, Article 10.32.3 shall govern.

10.32.5.2 Malleable Castings

Malleable castings shall conform to specifications forMalleable Iron Castings, ASTM A 47 Grade 35018. Thefollowing allowable stresses in pounds per square inchshall be used:

Tension...............................................................18,000Bending in Extreme Fiber..................................18,000Modulus of Elasticity................................. 25,000,000

10.32.5.3 Cast Iron

Cast iron castings shall conform to specifications forGray Iron Castings, AASHTO M 105 (ASTM A 48), Class30B. The following allowable stresses in pounds persquare inch shall be used:

Bending in Extreme Fiber................................... 3,000Shear ....................................................................3,000Direct Compression, Short Columns ................. 12,000

10.32.5.4 Bronze or Copper-Alloy

10.32.5.4.1 Bronze castings, AASHTO M 107(ASTM B 22), Copper Alloys 913 or 911, or Copper-Alloy Plates, AASHTO M 108 (ASTM B 100), shall bespecified.

10.32.5.4.2 The allowable unit-bearing stress inpounds per square inch on bronze castings or copper-alloyplates shall be 2,000.


TABLE 10.32.5.1A Allowable Stresses-Cast Steel and Ductile Iron

AASHTO Designation M 103 M 192 M 192 M 163 NoneASTM Designation A 27 A 486 A 486 A 743 A 536Class or Grade 70-36 70 90 120 CA-15 60-40-18Minimum Yield Point, Fy 36,000 60,000 95,000 65,000 40,000Axial Tension 14,500 22,500 34,000 24,000 16,000Tension in Extreme Fibers 14,500 22,500 34,000 24,000 16,000Axial Compression, Short Columns 20,000 30,000 45,000 32,000 22,000Compression in Extreme Fibers 20,000 30,000 45,000 32,000 22,000Shear 9,000 13,500 21,000 14,000 10,000Bearing, Steel Parts in Contact 30,000 45,000 68,000 48,000 33,000Bearing on Pins not Subject to Rotation 26,000 40,000 60,000 43,000 28,000Bearing on Pins Subject to Rotation 13,000 20,000 30,000 21,500 14,000

(such as used in rockers and hinges)

10.32.6 Bearing on Masonry

10.32.6.1 The allowable unit-bearing stress inpounds per square inch on the following types of masonryshall be:

Granite....................................................................800Sandstone and Limestone .......................................400

10.32.6.2 The above bridge seat unit stress will applyonly where the edge of the bridge seat projects at least 3inches (average) beyond the edge of shoe or plate. Other-wise, the unit stresses permitted will be 75% of the aboveamounts.

10.32.6.3 For allowable unit-bearing stress on con-crete masonry, refer to Article 8.15.2.1.3.

10.33 ROLLED BEAMS

10.33.1 General

10.33.1.1 Rolled beams, including those with weldedcover plates, shall be designed by the moment of inertiamethod. Rolled beams with riveted cover plates shall bedesigned on the same basis as riveted plate girders.

10.33.1.2 The compression flanges of rolled beamssupporting timber floors shall not be considered to belaterally supported by the flooring unless the floor and fas-tenings are specially designed to provide adequate support.

10.33.2 Bearing Stiffeners

Suitable stiffeners shall be provided to stiffen the websof rolled beams at bearings when the unit shear in the webadjacent to the bearing exceeds 75% of the allowableshear for girder webs. See the related provisions of Arti-cle 10.34.6.

10.34 PLATE GIRDERS

10.34.1 General

10.34.1.1 Girders shall be proportioned by the mo-ment of inertia method. For members primarily in bend-ing, the entire gross section shall be used when calculat-ing tensile and compressive stresses. Holes forhigh-strength bolts or rivets and/or open holes not ex-ceeding 1 1/4 inches, may be neglected provided the arearemoved from each flange does not exceed 15% of thatflange. That area in excess of 15% shall be deducted fromthe gross area.

10.34.1.2 The compression flanges of plate girderssupporting timber floors shall not be considered to belaterally supported by the flooring unless the floor andfastenings are specially designed to provide support.

10.34.2 Flanges

10.34.2.1 Welded Girders

10.34.2.1.1 Each flange may comprise a series ofplates joined end to end by full penetration butt welds.Changes in flange areas may be accomplished by varyingthe thickness and/or width of the flange plate, or by addingcover plates. Where plates of varying thicknesses orwidths are connected, the splice shall be made in accor-dance with Article 10.18 and welds ground smooth beforeattaching to the web. The compression-flange width, b, onfabricated I-shaped girders preferably shall not be lessthan 0.2 times the web depth, but in no case shall it be lessthan 0.15 times the web depth. If the area of the compres-sion flange is less than the area of the tension flange, theminimum flange width may be based on two times thedepth of the web in compression rather than the webdepth. The compression-flange thickness, t, preferablyshall not be less than 1.5 times the web thickness. The


width-to-thickness ratio, b/t, of flanges subject to tensionshall not exceed 24.

10.34.2.1.2 When cover plates are used, they shall bedesigned in accordance with Article 10.13.

10.34.2.1.3 The ratio of compression flange platewidth to thickness shall not exceed the value determinedby the formula

b _ 3,250but in no case shall (10-19)

t fb b/t exceed 24

10.34.2.1.4 Where the calculated compressive bend-ing stress equals .55 F Y the (b/t) ratios for the variousgrades of steel shall not exceed the following:

36,000 psi, Y.P. Min. b/t = 2350,000 psi, Y.P. Min. b/t = 2070,000 psi, Y.P. Min. b/t = 1790,000 psi, Y.P. Min. b/t = 15

100,000 psi, Y.P. Min. b/t = 14

In the above b is the flange plate width, t is the thickness,and fb is the calculated maximum compressive bendingstress. (See Article 10.40.3 for Hybrid Girders.)

10.34.2.1.5 In the case of a composite girder the ratioof the top compression flange plate width to thicknessshall not exceed the value determined by the formula

b _ 3,860 but in no case shallt F b/t exceed 24

(10-20)

where fde1 is the top flange compressive stress due to non-composite dead load.

10.34.2.2 Riveted or Bolted Girders

10.34.2.2.1 Flange angles shall form as large a partof the area of the flange as practicable. Side plates shallnot be used except where flange angles exceeding 7/8 inchin thickness otherwise would be required.

10.34.2.2.2 Width of outstanding legs of flangeangles in compression, except those reinforced byplates, shall not exceed the value determined by the for-mula

b ' _ 1,625 but in no case shall (10-21)t , b '/t exceed 12

10.34.2.2.3 Where the calculated compressive bend-ing stress equals 0.55 FY , the b ' /t ratios for the variousgrades of steel shall not exceed the following:

36,000 psi, Y.P. Min. b'/t = 1150,000 psi, Y.P. Min. b/t = 1070,000 psi, Y.P. Min. b/t = 8.590,000 psi, Y.P. Min. b/t = 7.5

100,000 psi, Y.P. Min. b'/t = 7

10.34.2.2.4 In the case of a composite girder thewidth of outstanding legs of top flange angles in com-pression, except those reinforced by plates, shall not ex-ceed the value determined by the following formula

b' _ 1,930 but in no case shall (10-22)t fd r, b'/t exceed 12

In the above b ' is the width of a flange angle, t is the thick-ness, fb is the calculated maximum compressive stress,and fdf, is the top flange compressive stress due to non-composite dead load.

10.34.2.2.5 The gross area of the compressionflange, except for composite design, shall be not less thanthe gross area of the tension flange.

10.34.2.2.6 Flange plates shall be of equal thickness,or shall decrease in thickness from the flange angles out-ward. No plate shall have a thickness greater than that ofthe flange angles.

10.34.2.2.7 At least one cover plate of the topflange shall extend the full length of the girder exceptwhen the flange is covered with concrete. Any cover platethat is not full length shall extend beyond the theo-retical cutoff point far enough to develop the capacityof the plate or shall extend to a section where the stressin the remainder of the girder flange is equal to the al-lowable fatigue stress, whichever is greater. The theo-retical cutoff point of the cover plate is the section atwhich the stress in the flange without that cover plateequals the allowable stress, exclusive of fatigue con-siderations.

10.34.2.2.8 The number of fasteners connecting theflange angles to the web plate shall be sufficient to de-velop the increment of flange stress transmitted to theflange angles, combined with any load that is applied di-rectly to the flange.

10.34.2.2.9 Legs of angles 6 inches or greater inwidth, connected to web plates, shall have two lines of


fasteners. Cover plates over 14 inches wide shall havefour lines of fasteners.

10.34.3 Thickness of Web Plates

10.34.3.1 Girders Not Stiffened Longitudinally

10.34.3.1.1 The web plate thickness of plate girderswithout longitudinal stiffeners shall not be less than thatdetermined by the formula

twD23,000

(See Figure 10.34.3.1A.) (10-23)

but in no case shall the thickness be less than D/170

10.34.3.1.2 Where the calculated compressive bend-ing stress in the flange equals the allowable bendingstress, the thickness of the web plate (with the web stiff-ened or not stiffened, depending on the requirements fortransverse stiffeners) shall not be less than (where the Y.P.is for the flange material)

36,000 psi, Y.P. Min. D/16550,000 psi, Y.P. Min. D/14070,000 psi, Y.P. Min. D/11590,000 psi, Y.P. Min. D/105

100,000 psi, Y.P. Min. D/100

10.34.3.2 Girders Stiffened Longitudinally

10.34.3.2.1 The web plate thickness of plate girdersequipped with longitudinal stiffeners shall not be less thanthat determined by the formula

_ D fbtw4, 050 Vk=

(10–24)

2 zfor DS >_ 0.4 k = 5.17( D J >9( D )

l J D,

2

for ds < 0.4 k =11.64 D

D~ D, –d s

but in no case shall the thickness be less than D/340. Forsymmetrical girders see Figure 10.34.3.1.A.

In the above, D (depth of the web) is the clear unsup-ported distance in inches between the flange compo-nents, t,,, is the web thickness, k is the buckling coeffi-cient, d, is the distance from the centerline of a platelongitudinal stiffener or the gage line of an angle longi-tudinal stiffener to the inner surface or the leg of the

110 220p

wd E

3 100 200 o3

I_~ON ~ so

4`f }-gyp rnn

tao 'm

tw=

1/ „'2o f t 6

80d

160 E9

t ,-7/16” } t" NC

- t d

Ic70

-N,140 a

3H J+ N G

dd CV °

U.~

C m 60 120 a

C d t w=s/1s° tN T

3o

wM

3 yC

o50V i 100 co N

Lw « ~ a

Om 40 80 oy4

fb (ksi)

WEB THICKNESS AND GIRDER DEPTH-(a function of bending stress)

D = depth of webt w = thickness of webfb = calculated compressive bending stress in flange

FIGURE 10.34.3.1A Web Thickness vs. Girder Depth for

Noncomposite Symmetrical Sections

compression flange component, D c is the depth of theweb in compression calculated by summing the stressesfrom the applicable stages of loading, and fb is the calcu-lated flange bending stress in the compression flange.The depth of web in compression, D,, in composite sec-tions subjected to negative bending may be taken asthe depth of the web in compression of the compositesection without summing the stresses from the variousstages of loading. When both edges of the web are incompression, k shall be taken equal to 7.2.

10.34.3.2.2 Where the calculated bending stress inthe flange equals the allowable bending stress, the thick-ness of the web plate in a symmetrical girder stiffenedwith transverse stiffeners in combination with one longi-tudinal stiffener located a distance D/5 from the compres-sion flange shall not be less than (where the Y.P. is for theflange material)

36,000 psi, Y.P. Min. D/32750,000 psi, Y.P. Min. D/27870,000 psi, Y.P. Min. D/235

130 260

120 240tw = 11/16

" . » _ t 1--t.t ;_~

30 600 10 20 30 40 50

tw=3/4„ t+


90,000 psi, Y.P. Min. D/207100,000 psi, Y.P. Min. D/196

In the above, D (depth of web) is the clear unsupporteddistance in inches between flange components.

10.34.4 Transverse Intermediate Stiffeners

10.34.4.1 Transverse intermediate stiffeners maybe omitted if the average calculated unit-shearing stressin the gross section of the web plate at the point con-sidered, f,,, is less than the value given by the followingequation:

F _ 7,33 x 10' FY

(D/tw)2 3(10-25)

where

D = unsupported depth of web plate between flangesin inches;

tw = thickness of the web plate in inches;F„ = allowable shear stress in psi.

10.34.4.2 Where transverse intermediate stiffenersare required, the spacing of the transverse intermediatestiffener shall be such that the actual shearing stress willnot exceed the value given by the following equation; themaximum spacing is further limited to 3D and is subjectto the handling requirement below:

F, =3Y

C+0.87(1-C)

(10-26)1+(d o /D)

The constant C is equal to the buckling shear stressdivided by the shear yield stress, and is determined asfollows:

for D <6, 000

tw Fy

C=1.0

for

D/tw > 7,500;FY

C—4.5x107k

(10-28)(D/t w ) Fy

where

k=5+5

+(do / D)

do = spacing of intermediate stiffenerFy = yield strength of the web plate

(F y/3) in Equation (10-26) can be replaced by the allow-able shearing stress given in Table 10.32. IA.

Transverse stiffeners shall be required if D/t w is greaterthan 150. The spacing of these stiffeners shall not exceedthe handling requirement D[260/(D/t w)]

2 .

10.34.4.3 The spacing of the first intermediate stiff-ener at the simple support end of a girder shall be such thatthe shearing stress in the end panel shall not exceed thevalue given by the following equation (the maximumspacing is limited to 1.5D):

F v = CFy/3 <_ Fy/3 (10-29)

10.34.4.4 If a girder panel is subjected to simultane-ous action of shear and bending moment with the magni-tude of the shear stress higher than 0.6 Fv, the bending ten-sile stress, Fs , shall be limited to

Fs = (.754 — .34fv/Fv )F y (10-30)

where

f„ = average calculated unit-shearing stress at thesection; live load shall be the load to producemaximum moment at the section under consid-eration

F„ = value obtained from Equation (10-26).

for

10.34.4.5 Where the calculated shear stress equals theallowable shear stress, transverse intermediate stiffenersmay be omitted if the thickness of the web is not less than

6'00 k5 (D/t w ) < 7,50~k

Y 1 y (10-27)

C _ 6, 000

(D/tq,)~F_y

36,000 psi, Y.P. Min. D/7850,000 psi, Y.P. Min. D/6670,000 psi, Y.P. Min. D/5690,000 psi, Y.P. Min. D/50

100,000 psi, Y.P. Min. D/47


10.34.4.6 Intermediate stiffeners preferably shall bemade of plates for welded plate girders and shall be madeof angles for riveted plate girders. They may be in pairs,one stiffener fastened on each side of the web plate, witha tight fit at the compression flange. They may, however,be made of a single stiffener fastened to one side of theweb plate. Stiffeners provided on only one side of the webmust be in bearing against, but need not be attached to, thecompression flange for the stiffener to be effective. How-ever, transverse stiffeners which connect diaphragms orcrossframes to the beam or girder shall be rigidly con-nected to both the top and bottom flanges.

10.34.4.7 The moment of inertia of any type of trans-verse stiffener with reference to the plane defined in Arti-cle 10.34.4.8 shall not be less than

I = dj W'J (10-31)

where

J = 2.5 (D/d,,) 2 — 2, but not less than 0.5 (10-32)

In these expressions,

I = minimum permissible moment of inertia of anytype of transverse intermediate stiffener in inchee;

J = required ratio of rigidity of one transverse stiffenerto that of the web plate;

d,, = distance between stiffeners in inches;D = unsupported depth of web plate between flange

components in inches;t,,, = thickness of the web plate in inches.

The gross cross-sectional area of intermediate trans-verse stiffeners shall be greater than

A= I0.15BD

(1—C)(LV

I -18~ Fyweb tµ (10 — 32a)

tw Fv J F

cr

9,025,000where F

cr =TYt'-

where

< Fystiffener (10 — 32b)

Fy stiffener is the yield strength of the stiffener; B = 1.0for stiffener pairs, 1.8 for single angles, and 2.4 for singleplates; and C is computed by Article 10.34.4.2. Whenvalues computed by Equation (10-32a) approach zero orare negative, then transverse stiffeners need only meet therequirements of Equation (10-31), and the requirementsof Article 10.34.4. 10,

10.34.4.8 When stiffeners are in pairs, the momentof inertia shall be taken about the center line of the webplate. When single stiffeners are used, the moment ofinertia shall be taken about the face in contact with theweb plate.

10.34.4.9 Transverse intermediate stiffeners need notbe in bearing with the tension flange. The distance be-tween the end of the stiffener weld and the near edge ofthe web-to-flange fillet welds shall not be less than 4t w ormore than 6t w. Stiffeners at points of concentrated loadingshall be placed in pairs and should be designed in accor-dance with Article 10. 34.6. However, transverse stiffenerswhich connect diaphragms or crossframes to the beam orgirder shall be rigidly connected to both the top and bot-tom flanges.

10.34.4.10 The width of a plate or the outstandingleg of an angle intermediate stiffener shall not be less than2 inches plus 1/3o the depth of the girder, and it shall prefer-ably not be less than 1

/4 the full width of the girder flange.The thickness of a plate or the outstanding leg of an angleintermediate stiffener shall not be less than 1/16 its width.Intermediate stiffeners may be AASHTO M 270 Grade 36steel,

10.34.5 Longitudinal Stiffeners

10.34.5.1 The optimum distance, d,, of a plate longi-tudinal stiffener or the gage line of an angle longitudinalstiffener from the inner surface or the leg of the compres-sion flange component is D/5 for a symmetrical girder.The optimum distance, ds , for an unsymmetrical compos-ite girder in positive-moment regions may be determinedfrom the equation given below:

d s = 1(10-32b)

Dcs 1+1.5f

DL+LLfDL

where D,s is the depth of the web in compression of thenoncomposite steel beam or girder, fDL is the noncom-posite dead-load stress in the compression flange, andfDL+LL is the total noncomposite and composite dead-

load plus the composite live-load stress in the compres-sion flange at the most highly stressed section of theweb. The optimum distance, d s, of the stiffener in negative-moment regions of composite sections is 2D,/5, whereD e is the depth of the web in compression of the com-posite section at the most highly stressed section ofthe web.

The longitudinal stiffener shall be proportioned so that

zI=DO 2.4 d

DO -0.13 (10-33)

W (

2

where

I = minimum moment of inertia of the longitudinalstiffener about its edge in contact with the web

°;plate in inches


D = unsupported distance between flange compo-nents in inches;

t, = thickness of the web plate in inches;d,, = actual distance between transverse stiffeners in

inches.

10.34.5.2 The thickness of the longitudinal stiffeneri s shall not be less than

2, 600(10-34)

where

b' = width of stiffenerF, = yield strength of the longitudinal stiffener

10.34.5.3 The stress in the stiffener shall not begreater than the basic allowable bending stress for the ma-terial used in the stiffener.

10.34.5.4 Longitudinal stiffeners are usually placedon one side only of the web plate. They need not be con-tinuous and may be cut at their intersections with thetransverse stiffeners.

10.34.5.5 For longitudinally stiffened girders, trans-verse stiffeners shall be spaced a distance, do, accordingto shear capacity as specified in Article 10.34.4.2, but notmore than 1.5 times the web depth. The handling require-ment given in Article 10.34.4.2 shall not apply to longitu-dinally stiffened girders. The spacing of the first trans-verse stiffener at the simple support end of alongitudinally stiffened girder shall be such that the shear-ing stress in the end panel does not exceed the value givenin Article 10.34.4.3. The maximum spacing of the firsttransverse stiffener at the simple support end of a longitu-dinally stiffened girder is limited to 1.5 times the webdepth. The total web depth D shall be used in determiningthe shear capacity of longitudinally stiffened girders inArticles 10.34.4.2 and 10.34.4.3.

10.34.5.6 Transverse stiffeners for girder panels withlongitudinal stiffeners shall be designed according to Ar-ticle 10.34.4.7.


10.34.6.1 Welded Girders

Over the end bearings of welded plate girders andover the intermediate bearings of continuous welded plategirders there shall be stiffeners. They shall extend asnearly as practicable to the outer edges of the flangeplates. They preferably shall be made of plates placed

on both sides of the web plate. Bearing stiffeners shallbe designed as columns, and their connection to the webshall be designed to transmit the entire end reac-tion to the bearings. For stiffeners consisting of twoplates, the column section shall be assumed to comprisethe two plates and a centrally located strip of the web platewhose width is equal to not more than 18 timesits thickness. For stiffeners consisting of four or moreplates, the column section shall be assumed to comprisethe four or more plates and a centrally located strip ofthe web plate whose width is equal to that enclosed bythe four or more plates plus a width of not more than 18times the web plate thickness. (See Article 10.40 forHybrid Girders.) The radius of gyration shall be computedabout the axis through the center line of the web plate. Thestiffeners shall be ground to fit against the flange throughwhich they receive their reaction, or attached to the flangeby full penetration groove welds. Only the portions of thestiffeners outside the flange-to-web plate welds shall beconsidered effective in bearing. The thickness of the bear-ing stiffener plates shall not be less than

b' Fy

12 33,000(10-35)

The allowable compressive stress and the bearing pres-sure on the stiffeners shall not exceed the values specifiedin Article 10.32.

10.34.6.2 Riveted or Bolted Girders

Over the end bearings of riveted or bolted plate girdersthere shall be stiffener angles, the outstanding legs ofwhich shall extend as nearly as practicable to the outeredge on the flange angle. Bearing stiffener angles shallbe proportioned for bearing on the outstanding legs offlange angles, no allowance being made for the portionsof the legs being fitted to the fillets of the flange angles.Bearing stiffeners shall be arranged, and their con-nections to the web shall be designed to transmit theentire end reaction to the bearings. They shall not becrimped. The thickness of the bearing stiffener anglesshall not be less than

b'F

33, 000(10-36)

The allowable compressive stress and the bearing pres-sure on the stiffeners shall not exceed the values specifiedin Article 10.32.


10.35 TRUSSES

10.35.1 Perforated Cover Plates and Lacing Bars

The shearing force normal to the member in the planesof lacing or continuous perforated plates shall be assumeddivided equally between all such parallel planes. Theshearing force shall include that due to the weight of themember plus any other external force. For compressionmembers, an additional force shall be added as obtainedby the following formula:

V=—P 100 + (f/r)Fy(10-37)

100 f / r + 10 3,300, 000

In the above expression

V = normal shearing force in pounds;P = allowable compressive axial load on members in

pounds;C = length of member in inches;r = radius of gyration of section about the axis per-

pendicular to plane of lacing or perforated platein inches;

Fy = specified minimum yield point of type of steelbeing used.

10.35.2 Compression Members—Thickness ofMetal

10.35.2.1 Compression members shall be so designedthat the main elements of the section will be connecteddirectly to the gusset plates, pins, or other members.

10.35.2.2 The center of gravity of a built-up sectionshall coincide as nearly as practicable with the center ofthe section. Preferably, segments shall be connected bysolid webs or perforated cover plates.

10.35.2.3 Plates supported on one side, outstandinglegs of angles and perforated plates—for outstandingplates, outstanding legs of angles, and perforated plates atthe perforations, the b/t ratio of the plates or angle seg-ments when used in compression shall not be greater thanthe value obtained by use of the formula

b _ 1,625(10-38)

t fa

but in no case shall b/t be greater than 12 for main mem-bers and 16 for secondary members.

(Note: b is the distance from the edge of plate or edge ofperforation to the point of support.)

10.35.2.4 When the compressive stress equals thelimiting factor of 0.44 F y , the b/t ratio of the segments in-dicated above shall not be greater than the ratios shownfor the following grades of steel:


100,000 psi, Y.P. Min. b/t = 7.5

10.35.2.5 Plates supported on two edges or webs ofmain component segments—for members of box shapeconsisting of main plates, rolled sections, or made upcomponent segments with cover plates, the b/t ratio of themain plates or webs of the segments when used in com-pression shall not be greater than the value obtained byuse of the formula

b _ 4,000(10-39)

t fa

but in no case shall b/t be greater than 45.(Note: b is the distance between points of support for theplate and between roots of flanges for the webs of rolledsegments.)

10.35.2.6 When the compressive stresses equal thelimiting factor of 0.44 Fy , the b/t ratio of the plates andsegments indicated above shall not be greater than the ra-tios shown for the following grades of steel:


100,000 psi, Y.P. Min. b/t = 19

10.35.2.7 Solid cover plates supported on two edgesor webs connecting main members or segments—formembers of H or box shapes consisting of solid coverplates or solid webs connecting main plates or segments,the b/t ratio of the solid cover plates or webs when used incompression shall not be greater than the value obtainedby use of the formula

b _ 5,000(10-40)

t fa

but in no case shall b/t be greater than 50.


(Note: b is the unsupported distance between points ofsupport.)

10.35.2.8 When the compressive stresses equal thelimiting factor of 0.44 Fy , the b/t ratio of the cover plateand webs indicated above shall not be greater than the ra-tios shown for the following grades of steel:

36,000 psi, Y.P. Min, b/t = 4050,000 psi, Y.P. Min. b/t = 3470,000 psi, Y.P. Min, b/t = 2890,000 psi, Y.P. Min. b/t = 25

100,000 psi, Y.P. Min. b/t = 24

10.35.2.9 Perforated cover plates supported on twoedges—for members of box shapes consisting of perfo-rated cover plates connecting main plates or segments, theb/t ratio of the perforated cover plates when used in com-pression shall not be greater than the value obtained byuse of the formula

b _ 6,000(10-41)

t fa

rolled segments the point of support may be taken as theweld whenever the ratio of outstanding flange width toflange thickness of the rolled segment is less than seven.Otherwise, point of support shall be the root of flange ofrolled segment. Terminations of the butt welds are to beground smooth.

10.36 COMBINED STRESSES

All members subjected to both axial compression andbending stresses shall be proportioned to satisfy the fol-lowing requirements

fa + C'j'x +C, yfby

1.0 (10-42)Fa 1 — fa F

fabX 1 — , } F byF ex Fey /

and

fa + f b + f by < 1.0 (at points of support)0.472Fy

FbX

Fby

(10-43)

where

but in no case shall b/t be greater than 55.(Note: b is the distance between points of support. Atten-tion is directed to requirements for plate thickness at per-forations, namely, plate supported on one side, which alsoshall be satisfied.)

10.35.2.10 When the compressive stresses equal thelimiting factor of 0.44 FY , the b/t ratio of the perforatedcover plates shall not be greater than the ratios shown forthe following grades of steel:


100,000 psi, Y.P. Min. b/t = 29

In the above expressions

fa = computed compressive stress;b = width (defined as indicated for each expres-

sion);= plate or web thickness.

10.35.2.11 The point of support shall be the inner lineof fasteners or fillet welds connecting the plate to the mainsegment. For plates butt welded to the flange edge of

F,71 )

e

F.S. (KbLb/rb)~

(10-44

fa = computed axial stress;fbX or fby = computed compressive bending stress

about the x axis and y axis, respectively;F a = axial stress that would be permitted if axial

force alone existed, regardless of the planeof bending;

FbX, Fby = compressive bending stress that would bepermitted if bending moment alone existedabout the x axis and the y axis, respec-tively, as evaluated according to Table10.32.1A;

F e = Euler buckling stress divided by a factor ofsafety;

E = modulus of elasticity of steel;Kb = effective length factor in the plane of bend-

ing (see Appendix C);Lb = actual unbraced length in the plane of

bending;rb = radius of gyration in the plane of bending;C., C.Y = coefficient about the x axis and y axis, re-

spectively, whose value is taken fromTable 10.36A;

F.S. = factor of safety = 2.12.


TABLE 10.36A Bending-Compression Interaction Coefficients

Loading Conditions Remarks Cm

pM1 Mb PComputed moments maximum at end; joint translation 0.85

not prevented Lb

MI M2Computed moments maximum at end; no transverse p p (0.4)Mt + 0.61loading, joint translation prevented Lb M2 J

Mi Ma

Transverse loading; joint translation prevented PLb a

p0.85

P. ~p

Transverse loading; joint translation prevented , .M 1.0

M l = smaller end moment.M I /M2 is positive when member is bent in single curvature.MI /M2 is negative when member is bent in reverse curvature.In all cases Cm may be conservatively taken equal to 1.0.

10.37 SOLID RIB ARCHES 10.37.1.2 The arch rib shall be proportioned to sat-isfy the following requirement:

10.37.1 Moment Amplification and Allowable Stressfa +fb < (10-47)

10.37.1.1 Live load plus impact moments that are de- Fa Fb

termined by an analysis which neglects arch rib deflectionshall be increased by an amplification factor A F where

1 fa = the computed axial stress;AF= 1 _ 1.70T

(10-45)

fb = the calculated bending stress, including momentAFe amplification, at the extreme fiber;

Fa = the allowable axial unit stress;where Fb = the allowable bending unit stress.

T = arch rib thrust at the quarter point from dead plus10.37.1.3 For buckling in the vertical planelive plus impact loading;

z zFe =

E(Euler buckling stress) (10-46) (KL

/FY(KL)2

r

_ F ` r JFa

2.121 — 47r2E (10-48)

L = one-half of the length of the arch rib;A = area of cross section;r = radius of gyration;

K = factor to account for effective length.

K Values for Use in Calculating F e and F.

Rise to Span 3-Hinged 2-HingedRatio Arch Arch Fixed Arch

0.1–0.2 1.16 1.04 0.70

0.2–0.3 1.13 1.10 0.70

0.3–0.4 1.16 1.16 0.72

where KL is as defined above.

10.37.1.4 The effects of lateral slenderness should beinvestigated. Tied arch ribs, with the tie and roadway sus-pended from the rib, are not subject to moment amplifica-tion, and F a shall be based on an effective length equal tothe distance along the arch axis between suspenders, forbuckling in the vertical plane. However, the smaller cross-sectional area of cable suspenders may result in an effec-tive length slightly longer than the distance between sus-penders.


10.37.2 Web Plates

10.37.2.1 The depth to thickness ratio D/tw of theweb plates, having no longitudinal stiffeners, shall not begreater than the following:

D _ 5, 000maximum D/t w = 60 (10-49)

t w fa

where tw = web thickness.

10.37.2.2 If one longitudinal stiffener is used at mid-depth of the web, maximum D/t a, shall be as follows:

D _ 7,500maximum D/tw = 90 (10-50)

tw fa

and the moment of inertia of the stiffener about an axisparallel to the web and at the base of the stiffener shall beequal to

I, = 0.75 De, (10-51)

10.37.2.3 If two longitudinal stiffeners are used atthe one-third points of the web depth D, maximum D/t µ,shall be as follows:

D _ 10, 000maximum D/t w =120 (10-52)

t w fa

and the moment of inertia of each stiffener shall be

IS = 2.2 DtW

(10-53)

10.37.2.4 The width to thickness ratio b'/t s of anyoutstanding element of the web stiffeners shall not exceedthe following:

b' _ 1,625maximum b '/t, =12 (10-54)

i s fa +3

10.37.2.5 Web plate equations apply between limits

0.2 5b

<– 0.7 (10-55)f

a+ f

b

10.37.3 Flange Plates

10.37.3.1 The b/tf ratio for the width of flange platesbetween webs shall be not greater than

b' _ 4,250maximum blt f = 47 (10-56)

tf

fa

+ fb

10.37.3.2 The b ' /tf ratio for the overhang width offlange plates shall be not greater than

b ' 1,625_'

maximum b '/t f =12 (10-57)t

ffa

+ fb

10.38 COMPOSITE GIRDERS

10.38.1 General

10.38.1.1 This section pertains to structures com-posed of steel girders with concrete slabs connected byshear connectors.

10.38.1.2 General specifications pertaining to the de-sign of concrete and steel structures shall apply to struc-tures utilizing composite girders where such specifica-tions are applicable. Composite girders and slabs shall bedesigned and the stresses computed by the composite mo-ment of inertia method and shall be consistent with thepredetermined properties of the various materials used.

10.38.1.3 The ratio of the moduli of elasticity of steel(29,000,000 psi) to those of normal weight concrete (W =145 pcf) of various design strengths shall be as follows:

f, = unit ultimate compressive strength of concrete asdetermined by cylinder tests at the age of 28 daysin pounds per square inch.

n = ratio of modulus of elasticity of steel to that ofconcrete. The value of n, as a function of the ul-timate cylinder strength of concrete, shall be as-sumed as follows:

f, = 2,000–2,300 n = 112,400–2,800 = 102,900–3,500 = 93,600–4,500 = 84,600–5,900 = 76,000 or more = 6

10.38.1.4 The effect of creep shall be considered inthe design of composite girders which have dead loadsacting on the composite section. In such structures,stresses and horizontal shears produced by dead loads act-ing on the composite section shall be computed for n asgiven above or for this value multiplied by 3, whichevergives the higher stresses and shears.


10.38.1.5 If concrete with expansive characteristicsis used, composite design should be used with caution andprovision must be made in the design to accommodate theexpansion.

10.38.1.6 Composite sections in simple spans andthe positive moment regions of continuous spans shouldpreferably be proportioned so that the neutral axis liesbelow the top surface of the steel beam. Concrete on thetension side of the neutral axis shall not be considered incalculating resisting moments. In the negative moment re-gions of continuous spans, only the slab reinforcementcan be considered to act compositely with the steel beamsin calculating resisting moments. Mechanical anchoragesshall be provided in the composite regions to developstresses on the plane joining the concrete and the steel.Concrete on the tension side of the neutral axis may beconsidered in computing moments of inertia for deflectioncalculations, for determining stiffness factors used in cal-culating moments and shears, and for computing fatiguestress ranges and fatigue shear ranges as permitted underthe provisions of Articles 10.3.1 and 10.38.5.1.

10.38.1.7 The steel beams or girders, especially if notsupported by intermediate falsework, shall be investigatedfor stability and strength for the loading applied during thetime the concrete is in place and before it has hardened.The casting or placing sequence specified in the plans forthe composite concrete deck shall be considered when cal-culating the moments and shears on the steel section. Themaximum flange compression stress shall not exceed thevalue specified in Table 10.32.IA for partially supportedor unsupported compression flanges multiplied by a factorof 1.4, but not to exceed 0.55Fy . The sum of the noncom-posite and composite dead-load shears in the web shall notexceed the shear-buckling capacity of the web multipliedby 1.35, nor the allowable shear stress, as follows:

F, = 0.45CFy <_ 0.33Fy (10-57a)

where C is specified in Article 10.34.4.2.

10.38.2 Shear Connectors

10.38.2.1 The mechanical means used at the junctionof the girder and slab for the purpose of developing theshear resistance necessary to produce composite actionshall conform to the specifications of the respective mate-rials as provided in Division II. The shear connectors shallbe of types that permit a thorough compaction of the con-crete in order to ensure that their entire surfaces are incontact with the concrete. They shall be capable of resist-ing both horizontal and vertical movement between theconcrete and the steel.

10.38.2.2 The capacity of stud and channel shearconnectors welded to the girders is given in Article10.38.5. Channel shear connectors shall have at least3/6-inch fillet welds placed along the heel and toe of thechannel.

10.38.2.3 The clear depth of concrete cover over thetops of the shear connectors shall be not less than 2 inches.Shear connectors shall penetrate at least 2 inches abovebottom of slab.

10.38.2.4 The clear distance between the edge of agirder flange and the edge of the shear connectors shall benot less than 1 inch. Adjacent stud shear connectors shallnot be closer than 4 diameters center to center.

10.38.3 Effective Flange Width

10.38.3.1 In composite girder construction the as-sumed effective width of the slab as a T-beam flange shallnot exceed the following:

(1) One-fourth of the span Iength of the girder.(2) The distance center to center of girders.(3) Twelve times the least thickness of the slab.

10.38.3.2 For girders having a flange on one sideonly, the effective flange width shall not exceed ihz of thespan length of the girder, or six times the thickness of theslab, or one-half the distance center to center of the nextgirder.

10.38.4 Stresses

10.38.4.1 Maximum compressive and tensilestresses in girders that are not provided with temporarysupports during the placing of the permanent dead loadshall be the sum of the stresses produced by the dead loadsacting on the steel girders alone and the stresses producedby the superimposed loads acting on the composite girder.When girders are provided with effective intermediatesupports that are kept in place until the concrete has at-tained 75% of its required 28-day strength, the dead andlive load stresses shall be computed on the basis of thecomposite section.

10.38.4.2 A continuous composite bridge may bebuilt with shear connectors either in the positive momentregions or throughout the length of the bridge. The posi-tive moment regions may be designed with compositesections as in simple spans. Shear connectors shall beprovided in the negative moment portion in which the re-inforcement steel embedded in the concrete is considereda part of the composite section. In case the reinforcement


steel embedded in the concrete is not used in computingsection properties for negative moments, shear connectorsneed not be provided in these portions of the spans, butadditional anchorage connectors shall be placed in the re-gion of the point of dead load contra-flexure in accordancewith Article 10.38.5.1.3. Shear connectors shall be pro-vided in accordance with Article 10.38.5.

10.38.5.1 Horizontal Shear

The maximum pitch of shear connectors shall not ex-ceed 24 inches except over the interior supports of con-tinuous beams where wider spacing may be used to avoidplacing connectors at locations of high stresses in the ten-sion flange.

Resistance to horizontal shear shall be provided by me-chanical shear connectors at the junction of the concreteslab and the steel girder. The shear connectors shall bemechanical devices placed transversely across the flangeof the girder spaced at regular or variable intervals. Theshear connectors shall be designed for fatigue* andchecked for ultimate strength.

*Reference is made to the paper titled "Fatigue Strength of Shear Con-nectors," by Roger G. Slutter and John W. Fisher, in Highway ResearchRecord, No. 147, published by the Highway Research Board, Washing-ton, D.C., 1966.

10.38.5.1.1 Fatigue

The range of horizontal shear shall be computed by theformula

Sr ^ VIQ (10-58)

= range of horizontal shear, in kips per inch, at thejunction of the slab and girder at the point in thespan under consideration;

=range of shear due to live loads and impactin kips; at any section, the range of shear shallbe taken as the difference in the minimum andmaximum shear envelopes (excluding dead loads);

= statical moment about the neutral axis of thecomposite section of the transformed concretearea, in' . Between points of dead-load con-traflexure, the statical moment about the neutralaxis of the composite section of the area of rein-forcement embedded in the concrete may be usedunless the transformed concrete area is consideredto be fully effective for negative moment in com-puting the longitudinal range of stress;

= moment of inertia of the transformed compositesection, ina . Between points of dead-load con-traflexure, the moment of inertia of the steelgirder including the area of reinforcement em-bedded in the concrete may be used unless thetransformed concrete area is considered to befully effective for negative moment in comput-ing the longitudinal range of stress.

(In the formula, the concrete area is transformed into anequivalent area of steel by dividing the effective concreteflange width by the modular ratio, n.)

The allowable range of horizontal shear, Z r , in poundson an individual connector is as follows:

Channels

Z, = Bw (10-59)

Welded studs (for H/d > 4)

Z, = a d2 (10-60)

where

w = length of a channel shear connector, in inches,measured in a transverse direction on the flangeof a girder;

d = diameter of stud in inches;a = 13,000 for 100,000 cycles

10,600 for 500,000 cycles7,850 for 2,000,000 cycles5,500 for over 2,000,000 cycles;

10.38.4.3 The minimum longitudinal reinforcementincluding the longitudinal distribution reinforcementmust equal or exceed 1 % of the cross-sectional area of theconcrete slab whenever the longitudinal tensile stress inthe concrete slab due to either the construction loads or thedesign loads exceeds f f specified in Article 8.15.2.1.1. Thearea of the concrete slab shall be taken equal to the struc-tural thickness times the entire width of the bridge deck.The required reinforcement shall be No. 6 bars orsmaller spaced at not more than 12 inches. Two-thirds ofthis required reinforcement is to be placed in the top layerof slab. Placement of distribution steel as specified in Ar-ticle 3.24. 10 is waived.

10.38.4.4 When shear connectors are omitted fromthe negative moment region, the longitudinal reinforce-ment shall be extended into the positive moment regionbeyond the anchorage connectors at least 40 times the re-inforcement diameter. For epoxy-coated bars, the lengthto be extended into the positive moment region beyondthe anchorage connectors should be modified to complywith Article 8.25.2.3.

10.38.5 Shear


B = 4,000 for 100,000 cycles3,000 for 500,000 cycles2,400 for 2,000,000 cycles2,100 for over 2,000,000 cycles;

H = height of stud in inches.

The required pitch of shear connectors is determinedby dividing the allowable range of horizontal shear of allconnectors at one transverse girder cross-section ().~Zr) bythe horizontal range of shear S r, but not to exceed the max-imum pitch specified in Article 10.38.5.1. Over the inte-rior supports of continuous beams the pitch may be mod-ified to avoid placing the connectors at locations of highstresses in the tension flange provided that the total num-ber of connectors remains unchanged.

10.38.5.1.2 Ultimate Strength_

The number of connectors so provided for fatigue shallbe checked to ensure that adequate connectors are pro-vided for ultimate strength.

The number of shear connectors required shall equal orexceed the number given by the formula

N 1 = QS (10-61)

The number of connectors, N2, required between thepoints of maximum positive moment and points of adja-cent maximum negative moment shall equal or exceed thenumber given by the formula

N 2 =P+P3

(10-64)u

At points of maximum negative moment the force inthe slab is taken as

P 3 = AsFy* (10-65)

where

As = total area of longitudinal reinforcing steel atthe interior support within the effective flangewidth;

Fy* = specified minimum yield point of the reinforc-ing steel.

The ultimate strength of the shear connector is given asfollows:

Channels

S u = 550 (h+

2)

W f~ (10-66)

where Welded studs (for H/d > 4)

N, = number of connectors between points of maxi-mum positive moment and adjacent end sup-ports;

% = ultimate strength of the shear connector as givenbelow;

= reduction factor = 0.85;P = force in the slab as defined hereafter as P 1 or

P2 .

At points of maximum positive moment, the force inthe slab is taken as the smaller value of the formulas

P l = A,Fy (10-62)

or

P2 = 0.85f~lbt 5 (10-63)

where

AS = total area of the steel section including cover-plates;

F, = specified minimum yield point of the steel beingused;

fc' = compressive strength of concrete at age of 28

days;b =effective flange width given in Article 10.38.3;is = thickness of the concrete slab.

S„ = 0.4d 2 fc E c 5 60, 000A SC(10-67)

where

Ec = modulus of elasticity of the concrete in poundsper square inch;

E c =w3/2

3 3IC

(10-68)

S„ = ultimate strength of individual shear connector inpounds;

As , = cross-sectional area of a stud shear connector insquare inches;

h = average flange thickness of the channel flange ininches;

t = thickness of the web of a channel in inches;W = length of a channel shear connector in inches;f,' = compressive strength of the concrete in 28 days

in pounds per square inch;d = diameter of stud in inches;w = unit weight of concrete in pounds per cubic foot.

*When reinforcement steel embedded in the top slab is not used incomputing section properties for negative moments, P 3 is equal to zero.


10.38.5.1.3 Additional Connectors to Develop SlabStresses

The number of additional connectors required at pointsof contraflexure when reinforcing steel embedded in theconcrete is not used in computing section properties fornegative moments shall be computed by the formula

N, = AIf,/Z, (10-69)

where

Nc = number of additional connectors for each beamat point of contraflexure;

A'r = total area of longitudinal slab reinforcing steelfor each beam over interior support;

fr = range of stress due to live load plus impact inthe slab reinforcement over the support (in lieuof more accurate computations, f, may be takenas equal to 10,000 psi);

Zr = allowable range of horizontal shear on an indi-vidual shear connector.

The additional connectors, N,, shall be placed adjacentto the point of dead load contraflexure within a distanceequal to one-third the effective slab width, i.e., placed ei-ther side of this point or centered about it. It is preferableto locate field splices so that they clear the connectors.

10.38.5.2 Vertical Shear

The intensity of unit-shearing stress in a compositegirder may be determined on the basis that the web of thesteel girder carries the total external shear, neglecting theeffects of the steel flanges and of the concrete slab.The shear may be assumed to be uniformly distributedthroughout the gross area of the web.

10.38.6 Deflection

10.38.6.1 The provisions of Article 10.6 in regard todeflections from live load plus impact also shall be ap-plicable to composite girders.

10.38.6.2 When the girders are not provided withfalsework or other effective intermediate support during theplacing of the concrete slab, the deflection due to the weightof the slab and other permanent dead loads added before theconcrete has attained 75% of its required 28-day strengthshall be computed on the basis of noncomposite action.

10.39 COMPOSITE BOX GIRDERS

10.39.1 General

10.39.1.1 This section pertains to the design of sim-ple and continuous bridges of moderate length supported

by two or more single cell composite box girders. The dis-tance center-to-center of flanges of each box should be thesame and the average distance center-to-center of flangesof adjacent boxes shall be not greater than 1.2 times andnot less than 0.8 times the distance center-to-center offlanges of each box. In addition to the above, when nonpa-rallel girders are used, the distance center-to-center of ad-jacent flanges at supports shall be not greater than 1.35times and not less than 0.65 times the distance center-to-center of flanges of each box. The cantilever overhang ofthe deck slab, including curbs and parapets, shall be lim -

ited to 60% of the average distance center-to-center offlanges of adjacent boxes, but shall in no case exceed 6feet.

10.39.1.2 The provisions of Division I, Design, shallgovern where applicable, except as specifically modifiedby Articles 10.39.1 through 10.39.8.

10.39.2 Lateral Distribution of Loads for BendingMoment

10.39.2.1 The live load bending moment for eachbox girder shall be determined by applying to the girder,the fraction WL of a wheel load (both front and rear), de-termined by the following equation:

WL = 0.1 + 1.7R + 0.85 (10-70)W

where

R =N,,

(10-71)Number of Box Girders

N,N = W,/12 reduced to the nearest whole number;W, = roadway width between curbs in feet, or barriers

if curbs are not used. R shall not be less than 0.5or greater than 1.5.

10.39.2.2 The provision of Article 3.12, Reduction ofLoad Intensity, shall not apply in the design of box gird-ers when using the design load WL given by the aboveequation.

10.39.3 Design of Web Plates

10.39.3.1 Vertical Shear

The design shear V, for a web shall be calculated usingthe following equation:

Vµ, = V„/cos 0 (10-72)


where

V, = vertical shear;= angle of inclination of the web plate to the verti-

cal.

10.39.3.2 Secondary Bending Stresses

10,39.3.2.1 Web plates maybe plumb (90°to bottomof flange) or inclined. If the inclination of the web platesto a plane normal to the bottom flange is no greater than 1to 4, and the width of the bottom flange is no greater than20% of the span, then the transverse bending stresses re-sulting from distortion of the span, and the transversebending stresses resulting from distortion of the girdercross section and from vibrations of the bottom plate neednot be considered. For structures in this category trans-verse bending stresses due to supplementary loadings,such as utilities, shall not exceed 5,000 psi.

10.39.3.2.2 For structures exceeding these limits, adetailed evaluation of the transverse bending stresses dueto all causes shall be made. These stresses shall be limitedto a maximum stress or range of stress of 20,000 psi.

10.39.4 Design of Bottom Flange Plates

10.39.4.1 Tension Flanges

10.39.4.1.1 In cases of simply supported spans, thebottom flange shall be considered completely effective inresisting bending if its width does not exceed one-fifth thespan length. If the flange plate width exceeds one-fifth ofthe span, an amount equal to one-fifth of the span onlyshall be considered effective.

10.39.4.1.2 For continuous spans, the criteria aboveshall be applied to the lengths between points of con-traflexure.

10.39.4.2 Compression Flanges Unstiffened

10.39.4.2.1 Unstiffened compression flanges de-signed for the basic allowable stress of 0.55 F

Yshall have

a width to thickness ratio equal to or less than the valueobtained by the use of the formula

b 6,140=

Fy(10-73)

t

where

b = flange width between webs in inches;t = flange thickness in inches.

10.39.4.2.2 For greater b/t ratios, but not exceeding13, 300 j, the stress in an unstiffened bottom flange shallnot exceed the value determined by the use of the formula

fb = 0.55Fy – 0.224Fy X

~13,300- b

1–sin x t

2 7,160 (10-74)

10.39.4.2.3 For values of b/t exceeding 13,300/,the stress in the flange shall not exceed the value given bythe formula

2

fb =57.6(b) x10 6(10-75)

10.39.4.2.4 The b/t ratio preferably should not ex-ceed 60 except in areas of low stress near points of deadload contraflexure.

10.39.4.2.5 Should the b/t ratio exceed 45, longitudi-nal stiffeners should be considered.

10.39.4.2.6 Unstiffened compression flanges shallalso satisfy the provisions of Article 10.39.4.1. The effec-tive flange plate width shall be used to calculate the flangebending stress. The full flange plate width shall be used tocalculate the allowable bending stress.

10.39.4.3 Compression Flanges StiffenedLongitudinally*

10.39.4.3.1 Longitudinal stiffeners shall be at equalspacings across the flange width and shall be proportionedso that the moment of inertia of each stiffener about anaxis parallel to the flange and at the base of the stiffener isat least equal to

I, = tfw (10-76)

where

= 0.07 k1n4 for values of n greater than 1;= 0.125 k 3 for a value of n = 1;

tf = thickness of the flange;w = width of flange between longitudinal stiffeners or

distance from a web to the nearest longitudinalstiffener;

n = number of longitudinal stiffeners;k = buckling coefficient which shall not exceed 4.

*In solving these equations a value of k between 2 and 4 generallyshould be assumed.

10.39.4.3.1 DIVISION I-DESIGN 309

k=4 k=4 k=4

v Vn

cC

v

cNO STIFFENERS REQUIREDFcr =F y fb=0.55Fy bey = 6,140

Fcr = 0.96 Fy, fb = 0.53 Fy,b

47-y = 8,200

Fcr = 0.85 Fy , fb = 0.47 Fy,t4—Fy = 10,060

NOTE: V) k = 2.56 k =2.56 k =2.56Fcr refers to Load Factor Designb refers to Working Stress Design c Cl)Fy is in Ib/in

2 c+)i „

c c

C;.. C 0U

.O4

It a i~.'~

4V

I40

WITHOUTTRANSVERSE o 0STIFFENERS ,

k=4 k=4 jk = 4

/Clv k =2 .25 ~' k=2.25 k = 2.25

WITH TRANSVERSE STIFFENERS

n = 2,Is=2.67bt'00,

k=4 k=4 =4 n=3,Is=2.00bt'n = 4, Is = 1,60 bt3

k = 1.78 n=5,Is=1.33bt3

n"~ =1.78 k=1.7810000 15000 20000 25000 30000 35000 40000

b~Fpy

FIGURE 10.39.4.3A. Longitudinal Stiffeners—Box Girder Compression Flange

0.5000


0.09k, = 2

hIt E (fs = 0.55 Fy)b 2 A F (Fs = F) c

NOTE;fs refers to Working Stress Design b lAfFy

I t E. (fs = 0.53-(Fs = 0.96

Fy)Fy)

Fs refers to Load Factor DesignFy is in IbAnz k, = 2.78

k, = 4

D

c tk

k, = 1.78

k, = 2.56k,= 4

c

N NIt E , (fs 0.47 Fy)

kb 2 fy- (Fs 0.85 Fy)

Xk

---b A = 0.47 Fy )rL k, = 2.25

c~

, 2 n n ; 3 (Fs = 0.85 Fy)n' ' 3 t~ ' ` 3

ck,=4

k,=1.78 , = 2. n= 4

n= 4

b{fs=0.53Fy) k,=4 n= 5(Fs = 0.96Fy) n~ k,=2.78 k,=4

a (fs = 0.55 Fy)b (Fs = Fy )

Is for longitudinal stiffeners = 8t3 w (in .o)

bT

y

D.08

0.07

0.06

0.05

0.04

It EBzA(Fy

0.03

0.02

0.01

0 010,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000

FIGURE 10.39.4.313 Spacing and Size of Transverse Stiffeners (for Flange Stiffened Longitudinally and transversely)


10.39.4.3.2 For the flange, including stiffeners, to bedesigned for the basic allowable stress of 0.55 F Y , the ratiow/t shall not exceed the value given by the formula

w _ 3, 070 ~_k (10-77)t J—

Y

10.39.4.3.3 For greater values of w/t but not exceed-ing 60 or (6,650 whichever is less, the stress inthe flange, including stiffeners, shall not exceed the valuedetermined by the formula

fb = 0.55F Y - 0.224F Y X

6, 650w

~Fy-1 -sin 7r x

t (10-78)2 3, 580

10.39.4.3.4 For values of w/t exceeding (6,650 V /k-)/N/Ty but not exceeding 60, the stress in the flange, in-cluding stiffeners, shall not exceed the value given by theformula

fb = 14.4 k(t/w)2 X 106 (10-79)

10.39.4.3.5 When longitudinal stiffeners are used, itis preferable to have at least one transverse stiffenerplaced near the point of dead load contraflexure. The stiff-ener should have a size equal to that of a longitudinal stiff-ener.

10.39.4.3.6 If the longitudinal stiffeners are placed attheir maximum w/t ratio to be designed for the basic al-lowable design stresses of 0.55 F Y and the number of lon-gitudinal stiffeners exceeds 2, then transverse stiffenersshould be considered.

10.39.4.3.7 Compression flanges stiffened longitudi-nally shall also satisfy the provisions of Article 10.39.4.1.The effective flange plate width shall be used to calculatethe flange bending stress. The full flange plate width shallbe used to calculate the allowable bending stress.

10.39.4.4 Compression Flanges StiffenedLongitudinally and Transversely

10.39.4.4.1 The longitudinal stiffeners shall be atequal spacings across the flange width and shall be pro-portioned so that the moment of inertia of each stiffenerabout an axis parallel to the flange and at the base of thestiffener is at least equal to

1, = 8 tfw (10-80)

10.39.4.4.2 The transverse stiffeners shall be propor-tioned so that the moment of inertia of each stiffener aboutan axis through the centroid of the section and parallel toits bottom edge is at least equal to

It =0.10(n+1)3w3 Eof

(10-81)

where

Af = area of bottom flange including longitudinal

stiffeners;a = spacing of transverse stiffeners;f, = maximum longitudinal bending stress in the

flange of the panels on either side of the trans-verse stiffener;

E = modulus of elasticity of steel.

10.39.4.4.3 For the flange, including stiffeners, to bedesigned for the basic allowable stress of 0.55 F Y , the ratiow/t for the longitudinal stiffeners shall not exceed thevalue given by the formula

w _ 3, 070 kl (10-82)t

Y

where

k i= [1+(a/b)2]z +87.3

(10-83)(n+1)2(a/b)2[1+0.1(n+1)]

10.39.4.4.4 For greater values of w/t, but not ex-ceeding 60 or (6,650 V—k,)/N/—F,, whichever is less, thestress in the flange, including stiffeners, shall not exceedthe value determined by the formula

fb = 0.55F, 0.224F Y X

~6,650 %/k7 -

w

1 - sin?r

X t (10-84)2 3,580

10.39.4.4.5 For values of w/t exceeding (6,650N/7k)/V'F, but not exceeding 60, the stress in the flange,including stiffeners, shall not exceed the value given bythe formula


I

2fb =14.4k,

( W)— x 10 6 (10–85)

10.39.4.4.6 The maximum value of the buckling co-efficient, k,, shall be 4. When k l has its maximum value,the transverse stiffeners shall have a spacing, a, equal toor less than 4w. If the ratio alb exceeds 3, transverse stiff-eners are not necessary.

10.39.4.4.7 The transverse stiffeners need not beconnected to the flange plate but shall be connected to thewebs of the box and to each longitudinal stiffener. Theconnection to the web shall be designed to resist the ver-tical force determined by the formula

R =FySs

(10–86)2b

where S, = section modulus of the transverse stiffener.

10.39.4.4.8 The connection to each longitudinalstiffener shall be designed to resist the vertical force de-termined by the formula

R, =FyS,

(10–87)nb

10.39.4.4.9 Compression flanges stiffened longitudi-nally and transversely shall also satisfy the provisions ofArticle 10.39.4.1. The effective flange plate width shallbe used to calculate the flange bending stress. The fullflange plate width shall be used to calculate the allowablebending stress.

10.39.4.5 Compression Flange Stiffeners,General

10.39.4.5.1 The width to thickness ratio of any out-standing element of the flange stiffeners shall not exceedthe value determined by the formula

b' 2,600, _ (10–88)t

where

b ' = width of any outstanding stiffener elementt' = thickness of outstanding stiffener elementF

v= yield strength of outstanding stiffener ele-

ment.

10.39.4.5.2 Longitudinal stiffeners shall be extendedto locations where the maximum stress in the flange doesnot exceed that allowed for base metal adjacent to or con-nected by fillet welds.

10.39.5 Design of Flange to Web Welds

The total effective thickness of the web-flange weldsshall be not less than the thickness of the web, except,when two or more interior intermediate diaphragms perspan are provided, the minimum size fillet welds specifiedin Article 10.23.2.2 may be used. Regardless of the typeweld used, welds shall be deposited on both sides of theconnecting flange or web plate.

10.39.6 Diaphragms

10.39.6.1 Diaphragms, cross-frames, or other meansshall be provided within the box girders at each support toresist transverse rotation, displacement, and distortion.

10.39.6.2 Intermediate diaphragms or cross-framesare not required for steel box girder bridges designed inaccordance with this specification.

10.39.7 Lateral Bracing

Generally, no lateral bracing system is required be-tween box girders. A horizontal wind load of 50 poundsper square foot shall be applied to the area of the super-structure exposed in elevation. Half of the resulting forceshall be applied in the plane of the bottom flange. The sec-tion assumed to resist the horizontal load shall consist ofthe bottom flange acting as a web and 12 times the thick-ness of the webs acting as flanges. A lateral bracing sys-tem shall be provided if the combined stresses due to thespecified horizontal force and dead load of steel and deckexceed 150% of the allowable design stress.

10.39.8 Access and Drainage

Consistent with climate, location, and materials, con-sideration shall be given to the providing of manholes, orother openings, either in the deck slab or in the steel boxfor form removal, inspection, maintenance, drainage, etc.

10.40 HYBRID GIRDERS

10.40.1 General

10.40.1.1 This section pertains to the design ofgirders that utilize a lower strength steel in the web


100

0.50_ .7

Y = 1.00

OC = 0.72

Q 7;

701.0 1.5 2.0 2.5 3.0 3.5 4.0

10.40.1.2 The provisions of Division I, Design, shallgovern where applicable, except as specifically modifiedby Articles 10.40.1 through 10.40.4.


10.40.2.1 Bending

10.40.2.1.1 The bending stress in the web may ex-ceed the allowable stress for the web steel provided thatthe stress in each flange does not exceed the allowablestress from Articles 10.3 or 10.32 for the steel in thatflange multiplied by the reduction factor, R.

R=1—RW(1-(X)2(3—W+Wa)(10-89)

6+RW(3 — W)

RATIO OF WEB AREA TO TENSION FLANGE AREA,p

FIGURE 10.40.2.IA

)0

~5

90= 0.50

= 0.75BS

OC = 0.501° .00

80

75

7n1.0 1.5 2.0 2.5 3.0 3.5 4.0

RATIO OF WEB AREA TO TENSION FLANGE AREA, P

FIGURE 10.40.2.1B

than in one or both of the flanges. It applies to compositeand noncomposite plate girders, and composite boxgirders. At any cross section where the bending stress ineither flange exceeds 55% of the minimum specifiedyield strength of the web steel, the compression-flangearea shall not be less than the tension-flange area. Thetop-flange area shall include the transformed area of anyportion of the slab or reinforcing steel that is consideredto act compositely with the steel girder.

(See Figure 10.40.2. IA and 10.40.2.1B.)

where:

of = minimum specified yield strength of the web di-vided by the minimum specified yield strength ofthe tension flange;*

(3 = area of the web divided by the area of the tensionflange;*

LGr = distance from the outer edge of the tensionflange* to the neutral axis (of the transformedsection for composite girders) divided by thedepth of the steel section.

10.40.2.1.2 The bending stress in the concrete slab incomposite girders shall not exceed the allowable stress forthe concrete multiplied by R.

10.40.2.1.3 R shall be taken as 1.0 at sections wherethe bending stress in both flanges does not exceed the al-lowable stress for the web.

10.40.2.1.4 Longitudinal web stiffeners preferablyshall not be located in yielded portions of the web.

10.40.2.2 Shear

The design of the web for a hybrid girder shall be incompliance with Article 10.34.3 except that Equation(10-26) of Article 10.34.4.2 for the allowable averageshear stress in the web of transversely stiffened nonhybridgirders shall be replaced by the following equation for theallowable average shear stress in the web of transverselystiffened hybrid girders:

*Bottom flange of orthotropic deck bridges.


F,, = CFY / 3 <_ Fy / 3 (10-90)

where FY is equal to the specified minimum yield strengthof the web. The provisions of Article 10.34.4.4, and theequation for A in Article 10.34.4.7 are not applicable tohybrid girders.

10.40.2.3 Fatigue

Hybrid girders shall be designed for the allowablefatigue stress range given in Article 10.3 and Table 10.3. IA.

10.40.3 Plate Thickness Requirements

In calculating the maximum width-to-thickness ratioof the flange plate according to Article 10.34.2, fb shall betaken as the lesser of the calculated bending stress in thecompression flange divided by the reduction factor, R, or theallowable bending stress for the compression flange.

10.40.4 Bearing Stiffener Requirements

In designing bearing stiffeners at interior supports ofcontinuous hybrid girders for which a is less than 0.7, nopart of the web shall be assumed to act in bearing.

10.41 ORTHOTROPIC•DECKSUPERSTRUCTURES

10.41.1 General

10.41.1.1 This section pertains to the design of steelbridges that utilize a stiffened steel plate as a deck. Usu-ally the deck plate is stiffened by longitudinal ribs andtransverse beams; effective widths of deck plate act as thetop flanges of these ribs and beams. Usually the deck in-cluding longitudinal ribs, acts as the top flange of the mainbox or plate girders. As used in Articles 10.41.1 through10.41.4.10, the terms rib and beam refer to sections thatinclude an effective width of deck plate.

10.41.1.2 The provisions of Division I, Design, shallgovern where applicable, except as specifically modifiedby Articles 10.41.1 through 10.41.4. 10.

An appropriate method of elastic analysis, such as theequivalent-orthotropic-slab method or the equivalent-gridmethod, shall be used in designing the deck. The equiva-lent stiffness properties shall be selected to correctly sim-ulate the actual deck. An appropriate method of elasticanalysis, such as the thin-walled-beam method, that ac-counts for the effects of torsional distortions of the cross-sectional shape shall be used in designing the girders of or-thotropic-deck box-girder bridges. The box-girder designshall be checked for lane or truck loading arrangementsthat produce maximum distortional (torsional) effects.

10.41.1.3 For an alternate design method (StrengthDesign), see Article 10.60.

10.41.2 Wheel Load Contact Area

The wheel loads specified in Article 3.7 shall be uni-formly distributed to the deck plate over the rectangulararea defined below:

Width LengthWheel Load Perpendicular in Direction

(kip) to Traffic (inches) of Traffic (inches)

8 20+2t 8+2t12 20+2t 8+2t16 24+2t 8+2t

In the above table, t is the thickness of the wearing sur-face in inches.

10.41.3 Effective Width of Deck Plate

10.41.3.1 Ribs and Beams

The effective width of deck plate acting as the topflange of a longitudinal rib or a transverse beam may becalculated by accepted approximate methods.*

10.41.3.2 Girders

10.41.3.2.1 The full width of deck plate maybe con-sidered effective in acting as the top flange of the girdersif the effective span of the girders is not less than: (1) 5times the maximum distance between girder webs and (2)10 times the maximum distance from edge of the deck tothe nearest girder web. The effective span shall be takenas the actual span for simple spans and the distance be-tween points of contraflexure for continuous spans. Alter-natively, the effective width may be determined by ac-cepted analytical methods.

10.41.3.2.2 The effective width of the bottom flangeof a box girder shall be determined according to the pro-visions of Article 10.39.4.1.


10.41.4.1 Local Bending Stresses in Deck Plate

The term local bending stresses refers to the stressescaused in the deck plate as it carries a wheel load to theribs and beams. The local transverse bending stressescaused in the deck plate by the specified wheel load plus30% impact shall not exceed 30,000 psi unless a higher al-lowable stress is justified by a detailed fatigue analysis or

*"Design Manual for Orthotropic Steel Plate Deck Bridges," AISC,1963, or "Orthotropic Bridges, Theory and Design," by M.S. Troitsky,Lincoln Arc Welding Foundation, 1967.


by applicable fatigue-test results. For deck configurationsin which the spacing of transverse beams is at least 3 timesthe spacing of longitudinal-rib webs, the local longitudi-nal and transverse bending stresses in the deck plate neednot be combined with the other bending stresses coveredin Articles 10.41.4.2 and 10.41.4.3.

10.41.4.2 Bending Stresses in Longitudinal Ribs

The total bending stresses in longitudinal ribs due to acombination of (1) bending of the rib and (2) bending ofthe girders may exceed the allowable bending stresses inArticle 10.32 by 25%. The bending stress due to each ofthe two individual modes shall not exceed the allowablebending stresses in Article 10.32.

10.41.4.3 Bending Stresses in Transverse Beams

The bending stresses in transverse beams shall not ex-ceed the allowable bending stresses in Article 10.32.

10.41.4.4 Intersections of Ribs, Beams, andGirders

Connections between ribs and the webs of beams,holes in the webs of beams to permit passage of ribs,connections of beams to the webs of girders, and ribsplices may affect the fatigue life of the bridge when theyoccur in regions of tensile stress. Where applicable, thenumber of cycles of maximum stress and the allowable fa-tigue stresses given in Article 10.3 shall be applied in de-signing these details; elsewhere, a rational fatigue analy-sis shall be made in designing the details. Connectionsbetween webs of longitudinal ribs and the deck plate shallbe designed to sustain the transverse bending fatiguestresses caused in the webs by wheel loads.

10.41.4.5 Thickness of Plate Elements

10.41.4.5.1 Longitudinal Ribs and Deck Plate

Plate elements comprising longitudinal ribs, anddeck-plate elements between webs of these ribs, shallmeet the minimum thickness requirements of Article10.35.2. The quantity f, may be taken as 75% of the sumof the compressive stresses due to (1) bending of the riband (2) bending of the girder, but not less than the com-pressive stress due to either of these two individual bend-ing modes.

10.41.4.5.2 Girders and Transverse Beams

Plate elements of box girders, plate girders, and trans-verse beams shall meet the requirements of Articles10.34.2 to 10.34.6 and 10.39.4.

10.41.4.6 Maximum Slenderness ofLongitudinal Ribs

The slenderness, L1r, of a longitudinal rib shall not ex-ceed the value given by the following formula unless itcan be shown by a detailed analysis that overall bucklingof the deck will not occur as a result of compressive stressinduced by bending of the girders

L _ 1, 500 2, 700F

Cr max1,000

F– F2 (10-91)

Y Y

where

L = distance between transverse beams;r = radius of gyration about the horizontal centroidal

axis of the rib including an effective width ofdeck plate;

F = maximum compressive stress in psi in the deckplate as a result of the deck acting as the topflange of the girders; this stress shall be taken aspositive;

Fy = yield strength of rib material in psi.

10.41.4.7 Diaphragms

Diaphragms, cross frames, or other means shall beprovided at each support to transmit lateral forces tothe bearings and to resist transverse rotation, displace-ment, and distortion. Intermediate diaphragms orcross frames shall be provided at locations consistentwith the analysis of the girders. The stiffness and strengthof the intermediate and support diaphragms or crossframes shall be consistent with the analysis of thegirders.

10.41.4.8 Stiffness Requirements

10.41.4.8.1 Deflections

The deflections of ribs, beams, and girders due to liveload plus impact may exceed the limitations in Article10.6 but preferably shall not exceed 1/5oo of their span. Thecalculation of the deflections shall be consistent with theanalysis used to calculate the stresses.

To prevent excessive deterioration of the wearing sur-face, the deflection of the deck plate due to the specifiedwheel load plus 30% impact preferably shall be less than1/3oo of the distance between webs of ribs. The stiffeningeffect of the wearing surface shall not be included in cal-culating the deflection of the deck plate.

10.41.4.8.2 Vibrations

The vibrational characteristics of the bridge shall beconsidered in arriving at a proper design.


10.41.4.9 Wearing Surface

A suitable wearing surface shall be adequately bondedto the top of the deck plate to provide a smooth, nonskidriding surface and to protect the top of the plate againstcorrosion and abrasion. The wearing surface materialshall provide (1) sufficient ductility to accommodate,without cracking or debonding, expansion and contrac-tion imposed by the deck plate, (2) sufficient fatiguestrength to withstand flexural cracking due to deck-platedeflections, (3) sufficient durability to resist rutting, shov-ing, and wearing, (4) imperviousness to water and motor-

vehicle fuels and oils, and (5) resistance to deteriorationfrom deicing salts, oils, gasolines, diesel fuels, andkerosenes.

10.41.4.10 Closed Ribs

Closed ribs without access holes for inspection, clean-ing, and painting are permitted. Such ribs shall be sealedagainst the entrance of moisture by continuously welding(1) the rib webs to the deck plate, (2) splices in the ribs,and (3) diaphragms, or transverse beam webs, to the endsof the ribs.

Part DSTRENGTH DESIGN METHOD

LOAD FACTOR DESIGN

10.42 SCOPE

Load factor design is a method of proportioning struc-tural members for multiples of the design loads. To ensureserviceability and durability, consideration is given to thecontrol of permanent deformations under overloads, to thefatigue characteristics under service loadings, and to thecontrol of live load deflections under service loadings. SeePart C—Service Load Design Method—Allowable StressDesign for an alternate design procedure.

10.43 LOADS

10.43.1 Service live loads are vehicles which may oper-ate on a highway legally without special load permit.

10.43.2 For design purposes, the service loads aretaken as the dead, live, and impact loadings described inSection 3.

10.43.3 Overloads are the live loads that can be allowedon a structure on infrequent occasions without causingpermanent damage. For design purposes, the maximumoverload is taken as 5(L + I)/3.

10.43.4 The maximum loads are the loadings specifiedin Article 10.47.

10.44 DESIGN THEORY

10.44.1 The moments, shears, and other forces shall bedetermined by assuming elastic behavior of the structureexcept as modified in Article 10.48.1.3.

10.44.2 The members shall be proportioned by themethods specified in Articles 10.48 through 10.56 so that

their computed maximum strengths shall be at least equalto the total effects of design loads multiplied by their re-spective load factors specified in Article 3.22.

10.44.3 Service behavior shall be investigated as speci-fied in Articles 10.57 through 10.59.

10.45 ASSUMPTIONS

10.45.1 Strain in flexural members shall be assumed di-rectly proportional to the distance from the neutral axis.

10.45.2 Stress in steel below the yield strength, F Y,of the grade of steel used shall be taken as 29,000,000 psitimes the steel strain. For strain greater than thatcorresponding to the yield strength, F,,, the stress shallbe considered independent of strain and equal to the yieldstrength, F, This assumption shall apply also to the lon-gitudinal reinforcement in the concrete floor slab in theregion of negative moment when shear connectors areprovided to ensure composite action in this region.

10.45.3 At maximum strength the compressive stress inthe concrete slab of a composite beam shall be assumedindependent of strain and equal to 0.85f,.

10.45.4 Tensile strength of concrete shall be neglectedin flexural calculations, except as permitted under the pro-visions of Articles 10.57.2, 10.58.1, and 10.58.2.2.

10.46 DESIGN STRESS FOR STRUCTURALSTEEL

The design stress for structural steel shall be the spec-ified minimum yield point or yield strength, F5„ of the steelused as set forth in Article 10.2.


10.47 MAXIMUM DESIGN LOADS

The maximum moments, shears, or forces to be sus-tained by a stress-carrying member shall be computed forthe load combinations specified in Article 3.22. Each partof the structure shall be proportioned for the group loadsthat are applicable and the maximum design required bythe group loading combinations shall be used.

10.48 FLEXURAL MEMBERS

Flexural members are subject to the following require-ments in this article in addition to any applicable require-ments from Articles 10.49 through 10.61 that may super-sede these requirements. The compression-flange width,b, on fabricated I-shaped girders preferably shall not beless than 0.2 times the web depth, but in no case shall it beless than 0.15 times the web depth. If the area of the com-pression flange is less than the area of the tension flange,the minimum flange width may be based on two times thedepth of the web in compression rather than the webdepth. The compression-flange thickness, t, preferablyshall not be less than 1.5 times the web thickness. Thewidth-to-thickness ratio, b/t, of flanges subject to tensionshall not exceed 24.

10.48.1 Compact Sections

Sections of properly braced constant-depth flexuralmembers without longitudinal web stiffeners, withoutholes in the tension flange and with high resistance tolocal buckling qualify as compact sections.

Sections of rolled or fabricated flexural membersmeeting the requirements of Article 10.48.1.1 below shallbe considered compact sections and the maximumstrength shall be computed as

M~ = FYZ (10-92)

where F Y is the specified yield point of the steel beingused, and Z is the plastic section modulus.*

10.48.1.1 Compact sections shall meet the followingrequirements: (For certain frequently used steels these re-quirements are listed in Table 10.48.1.2A.)

(a) Compression flange

b < 4,110(10-93)

t

*Values for rolled sections are listed in the Manual of Steel Construc-tion, Ninth Edition, 1989, American Institute of Steel Construction. Ap-pendix D shows the method of computing Z as presented in the Com-mentary of AISI Bulletin 15.

where b is the flange width and t is the flange thickness.

(b) Web thickness

D < 19,230(10-94)

t W

where D is the clear distance between the flanges andI, is the web thickness.

When both b/t and D/t, exceed 75% of the above lim-its, the following interaction equation shall apply

D +4.68 Cb~33,650 (10-95)

w Fyf

where Fyf is the yield strength of the compression flange.

(c) Spacing of lateral bracing for compression flange

L b < [3.6–2.2(M I /M„)] x 106(10-96)

ry Fy

where L b is the distance between points of bracing of thecompression flange, Ty is the radius of gyration of thesteel section with respect to the Y-Y axis, M, is thesmaller moment at the end of the unbraced length of themember, and M„ is the ultimate moment from Equation(10-92) at the other end of the unbraced length: (M,/M„)is positive when moments cause single curvature be-tween brace points. (M,/M„) is negative when momentscause reverse curvature between brace points.

The required lateral bracing shall be provided bybraces capable of preventing lateral displacement andtwisting of the main members or by embedment of thetop and sides of the compression flange in concrete.

(d) Maximum axial compression

P < 0.15 FYA (10-97)

where A is the area of the cross section. Members withaxial loads in excess of 0.15F Y A should be designed asbeam-columns as specified in Article 10.54.2.

10.48.1.2 Article 10.48.1 is applicable to steels witha demonstrated ability to reach MP . Steels such asAASHTO M 270 Grades 36, 50, and 50W (ASTM A 709Grades 36, 50, and 50W), and AASHTO M 270 GradeHPS70W (ASTM A 709 Grade HPS70W) meet these re-quirements. The limitations set forth in Article 10.48.1 aregiven in Table 10.48.1.2A.

10.48.1.3 In the design of a continuous beam withcompact negative-moment support sections of AASHTO


TABLE 10.48.1.2A Limitations for Compact Sections

Fy (psi) 36,000 50,000 70,000

b/t 21.7 18.4 15.5

D/t, 101 86 72

Lb ry (MI/M„ = 0*) 100 72 51

Lb/ry (MI/M„ = 1*) 39 28 20* For values of MfM, other than 0 and 1, use Equation (10-96).

M 270 Grades 36, 50 and 50W (ASTM A 709 Grades 36,50, and 50W) steel complying with the provision of Arti-cle 10.48.1.1, negative moments over such supports atOverload and Maximum Load determined by elasticanalysis may be reduced by a maximum of 10%. Such re-ductions shall be accompanied by an increase in momentsthroughout adjacent spans statically equivalent and oppo-site in sign to the decrease of negative moments at the ad-jacent supports. For example, the increase in moment at thecenter of the span shall equal the average decrease of themoments at the two adjacent supports. The reduction shallnot apply to the negative moment of a cantilever.

This 10% redistribution of moment shall not apply tocompact sections of AASHTO M 270 Grade HPS70W orGrade 70W (ASTM A 709 Grade HPS70W or Grade70W) steel.

10.48.2 Braced Noncompact Sections

For sections of rolled or fabricated flexural membersnot meeting the requirements of Article 10.48.1.1 butmeeting the requirements of Article 10.48.2.1 below, themaximum strength shall be computed as the lesser of

MU = FFS. (10-98)

or

M. = FS.~R b (10-99)

subject to the requirement of Article 10.48.2.1(c) where

lz

F~, 4,400b I Fy

b =compression flange widtht = compression flange thicknessS Xt = section modulus with respect to tension flange

(in.)SX,= section modulus with respect to compression

flange (in.)

Rb = flange-stress reduction factor determined from theprovisions of Article 10.48.4.1, with fb substitutedfor the term M,/S., when Equation (10-103b)applies

fb = factored bending stress in the compressionflange, but not to exceed Fy

10.48.2.1 The above equations are applicable tosections meeting the following requirements:

(a) Compression flange

b < 24 (10-100)t

(b) Web thickness

The web thickness shall meet the requirement given byEquation (10-104) or Equation (10-109), as applicable,subject to the corresponding requirements of Article10.49.2 or 10.49.3. For unstiffened webs, the webthickness shall not be less than D/150.

(c) Spacing of lateral bracing for compression flange

Lb20, 000, OOOAe

(10-101)~ FY

d

where d is the depth of beam or girder, and A f is theflange area. If Equation (10-101) is not satisfied, M„calculated from Equation (10-99) shall not exceed M,calculated from the provisions of Article 10.48.4.1.

(d) Maximum axial compression

P < 0.15 FY A. (10-102)

Members with axial loads in excess of 0.15 F Y A shouldbe designed as beam-columns as specified in Article10.54.2.

10.48.2.2 The limitations set forth in Article10.48.2.1 above are given in Table 10.48.2. IA.

10.48.3 Transitions

The maximum strength of sections with geometricproperties falling between the limits of Articles 10.48.1

TABLE 10.48.2.IA Limitations for Braced NoncompactSections

F,(psi) 36,000 50,000 70,000 90,000 100,000

b/t * 23.2 19.7 16.6 14.7 13.9Lb dA f 556 400 286 222 200

D/t„. Refer to Articles 10.48.5.1, 10.48.6.1, 10.49.2,

or 10.49.3, as applicable. For unstiffened webs, the

limit is 150.

* Limits shown are for Fcr = Fy. Refer also to Articles 10.48.2 and10.48.2.1(a).


and 10.48.2 may be computed by straight-line interpola-tion, except that the web thickness must always satisfy Ar-ticle 10.48.1.1(b).

10.48.4 Partially Braced Members

Members not meeting the lateral bracing requirementof Article 10.48.2.1(c) shall be braced at discrete locationsspaced at a distance, Lb, such that the maximum strengthof the section under consideration satisfies the require-ments of Article 10.48.4.1. Bracing shall be provided suchthat lateral deflection of the compression flange is restrainedand the entire section is restrained against twisting.

10.48.4.1 If the lateral bracing requirement of Arti-cle 10.48.2.1(c) is not satisfied and the ratio of the mo-ment of inertia of the compression flange to the momentof inertia of the member about the vertical axis of the web,Iy,/I y , is within the limits of 0.1 < I,,/I, <_ 0.9, the maxi-mum strength for the limit state of lateral-torsional buck-ling shall be computed as

M. = M~Rb (10-103a)

Rb = 1 for longitudinally stiffened girders if the webslenderness satisfies the following requirement:

D <_ 5,460~__k

tw

fb

where1z

for Dc )))>–0.4 k=5.17(D

z

>–9(Dd, D

C

A,, = area of compression flange On.');M, = lateral torsional buckling moment, or yield

moment, defined below (lb-in.);S. = section modulus with respect to compression

flange (in.' ). Use S,,c for live load for a com-posite section;

A = 15,400 for all sections where D, is less thanor equal to D/2;

= 12,500 for sections where D, is greater thanD/2.

The moment capacity, Mr , cannot exceed the yield mo-ment, M y . In addition M r

cannot exceed the lateral tor-sional buckling moment given below:

For sections with D° <– or with longitudinally

stiffened webs w y

l l z

Mr

= 91 x 106Cb(Ly

I 0 .87 aI <M y

Lb / Lb /

(10-1 03c)

For sections with < (D c )

r W

for L b 5 L P

for ds < 0.4 k =11.641D

z

D C D c – d s

ds = the distance from the centerline of a platelongitudinal stiffener or the gage line of anangle longitudinal stiffener to the inner surfaceor the leg of the compression flange component.

fb = factored bending stress in the compressionflange

forWhen both edges of the web are in compression,

k shall be taken equal to 7.2.

Otherwise, for girders with or without longitudinal stiff-eners, Rb shall be calculated as

AR b = 1 – 0.002

` ~W

` – 1.0t,

~SX~

(10-103b)

D, = depth of the web in compression (in.). Forcomposite beams and girders, D, shall becalculated in accordance with the provisionsspecified in Article 10.50(b).

t,, = thickness of web (in.);

M r =MY

(10 -103d)

Lr>Lb>Lp

( 11

M r =C t Fy S,« ~1–0.5 ILb –LP

I

J

(10-103e)L r –L

P J

(572 x lO6IY0)1/2d

L~ =I (10-103f)Fy S

Xc

L b > Lrz

M( =CbF

y~xo CLr J (10-103g)l b)

Lb = unbraced length of the compression flange,in.

LP = 9,500r'/VF—,, in.r ' = radius of gyration of compression flange

about the vertical axis in the plane of theweb, in.

Iyc= moment of inertia of compression flange

about the vertical axis in the plane of theweb, in.°

d = depth of girder, in.

for


J =[(bt3 ), + (be), + DtN,3 ]

where b and t repre-

sent the flange width and thickness of thecompression and tension flange, respectively,m.

Cb = 1.75 + 1.05 (M,/M 2 ) + 0.3(M,/M 2 ) 2 < 2.3where M, is the smaller and M2 the largerend moment in the unbraced segment of thebeam; M,/M2 is positive when the momentscause reverse curvature and negative whenbent in single curvature.

Cb = 1.0 for unbraced cantilevers and for mem-bers where the moment within a significantportion of the unbraced segment is greaterthan or equal to the larger of the segment endmoments.*

The compression flange shall satisfy the requirement of Ar-ticle 10.48.2.1(a). The web thickness shall meet therequirement given by Equation (10-104) or Equation(10-109), as applicable, subject to the correspondingrequirements of Article 10.49.2 or 10.49.3. For unstiffenedwebs, the web thickness shall not be less than D/150.

10.48.4.2 Members with axial loads in excess of0.15FYA should be designed as beam-columns as specifiedin Article 10.54.2.

10.48.5 Transversely Stiffened Girders

10.48.5.1 For girders not meeting the shear require-ments of Article 10.48.8.1 (Equation 10-113) transversestiffeners are required for the web. For girders with trans-verse stiffeners but without longitudinal stiffeners thethickness of the web shall meet the requirement:

D < 36,500tw ~ (10-104)

subject to the web thickness requirement of Article10.49.2. For different grades of steel this limit is

D/tw F,(psi)

192 36,000163 50,000138 70,000122 90,000115 100,000

* For the use of larger Cb values, see Structural Stability ResearchCouncil Guide to Stability Design Criteria forMetal Structures, 4th Ed.,pg. 135.

If the web slenderness D/t,,, exceeds the upper limit, eitherthe section shall be modified to comply with the limit, or alongitudinal stiffener shall be provided.

10.48.5.2 The maximum bending strength of trans-versely stiffened girders meeting the requirements of Ar-ticle 10.48.5.1 shall be computed by Articles 10.48.1,10.48.2, 10.48.4.1, 10.50, 10.51, or 10.53, as applicable,subject to the requirements of Article 10.48.8.2.

10.48.5.3 The shear capacity of transversely stiff-ened girders shall be computed by Article 10.48.8. Thewidth-to-thickness ratio of transverse stiffeners shall besuch that

b' <— 16 (10-105)t

where b ' is the projecting width of the stiffener.The gross cross-sectional area of intermediate trans-

verse stiffeners shall not be less than

A = C0.15BD

(1— C) —I -18 I FY

°eb

tK (10 -106a)tw

(

V V. J J Fcr

where F,, =9,025,000

< F (10 -106b)crb,

2 ystiffener

Ct)

where Fy stiffener is the yield strength of the stiffener;B = 1.0 for stiffener pairs, 1.8 for single angles, and 2.4for single plates; and C is computed by Article 10.48.8.1.When values computed by Equation (10-106a) approachzero or are negative, then transverse stiffeners need onlymeet the requirements of Equations (10-105) and (10-107),and Article 10.34.4.10.

The moment of inertia of transverse stiffeners withreference to the plane defined below shall be not lessthan

I = djw3 J (10-107)

where

J = 2.5(D/dn)2 — 2, but not less than 0.5 (10-108)

do = distance between transverse stiffeners

When stiffeners are in pairs, the moment of inertiashall be taken about the center line of the web plate. Whensingle stiffeners are used, the moment of inertia shall betaken about the face in contact with the web plate.

Transverse stiffeners need not be in bearing with thetension flange. The distance between the end of the stiff-ener weld and the near edge of the web-to-flange filletweld shall not be less than 4tw or more than 6ta,. Stiffeners


provided on only one side of the web must be in bearingagainst, but need not be attached to, the compressionflange for the stiffener to be effective. However, trans-verse stiffeners which connect diaphragms or crossframesto the beam or girder shall be rigidly connected to both thetop and bottom flanges.

10.48.6 Longitudinally Stiffened Girders

10.48.6.1 Longitudinal stiffeners shall be required onsymmetrical girders when the web thickness is less thanthat specified by Article 10.48.5.1 and shall be placed at adistance D/5 from the inner surface of the compressionflange.

The web thickness of plate girders with transversestiffeners and one longitudinal stiffener shall meet therequirement:

D < 73,000(10-109)

t W Fy

For different grades of steel, this limit is

D/t,,, F y(psi)

385 36,000326 50,000276 70,000243 90,000231 100,000

Singly symmetric girders are subject to the requirementsof Article 10.49.3.

10.48.6.2 The maximum bending strength of longi-tudinally stiffened girders meeting the requirements ofArticle 10.48.6.1 shall be computed by Articles 10.48.2,10.48.4.1, 10.50.1.2, 10.50.2.2, 10.51, or 10.53, as ap-plicable, subject to the requirements of Article 10.48.8.2.

10.48.6.3 The shear capacity of girders with onelongitudinal stiffener shall be computed by Article10.48.8.

The dimensions of the longitudinal stiffener shall besuch that

(a) the thickness of the longitudinal stiffener is notless than that given by Article 10.34.5.2, and the fac-tored bending stress in the longitudinal stiffener is notgreater than the yield strength of the longitudinalstiffener.(b) the rigidity of the stiffener is not less than:

2

I_Dt 3 2.4~ d—D°~ -0.13 (10-110)

where:

I = moment of inertia of the longitudinal stiffenerabout its edge in contact with the web plate, in

'.

(c) the radius of gyration of the stiffener is not lessthan.

r >d 0 F

23,000(10-111)

In computing the r value above, a centrally located webstrip not more than 18t,, in width shall be considered as apart of the longitudinal stiffener. Transverse stiffeners forgirder panels with longitudinal stiffeners shall be designedaccording to Article 10.48.5.3. In addition, the section mod-ulus of the transverse stiffener shall be not less than

s, = 3 (DId o)S, (10-112)

where D is the total panel depth (clear distance betweenflange components) and S t is the section modulus of thelongitudinal stiffener.


Bearing stiffeners shall be designed for beams andgirders as specified in Articles 10.33.2 and 10.34.6.

10.48.8 Shear

10.48.8.1 The shear capacity of webs of rolled orfabricated flexural members shall be computed as follows:

For unstiffened webs, the shear capacity shall be lim-ited to the plastic or buckling shear force as follows:

VU = CVp (10-113)

For stiffened web panels complying with the provisionsof Article 10.48.8.3, the shear capacity shall be determinedby including post-buckling resistance due to tension-fieldaction as follows:

V. = VP C+0.87(1-C)

(10-114)1+ (do /D) 2

VP

is equal to the plastic shear force and is determinedas follows:

V P = 0.58Fy Dtw (10-115)

The constant C is equal to the buckling shear stressdivided by the shear yield stress, and is determined asfollows:


for D <6, 000

tw

Fy

C=1.0

for6, 000 -~_k < D < 7, 500

t, Fy

C– 6,000(10-116)

C '

D ) ~—Fy

forD > 7,500,Fk

tw

J—Y

C=4.5x z0'k

(10-117)D

Ct

w )2

FY

where the buckling coefficient, k = 5 + [5 - (do/D) 2 ],except k shall be taken as 5 for unstiffened beams andgirders.

D = clear, unsupported distance between flangecomponents;

do = distance between transverse stiffeners;Fy = yield strength of the web plate.

10.48.8.2 If a girder panel is controlled by Equation(10-114) and is subjected to the simultaneous action ofshear and bending moment with the magnitude of the mo-ment greater than 0.75M., the shear shall be limited to notmore than

V/Vu = 2.2 — (1.6M/K) (10-118)

If girder panel of a composite noncompact section iscontrolled by Equation (10-114) and is subjected to the si-multaneous action of shear and bending moment with themagnitude of the factored bending stress f, greater than0.75 Fo , the shear shall instead be limited to not more than:

V/V„ =2.2—(1.6fs/Fu ) (10—118a)

where f, = factored bending stress in either the top orbottom flange, whichever flange has thelarger ratio of (f,/F„)

F,, = maximum bending strength of either the topor bottom flange, whichever flange has thelarger ratio of (f,/F„)

10.48.8.3 Where transverse intermediate stiffenersare required, transverse stiffeners shall be spaced at a dis-tance, d o , according to shear capacity as specified in Arti-cle 10.48.8.1, but not more than 3D. Transverse stiffenersmay be omitted in those portions of the girders where themaximum shear force is less than the value given by Ar-

ticle 10.48.8.1, Equation (10-113), subject to the handlingrequirement below.

Transverse stiffeners shall be required if D/t µ, is greaterthan 150. The spacing of these stiffeners shall not exceedthe handling requirement D[260/(D/t w)] 2 .

For longitudinally stiffened girders, transverse stiffen-ers shall be spaced a distance, do , according to shear ca-pacity as specified in Article 10.48.8.1, but not more than1.5 times the web depth. The handling requirement givenabove shall not apply to longitudinally stiffened girders.The total web depth D shall be used in determining theshear capacity of longitudinally stiffened girders in Arti-cle 10.48.8.1 and in Equation (10-119).

The first stiffener space at the simple support end of atransversely or longitudinally stiffened girder shall be suchthat the shear force in the end panel will not exceed the plas-tic or buckling shear force given by the following equation

Vo = CVp (10-119)

For transversely stiffened girders, the maximum spacingof the first transverse stiffener is limited to 1.5D. For lon-gitudinally stiffened girders, the maximum spacing of thefirst transverse stiffener is also limited to 1.51).

10.49 SINGLY SYMMETRIC SECTIONS

10.49.1 General

For sections symmetric about the vertical axis but un-symmetric with respect to the horizontal centroidal axis,the provisions of Articles 10.48.1 through 10.48.4 shall beapplicable.

10.49.2 Singly Symmetric Sections with TransverseStiffeners

Girders with transverse stiffeners shall be designed andevaluated by the provisions of Article 10.48.5 except thatwhen D,, the clear distance between the neutral axis andthe compression flange, exceeds D/2 the web thickness,tW , shall meet the requirement

D c 18,250(10-120)

t W

If the web slenderness D,/tw exceeds the upper limit,either the section shall be modified to comply with thelimit, or a longitudinal stiffener shall be provided.

10.49.3 Longitudinally Stiffened Singly SymmetricSections

10.49.3.1 Longitudinal stiffeners shall be required onsingly symmetric sections when the web thickness is lessthan that specified by Article 10.49.2.


10.49.3.2 For girders with one longitudinal stiffenerand transverse stiffeners, the provisions of Article 10.48.6for symmetrical sections shall be applicable in addition tothe following:

(a) The optimum distance, ds , of a plate longitudinalstiffener or the gage line of an angle longitudinal stiff-ener from the inner surface or the leg of the compres-sion flange component is D/5 for a symmetrical girder.The optimum distance, d s, for a singly symmetric com-posite girder in positive-moment regions may be de-termined from the equation given below

d 5 _ 1 (10-121)D0S 1+1.5

fDL+LL

fDL

where D, s is the depth of the web in compression of thenoncomposite steel beam or girder, fDL is the non-composite dead-load stress in the compression flange,and fDL+LL is the total noncomposite and compositedead-load plus the composite live-load stress in thecompression flange at the most highly stressed sectionof the web. The optimum distance, d s, of the stiffenerin negative-moment regions of composite sections is2D,/5, where D, is the depth of the web in compressionof the composite section at the most highly stressedsection of the web.(b) When Dc exceeds D/2, the web thickness, t„„ shallmeet the requirement

D c 36,500(10-122)

tµ, f l y

10.49.4 Singly Symmetric Braced NoncompactSections

Singly symmetric braced, noncompact sections ofrolled or fabricated flexural members shall be designedand evaluated by the provisions of Article 10.48.2.

10.49.5 Partially Braced Members with SinglySymmetric Sections

The maximum strength of singly symmetric sectionsmeeting all requirements of Article 10.48.2.1, exceptfor the lateral bracing requirement given by Equation(10-101), shall be computed as the lesser of M. calculatedfrom Equation (10-98) or M. calculated from Equation(10-99), with M. calculated from Equation (10-99) not toexceed M„ calculated from the provisions of Article10.48.4.1.

10.50 COMPOSITE SECTIONS

Composite sections shall be so proportioned that thefollowing criteria are satisfied.

(a) The maximum strength of any section shall not beless than the sum of the computed moments at that sec-tion multiplied by the appropriate load factors.(b) The web of the steel section shall be designed tocarry the total external shear and must satisfy the ap-plicable provisions of Articles 10.48 and 10.49. Thevalue of D, shall be taken as the clear distance betweenthe :neutral axis and the compression flange. In posi-tive-moment regions, the value of D, shall be calcu-lated by summing the stresses due to the appropriateloadings acting on the respective cross sections sup-porting the loading. The depth of web in compression,D,, in composite sections subjected to negative bend-ing may be taken as the depth of the web in com-pression of the composite section without summing thestresses from the various stages of loading. The webdepth in compression, D,p , of sections meeting theweb compactness and ductility requirements of Article10.50.1.1.2 under the maximum design loads shall becalculated from the fully plastic cross section ignoringthe sequence of load application. Girders with a webslenderness exceeding the limits of Article 10.48.5.1 or10.49.2 shall either be modified to comply with theselimits or else shall be stiffened by one longitudinalstiffener.(c) The moment capacity at first yield shall be com-puted considering the application of the dead and liveloads to the steel and composite sections.(d) The steel beam or girder shall satisfy the con-structibility requirements of Article 10.61.

b -FY t fl ngea~C

is T'T

--~ C'

ttf D Fy Yd y web

Fy bottomF

Yflange

Cross-Section Stress distribution

PLASTIC STRESS DISTRIBUTION

FIGURE 10.50A


10.50.1 Positive Moment Sections

10.50.1.1 Compact Sections

The maximum strength, M,,, of compact composite sec-tions in positive-moment regions shall be computed in ac-cordance with Article 10.50.1.1.2. The steel shall have thedemonstrated ability to reach M P . Steels such as AASHTOM 270 Grades 36, 50, and 50W (ASTM A 709 Grades 36,50, and 50W), and AASHTO M 270 Grade HPS70W(ASTM A 709 Grade HPS70W) meet these requirements.

10.50.1.1.1 The resultant moment of the fully plasticstress distribution may be computed as follows:

(a) The compressive force in the slab, C, is equal to thesmallest of the values given by the following Equations:

C = 0.85f,' bts + (AF y ) (10-123)

where b is the effective width of slab, specified in Ar-ticle 10.38.3, is is the slab thickness, and (AFy), is theproduct of the area and yield point of that part of rein-forcement which lies in the compression zone of theslab.

C = (AFy)bf + (AFy) + (AF~,) w (10-124)

where (AFy)bf is the product of area and yield pointfor bottom flange of steel section (including coverplate if any), (AFy)tf is the product of area and yieldpoint for top flange of steel section, and (AF y), isthe product of area and yield point for web of steel sec-tion.(b) The depth of the stress block is computed from thecompressive force in the slab.

C– (AFy ),a (10-125)

0.85fc'b

(c) When the compressive force in the slab is less thanthe value given by Equation (10-124), the top portion ofthe steel section will be subjected to the compressiveforce C ' (Figure 10.50A) given by the following equa-tion:

C _ F(AFy)–C(10-126)

2

(d) The location of the neutral axis within the steelsection measured from the top of the steel section maybe determined as follows:

for C ' < (AFy ),f

Cy =

't tf (10-127)

(AFy )tf

for C ' >– (AFy ),f

–t +C –(AFy)cf

D (10-128)Y – t tf ( AFy)W

(e) The maximum strength of the section in bending isthe first moment of all forces about the neutral axis, tak-ing all forces and moment arms as positive quantities.

10.50.1.1.2 Composite sections of constant-depthmembers in positive-moment regions without longitudi-nal web stiffeners and without holes in the tension flangeshall qualify as compact when the web of the steel sectionsatisfies the following requirement:

2D cP < 19,230(10-129)

_Fyt W

whereD,P

is the depth of the web in compression at theplastic moment calculated in accordance with Article10.50.1.1.1, and tw is the web thickness. Equation (10-129)is satisfied if the neutral axis at the plastic moment islocated above the web; otherwise D,P shall be computedas y from Equation (10-128) minus ttf. Also, the distancefrom the top of the slab to the neutral axis at the plasticmoment, D P, shall satisfy

D'DP <5 (10-129a)

where

D'_R(d+t s +tb)

7.5R = 0.9 for Fy = 36,000 psi;

= 0.7 for Fy = 50,000 and 70,000 psi;d = depth of the steel beam or girder;is = thickness of the slab;th = thickness of the concrete haunch above the beam

or girder top flange.

Equation (10-129a) need not be checked for sectionswhere the maximum flange stress does not exceed thespecified minimum flange yield stress.

The maximum bending strength, M,,, of compact com-posite sections in simple spans or in the positive-momentregions of continuous spans with compact noncompositeor composite negative-moment pier sections shall betaken as


for D. <_ D'

M u = MP

(10-129b)

for D' < DP <_ 5D'

5MP

0.85M 0.85M — M DM=

p

4 y+4

pDp) (10 -129c)

where

Mp = plastic moment capacity of the composite posi-tive moment section calculated in accordancewith Article 10.50.1.1.1;

My = moment capacity at first yield of the compositepositive moment section calculated as F Y timesthe section modulus with respect to the tensionflange. The modular ratio, n, shall be used tocompute the transformed section properties.

In continuous spans with compact composite positive-moment sections, but with noncompact noncomposite orcomposite negative-moment pier sections, the maximumbending strength, Mu , of the composite positive-momentsections shall be taken as either the moment capacity atfirst yield determined as specified in Article 10.50(c), or as

Mu = MY + A(Mu — M,), je, (10-129d)

where

= the moment capacity at first yield ofthe compact positive moment sectioncalculated in accordance with Article10.50(c);

— Ms ) P, er = moment capacity of the noncompactsection at the pier, Mu , given by Arti-cle 10.48.2 or Article 10.48.4, minusthe elastic moment at the pier, M S , forthe loading producing maximum pos-itive bending in the span. Use thesmaller value of the difference for thetwo-pier sections for interior spans;

= 1 for interior spans;= distance from end support to the loca-

tion of maximum positive moment di-vided by the span length for end spans.

M. computed from Equation (10-129d) shall not exceedthe applicable value of M u computed from either Equation(10-129b) or Equation (10-129c).

For continuous spans where the maximum bendingstrength of the positive-moment sections is determinedfrom Equation (10-129d), the maximum positive moment

in the span shall not exceed My, for the loading which pro-duces the maximum negative moment at the adjacentpier(s).

For composite sections in positive-moment regions notsatisfying the requirements of Equation (10-129) or Equa-tion (10-129a), or of variable-depth members or with lon-gitudinal web stiffeners, or with holes in the tensionflange, the maximum bending strength shall be deter-mined as specified in Article 10.50.1.2.

10.50.1.2 Noncompact Sections

10.50.1.2.1 When the steel section does not satisfythe compactness requirements of Article 10.50.1.1.2, thesum of the bending stresses due to the appropriate load-ings acting on the respective cross sections supporting theloadings shall not exceed the maximum strength, F u, ofthe tension flange taken equal to FY or the maximumstrength, Fu , of the compression flange taken equal toFyRb , where R b is the flange-stress reduction factor deter-mined from the provisions of Article 10.48.4.1. When Rb

is determined from Equation (10-103b), fb shall be substi-tuted for the term Mr/S Xe and

Afcshall be taken as the ef-

fective combined transformed area of the top flange andconcrete deck that yields D e calculated in accordance withArticle 10.50(b). fb is equal to the factored bending stressin the compression flange, but not to exceed F y . The re-sulting Rb factor shall be distributed to the top flange andconcrete deck in proportion to their relative stiffness. Theprovisions of Article 10.48.2.1(b) shall apply.

10.50.1.2.2 When the girders are not provided withtemporary supports during the placing of dead loads, thesum of the stresses produced by 1.30D, acting on the steelgirder alone with 1.30(D e + 5(L + I)/3) acting on thecomposite girder shall not exceed yield stress at any point,where D S and De are the moments caused by the dead loadacting on the steel girder and composite girder, respec-tively.

10.501.2.3 When the girders are provided with ef-fective intermediate supports that are kept in place untilthe concrete has attained 75% of its required 28-daystrength, stresses produced by the loading, 1.30(D + 5(L+ I)/3), acting on the composite girder, shall not exceedyield stress at any point.

10.50.2 Negative Moment Sections

The maximum bending strength of composite sectionsin negative moment regions shall be computed in accor-dance with Article 10.50.2.1 or 10.50.2.2, as applicable.

M y

(M

u

A


It shall be assumed that the concrete slab does not carrytensile stresses. In cases where the slab reinforcement iscontinuous over interior supports, the reinforcement maybe considered to act compositely with the steel section.


Composite sections of constant-depth members in nega-tive bending without longitudinal web stiffeners and with-out holes in the tension flange qualify as compact when theirsteel section meets the requirements of Article 10.48.1.1,and has the demonstrated ability to reach M, Steels such asAASHTO M 270 Grades 36, 50, and 50W (ASTM A 709Grades 36, 50, and 50W), and AASHTO M 270 GradeHPS70W (ASTM A 709 Grade HPS70W) meet these re-quirements. M. shall be computed as the resultant momentof the fully plastic stress distribution acting on the sectionincluding any composite rebars.

If the distance from the neutral axis to the compressionflange exceeds D/2, the compact section requirementsgiven by Equations (10-94) and (10-95) must be modifiedby replacing D with the quantity 2D,p , where D, p is thedepth of the web in compression at the plastic moment.

10.50.2.2 Noncompact Sections

When the steel section does not satisfy the compactnessrequirements of Article 10.50.2.1 but does satisfy all the re-quirements of Article 10.48.2.1, the sum of the bendingstresses due to the appropriate loadings acting on the re-spective cross sections supporting the loadings shall not ex-ceed the maximum strength, F,,, of the tension flange takenequal to F y or the maximum strength, FU , of the compres-sion flange taken equal to F,,Rb, where Fir is the criticalcompression flange stress specified in Article 10.48.2 andRb is the flange-stress reduction factor determined from theprovisions of Article 10.48.4.1. When Rb is determinedfrom Equation (10-103b), fb shall be substituted for the termM,IS Xc. fb is equal to the factored bending stress in the com-pression flange, but not to exceed F y . When all requirementsof Article 10.48.2.1 are satisfied, except for the lateral brac-ing requirement given by Equation (10-101), F,, of thecompression flange shall be taken equal to F,rRb, but not toexceed M„/S X ,, where M. and S., are determined accordingto the provisions of Article 10.48.4.1. In determining thefactor C b in Article 10.48.4.1, the smaller and larger valuesof fb at each end of the unbraced segment of the girder shallbe substituted for the smaller and larger end moments, M l

and Mz, respectively.

10.50.2.3

The minimum longitudinal reinforcement includingthe longitudinal distribution reinforcement must equal orexceed 1 % of the cross-sectional area of the concrete slab

whenever the longitudinal tensile stress in the concreteslab due to either the factored construction loads or theoverload specified in Article 10.57 exceeds 0.9f I, where f,is the modulus of rupture specified in Article 8.15.2.1.1.The area of the concrete slab shall be taken equal to thestructural thickness times the entire width of the bridgedeck. The required reinforcement shall be No. 6 bars orsmaller spaced at not more than 12 inches. Two-thirds ofthis required reinforcement is to be placed in the top layerof slab. Placement of distribution steel as specified in Ar-ticle 3.24. 10 is waived.

10.50.2.4

When shear connectors are omitted from the negativemoment region, the longitudinal reinforcement shall beextended into the positive moment region beyond the an-chorage connectors at least 40 times the reinforcement di-ameter.

10.51 COMPOSITE BOX GIRDERS*

This section pertains to the design of simple and con-tinuous bridges of moderate length supported by two ormore single-cell composite box girders. The distance cen-ter-to-center flanges of adjacent boxes shall be not greaterthan 1.2 times and not less than 0.8 times the distance cen-ter-to-center of the flanges of each box. In addition to theabove, when nonparallel girders are used the distance cen-ter-to-center of adjacent flanges at supports shall be notgreater than 1.35 times and not less than 0.65 times thedistance center-to-center of the flanges of each box. Thecantilever overhang of the deck slab, including curbs andparapet, shall be limited to 60% of the distance betweenthe centers of adjacent top steel flanges of adjacent boxgirders, but in no case greater than 6 feet.

10.51.1 Maximum Strength

The maximum strength of box girders shall be deter-mined according to the applicable provisions of Articles10.48, 10.49, and 10.50. In addition, the maximumstrength of the negative moment sections shall be limitedby

M~ = F,,S (10-130)

where F, is the buckling stress of the bottom flange plateas given in Article 10.51.5.

*For information regarding the design of long-span steel box girderbridges, Report No. FHWA-TS-80-205, "Proposed Design Specifica-tions for Steel Box Girder Bridges " is available from the Federal High-way Administration.


10.51.2 Lateral Distribution

The live-load bending moment for each box girdershall be determined in accordance with Article 10.39.2.

13,300- b F,c= t (10-135)

7,160

10.51.5.3 For values of10.51.3 Web Plates

The design shear Vµ, for a web shall be calculated usingthe following equation

V W = V/cos 0 (10-131)

where V = one-half of the total vertical shear force on onebox girder, and 0 = the angle of inclination of the webplate to the vertical.

The inclination of the web plates to the vertical shallnot exceed 1 to 4.

10.51.4 Tension Flanges

In the case of simply supported spans, the bottomflange shall be considered fully effective in resisting bend-ing if its width does not exceed one-fifth the span length.If the flange plate width exceeds one-fifth of the span,only an amount equal to one-fifth of the span shall be con-sidered effective.

For continuous spans, the requirements above shall beapplied to the distance between points of contraflexure.

10.51.5 Compression Flanges

10.51.5.1 Unstiffened compression flanges designedfor the yield stress, FY , shall have a width-to-thickness ratioequal to or less than the value obtained from the formula

b 6,140t = ~- (10-132)

where b = flange width between webs in inches, and t =flange thickness in inches.

10.51.5.2 For greater b/t ratios,

6,140 < b < 13,300(10-133)F t F lY

the buckling stress of an unstiffened bottom flange isgiven by the formula

Foy = 0.592Fy Cl + 0.687 sin 2 ) (10-134)

in which c shall be taken as

13,300(14-136)t

~ y

the buckling stress of the flange is given, by the formula

F,, = 105(t/b)2 X 10 6 (10-137)

10.51.5.4 If longitudinal stiffeners are used, theyshall be equally spaced across the flange width and shallbe proportioned so that the moment of inertia of each stiff-ener about an axis parallel to the flange and at the base ofthe stiffener is at least equal to

I, = (~ t3w (10-138)

where

= 0.07k3 n4 when n equals 2, 3, 4, or 5;= 0.125k3 when n = 1;

w = width of flange between longitudinal stiffeners ordistance from a web to the nearest longitudinalstiffener;

n = number of longitudinal stiffeners;k = buckling coefficient which shall not exceed 4.

10.51.5.4.1

For a longitudinally stiffened flange designed for theyield stress Fy , the ratio w/t shall not exceed the valuegiven by the formula

w = 3,070(10-139)

t

10.51.5.4.2 For greater values of w/t

3,070 -~k- < w 56,650 ~

(10-140)—t

the buckling stress of the flange, including stiffeners, isgiven by Article 10.51.5.2 in which c shall be taken as

6, 650 -Ak- -w

c= t (10-141)3,580-Fk


10.51.5.4.3 For values of

w>6,650~_k(10-142)

t FY-

the buckling stress of the flange, including stiffeners, isgiven by the formula

F,r = 26.2k(t/w)2 X 106 (10-143)

10.51.5.4.4 When longitudinal stiffeners are used, itis preferable to have at least one transverse stiffenerplaced near the point of dead load contraflexure. The stiff-ener should have a size equal to that of a longitudinal stiff-ener. The number of longitudinal stiffeners preferablyshall not exceed 2. If the number of longitudinal stiffen-ers exceeds 2, then the use of additional transverse stiff-eners should be considered.

10.51.5.5 The width-to-thickness ratio of any out-standing element of the flange stiffeners shall not exceedthe value determined by the formula

b' _ 2,600(10-144)

t' jF–Y

where

b' = width of any outstanding stiffener element,and;

t ' = thickness of outstanding stiffener element;F, = yield strength of outstanding stiffener ele-

ment.

10.51.5.6 Compression flanges shall also satisfy theprovisions of Article 10.51.4. The effective flange platewidth shall be used to calculate the factored flange bend-ing stress. The full flange plate width shall be used to cal-culate the buckling stress of the flange.

10.51.6 Diaphragms

Diaphragms, cross-frames, or other means shall beprovided within the box girders at each support to resisttransverse rotation, displacement, and distortion.

Intermediate diaphragms or cross-frames are not re-quired for box girder bridges designed in accordance withthis specification.

10.51.7 Design of Flange to Web Welds

The total effective thickness of the web-flange weldsshall not be less than the thickness of the web, except,

when two or more interior intermediate diaphragms perspan are provided, the minimum size fillet welds specifiedin Article 10.23.2.2 may be used. Regardless of the typeweld used, welds shall be deposited on both sides of theconnecting flange or web plate.

10.52 SHEAR CONNECTORS

10.52.1 General

The horizontal shear at the interface between the con-crete slab and the steel girder shall be provided for by me-chanical shear connectors throughout the simple spansand the positive moment regions of continuous spans. Inthe negative moment regions, shear connectors shall beprovided when the reinforcing steel embedded in the con-crete is considered apart of the composite section. In casethe reinforcing steel embedded in the concrete is not con-sidered in computing section properties of negative mo-ment sections, shear connectors need not be provided inthese portions of the span, but additional connectors shallbe placed in the region of the points of dead load con-traflexure as specified in Article 10.38.5.1.3.

10.52.2 Design of Connectors

The number of shear connectors shall be determined inaccordance with Article 10.38.5.1.2 and checked for fa-tigue in accordance with Articles 10.38.5.1.1 and10.38.5.1.3.

10.52.3 Maximum Spacing

The maximum pitch shall not exceed 24 inches exceptover the interior supports of continuous beams wherewider spacing may be used to avoid placing connectors atlocations of high stresses in the tension flange.

10.53 HYBRID GIRDERS

This section pertains to the design of girders that uti-lize a lower strength steel in the web than in one or bothof the flanges. It applies to composite and noncompositeplate girders and to composite box girders. At any crosssection where the bending stress in either flange caused bythe maximum design load exceeds the minimum specifiedyield strength of the web steel, the compression-flangearea shall not be less than the tension-flange area. The top-flange area shall include the transformed area of any por-tion of the slab or reinforcing steel that is considered to actcompositely with the steel girder.

The provisions of Articles 10.48 through 10.52,10.57.1, and 10.57.2 shall apply to hybrid beams and gird-


ers except as modified below. In all equations of these ar-ticles, F Y shall be taken as the minimum specified yieldstrength of the steel of the element under considerationwith the following exceptions

(1) In Articles 10.48.1.1(b), 10.48.4.1, 10.48.5.1,10.48.6.1, 10.49.2, 10.49.3.2(b), and 10.50.1.1.2, use F Y

of the compression flange.(2) Articles 10.57.1 and 10.57.2 shall apply to theflanges, but not to the web of hybrid girders.

The provision specified in Article 10.40.4 shall alsoapply. Longitudinal web stiffeners preferably shall not belocated in yielded portions of the web.

10.53.1 Noncomposite Hybrid Sections


The equation of Article 10.48.1 for the maximumstrength of compact sections shall be replaced by theexpression

M u = FYfZ (10-145)

where FYf is the specified minimum yield strength of theflange, and Z is the plastic section modulus.

In computing Z, the web thickness shall be multipliedby the ratio of the minimum specified yield strength of theweb, FYW , to the minimum specified yield strength of theflange, FYf.

10.53.1.2 Braced Noncompact Sections

The equations of Article 10.48.2 for the maximumstrength of braced noncompact sections shall be replacedby the expressions

M~ = F YfSX,R (10-146)

M. = Fer S Xc RbR (10 -146a)

For symmetrical sections

R=12+(3(3p–p3)(10-147)

12+20

where

p = FYW/Fyf

R = AW/Af

For unsymmetrical sections

R =1—C

RW(1—P)2(3—W+PW) (10-148)6

+RW(3— W)

where tV is the distance from the outer fiber of the tensionflange to the neutral axis divided by the depth of the steelsection. R shall be taken as 1.0 at sections where the stressin both flanges caused by the maximum design loads doesnot exceed the specified minimum yield strength of the web.

10.53.1.3 Partially Braced Members

The strength of noncompact hybrid sections of par-tially braced members not satisfying the lateral bracing re-quirement given by Equation (10-101) shall be calculatedas the lesser of M„ calculated from Equation (10-146) orM„ calculated from Equation (10-146a). M„ calculatedfrom Equation (10-146a) is not to exceed M. calculatedfrom the provisions of Article 10.48.4.1 with Equation(10-103a) replaced by the expression

Mu = M rReR (10-148a)

and the yield moment calculated as

MY = FYfS R (10-148b)

where the appropriate R is determined from Article10.53.1.2 above, and Re is determined by Equation (10-103b).

10.53.2 Composite Hybrid Sections

The maximum strength of a compact composite sectionshall be computed as specified in Article 10.50.1.1.2 or Ar-ticle 10.50.2.1, as applicable, using the specified minimumyield strength of the element under consideration to com-pute the plastic moment capacity. The yield moment in Ar-ticle 10.50.1.1.2 shall be multiplied by R (for unsymmet-rical sections) from Article 10.53.1.2, with th calculated asspecified below for noncompact composite sections.

The maximum strength of a noncompact compositesection shall be taken as the maximum strength computedfrom Article 10.50.1.2 or Article 10.50.2.2, as applicable,rimes R (for unsymmetrical sections) from Article10.53.1.2, in which ip is the distance from the outer fiberof the tension flange to the neutral axis of the transformedsection divided by the depth of the steel section.

10.53.3 Shear

Equation (10-114) of Article 10.48.8.1 for the shear ca-pacity of transversely stiffened girders shall be replacedby the expression


V~ = VPC (10-149) 10.54.1.2 Effective Length

The provisions of Article 10.48.8.2, and the equationfor A in Article 10.48.5.3 are not applicable to hybridgirders.

10.54 COMPRESSION MEMBERS

10.54.1 Axial Loading

10.54.1.1 Maximum Capacity

The maximum strength of concentrically loadedcolumns shall be computed as

P„ = 0.85A,Fc, (10-150)

where AS is the gross effective area of the column crosssection and F,, is determined by one of the following twoformulas *:

zFir=Fy 1

–47zzE~Krc)

(10-151)

forFFYr

(10-152)

2

Fcr = E

11z

(10-153)

C r c l

forKL~

FFYr(10-154)

where

K = effective length factor in the plane of buckling;L, = length of the member between points of support

in inches;r = radius of gyration in the plane of buckling in

inches;F,, = yield stress of the steel in pounds per square inch;E = 29,000,000 pounds per square inch;F,, = buckling stress in pounds per square inch.

*Singly symmetric and unsymmetric compression members, such asangles or tees, and doubly symmetric compression members, such ascruciform or built-up members with very thin walls, may also requireconsideration of flexural-torsional and torsional buckling. Refer to theManual of Steel Construction, Ninth Edition, 1989, American Instituteof Steel Construction.

The effective length factor K shall be determined asfollows

(a) For members having lateral support in both direc-tions at its ends

K = 0.75 for riveted, bolted, or welded end connec-tions;

K = 0.875 for pinned ends.

(b) For members having ends not fully supported lat-erally by diagonal bracing or an attachment to an adja-cent structure, the effective length factor shall be de-termined by a rational procedure.**

10.54.2 Combined Axial Load and Bending

10.54.2.1 Maximum Capacity

The combined maximum axial force P and the maximumbending moment M acting on a beam-column subjected toeccentric loading shall satisfy the following equations:

O.SSA +MCP

< 1.0 (10 -155)sFcr M

u I —l A s Fe

P + M <_ 1.0 (10-156)0.85A S Fy M p

where:

Fir = buckling stress as determined by the equations ofArticle 10.54.1.1;

M„ = maximum strength as determined by Articles10.48.1, 10.48.2, or 10.48.4;

Fe = Enz

z = the Euler Buckling stress

Co in the plane of bending;

r(10-157)

C = equivalent moment factor, as defined below;M

P= FyZ, the full plastic moment of the section;

Z = plastic section modulus;

= effective slenderness ratio in the plane of-KLr

bending.

**B. G. Johnston, Guide to Stability Design Criteria for Metal Struc-tures, John Wiley and Sons, Inc., New York, 1976.


10.54.2.2 Equivalent Moment Factor C

If the ends of the beam-column are restrained fromsidesway in the plane of bending by diagonal bracing orattachment to an adjacent laterally braced structure, thenthe value of equivalent moment factor, C, may be com-puted by the formula

C = 0.6 + 0.4a (10-158)

where a is the ratio of the numerically smaller to the largerend moment. The ratio a is positive when the two end mo-ments act in an opposing sense (i.e., one acts clockwiseand the other acts counterclockwise) and negative whenthey act in the same sense. In all cases, factor C may betaken conservatively as unity.

10.55 SOLID RIB ARCHES

See Article 3.2 for load factors and combinations. UseService Load Design Method for factored loads and theformulas changed as follows:

10.55.1 Moment Amplification and AllowableStresses

AF1.18T (10-159)

1AFe

The b ' /t, ratio for the stiffeners shall be

b _ 2,200 bmaximum =12 (10 -164)

is fa + f

3

i s

10.55.3 Flange Plates

b ' _ 5,700for width between webs (10 -165)

t f fa + fb

b ' _ 2,200for overhang widths,

t f fa + fb maximum b'/t f =12 (10-166)

10.56 SPLICES, CONNECTIONS, AND DETAILS

10.56.1 Connectors

10.56.1.1 General

Connectors and connections shall be proportioned sothat their design resistance, (~R, (maximum strength mul-tiplied by a resistance factor) as given in this Article, asapplicable, shall be at least equal to the effects of serviceloads multiplied by their respective load factors as speci-fied in Article 3.22.

10.56.1.2 Weldsz

YFY rFa

1.181

4,rrzEand Fe = FY

(10-160)

10.55.2 Web Plates

No longitudinal stiffener

D/tw – 6,750– (10-161)

a

One longitudinal stiffener

D/tw =10,150

(10-162)A

Two longitudinal stiffeners

D/t w = 13,500(10-163)

a

The ultimate strength of the weld metal in groove andfillet welds shall be equal to or greater than that of the basemetal, except that the designer may use electrode classifi-cations with strengths less than the base metal when de-tailing fillet welds for quenched and tempered steels.However, the welding procedure and weld metal shall beselected to ensure sound welds. The effective weld areashall be taken as defined in ANSI/AASHTO/AWS D1.5Bridge Welding Code, Article 2.3.

10.56.1.3 Bolts and Rivets

10.561.3.1 In proportioning fasteners, the cross sec-tional area based upon nominal diameter shall be used.

10.56.1.3.2 The design force, 4R, in kips, forAASHTO M 164 (ASTM A 325) and AASHTO M 253(ASTM A 490) high-strength bolts subject to applied axialtension or shear is given by

(~R = (FAb (10-166a)


TABLE 10.56A Design Strength of Connectors

Type of Fastener Strength (,OF)

Groove Weld' 1.00 FyFillet Weldb 0.45 F„

Low-Carbon Steel BoltsASTM A 307

Tension 30 ksiShear on Bolt with

Threads in Shear Plane d 18 ksi

Power-Driven RivetsASTM A 502

Shear—Grade 1 25 ksiShear—Grade 2 30 ksi

High-Strength BoltsAASHTO M 164(ASTM A 325)

Applied Static Tension` 68 ksiShear on Bolt with

Threads in Shear Plane ',d,e 35 ksi

AASHTO M 253(ASTM A 490)

Applied Static Tension 85 ksiShear on Bolt with

Threads in Shear Planed,e 43 ksi

'Fy = yield point of connected material.'F„ = minimum strength of the welding rod metal.`The tensile strength of M 164 (A 325) bolts decreases for diameters greater than 1 inch.

The design values listed are for bolts up to 1-inch in diameter. The design values shall bemultiplied by 0.875 for diameters greater than 1 inch.

d Tabulated values shall be reduced by 20 percent in bearing-type connections whose lengthbetween extreme fasteners in each of the spliced parts measured parallel to the line of axial forceexceeds 50 inches. For flange splices, the 50-inch length is to be measured between the extremebolts on only one side of the connection.

e lf material thickness or joint details preclude threads in the shear plane, multiply values by1.25.

where

(~F = design strength per bolt area as given in Table10.56A for appropriate kind of load, ksi;

Ab = area of bolt corresponding to nominal diameter,sq in.

The design bearing force, (~R, on the connected mate-rial in standard, oversized, short-slotted holes loaded inany direction, or long-slotted holes parallel to the appliedbearing force shall be taken as

(~R = 0.9LJF~ < 1.8dtF„ (10-166b)

The design bearing force, (~R, on the connected mate-rial in long-slotted holes perpendicular to the appliedbearing force shall be taken as

(~R = 0.75LJF u < 1.5dtF„ (10-166c)

The design bearing force for the connection is equal tothe sum of the design bearing forces for the individualbolts in the connection.

In the foregoing

(~R = design bearing force, kips.F„ = specified minimum tensile strength of the con-

nected material, ksi.L, = clear distance between the holes or between the

hole and the edge of the material in the directionof the applied bearing force, in.

d = nominal diameter of bolt, in.t = thickness of connected material, in.

10.56.1.3.3 High-strength bolts preferably shall beused for fasteners subject to tension or combined shearand tension.

For combined tension and shear, bolts and rivets shallbe proportioned so that the tensile stress does not exceed


for fv (Fv <– 0.33

Ft = Ft (10-167)

for fv/Fv > 0.33

Ft =Ft 1–(fv /Fv (10-167a)

where

fv = computed rivet or bolt stress in shear, ksi;F„ = design shear strength of rivet or bolt from Table

10.56A, ksi;F, = design tensile strength of rivet or bolt from Table

10.56A, ksi;F,' = reduced design tensile strength of rivet or bolt

due to the applied shear stress, ksi.

10.56.1.4 Slip-Critical Joints

Slip-critical joints shall be designed to prevent slip atthe overload in accordance with Article 10.57.3, but as aminimum the bolts shall be capable of developing theminimum strength requirements in shear and bearing ofArticle 10.56.1.3 under the maximum design loads.

Potential slip of joints should be investigated at inter-mediate load stages especially those joints located in com-posite regions.

10.56.2 Bolts Subjected to Prying Action byConnected Parts

Bolts required to support applied load by means of di-rect tension shall be proportioned for the sum of the ex-ternal load and tension resulting from prying action pro-duced by deformation of the connected parts. The totaltension should not exceed the values given in Table10.56A.

The tension due to prying actions shall be computed as

Q_ [3b _]T (10-168)

8a 20

where

Q = prying tension per bolt (taken as zero when nega-tive);

T = direct tension per bolt due to external load;a = distance from center of bolt to edge of plate;b = distance from center of bolt to toe of fillet of con-

nected part;t = thickness of thinnest part connected in inches.

10.56.3 Rigid Connections

10.56.3.1 All rigid frame connections, the rigidity ofwhich is essential to the continuity assumed as the basisof design, shall be capable of resisting the moments,shears, and axial loads to which they are subjected bymaximum loads.

10.56.3.2 The beam web shall equal or exceed thethickness given by

t wM ° (10-169)

( Fy dbd c

where

M, = column moment;db =beam depth;d, =column depth.

When the thickness of the connection web is less thanthat given by the above formula, the web shall bestrengthened by diagonal stiffeners or by a reinforcingplate in contact with the web over the connection area.

At joints where the flanges of one member are rigidlyframed into one flange of another member, the thicknessof the web, tw, supporting the latter flange and the thick-ness of the latter flange, t,, shall be checked by the for-mulas below. Stiffeners are required on the web of the sec-ond member opposite the compression flange of the firstmember when

t w < Af (10-170)tb + 5k

and opposite the tension flange of the first memberwhen

t ' <0.4~A_f (10-171)

where

tw = thickness of web to be stiffened;k = distance from outer face of flange to toe of web

fillet of member to be stiffened;t b = thickness of flange delivering concentrated force;t, = thickness of flange of member to be stiffened;Af = area of flange delivering concentrated load.

10.57 OVERLOAD

For AASHTO H or HS loadings, the overload is definedas D + 5(L+I)13, except for beams and girders designed


TABLE 10.57A Design Slip Resistance for Slip-Critical Connections(Slip Resistance per Unit of Bolt Area, 4F, = 4)Tb µ, ksi)

Hole Type and Direction of Load Application

Any Direction Transverse Parallel

Oversize andStandard Short Slot Long Slots Long Slots

AASHTO AASHTO AASHTO AASHTO AASHTO AASHTO AASHTO AASHTOM 164 M 253 M 164 M 253 M 164 M 253 M 164 M 253

(ASTM (ASTM (ASTM (ASTM (ASTM (ASTM (ASTM ASTMContact Surface of Bolted Parts A 325)' A490) A 325)' A 490) A 325)' A490) A 325)' A 490)Class A (Slip Coefficient 0.33) 21 26 18 22 15 18 13 16

Clean mill scale and blast-cleaned surfaces with Class Acoatings'

Class B (Slip Coefficient 0.50) 32 40 27 34 22 28 19 24Blast-cleaned surfaces andblast-cleaned surfaces withClass B coatings'

Class C (Slip Coefficient 0.33) 21 26 18 22 15 18 13 16Hot-dip galvanized surfacesroughened by wire brushingafter galvanizing.

The tensile strength of M 164 (A 325) bolts decreases for diameters greater than 1 inch. The design values listed are for bolts up to f-inch diameter. The design values shall be multiplied by 0.875 for diameters greater than 1 inch.

bCoatings classified as Class A or Class B include those coatings which provide a mean slip coefficient not less than 0.33 or 0.50,

respectively, as determined by Testing Method to Determine the Slip Coefficient for Coatings Used in Bolted Joints. See Article 10.32.3.2.3.

for the Group IA load combination specified in Article3.5.1 for which overload is defined as D + 2.2(L+1) with(L+I) assumed to occupy a single lane without concur-rent loading in any other lane. For beams and girders de-signed for an overload vehicle selected by the operatingagency in accordance with the Group IB load combina-tion, the overload is defined as D + (L+I). If moment re-distribution is permitted under the provisions of Article10.48.1.3, the limitations specified in Articles 10.57.1and 10.57.2 shall apply to the modified moments, but notto the original moments. Web bend-buckling shall bechecked for the overload according to Equation (10-173).For composite sections, D, shall be calculated in accor-dance with Article 10.50(b). Sections that do not satisfyEquation (10-173) shall be modified to comply with therequirement.

10.57.1 Noncomposite Sections

stresses, the presence or absence of temporary supportsduring the construction shall be considered. For memberswith shear connectors provided throughout their entirelength that also satisfy the provisions of Article10.50.2.3, the overload flange stresses caused by loadsacting on the appropriate composite section may be com-puted assuming the concrete deck to be fully effective forboth positive and negative moment. For this case, the re-sulting stresses shall be combined with the stresses dueto loads acting on the noncomposite section to calculateD, for checking web bend buckling.

10.57.3 Slip-Critical Joints

10.57.3.1 In addition to the requirements of Arti-cles 10.56.1.3.1 and 10.56.1.3.2 for fasteners, the forcecaused by D + 5(L + I)13 on a slip-critical joint shall notexceed the design slip force (ER s) given by

At noncomposite sections, the maximum overloadflange stress shall not exceed 0.81 7

y .

(~Rg = (~FsA bNA (10-172a)

where

10.57.2 Composite Sections

At composite sections, the maximum overload flangestress shall not exceed 0.95F y . In computing dead load

(~Fs = (~ Tbµ, design slip resistance per unit of bolt areagiven in Table 10.57A, ksi;

Ab = area corresponding to the nominal body area ofthe bolt, sq in.;


Nb = number of bolts in the joint;N, = number of slip planes;Tb = specified tension in the bolt;g = slip coefficient;

= 0.33 for clean mill scale and Class A coatings= 0.50 for blast-cleaned surfaces and Class B

coatings;= 0.33 for hot-dip galvanized and roughened

surfaces;= 1.0 for standard holes;= 0.85 for oversized and short slotted holes;= 0.70 for long slotted holes loaded transversely;= 0.60 for long slotted holes loaded longitudinally.

Class A, B, or C surface conditions of the bolted parts asdefined. in Table 10.57A shall be used in joints designatedas slip-critical except as permitted in Article 10.57.3.2.

10.57.3.2 Subject to the approval of the Engineer,coatings providing a slip coefficient less than 0.33 may beused provided the mean slip coefficient is established bytest in accordance with the requirements of Article10.57.3.3, and the slip resistance per unit area established.The slip resistance per unit area shall be taken as equal tothe slip resistance per unit area from Table 10.57A forClass A coatings as appropriate for the hole type and bolttype times the slip coefficient determined by test dividedby 0.33..

10.57.3.3 Paint, used on the faying surfaces of con-nections specified to be slip critical, shall be qualified bytest in accordance with "Test Method to Determine theSlip Coefficient for Coatings Used in Bolted Joints" asadopted by the Research Council on Structural Connec-tions. See Appendix A of Allowable Stress Design Speci-fication for Structural Joints Using ASTMA 325 orA 490Bolts, published by the Research Council on StructuralConnections.

10.57.3.4 For combined shear and tension in slip crit-ical joints where applied forces reduce the total clampingforce on the friction plane, the design slip force shall not ex-ceed the value ERs

' obtained from the following equation:

ERs = ~R, (1 — 1.88f,/F,,) (10-172b)

where

ft = computed tensile stress in the bolt due to ap-plied loads including any stress due to pryingaction, ksi;

ER, = design slip force specified in Equation (10-172a),kips;

F„ = 120 ksi for M 164 (A 325) bolts up to 1-inchdiameter;

= 105 ksi for M 164 (A 325) bolts over 1-inchdiameter;

= 150 ksi for M 253 (A 490) bolts.

10.58 FATIGUE

10.58.1 General

The analysis of the probability of fatigue of steel mem-bers or connections under service loads and the allowablerange of stress for fatigue shall conform to Article 10.3,except that the limitation imposed by the basic criteriagiven in Article 10.3.1 shall not apply. For members withshear connectors provided throughout their entire lengththat also satisfy the provisions of Article 10.50.2.3, therange of stress may be computed using the composite sec-tion assuming the concrete deck to be fully effective forboth positive and negative moment.

10.58.2 Composite Construction

10.58.2.1 Slab Reinforcement

When composite action is provided in the negative mo-ment region, the range of stress in slab reinforcement shallbe limited to 20,000 psi.

10.58.2.2 Shear Connectors

The shear connectors shall be designed for fatigue inaccordance with Article 10.38.5.1.

10.58.3 Hybrid Beams and Girders

Hybrid girders shall be designed for fatigue in accor-dance with Article 10.3.

10.59 DEFLECTION

The control of deflection of steel or of composite steeland concrete structures shall conform to the provision ofArticle 10.6.

10.60 ORTHOTROPIC SUPERSTRUCTURES

A rational analysis based on the Strength DesignMethod, in accordance with the specifications, will beconsidered as compliance with the specifications.


10.61 CONSTRUCTIBILITY

The moment and shear capacity of a steel beam or girdershall meet the requirements specified below to control localbuckling of the web and compression flange, and to preventlateral torsional buckling of the cross section under thenoncomposite dead load prior to hardening of the deckslab. The casting or placing sequence of the concrete deckspecified in the plans shall be considered in determining theapplied moments and shears. A load factor of y = 1.3 shallbe used in calculating the applied moments and shears.

10.61.1 Web Bend Buckling

The maximum factored noncomposite dead load com-pressive bending stress in the web shall not exceed thevalue given below:

26,200,OOOak~ (10-173)fb ~

D zF

yW

(tW )

where

FyW = specified minimum yield strength of the webDc = depth of the web of the steel beam or girder in

compressionD = web depthtW = thickness of webk = 9(D/Df for members without a longitudinal

stiffenera = 1.3 for members without a longitudinal stiffenera = 1.0 for members with a longitudinal stiffener

Sections without longitudinal stiffeners that do not satisfyEquation (10-173) shall either be modified to comply withthe requirement or a longitudinal stiffener shall be addedto the web at a location on the web that satisfies both Equa-tion (10-173) and all strength requirements, which may ormay not correspond to the optimum location of the longi-tudinal stiffener specified in Article 10.49.3.2(a). For lon-gitudinally stiffened girders, the buckling coefficient, k, iscalculated as

r l2

for Dc >_0.4 k=5.171a

I >_9Iz

Dc

zfor

D<0.4 k=11.64D

D d

s

where

d, = the distance from the centerline of a plate longi-tudinal stiffener or the gage line of an angle lon-gitudinal stiffener to the inner surface or the leg ofthe compression flange component.

For members with or without a longitudinal stiffener,k shall be taken equal to 7.2 when both edges of the webare in compression.

The web thickness requirements specified in Articles10.48.5.1, 10.48.6.1, 10.49.2, and 10.49.3.2(b) shall notbe applied to the constructibility load case.

10.61.2 Web Shear Buckling

The sum of the factored noncomposite and compositedead-load shears shall not exceed the shear buckling ca-pacity of the web specified in Article 10.48.8.1 (Equation10-113).

10.61.3 Lateral-Torsional Buckling of the CrossSection

The maximum factored non-composite dead-load mo-ment shall not exceed the value of M. calculated for thesteel beam or girder using the equations specified in Arti-cle 10.48.4.1, nor M y .

10.61.4 Compression Flange Local Buckling

The ratio of the top compression flange width to thick-ness in positive-moment regions shall not exceed thevalue determined by the formula

b _ 4,400_< 24 (10-174)

t id

where fdf is the top-flange compressive stress due to thefactored noncomposite dead load divided by the factor R b

specified in Article 10.48.4.1, but not to exceed F Y.

Section 11

ALUMINUM DESIGN

11.1 GENERAL

The purpose of this section is to provide a location forindexing aluminum design, material fabrication, and con-struction specifications.

11.2 BRIDGES

The Specifications forAluminum Structures, Fifth Edi-tion, December 1986, published by the Aluminum Asso-ciation, Inc., as it applies to "Bridge and Similar TypeStructures," are intended to serve as a standard or guidefor the preparation of plans and specifications and as a ref-erence for designers, fabricators, and erectors of alu-minum bridge and railing structures and their aluminumstructural components. Welding shall conform to Section10 of the current AWS D1.2 Structural Welding Code—Aluminum, and workmanship requirements for Class IIstructures.

11.3 SOIL-METAL PLATE INTERACTIONSYSTEMS

The design of aluminum soil-metal plate interactionsystems shall be in accordance with Section 12. Fabrica-tion and installation shall be in accordance with Section23—Division Il.

11.4 STRUCTURAL SUPPORTS FOR HIGHWAYSIGNS, LUMINAIRES, AND TRAFFICSIGNALS

The AASHTO Standard Specifications for StructuralSupports for Highway Signs, Luminaires and Traffic Sig-nals shall be used for the design and preparation of plansand specifications, fabrication, and erection of aluminumsign supports, luminaires, and traffic signals. Weldingshall conform to Section 10 of the current AWS D1.2Structural Welding Code Aluminum, and workmanshiprequirements for Class I structures. Special considerationmay be given to certain support structures, which may bedesigned and fabricated according to the provisions of Ar-ticle 11.2, Bridges.

11.5 BRIDGE RAILING

The design of aluminum bridge railing shall be gov-erned by Article 2.7; the fabrication and erection shallconform to Section 6 of the Specifications for AluminumStructures, Fifth Edition, 1986; and the welding shall con-form to Section 10 of the current AWS D1.2 StructuralWelding Code Aluminum, and workmanship require-ments for Class II Structures. The AASHTO RoadsideDesign Guide should be consulted for guidance on thesafety considerations in the design of bridge rail.

337

Section 12

SOIL-CORRUGATED METAL STRUCTUREINTERACTION SYSTEMS

12.1 GENERAL

12.1.1 Scope

The specifications of this Section are intended for thestructural design of corrugated metal structures. It must berecognized that a buried flexible structure is a compositestructure made up of the metal ring and the soil envelope,and that both materials play a vital part in the structuraldesign of flexible metal structures.

Only Article 12.7 is applicable to structural plate boxculverts.

12.1.2 Notations

A = required wall area (Article 12.2. 1)A = area of pipe wall (Article 12.3. 1)AL = total axle load on single axle or tandem axles (Ar-

ticles 12.8.4.3.2 and 12.8.4.4)C, = number of axles coefficient (Article 12.8.4.3.2)C2 = number of wheels per axle coefficient (Article

12.8.4.3.2)Cdt = dead load adjustment coefficient (Article

12.8.4.3.2)Cee = live load adjustment coefficient (Article

12.8.4.3.2)D = straight leg of haunch (Article 12.8.2)E m = modulus of elasticity of metal (Articles 12.2.2 and

12.3.2)Ems, = modulus of elasticity of pipe material (Articles

12.2.4 and 12.3.4)FF = flexibility factor (Articles 12.2.4 and 12.3.4)fa = allowable stress-specified minimum yield point

divided by safety factor (Article 12.2. 1)f, = critical buckling stress (Articles 12.2.2 and 12.3.2)f„ = specified minimum tensile strength (Articles

12.2.2 and 12.3.2)f, = specified minimum yield point (Article 12.3. 1)H = height of cover above crown (Article 12.8.4.4)I = moment of inertia, per unit length, of cross section

of the pipe wall (Articles 12.2.4 and 12.3.4)

k = soil stiffness factor (Articles 12.2.2 and 12.3.2)Ma l = dead load factored moment (Article 12.8.4.3.3)M„ = live load factored moment (Article 12.8.4.3.3)M PC = crown plastic moment capacity (Article

12.8.4.3.3)MPh = haunch plastic moment capacity (Article

12.8.4.3.3)P = design load (Article 12.1.4)P = proportion of total moment carried by the crown.

Limits for P are given in Table 12.7.41) (Article12.8.4.3.3)

r = radius of gyration of corrugation (Articles 12.2.2and 12.3.2)

r, = radius of crown (Table 12.8.2A)rh = radius of haunch (Table 12.8.2A)R = rise of box culvert (Articles 12.7.2 and 12.8.4.4)Rh = haunch moment reduction factor (Article

12.8.4.3.3)S = diameter of span (Articles 12.1.4, 12.2.2, 12.8.2,

and 12.8.4.4)s = pipe diameter or span (Articles 12.2.4, 12.3.2, and

12.3.4)SF = safety factor (Article 12.2.3)SS = required seam strength (Articles 12.2.3 and

12.3.3)T = thrust (Article 12.1.4)TL = thrust, load factor (Articles 12.3.1 and 12.3.3)T s = thrust, service load (Articles 12.2.1 and 12.2.3)t = length of stiffening rib on leg (Article 12.8.2)V = reaction acting in leg direction (Article 12.8.4.4)0 = haunch radius included angle (Table 12.8.2A)y = unit weight of backfill (Articles 12.8.4.3.2 and

12.8.4.4)= capacity modification factor (Articles 12.3.1 and

12.3.3)

12.1.3 Loads

Design load, P, shall be the pressure acting on the struc-ture. For earth pressures, see Article 3.20. For live load,see Articles 3.4 to 3.7, 3.11, 3.12, and 6.4, except that the

339


words "When the depth of fill is 2 feet or more" in Article6.4.1 need not be considered. For loading combinations,see Article 3.22.

12.1.4 Design

12.1.4.1 The thrust in the wall shall be checked bythree criteria. Each considers the mutual function of themetal wall and the soil envelope surrounding it. The cri-teria are:

(a) Wall area;(b) Buckling stress;(c) Seam strength (structures with longitudinal seams).

12.1.4.2 The thrust in the wall is:

T = P xS

(12-I)

where:

P = design load, in pounds per square foot;S = diameter or span, in feet;T = thrust, in pounds per foot.

12.1.4.3 Handling and installation strength shall besufficient to withstand impact forces when shipping andplacing the pipe.

12.1.5 Materials

The materials shall conform to the AASHTO specifi-cations referenced herein.

12.1.6 Soil Design

12.1.6.1 Soil Parameters

The performance of a flexible culvert is dependent onsoil structure interaction and soil stiffness.

The following must be considered:

(a) Soils:(1) The type and anticipated behavior of the foun-dation soil must be considered; i.e., stability forbedding and settlement under load.(2) The type, compacted density, and strengthproperties of the soil envelope immediately adjacentto the pipe must be established. Good side fill is ob-tained from a granular material with little or no plas-ticity and free of organic material, i.e., AASHTOclassification groups A-1, A-2, and A-3, compactedto a minimum 90% of standard density based onAASHTO Specification T 99 (ASTM D 698).

(3) The density of the embankment material abovethe pipe must be determined. See Article 6.2.

(b) Dimensions of soil envelope.

The general recommended criteria for lateral limits ofthe culvert soil envelope are as follows:

(1) Trench installations-2-feet minimum each sideof culvert. This recommended limit should be modifiedas necessary to account for variables such as poor insitu soils.(2) Embankment installations-one diameter or spaneach side of culvert.(3) The minimum upper limit of the soil envelope is 1foot above the culvert.

12.1.6.2 Pipe Arch Design

The design of the corner backfill shall account forcorner pressure which shall be considered to be approxi-mately equal to thrust divided by the radius of thepipe arch corner. The soil envelope around the corners ofpipe arches shall be capable of supporting this pressure.

12.1.6.3 Arch Design

12.1. 63.1 Special design considerations may be ap-plicable; a buried flexible structure may raise two impor-tant considerations. The first is that it is undesirable tomake the metal arch relatively unyielding or fixed com-pared with the adjacent sidefill. The use of massive foot-ings or piles to prevent any settlement of the arch is gen-erally not recommended.

Where poor materials are encountered, considerationshould be given to removing some or all of this poor ma-terial and replacing it with acceptable material.

The footing should be designed to provide uniformlongitudinal settlement, of acceptable magnitude from afunctional aspect. Providing for the arch to settle will pro-tect it from possible drag down forces caused by the con-solidation of the adjacent sidefill.

The second consideration is bearing pressure of soilsunder footings. Recognition must be given to the effect ofdepth of the base of footing and the direction of the foot-ing reaction from the arch.

Footing reactions for the metal arch are considered toact tangential to the metal plate at its point of connectionto the footing. The value of the reaction is the thrust in themetal arch plate at the footing.

12.1.6.3.2 Invert slabs and other appropriate mea-sures shall be provided to anticipate scour.

1 11.7 DIVISION I-DESIGN 341

12.1.7 Abrasive or Corrosive Conditions

Extra metal thickness, or coatings, may be required forresistance to corrosion and abrasion. For highly abrasiveconditions, a special design may be required.


When multiple lines of pipes or pipe arches greaterthan 48 inches in diameter or span are used, they shall bespaced so that the sides of the pipe shall be no closer thanone-half diameter or 3 feet, whichever is less, to permitadequate compaction of backfill material. For diametersup to and including 48 inches, the minimum clear spacingshall not be less than 2 feet.

12.1.9 End Treatment

Protection of end slopes may require special consid-eration where backwater conditions may occur, or whereerosion and uplift could be a problem. Culvert ends con-stitute ,a major run-off-the-road hazard if not properly de-signed. Safety treatment, such as structurally adequategrating that conforms to the embankment slope, exten-sion of culvert length beyond the point of hazard, or pro-vision of guardrail, are among the alternatives to be con-sidered.. End walls on skewed alignment require a specialdesign.

12.1.10 Construction and Installation

The construction and installation shall conform to Sec-tion 23--Division It.

12.2 ',SERVICE LOAD DESIGN

Service Load Design is a working stress method, as tra-ditionally used for culvert design.

12.2.1 Wall Area

A = TS/fa (12-2)

where:

A = required wall area in square inches per foot;T, = thrust, service load in pounds per foot;fa = allowable stress-specified minimum yield point,

pounds per square inch, divided by safety factor,fY/SF.

12.2.2 Buckling

Corrugations with the required wall area, A, shall bechecked for possible buckling. If the allowable bucklingstress, fJSF, is less than fa , the required area must be re-calculated using fJSF in lieu of fa. Formulae for buckling

are:

a (kS) 2

If S < kF224Em

then f,, = f,, - 48Em r (12-3)

If S < k 2fu

then for = (12E. (12-4)

u

where:

f„ = specified minimum tensile strength in pounds persquare inch;

fir = critical buckling stress in pounds per square inch;k = soil stiffness factor = 0.22;S = diameter or span in inches;r = radius of gyration of corrugation in inches;Em = modulus of elasticity of metal in pounds per

square inch.

12.2.3 Seam Strength

For pipe fabricated with longitudinal seams (riveted,spot-welded, bolted), the seam strength shall be sufficientto develop the thrust in the pipe wall.

The required seam strength shall be

SS = T,(SF) (12-5)

where:

SS = required seam strength in pounds per foot;T, = thrust in pipe wall in pounds per foot;SF = safety factor.

12.2.4 Handling and Installation Strength

Handling and installation rigidity is measured by aflexibility factor, FF, determined by the formula:

FF = s 2/EmI (12-6)

where:

FF= flexibility factor in inches per pound;s = pipe diameter or maximum span in inches;Em = modulus of elasticity of the pipe material in

pounds per square inch;


I = moment of inertia per unit length of cross section where:

of the pipe wall in inches to the 4th power per SS = required seam strength in pounds per foot;inch. TL =thrust multiplied by applicable factor, in pounds

per linear foot;

12.3 LOAD FACTOR DESIGN = capacity modification factor.

Load Factor Design is an alternative method of designbased on ultimate strength principles.

12.3.1 Wall Area

A = TL/(~fy (12-7)

where:

A = area of pipe wall in square inches per foot;T L = thrust, load factor in pounds per foot;fy = specified minimum yield point in pounds per

square inch;= capacity modification factor.

12.3.2 Buckling

If f,, is less than fy , A must be recalculated using f,, inlieu of fy :

If s < k2fEm then fir = fu - 48E

f

a(ks / r)

2(12-8)

u m

12If s > k

24E m then fir= ks /Er)2

(12-9)

where:

f„ = specified minimum metal strength in pounds persquare inch;

f,, = critical buckling stress in pounds per square inch;k = soil stiffness factor = 0.22;s = pipe diameter or span in inches;r = radius of gyration of corrugation in inches;Em = modulus of elasticity of metal in pounds per

square inch.


For pipe fabricated with longitudinal seams (riveted,spot-welded, bolted), the seam strength shall be sufficientto develop the thrust in the pipe wall. The required seamstrength shall be:


Handling rigidity is measured by a flexibility factor,FF, determined by the formula:

FF = sl/E.1 (12-11)

where:

FF = flexibility factor in inches per pound;s = pipe diameter or maximum span in inches;Em = modulus of elasticity of the pipe material in

pounds per square inch;I = moment of inertia per unit length of cross section

of the pipe wall in inches to the 4th power perinch.

12.4 CORRUGATED METAL PIPE

12.4.1 General

12.4.1.1 Corrugated metal pipe and pipe-archesmay be of riveted, welded, or lock seam fabricationwith annular or helical corrugations. The specifications are:

Aluminum SteelAASHTO M 36,

AASHTO M 190, M 196 M 190, M 245

12.4.1.2 Service Load Design-safety factor, SF

Seam strength = 3.0Wall area = 2.0Buckling = 2.0

12.4.1.3 Load Factor Design-capacitymodification factor, (~

For Helical pipe with lock seam or fully welded seam:

Wall area and buckling (~ = 1.0

For Annular pipe with spot welded, riveted or bolted seam:

Wall area and buckling = 1.0SS = TLJ(~ (12-10) Seam strength = 0.67

34312.4.1.4 DIVISION I-DESIGN

12.4.1.4 Flexibility Factor

(a) For steel conduits, FF should generally not exceedthe following values:%4-in. and %z-in. depth corrugation,FF = 4.3 X 10

-2

1-in. depth corrugation, FF = 3.3 X 10-2

(b) For aluminum conduits, FF should generally notexceed the following values:%4-in. and Y2-in. depth corrugations,FF = 3.1 X 10 -2 for 0.060 in. material thicknessFF = 6.1 X 10 -2 for 0.075 in. material thicknessFF = 9.2 X 10 -2 for all other material thicknesses1-in. depth corrugation, FF = 6 X 10-2

12.4.1.5 Minimum Cover

The minimum cover for design loads shall be Span/8but not less than 12 inches. (The minimum cover shall bemeasured from the top of a rigid pavement or the bottomof a flexible pavement.) For construction requirements,see Article 23.10-Division II.


Minimum Longitudinal Seam Strength

2 x 1/2 and 2-2/3 x 1/2 Corrugated Steel 3 x 1 Corrugated Steel Pipe-Pipe-Riveted or Spot Welded Riveted or Spot Welded

Single Double DoubleThickness Rivet Size Rivets Rivets Thickness Rivet Size Rivets

(in.) (in.) (kips/ft) (kips/ft) (in.) (in.) (kips/ft)

0.064 5116 16.7 21.6 0.064 3/8 28.70.079 5/16 18.2 29.8 0.079 3/8 35.70.109 3/8 23.4 46.8 0.109 7/16 53.00.138 3/8 24.5 49.0 0.138 7/16 63.70.168 3/8 25.6 51.3 0.168 7/16 70.7

2 x 1/2 and 2-2/3 x 1/2 CorrugatedAluminum Pipe-Riveted

Rivet Single DoubleThickness Size Rivets Rivets

(in.) (in.) (kips/ft) (kips/ft)

0.060 5/16 9.0 14.00.075 5/16 9.0 18.00.105 3/8 15.6 31.50.135 3/8 16.2 33.00.164 3/8 16.8 34.0


3 x 1 Corrugated Aluminum 6 x 1 Corrugated AluminumPipe-Riveted PipeRiveted

Double DoubleThickness Rivet Size Rivets Thickness Rivet Size Rivets

(in.) (in.) (kips/ft) (in.) (in.) (kips/ft)

0.060 3/8 16.5 0.060 1/2 16.00.075 3/8 20.5 0.075 1/2 19.90.105 1/2 28.0 0.105 1/2 27.90.135 1/2 42.0 0.135 1/2 35.90.164 1/2 54.5 0.167 1/2 43.5

12.4.3 Section Properties

12.4.3.1 Steel Conduits

1-1/2 x 1/4 Corrugation 2-2/3 x 1/2 Corrugation

Thickness A S r I x 10 -3 A S r I x 10-1

(in.) (sgin./ft) (in.) (in. 4/in.) (sqin./ft) (in.) (in. 4/in.)0.028 0.3040.034 0.3800.040 0.456 0.0816 0.253 0.465 0.1702 1.1210.052 0.608 0.0824 0.344 0.619 0.1707 1.5000.064 0.761 0.0832 0.439 0.775 0.1712 1.8920.079 0.950 0.0846 0.567 0.968 0.1721 2.3920.109 1.331 0.0879 0.857 1.356 0.1741 3.4250.138 1.712 0.0919 1.205 1.744 0.1766 4.5330.168 2.098 0.0967 1.635 2.133 0.1795 5.725

3 x 1 Corrugation 5 x 1 CorrugationThickness A g r I x 10- 1 A S r I x 10 -3

(in.) (sgin./ft) (in.) (in. 4/in.) (sgin./ft) (in.) (in. 4/in.)

0.064 0.890 0.3417 8.659 0.794 0.3657 8.8500.079 1.113 0.3427 10.883 0.992 0.3663 11.0920.109 1.560 0.3448 15.459 1.390 0.3677 15.6500.138 2.008 0.3472 20.183 1.788 0.3693 20.3170.168 2.458 0.3499 25.091 2.186 0.3711 25.092

12.4.3.2 Aluminum Conduits

1-1/2 x 1/4 Corrugation 2-2/3 x 1/2 CorrugationThickness AS r I x 10-3 A S r I x 10-3

(in.) (sq in./ft) (in.) (in. 4/in.) (sq in./ft) (in.) (in. 4/in.)

0.048 0.608 0.0824 0.3440.060 0.761 0.0832 0.349 0.775 0.1712 1.8920.075 .................................... 0.968 0.1721 2.3920.105 .................................... 1.356 0.1741 3.4250.135 .................................... 1.745 0.1766 4.5330.164 .................................... 2.130 0.1795 5.725

3 x 1 Corrugation 6 x IEffective

Thickness AS r I x 10-1 AS Area r I x 10-1

(in.) (sq in./ft) (in.) (in. 4/in.) (sq in./ft) (sq in./ft) (in.) (in. 4/in.)

0.060 0.890 0.3417 8.659 0.775 0.387 0.3629 8.5050.075 1.118 0.3427 10.883 0.968 0.484 0.3630 10.6310.105 1.560 0.3448 15.459 1.356 0.678 0.3636 14.3400.135 2.088 0.3472 20.183 1.744 0.872 0.3646 19.3190.164 2.458 0.3499 25.091 2.133 1.066 0.3656 23.760

34512.4.4 DIVISION I-DESIGN

12.4.4 Chemical and Mechanical Requirements 12.5.2 Soil Design

12.4.4.1 Aluminum-corrugated metal pipe and pipe-arch material requirements-AASHTO M 197

Mechanical Properties for Design

Minimum MinimumMaterial Tensile Yield Mod. of

Grade Strength Point Elast.(psi) (psi) (psi)

3004-H34 31,000 24,000 10 x 106

3004-H32 27,000 20,000 10 x 106

H34 temper must be used with riveted pipes to acheive seam strength.Both H32 and H34 temper material may be used with helical pipe.

12.4.4.2 Steel-corrugated metal pipe and pipe-archmaterial requirements-AASHTO M 218

M 246:


Minimum MinimumTensile Yield Mod. of

Strength Point Elast.(psi) (psi) (psi)

45,000 33,000 29 x 10 6

12.4.5 Smooth-Lined Pipe

Corrugated metal pipe composed of a smooth liner andcorrugated shell attached integrally at helical seamsspaced not more than 30 inches apart may be designed inaccordance with Article 12.1 on the same basis as a stan-dard corrugated metal pipe having the same corrugationsas the shell and a weight per foot equal to the sum of theweights per foot of liner and helically corrugated shell.The shell shall be limited to corrugations having a max-imum pitch of 3 inches and a thickness of not less than60% of the total thickness of the equivalent standardpipe.

12.5 SPIRAL RIB METAL PIPE

12.5.1 General

12.5.1.1 Spiral Rib metal pipe and pipe-arches arehelically formed from a single thickness of steel or alu-minum with outwardly projecting ribs and a lockseam.The specifications are

Aluminum: AASHTO M 196, M 190Steel: AASHTO M 36, M 245, M 190

12.5.2.1 Spiral Rib pipe and pipe-arches installed inembankment conditions shall have a granular soil backfillenvelope extending to a minimum of one span on eachside of the pipe and one foot above the pipe. This granu-lar soil envelope shall meet the material and compactionrequirements of Article 12.1.6.1 (a).

12.5.2.2 Spiral Rib pipe and pipe-arches installed instandard trench conditions shall have a backfill envelopethat

(a) Meets the material and compaction requirementsof Article 12.1.6.1 (a).(b) Extends a minimum of 2 feet each side of the pipeto the trench wall. To account for variable conditions,this recommendation shall be increased as required forpoor in situ soils. It may be decreased for trenches inrock or high-bearing strength in situ soils to the limitsrequired for backfill compaction. In this condition, theuse of cementitious grouts allows the envelope to bedecreased to 2 inches, each side of the pipe.(c) Extends a minimum of 1 foot above the crown ofthe pipe.

12.5.2.3 Pipe-Arch Design

The design of the corner backfill shall meet the re-quirements of Article 12.1.6.2.

12.5.2.4 Special Conditions

Design and installation shall meet the requirements ofArticle 12.1.7 for abrasive or corrosive conditions; Arti-cle 12.1.8 for minimum spacing of multiple runs; and Ar-ticle 12.1.9 for end treatment.

12.5.2.5 Construction and Installation

Construction and installation shall conform to Section23-Division II.

12.5.3 Design

12.5.3.1 Service load design shall conform to the re-quirements of Article 12.2-Safety Factor (SF) shall be:

Wall Area = 2.0Buckling = 2.0

12.5.3.1 Load factor design shall conform to the re-quirements of Article 12.3-Capacity modification factor,~), shall be

4 = 1.00


12.5.3.2 Flexibility Factor 12.5.4 Section Properties

(a) For steel conduits, FF should generally not exceed 12.5.4.1 Steel Conduits

the following values 3/4 X 3/4 x 7'/2 Configuration

(1) For installation conforming to Article 12.5.2.1 Thickness As r I x 1073

(in) (sq inlft) (in) (in4/in)

FF = 0.21711.33

for /4 X /4 X 7/2 configurations. 0.064 0.509 0.258 2.821FF = 0.140 10.33 for/4X 1 X 11%2 configurations. 0.079 0.712 0.250 3.701

(2) For installations conforming to Article 0.109 1.184 0.237 5.5370.138 1.717 0.228 7.433

12.5.2.23/4 x 1 x I V/2 Configuration

FF = 0.263 10- 31 for'/4 X '/4 X 7/2 configurations A. r I x 10-3

FF = 0.163 I0 33 for - /4 X 1 X 11 %z configurations. (sq in 3ft) fin) (ink /in)

0.374 0.383 4.580Note: 1 is the applicable moment of inertia value from Ar- 0.524 0.373 6.080ticle 12.5.4.1. 0.883 0.355 9.260

Note: Effective section properties at full yield stress.

(b) For aluminum conduits, FF should generally notexceed the following values

(1) For installations conforming to Article12.5.2.1

FF = 0.340I0.33

for -1/4 X '/4 X 7/2 configurations.

FF = 0.175I0.33

for 1/4 X 1 X 11 /2 configurations.

(2) For installations conforming to Article12.5.2.2

FF = 0.420 I 0.33 for 3/4 X 3/4 X 7/2 configurations.FF = 0.215 11 -31 for 3/4 X 1 X 11 /2 configurations.

Note: 1 is the applicable moment of inertia value from Ar-ticle 12.5.4.2.


The minimum cover for design loads shall be mea-sured from the top of rigid pavement or the bottom of flex-ible pavement such that

(a) For steel conduits the minimum cover shall bespan/4, but not less than 12 inches;(b) For aluminum conduits with spans of 48 inches orless, the minimum cover shall be span/2, but not lessthan 12 inches. For aluminum conduits with spansgreater than 48 inches, the minimum cover shall bespan/2.75, but not less than 24 inches.

For construction requirements, see Article 26.6-Division II.


Thickness(in)

3/4 X

3/4X 716 Configuration

A, r I x 10(sq inAt) (in) (in4/in)

0.060 0.415 0.272 2.5580.075 0.569 0.267 3.3720.105 0.914 0.258 5.0730.135 1.290 0.252 6.826

3/4 x 1 x 11 1/2 Configuration

A. r I x 10-3

(sq inift) (in) (in4/in)

0.312 0.396 4.0800.427 0.391 5.4500.697 0.380 8.3901.009 0.369 11.480

Note: Effective section properties at full yield stress.

12.5.5 Chemical and Mechanical Requirements

12.5.5.1 Steel Spiral Rib Pipe and Pipe-ArchRequirements-AASHTO M 218

Mechanical Properties for DesignMinimum Minimum

Tensile Yield Modulus ofStrength Point Elasticity

(psi) (psi) (psi)

45,000 33,000 29 x 106

12.5.5.2 Aluminum Spiral Rib Pipe and Pipe-Arch Requirements-AASHTO M 197


Minimum MinimumMaterial Tensile Yield Mod. of

Grade Strength Point Elast.

(psi) (psi ) (psi)

3004-1134 31,000 24,000 10 x 106

3004-H32 27,000 20,000 lox 10 6

H34 temper must be used with riveted pipes to acheive seam strength.Both H32 and H34 temper material may be used with helical pipe.

12.6 DIVISION I-DESIGN 347

12.6 STRUCTURAL PLATE PIPE STRUCTURES

12.6.1 General

12.6.1.1 Structural plate pipe, pipe-arches, andarches shall be bolted with annular corrugations only.

The specifications are

Aluminum SteelAASHTO M 219 AASHTO M 167

12.6.1.2 Service Load Design-safety factor, SF

Seam strength = 3.0Wall area = 2.0Buckling = 2.0

12.6.1.3 Load Factor Design-CapacityModification Factor, (~

Wall area and buckling = 1.0Seam strength = 0.67

12.6.1.4 Flexibility Factor

(a) For steel conduits, FF should generally not exceedthe following values

6 in. X 2 in. corrugation FF = 2.0 X 10 -2 (pipe)6 in. X 2 in. corrugation FF = 3.0 X 10

-2(pipe-

arch)6 in. X 2 in. corrugation FF = 3.0 X 10

-2(arch)

(b) For aluminum conduits, FF should generally notexceed the following values

9 in. X 2%2 in. corrugation FF = 2.5 X 10-2

(pipe)9 in. X 2%2 in. corrugation FF = 3.6 X 10 -2 (pipe-

arch)9 in. X 2%2 in. corrugation FF = 3.6 X 10 -2 (arch)


The minimum cover for design loads shall be Span/8but not less than 12 inches. (The minimum cover shall bemeasured from the top of a rigid pavement or the bottomof a flexible pavement.) For construction requirements,see Article 26.6-Division II.


Minimum Longitudinal Seam Strengths

6" x 2" Steel Structural Plate Pipe_Thickness Diameter 4 Bolts/ft 6 Bolts/ft 8 Bolts/ft

(in) (in.) (kips/ft) (kips/ft) (kips/ft)

0.109 3/4 43.00.138 314 62.00.168 3/4 81.00.188 3/4 93.00.218 3/4 112.00.249 3/4 132.00.280 3/4 144.0 180 1940.318 7/8 2350.380 7/8 285

9" x 2'A" Aluminum Structural Plate PipeSteel Bolts Aluminum

Bolts51/3 Bolts 5'/3 Bolts

Thickness Bolt Size Per ft Per ft(in.) (in.) (kips/ft) (kips/ft)

0.100 3/4 28.0 26.40.125 3/4 41.0 34.80.150 3/4 54.1 44.40.1 5 3/4 63.7 52.80.200 3/4 73.4 52.80.225 3/4 83.2 52.80.250 3/4 93.1 52.8


12.6.3.1 Steel Conduits

6" x 2" CorrugationsThickness AS r I x 10-3

(in.) (in./ft) (in.) (in."/in.)

0.109 1.556 0.682 60.4110.138 2.003 0.684 78.1750.168 2.449 0.686 96.1630.188 2.739 0.688 108.0000.218 3.199 0.690 126.9220.249 3.650 0.692 146.1720.280 4.119 0.695 165.8360.318 4.671 0.698 190.0000.380 5.613 0.704 232.000


Thickness(in.)

A.(sq in./ft)

9" x 2'/2" Corrugations

r I x 10-1

(in.) (in. 4/in.)

0.100 1.404 0.8438 83.0650.125 1.750 0.8444 103.9910.150 2.100 0.8449 124.8830.175 2.449 0.8454 145.8950.200 2.799 0.8460 166.9590.225 3.149 0.8468 188.1790.250 3.501 0.8473 209.434


12.6.4 Chemical and Mechanical Properties

12.6.4.1 Aluminum Structural Plate Pipe, Pipe-Arch, and Arch MaterialRequirements-AASHTO M 219, Alloy5052


Minimum MinimumTensile Yield Mod. of

Thickness Strength Point Elast.(in.) (psi) (psi) (psi)

0.100 to 0.175 35,000 24,000 10 x 106

0.176 to 0.250 3400 24,000 10 x 106

12.6.4.2 Steel Structural Plate Pipe, Pipe-Arch,and Arch Material Requirements-AASHTO M 167


Minimum MinimumTensile Yield Mod. ofStrength Point Elast.

(psi) (psi) (psi)

45,000 33,000 29 x 10 6

12.6.5 Structural Plate Arches

The design of structural plate arches should be basedon ratios of a rise to span of 0.3 minimum.

12.7 LONG-SPAN STRUCTURAL PLATESTRUCTURES

12.7.1 General

Long-span structural plate structures are short-spanbridges defined as follows:

12.7.1.1 Structural plate structures (pipe, pipe-arch,and arch) that exceed the maximum sizes imposed by Ar-ticle 12.6.

12.7.1.2 Special shapes of any size that involve a rel-atively large radius of curvature in crown or side plates.Vertical ellipses, horizontal ellipses, underpasses, lowprofile arches, high profile arches, and inverted pearshapes are the terms describing these special shapes.

12.7.1.3 Wall strength and chemical and mechanicalproperties shall be in accordance with Article 12.6. The

construction and installation shall conform to Section26-Division 11.

12.7.2 Structure Design

12.7.2.1 General

Long-span structures shall be designed in accordancewith Articles 12.1 and 12.6, and 12.2 or 12.3 except thatthe requirements for buckling and flexibility factor shallnot apply. The span in the formulae for thrust shall be re-placed by twice the top arc radius. Long-span structuresshall include acceptable special features. Minimum re-quirements are detailed in Table 12.7.2A.

TABLE 12.7.2A Minimum Requirements for Long-SpanStructures with Acceptable Special Features

1. TOP ARC MINIMUM THICKNESS

Top Radius (ft)

15 15-17 17-20 20-23 23-25

6„ x 2"CorrugatedSteel Plates 0.109 in. 0.138 in. 0.168 in. 0.218 in. 0.249 in.

H. MINIMUM COVER IN FEET

TOP RADIUS (FT)

SteelThickness'in inches 15 15-17 17-20 20-23 23-25

.109 2.5

.138 2.5 3.0

.168 2.5 3.0 3.0

.188 2.5 3.0 3.0

.218 2.0 2.5 2.5 3.0

.249 2.0 2.0 2.5 3.0 4.0

.280 2.0 2.0 2.5 3.0 4.0

III. GEOMETRIC LIMITS

A. Maximum Plate Radius-25 Ft.B. Maximum Central Angle of Top Arc = 80'C. Minimum Ratio, Top Arc Radius to Side Arc Radius = 2D. Maximum Ratio, Top Arc Radius to Side Arc Radius = 5*

*Note: Sharp radii generate high soil bearing pressures.Avoid high ratios when significant heights of fill areinvolved.

IV. SPECIAL DESIGNS

Structures not described herein shall be regarded as specialdesigns.

'When reinforcing ribs are used the moment of inertia of thecomposite section shall be equal to or greater than the moment ofinertia of the minimum plate thickness shown.

12.7.2.2 DIVISION I-DESIGN 349

0 0 0PIPE ARCH

ROUND VERTICAL ELLIPSE0ARCH

UNDERPASS HORIZONTALELLIPSE

LOW PROFILE ARCH

FIGURE 12.7.1A Standard Terminology of Structural Plate Shapes Including Long-Span Structures

12.7.2.2 Acceptable Special Features

(a) Continuous longitudinal structural stiffeners con-nected to the corrugated plates at each side of the toparc. Stiffeners may be metal or reinforced concrete ei-ther singly or in combination.(b) Reinforcing ribs formed from structural shapescurved to conform to the curvature of the plates, fas-tened to the structure as required to ensure integral ac-tion with the corrugated plates, and spaced at such in-tervals as necessary to increase the moment of inertiaof the section to that required by the design.

12.7.3 Foundation Design

12.7.3.1 Settlement Limits

Foundation design requires a geotechnical survey ofthe site to ensure that both the structure and the criti-cal backfill zone on each side of the structure will be

properly supported, within the following limits and con-siderations:

(1) Once the structure has been backfilled over thecrown, settlements of the supporting backfill relative tothe structure must be limited to control dragdownforces. If the sidefill will settle more than the structure,a detailed analysis may be required.(2) Settlements along the longitudinal centerline ofarch structures must be limited to maintain slope andpreclude footing cracks (arches). Where the structurewill settle uniformly with the adjacent soils, long spanswith full inverts can be built on a camber to achieve aproper final grade.(3) Differential settlements across the structure (fromspringline to springline) shall not exceed 0.01 (Span)2

/

rise in order to limit excessive rotation of the structure.More restrictive settlement limits may be required toprotect pavements, or to limit longitudinal differentialdeflections.


12.7.3.2 Footing Reactions (Arch Structures)

Footing reactions are calculated by simple statics tosupport the vertical loads. Soil load footing reactions(VDL ) are taken as the weight of the fill and pavementabove the springline of the structure.

Live loads, which provide relatively limited pressurezones acting on the crown of the structure are distributedto the footings.

Footing reactions may be taken as

Rv = (VDL + VLL ) Cos A (12.7.3.2-1)

RH = (VDL + VLL) Sin 0 (12.7.3.2-2)

where

R, = Vertical footing reaction component (K/ft)R H = Horizontal reaction component (K/ft)VDL = [HAS) - AT] a/2VLL = n(AL)/(LW + 2H 1)0 = Return angle of the structure (degrees)AL = Axle load (K) - 50% of all axles that can be

placed on the structure at one time32K for H 20/HS 2040K for H 25/HS 2550K for Tandem Axle160K for E80 Railroad Loading

AT = the area of the top portion of the structureabove the springline (ftz)

H, = Height of cover above the footing to traffic sur-face (ft.)

H2 = Height of cover from the structure's springlineto traffic surface (ft.)

LW = Lane width (ft.)

n =integer 2H, + 2 :s_: number of traffic lanesC LW

a = Unit weight of soil (k/ft3)

The width of the envelope, on each side of the structureshall be sized to limit shape change during constructionactivities outside the envelope and to control deflectionsunder service loads. (See Articles 12.7.4.2 and 12.7.4.3).

12,7.4.1 Soil Requirements

Granular type soils shall be used as structure backfill (theenvelope next to the metal structure). The order of prefer-ence of acceptable structure backfill materials is as follows:

(a) Well-graded sand and gravel; sharp, rough, or an-gular if possible.(b) Uniform sand or gravel.(c) Approved stabilized soil shall be used only underdirect supervision of a competent, experienced soilsEngineer. Plastic soils shall not be used.

The structure backfill material shall conform to one ofthe following soil classifications from AASHTO M 145,Table 2: for height of fill less than 12 feet, A-1, A-3, A-24,and A-2-5; for height of fill of 12 feet and more, A- 1, A-3.Structure backfill shall be placed and compacted to not lessthan 90% density per AASHTO T 180.

12.7.4.2 Construction Requirements

To control shape change from construction activitiesoutside the envelope in trench conditions, the structuralbackfill envelope shall extend to the trench wall and becompacted against it. Alternatively, the structural backfillmust extend an adequate distance to protect the shape of thestructure from construction loads. The remaining trenchwidth can be filled with suitable backfill material com-pacted to meet the requirements of Article 12.7.4.3. In em-bankment conditions, the minimum structural backfillwidth shall be 6 feet. Where dissimilar materials not meet-ing geotechnical filter criteria are used adjacent to eachother, a suitable geotextile must be used to avoid migration.

12.7.3.3 Footing Design12.7.4.3 Service Requirements

Reinforced concrete footings shall be designed in ac-cordance with Article 4.4 to limit settlements to the re-quirements of Article 12.7.3.1.

Footings should be sized to provide bearing pressuresequal to or greater than those exerted by the structuralbackfill on the foundation. This helps to ensure that if set-tlements do occur the footings and backfill will settle inapproximately equal amounts avoiding excessive drag-down loads on the structure.

12.7.4 Soil Envelope Design

Structural backfill material in the envelope around thestructure shall meet the requirements of Article 12.7.4.1.

To limit defections under service loads, the width ofthe envelope on each side of the structure,shall be ade-quate to limit horizontal compression strain to 1% of thestructure ' s span on each side of the structure. This is a de-sign limit-not a performance limit. Any span increasethat occurs is principally due to the consolidation of theside support materials as the structure is loaded duringbackfilling. These are construction movements that atten-uate when full cover is reached.

Limiting horizontal compression strain requires anevaluation of the width and quality of the structural back-fill material selected as well as the in situ, embankment orother fill materials within the zone, on each side of the


structure, that extends to a distance equal to the rise of thestructure plus its cover height (See Figure 12.7.4A).

Forces acting radially off the small radius corner arc ofthe structure at a distance d l from the structure can be cal-culated as

Pi = RT

d(12.7.4.3-1)

where

P t = the horizontal pressure from the structure at adistance d, from it (psf)

dl = distance from the structure (ft)T = Total dead load and live load thrust in the struc-

ture (Article 12.7.2.1-psf)R~ = Corner radius of the structure (ft)

The required envelope width beside the pipe, d, can becalculated for a known, allowable bearing pressure as

d= T - R,: (12.7.4.3-2)PBrg

where

d = required envelope width beside the structure (ft)PB,g = Allowable bearing pressure to limit compres-

sion (strain) in the trench wall or embankment(psf)

The structural backfill envelope shall continue abovethe crown to the minimum cover level for that structure or,if it is less, to the bottom of the pavement (or granular basecourse) or the bottom of any relief slab, etc.

12.7.5 End Treatment Design

End treatment selection and design is an integral partof the structural design. It ensures proper support of theends of the structure while providing protection fromscour, hydraulic uplift and loss of backfill due to erosionforces.

12.7.5.1 Standard Shell End Types

The standard end types for the corrugated plate shellare provided in Figure 12.7.5A. Step bevel, full bevel andskewed ends all involve cutting the plates within a ring.Each has its own structural considerations.

Step bevels cut the corner (and side on pear and highprofile arch shapes) plates on a diagonal (bevel) to matchthe fill slope. The following limits apply:

• The rise of the top step must be equal to or greaterthan the rise of the top arc; thus plates in the top arcare left uncut.

• The bottom step-for structures with inverts, must meet the re-

quirements for a top step.-for arches, must be a minimum of 6 inches.

H

MINIMUM LIMITSOF COMPACTED

NORMAL ROAD FILL

6 '

MIN

UJ _JU L'-Q

Y

D_ QO m

I QLn Me'~oJ Z

H

r` 7L-J

COMPACTED MINIMUM LIMITS OFNORMAL COMPACTED SELECT GRANULAR

ROAD FILL STRUCTURAL BACKFILL

6 ' NORMAL ROADFILL ABOVE

MINI-

MIN. COVER LEVEL

MIN.'COVERLEVEL

NATURAL LONGUNDISTURBED SPANEMBANKMENT - - - -

IL-J

FIGURE 12.7.4A Typical Structural Backfill Envelope and Zone of Structure Influence


Pv

Rt = top radius of the structureRc = corner radius of the structured = minimum structural backfill widthP = the horizontal pressure from the structure at

a distance d from it (psf)Pv = dead and live toad pressure (psf) on the crown

FIGURE 12.7.411 Assumed Pressure Distribution

• The slope of the cut plates generally shall be no flat-ter than 3:1.

• The upper edge of the cut plates must be bolted toand supported by a structural concrete slope collar,slope pavement, etc.

Full bevel ends are limited to special design only.Structures with full inverts must have a bottom step con-forming to the requirements for step bevel ends.

The bevel cut edge of all plates must be supported bya suitable, rigid concrete slope collar.

• Skew cut ends must be fully connected to and sup-ported by a reinforced concrete (or other rigid) head-wall. The headwall must extend an adequate dis-tance above the crown of the structure to be capableof reaching the ring compression thrust forces fromthe cut plates. In addition to normal active earth andlive load pressures, the headwall will react to a com-ponent of the radial pressure exerted by the structure(See Article 12.7.4.3).

12.7.5.2 Balanced Support

Soil support must be relatively balanced from sideto side, perpendicularly across the structure. In lieu ofa special design, slopes running perpendicularly acrossthe structure are limited to a maximum of 10%, for

cover heights of 10 feet or less, and to 15% for highercovers.

Unbalanced soil support occurs whenever a structure isskewed to an embankment. When this occurs, the fill mustbe warped (shaped) to maintain balanced support and toprovide an adequate width of backfill and embankmentsoil to support the ends.

In lieu of a special design, a flattened area running par-allel to the structure shall be provided to extend out a dis-tance of 1.5 (rise + cover) beyond the springline.

12.7.5.3 Hydraulic Protection

In hydraulic applications, the structure, which includesthe shell, footings, structural backfill envelope and otherfill materials within the zone influenced by the structuremust be protected.

12.7.5.3.1 Backfill Protection

Loss of backfill integrity through piping action must beconsidered. If materials prone to piping are used, thestructure and ends of the backfill envelope must be ade-quately sealed to control soil migration and/or infiltration.

12.7.5.3.2 Cut-Off (Toe) Walls

All hydraulic structures with full inverts require up-stream and downstream cut-off (toe) walls. Invert plates


END VIEW ELEVATION VIEW

(A) SQUARE ENDL.AY CAP,

SLOPE PAVEMENT,RIP RAP. ETC.AS REOWRIED

TOP STEP

REINFORCED CONCRETESLOPE COLLAR

2 rm.

BOTTOM STEP

ELEVATION VIEW

(B) STEP BEVEL

HEADWALL

"T CONCRETEPALL MUM=

SKEW END TEN

(C) SKEW CUT EN(REQUIRES FULL HEADWALL)

FIGURE 12.7.5A Standard Structure End Types

CLAY CAP,SLOPE PAVEMENT,

RIP RAP, M.AS REGUtRED -

REINFORCEDCONCRETE SLOPE COLLAR

AND TOE WALL

END VIEW

ELAN WLW


shall be bolted to cut-off walls at a maximum 20 inch cen-ter-to-center spacing using 3 /4 inch bolts.

The cut-off wall shall extend to an adequate depth tolimit hydraulic percolation to control up-lift forces(Article 12.7.5.3.3) and scour (Article 12.7.5.3.4).

12.7.5.3.3 Hydraulic Uplift

Hydraulic uplift is a design consideration for hydraulicstructures with full inverts where the design flow level inthe pipe may drop quickly. Resulting hydraulic gradients,with the water level higher in the backfill than in the pipe,must be limited to levels that will not buckle the invert orfloat the structure. Buckling may be evaluated using Arti-cle 12.7.2.3 assuming the span of the structure is twice theinvert radius. Where uplift can be a concern, design typi-cally employs adequate cut-off walls and other means toseal off water flow into the structural backfill.

12.7.5.3.4 Scour

Scour design shall meet the requirements of Article4.4.5.2. Where erodible soils are encountered, varying de-grees of conventional means of scour protection may beemployed to meet requirements.

Deep foundations such as piles or caissons are not tobe used without a special design that considers differen-tial settlement and provides a means to retain the struc-tural backfill if scour proceeds below the pile cap, etc.

12.7.6 Multiple Structures

Care must be exercised on the design of multiple,closely spaced structures to control unbalanced loading.Fills should be kept level over the series of structureswhen possible. Significant roadway grades across a seriesof structures require checking of the stability of the flexi-ble structures under the resultant unbalanced loading.

12.8 STRUCTURAL PLATE BOX CULVERTS

12.8.1 General

Structural plate box culverts (hereafter "box culverts")are composite reinforcing rib-plate structures of approxi-mate rectangular shape. Box culverts are intended forshallow covers and low wide waterway openings. Theshallow covers and extreme shapes of box culverts requirespecial design procedures. Requirements of Articles 12.1through 12.7 are not applicable to box culvert designs un-less included in Article 12.8 by specific reference.

12.8.1.1 Scope

Article 12.8 presents structural capacity requirementsfor box culverts based on the load factor method. Standard

shapes, soil requirements, and permissible product detailsfor box culverts in compliance with this specification aredefined.

12.8.2 Structural Standards

The design criteria presented in subsequent articles areapplicable only to structures in compliance with the stan-dards described in Article 12.8.

12.8.2.1 Structural plate box culverts shall be bolted.The box culvert materials specifications are

Aluminum SteelAASHTO M 219 AASHTO M 167

12.8.2.2 Reinforcing ribs shall be an aluminum orsteel structural section curved to fit the structural plates.Ribs shall be bolted to the plates so as to develop the plas-tic moment capacity required. Spacing between ribs shallnot exceed 2 feet on the crown and 4.5 feet on the haunch.Rib splices shall develop the plastic moment capacity re-quired at the location of the splice.

12.8.2.3 Plastic moment capacities of ribbed sectionsmay be computed using minimum yield strength valuesfor both rib and corrugated shell Such computed valuesmay be used for design only after they have been con-firmed by representative flexural test data. (Reference Ar-ticle 10.48.1).

12.8.3 Structure Backfill

12.8.3.1 Structure backfill material shall conform tothe requirements of Article 12.7.2.4, compacted to a min-imum 95% of standard density based on AASHTO T 99or 90% of standard density based on AASHTO T 180.

12.8.3.2 Specified structure backfill material shall be3 feet wide, minimum, at the footing and shall extend up-ward to the road base elevation.

TABLE 12.8.2A Geometric Requirementsfor Box Culverts

1. Span, (S), may vary from 8 ft-9 in. to 25 ft-5 in.II. Rise, (R), may vary from 2 ft-6 in. to 10 ft-6 in.

III. Radius of crown, (rj = 24 ft-9 1/2 in. maximumIV Radius of haunch, (rh) = 2 ft-6 in. minimumV 0 may vary from 50° to 70°

VI. Length of leg, (D), measured to the bottom of the plate, mayvary from 0.4 ft to 5.9 ft.

VII. Minimum length of rib on leg, (t), is either 19 in.; the length ofleg, (D), minus 3 in. or to within 3 in. of the top of a concretefooting, whichever is less.

12.8.4 DIVISION I-DESIGN 355

Crown

Haunch0

a

re rn R

t~

~-- End of Rib

i S I

FIGURE 12.8.2A Standard Terminology of StructuralPlate Box Culvert Shapes

12.8.4 Design

12.8.4.1 Analytical Basis for Design

Structural requirements for box culverts have been de-veloped from finite element analyses covering the rangeof structures allowed by Article 12.8.2.

12.8.4.1.1 Structural requirements are based onanalyses using two dimensional live loads equivalent toHS 20, 4-wheel, single-axle vehicles. Dead load of soilequals 120 pounds per cubic foot. Coefficients to adjust forother load conditions are contained in Article 12.8.4.3.2.

12.8.4.1.2 Backfill required in Article 12.8.3 is densegranular material. The analyses that provide the basis forthis specification were based on conservative soil proper-ties of low plasticity clay (CL) compacted to 90% of stan-dard AASHTO T 99.

12.8.4.2 Load Factor Method

The combined gamma and beta factors to be applied are

Dead load, load factor = 1.5Live load, load factor = 2.0

The capacity modification factor ~b is 1.00.

12.8.4.3 Plastic Moment Requirements

Analyses covering the range of box culvert shapes de-scribed in Article 12.8.2 have shown moment require-ments govern the design in all cases. Effects of thrust werefound to be negligible when combined with moment.

Metal box culverts act similar to rigid frames, distrib-uting moment between the crown and haunch on the basisof their relative stiffness. Within limits, increasing thestiffness of one component of the box (either crown orhaunch) reduces the portion of the total moment carriedby the other.

Article 12.8 provides for this moment distributionwithin the allowable limits of the moment proportioning

factor (P). P represents the proportion of the total momentthat can be carried by the crown of the box culvert andvaries with the relative moment capacities of the crownand haunch components. Limits for P are given in Table12.8.4D.

12.8.4.3.1 The sum of the crown and haunch deadload moments are

M DL = y x 10 -3 {S 3[0.0053 - 0.00024(S - 12)]+ 0.053 (H - 1.4)S2 1 (12-12)

where

M DL = The sum of the nominal crown and haunchdead load moments (kip-ft/ft)

S = Box culvert span in feet.y = Soil density (lbs/ft 3 )H = Height of cover from the box culvert rise to top

of pavement (ft)

12.8.4.3.2 The sum of the crown and haunch liveload moments are

MLL = CeeK,S/KZ (12-13)

where

MLL = The sum of the nominal crown and haunch liveload moments (kip-ft/ft)

Cee = Live load adjustment coefficient for axle loads,tandem axles, and axles with other than 4wheels;

CU = C,C2AL (12-14)

AL = Total axle load on single axle or tandem axles inkips;

C, = Adjustment coefficient for number of axles;C, = 1.0, for single axle;C, _ (0.5 + S/50), for tandem axles, (C l < 1.0);S = Box culvert span in feet;C2 = Adjustment coefficient for number of wheels

per axle. (Values for C2 are given in Table12.8.4A.)

H = Height of cover from the box culvert rise to topof pavement (ft.)

0.08K, = (H/S)02 , for 8 < S < 20 (12-15)

for 20 <- S <_ 26(12-16)

0.08 - 0.002(5 - 20)(14/S)o.2K, _


K2= 0.54H 2

-0.4H+5.05, for 1.4<_H<3.0(12-17)

K2 =1.90H+3, for3.0:~ H<_5.0 (12-18)

TABLE 12.8.4A C27 Adjustment Coefficient Values forNumber of Wheels Per Axle

Wheels Cover Depth, ftper

Axle 1.4 2.0 3.0 5.0

2 1.18 1.21 1.24 1.024 1.00 1.00 1.00 1.008 0.63 0.70 0.82 0.93

TABLE 12.8.4C Rh, Haunch Moment Reduction Values

Cover Depth, ft

1.4 2 3 4to5

0.66 0.74 0.87 1.00

If Equation (12-19) indicates a higher P factor thanpermitted by the ranges of Table 12.8.41), the actual crownis over designed, which is acceptable. However, in thiscase only the maximum value of P allowed by the tableshall be used to calculate the required haunch moment ca-pacity from Equation (12-20).

12.8.4.4 Footing Reactions

12.8.4.3.3 Crown plastic moment capacity (Mpc (~),and haunch plastic moment capacity (Mph (~), must beequal to or greater than the proportioned sum of loadadjusted dead and live load moments.

M PS > P[(C dl Mdt ) + (C 11M 11)] (12-19)

Mph ? (1.0 - P)[(C d1 M d1 ) + (RhC 11M 11 )1 (12-20)

where

P = Proportion of total moment carried by the crown.Limits for P are given in Table 12.8.41);

Rh =Haunch moment reduction factor from Table12.8.4E.

12.8.4.3.4 Article 12.8 can be used to check theadequacy of manufactured products for compliance withthe requirements of this specification. Using the actualcrown moment capacity provided by the box culvertunder consideration and the loading requirements of theapplication, Equation (12-19) is solved for the factor P.This factor should fall within the allowable range of Table12.8.41). Knowing the factor P, Equation (12-20) is thensolved for required haunch moment capacity, whichshould be less than or equal to the actual haunch momentcapacity provided.

TABLE 12.8.4B P, Crown Moment Proportioning Values

AllowableSpan ft Range of P

Less Than 10 0.55 to 0.7010-15 0.50 to 0.7015-20 0.45 to 0.7020-26 0.45 to 0.60

The reaction at the box culvert footing may be com-puted using the following equation

V = , y(HS/2,000 + S 2/40,000)+ AL/[8 + 2(H + R)] (12-21)

where

V = Reaction in kips per foot acting in the directionof the box culvert straight side;

y = Backfill unit weight in pounds per cubic foot;H = Height of cover over the crown in feet;S = Span of box culvert in feet;AL = Axle load in kips;R = Rise of box culvert in feet.

12.8.5 Manufacturing and Installation

12.8.5.1 Manufacture and assembly of structuralplates shall be in accordance with Articles 23.3.1.4,26.3.2, 26.3.3, 26.3.4, and 26.4.1. Reinforcing ribs shallbe attached as shown by the manufacturer. Bolts connect-ing plates, plates to ribs and rib splices shall be torqued to150-foot pounds.

12.8.5.2 Sidefill and overfill per Article 12.8.3 shallbe placed in uniform layers not exceeding 8 inches incompacted thickness at near optimum moisture withequipment and methods which do not damage or distortthe box culvert.

12.8.5.3 Following completion of roadway paving,crown deflection due to live load may be checked. After aminimum of 10 loading cycles with the design live load,the change in rise loaded with the design live load relativeto the rise unloaded, should not exceed %zoo of the boxculvert span.

Section 13

WOOD STRUCTURES

13.1 GENERAL AND NOTATIONS

13.1.1 General

The following information on wood design is generallybased on the National Design Specification for WoodConstruction (NDS ® ), 1991 Edition. Seethe 1991 Editionof the NDS ® for additional information.

13.1.2 Net Section

In determining the capacity of wood members, the netsection of the member shall be used. Unless otherwisenoted, the net section shall be determined by deducting fromthe gross section, the projected area of all material removedby boring, grooving, dapping, notching or other means.

13.1.3 Impact

In calculating live load stresses in wood, impact shallbe neglected unless otherwise noted. See Article 3.8.1.

13.1.4 Notations

a = coefficient based on support conditions for ta-pered columns (Article 13.7.3.4.2)

b = width of bending member (Article 13.6.4.3)c = coefficient based on sawn lumber, round timber

piles, glued laminated timber or structural com-posite lumber (Article 13.7.3.3.5)

CD = load duration factor (Article 13.5.5.2)C F = bending size factor for sawn lumber, struc-

tural composite lumber, and for glued lami-nated timber with loads applied parallel tothe wide face of the laminations (Article13.6.4.2)

C F = compression size factor for sawn lumber (foot-notes to Table 13.5. A)

CF = tension size factor for sawn lumber (footnotesto Table 13.5.1A) and structural compositelumber (footnotes to Tables 13.5.4A and13.5.413)

CH = sheer stress factor (footnotes to Table 13.5.1A)

CL = beam stability factor (Article 13.6.4.4)C M = wet service factor (Article 13.5.5.1)Cp = column stability factor (Article 13.7.3.3)Cv = volume factor for glued laminated timber with

loads applied perpendicular to the wide face ofthe laminations (Article 13.6.4.3)

Ce = bearing area factor (Article 13.6.6.3)Cf = form factor (Article 13.6.4.5)C

fu = flat use factor for sawn lumber (footnotes toTable 13.5. A)

C r = repetitive member factor for sawn lumber (foot-notes to Table 13.5.1A)

d = depth of member (Article 13.6.4.2.2)d,,,,, = maximum column face dimension (Article

13.7.3.4.2)dmi„ = minimum column face dimension (Article

13.7.3.4.2)diep = representative dimension for a tapered column

face (Article 13.7.3.4.2)E = tabulated modulus of elasticity (Article 13.6.3)E' = allowable modulus of elasticity (Article

13.6.3)Fe = tabulated unit stress in bending (Article 13.6.4.1)Fb = allowable unit stress in bending (Article 13.6.4.1)Fb = adjusted tabulated bending stress for beam sta-

bility (Article 13.6.4.4.5)Fe = tabulated unit stress in compression parallel to

grain (Article 13.7.3.2)F,' = allowable unit stress in compression parallel to

grain (Article 13.7.3.2)F* = adjusted tabulated stress in compression par-

allel to grain for column stability (Article13.7.3.3.5)

fe = actual unit stress in compression parallel to grain(Article 13.7.3.1)

Fe y = tabulated unit stress in compression perpendicu-lar to grain (Article 13.6.6.2)

Fc'L = allowable unit stress in compression perpendic-ular to grain (Article 13.6.6.2)

Fg = tabulated unit stress in bearing parallel to grain(Article 13.7.4.1)

Fb = allowable unit stress in bearing parallel to grain(Article 13.7.4.1)

357


F, = tabulated unit stress in tension parallel to grain(Article 13.8. 1)

Ft = allowable unit stress in tension parallel to grain(Article 13.8.1)

F„ = tabulated unit stress in shear parallel to grain(Article 13.6.5.3)

FV = allowable unit stress in shear parallel to grain(Article 13.6.5.3)

f„ = actual unit stress in shear parallel to grain (Arti-cle 13.6.5.2)

F B , = allowable unit stress for bearing on an inclinedsurface (Article 13.6.7)

K = column effective length factor (Article13.7.3.3.3)

KbE = material factor for beam stability (Article13.6.4.4.5)

K,E = material factor for column stability (Article13.7.3.3.5)

L = length of bending member between points ofzero moment (Article 13.6.4.3.1)

l = actual column length between points of lateralsupport (Article 13.7.3.3.3)

lb = length of bearing (Article 13.6.6.3)le = effective bending member length (Article

13.6.4.4.3)le = effective column length (Article 13.7.3.3.3)l„ = unsupported bending member length (Article

13.6.4.4.3)m = parameter for the specific material determined

in accordance with the requirements of ASTMD 5456 (Tables 13.5.4A and 13.5.4B)

RB = bending member slenderness ratio (Article13.6.4.4.4)

V = vertical shear (Article 13.6.5.2)VLD = maximum vertical shear at 3d or L/4 due to

wheel loads distributed laterally as specified formoment (Article 13.6.5.2)

VLL = distributed live load vertical shear (Article13.6.5.2)

VLu = maximum vertical shear at 3d or L/4 due

to undistributed wheel loads (Article 13.6.5.2)x = species variable for computing the volume fac-

tor (Article 13.6.4.3.1)0 = angle between the direction of load and the di-

rection of grain (Article 13.6.7)

13.2 MATERIALS

13.2.1.2 Dimensions

13.2.1.2.1 Structural calculations for sawn lumbershall be based on the net dimensions of the member forthe anticipated use conditions. These net dimensions de-pend on the type of surfacing, whether dressed, rough-sawn or full-sawn.

13.2.1.2.2 For dressed lumber, the net dry dimen-sions given in Table 13.2. shall be used for design, re-gardless of the moisture content at the time of manufac-ture or in use.

13.2.1.2.3 Where the design is based on rough, full-sawn or special sizes, the applicable moisture content anddimensions used in design shall be noted in the plans andspecifications.

TABLE 13.2.1A Net Dry Dimensionsfor Dressed Lumber

Nominal Dry Nominal DryThickness Thickness Width Width

Dimension Lumber (inches):2 1-1/2 2 1-1/2

2-1/2 2 3 2-1/2

3 2-1/2 4 3-1/2

3-1/2 3 5 4-1/2

4 3-1/2 6 5-1/2

4-1/2 4 8 7-1/4

10 9-1/4

12 11-1/4

14 13-1/4

16 15-1/4

Beams and Stringers and Posts and Timbers (inches):5 and 1/2 less 5 and 1/2 less

greater than greater thannominal nominal

13.2.2 Glued Laminated Timber

13.2.2.1 General

Glued laminated timber shall comply with the require-ments of AASHTO M 168 and shall be manufacturedusing wet-use adhesives.

13.2.1 Sawn Lumber13.2.2.2 Dimensions

13.2.1.1 General

Sawn lumber shall comply with the requirements ofAASHTO M 168.

13.2.2.2.1 Structural calculations for glued lami-nated timber shall be based on the net finished dimen-sions.


13.2.2.2.2 For Western Species and Southern Pine,the standard net finished widths shall be as given in Table13.2.2A. Other, nonstandard finished widths may be usedsubject to design requirements.

TABLE 13.2.2A Standard Net Finished Widths of GluedLaminated Timber Manufactured from

Western Species or Southern Pine

Nominal Western Species Southern PineWidth Net Finished Net Finished(in.) Width (in.) Width (in.)

4 3-1/8 36 5-1/8 58 6-3/4 6-3/4

10 8-3/4 8-1/212 10-3/4 10-1/214 12-1/4 1216 14-1/4 14

13.2.3 Structural Composite Lumber

13.2.3.1 General

Structural composite lumber, including laminated ve-neer lumber and parallel strand lumber, shall comply withthe requirements of ASTM D 5456 and shall be manufac-tured using wet-use adhesives which comply with re-quirements of ASTM D 2559.

13.2.3.2 Laminated Veneer Lumber

Laminated veneer lumber shall consist of a compositeof wood veneer sheet elements with wood fibers orientedprimarily along the length of the member. Veneer thick-ness shall not exceed 0.25 inches.

13.2.3.3 Parallel Strand Lumber

Parallel strand lumber shall consist of wood strand el-ements with wood fibers oriented primarily along thelength of the member. The least dimension at the strandsshall not exceed 0.25 inches and the average length shallbe a minimum of 150 times the least dimension.

13.2.3.4 Dimensions

Structural calculations for structural composite lumbershall be based on the net finished dimensions.

13.2.4 Piles

Wood piles shall comply with the requirements ofAASHTO M 168.

13.3 PRESERVATIVE TREATMENT

13.3.1 Requirement for Treatment

All wood used for structural purposes in exposed per-manent applications shall be pressure impregnated withwood preservative in accordance with the requirements ofAASHTO M 133.

13.3.2 Treatment Chemicals

All structural members that are not subject to directpedestrian contact shall preferably be treated with oil-typepreservatives. Members that are subject to direct pedes-trian contact, such as rails and footpaths, shall be treatedwith waterborne preservatives or oilborne preservatives inlight petroleum solvent. Direct pedestrian contact is con-sidered to be contact which may be made while the pedes-trian is situated anywhere in the access route provided forpedestrian traffic.

13.3.3 Field Treating

Insofar as is practicable, all wood members shall be de-signed to be cut, drilled, and otherwise fabricated prior topressure treatment with wood preservatives. When cut-ting, boring, or other fabrication is necessary after preser-vative treatment, exposed, untreated wood shall be speci-fied to be field treated in accordance with the requirementsof AASHTO M 133.

13.3.4 Fire Retardant Treatments

Fire-retardant chemicals shall not be used unless it isdemonstrated that they are compatible with the preserva-tive treatment. When fire retardants are used, design val-ues shall be reduced by the strength and stiffness reduc-tion factors specified by the fire retardant chemicalmanufacturer.

13.4 DEFLECTION

13.4.1 The term "deflection" as used herein shall be thedeflection computed in accordance with the assumptionsmade for loading when computing stress in the members.

13.4.2 Flexural members of bridge structures shall bedesigned to have adequate stiffness to limit deflections orany deformations that may adversely affect the strength orserviceability of the structure.


13.4.3 Members having simple or continuous spanspreferably should be designed so that the deflection due toservice live load does not exceed 11500 of the span.

13.4.4 For timber deck structures with timber girders orstringers of equal stiffness, and cross-bracing or di-aphragms sufficient in depth and strength to ensure lateraldistribution of loads, the deflection may be computed byconsidering all girders or stringers as acting together andhaving equal deflection. When the cross-bracing or di-aphragms are not sufficient to laterally distribute loads,deflection shall be distributed as specified for moment.

13.4.5 For concrete decks on wood girders or stringers,the deflection shall be assumed to be resisted by all beamsor stringers equally.

13.5 DESIGN VALUES

13.5.1 General

Stress and modulus of elasticity values used for design,referred to as allowable design values, shall be the tabu-lated values modified by all applicable adjustments re-quired by this Section. The actual stress due to loadingshall not exceed the allowable stress.

13.5.2 Tabulated Values for Sawn Lumber

13.5.2.1 Tabulated values for sawn lumber are givenin Table 13.5.1A for visually graded lumber and Table13.5. for mechanically graded lumber. Values for bear-ing parallel to grain are given in Table 13.5.2A. These val-ues are taken from the 1991 Edition of the NDS ® and rep-resent a partial listing of available species and grades.Refer to the 1991 Edition of the NDS ® for a more com-plete listing.

13.5.2.2 Stress Grades in Flexure

13.5.2.2.1 The tabulated unit bending stress for Di-mension (2 to 4 inches thick) and Post and Timber gradesapplies to material with the load applied either to the nar-row or wide face.

are graded to Beam and Stringer grade requirements, thetabulated unit bending stress for the applicable Beam andStringer grades may be used.

13.5.2.2.4 Beam and Stringer grades are normallygraded for use as a single, simple span. When used as acontinuous beam, the grading provisions customarily ap-plied to the middle third of the simple span length shall beapplied to the middle two-thirds of the length for two-spanbeams, and to the entire length for beams continuous overthree or more spans.

13.5.3 Tabulated Values for Glued LaminatedTimber

13.5.3.1 Tabulated values for glued laminated tim-ber of softwood species are given in Tables 13.5.3A and13.5.3B. Values for bearing parallel to grain are given inTable 13.5.2A. These values are taken from the 1993Edition of the American Institute of Timber Construc-tion, AITC 117-93 Design, "Standard Specifications forStructural Glued Laminated Timber of SoftwoodSpecies." Refer to AITC 117-93 Design for a more com-plete listing.

13.5.3.2 Tabulated values for hardwood species shallbe as given in the 1985 Edition of American Institute ofTimber Construction, AITC 119, "Standard Specificationsfor Hardwood Glued Laminated Timber."

13.5.3.3 Species other than those specifically in-cluded or referenced in this Section may be used, pro-vided that tabulated values are established for eachspecies in accordance with AASHTO M 168.

13.5.4 Tabulated Values for Structural CompositeLumber

13.5.4.1 Representative tabulated design values forstructural composite lumber are given in Table 13.5.4Afor laminated veneer lumber and Table 13.5.4B for paral-lel strand lumber.

13.5.5 Adjustments to Tabulated Design Values

13.5.5.1 Wet Service Factor, CM

13.5.2.2.2 The tabulated unit bending stress forDecking grades applies only when the load is applied tothe wide face.

13.5.2.2.3 The tabulated unit bending stress forBeam and Stringer grades applies only when the load isapplied to the narrow face. When Post and Timber sizes

13.5.5.1.1 Tabulated values for sawn lumber assumethat the material is installed and used under continuouslydry conditions where the moisture content of the wooddoes not exceed 19%. When the moisture content at in-stallation or in service is expected to exceed 19%, tab-ulated values shall be reduced by the wet service fac-

TABLE 13.5.1A Tabulated Design Values for Visually Graded Lumber and Timbers

Design Values in Pounds per Square Inch (psi)

Tension Shear Compression Compression ModulusParallel Parallel Perpendicular Parallel of Grading

Species and Size Bending to Grain to Grain to Grain to Grain Elasticity RulesCommercial Grade Classification Fb F, F„ F.1 F. E Agency

DOUGLAS FIR-LARCH

Select Structural 1450 1000 95 625 1700 1,900,000No. 1 & Btr 2"–4" thick 1150 775 95 625 1500 1,800,000 WWPANo. 1 1000 675 95 625 1450 1,700,000No. 2 2" & wider 875 575 95 625 1300 1,600,000 WCLIB

Dense Select Structural 1900 1100 85 730 1300 1,700,000Select Structural Beams and 1600 950 85 625 1100 1,600,000Dense No. 1 Stringers 1550 775 85 730 1100 1,700,000No. 1 1350 675 85 625 925 1,600,000No. 2 875 425 85 625 600 1,300,000 WCLIB

Dense Select Structural 1750 1150 85 730 1350 1,700,000Select Structural Posts and 1500 1000 85 625 1150 1,600,000Dense No. 1 Timbers 1400 950 85 730 1200 1,700,000No. 1 1200 825 85 625 1000 1,600,000No. 2 750 475 85 625 700 1,300,000

Dense Select Structural 1850 1100 85 730 1300 1,700,000Select Structural 1600 950 85 625 1100 1,600,000Dense No. 1 Beams and 1550 775 85 730 1100 1,700,000No. 1 Stringers 1350 675 85 625 925 1,600,000Dense No. 2 1000 500 85 730 700 1,400,000No.2 875 425 85 625 600 1,300,000 WWPA

Dense Select Structural 1750 1150 85 730 1350 1,700,000Select Structural 1500 1000 85 625 1150 1,600,000Dense No. 1 Posts and 1400 950 85 730 1200 1,700,000No.1 Timbers 1200 825 85 625 1000 1,600,000Dense No. 2 800 550 85 730 550 1,400,000No. 2 700 475 85 625 475 1,300,000

EASTERN SOFTWOODS

Select Structural 1250 575 70 335 1200 1,200,000 NELMANo. 1 2"–4" thick 775 350 70 335 1000 1,100,000No. 2 2" & wider 575 275 70 335 825 1,100,000 NSLB

z

TABLE 13.5.1A Tabulated Design Values for Visually Graded Lumber and Timbers (Continued) NDesign Values in Pounds per Square Inch (psi)


Species and Size Bending to Grain to Grain to Grain to Grain Elasticity RulesCommercial Grade Classification Fb Ft F„ F, F. E Agency

HEM-FIR

Select Structural 1400 900 75 405 1500 1,600,000No. 1 & Btr 2"-4" thick 1060 700 75 405 1350 1,500,000

WWPANo. 1 950 600 75 405 1300 1,500,000No. 2 T & wider 850 500 75 405 1250 1,300,000 WCLIB

Select Structural Beams and 1300 750 70 405 925 1,300,000No. 1 Stringers 1050 525 70 405 750 1,300,000

No.2 675 350 70 405 500 1,100,000 WCLIB

xSelect Structural Posts and 1200 800 70 405 975 1,300,000No.1 Timbers 975 650 70 405 850 1,300,000

No. 2 575 375 70 405 575 1,100,000 xSelect Structural Beams and 1250 725 70 405 925 1,300,000No. 1 Stringers 1050 525 70 405 775 1,300,000No.2 675 325 70 405 475 1,100,000 WWPA

dSelect Structural Posts and 1200 800 70 405 975 1,300,000No.l Timbers 950 650 70 405 850 1,300,000 cnNo.2 525 350 70 405 375 1,100,000

MIXED SOUTHERN PINE

Select Structural 2050 1200 100 565 1800 1,600,000

No. 1 27-4" thick 1450 875 100 565 1650 1,500,000

No.2 2"-4" wide 1300 775 90 565 1650 1,400,000

Select Structural 1850 1100 90 565 1700 1,600,000No. 1 27-4" thick 1300 750 90 565 1550 1,500,000

No.2 5"-6" wide 1150 675 90 565 1550 1,400,000SPIB

Select Structural 27-4"thick 1750 1000 90 565 1600 1,600,000No.1 1200 700 90 565 1450 1,500,000No.2 8" wide 1050 625 90 565 1450 1,400,000

Select Structural 20-4"thick 1500 875 90 565 160Q 1,600,000No.1 1050 600 90 565 1450 1,500,000

No.2 10" wide 925 550 90 565 1450 1,400,000 "'

TABLE 13.5.1A Tabulated Design Values for Visually Graded Lumber and Timbers (Continued)



Species and Size Bending to Grain to Grain to Grain to Grain Elasticity RulesCommercial Grade Classification Fb F t F,. F, F. E Agency

Select Structural 2"-4" thick 1400 825 90 565 1550 1,600,000No.1 975 575 90 565 1400 1,500,000No. 2 12" wide 875 525 90 565 1400 1,400,000

MIXED SOUTHERN PINE (Dry or Wet Service Conditions)

Select Structural 5" x 5" 1500 1000 110 375 900 1,300,000No. 1 & larger 1350 900 110 375 800 1,300,000 SPIBNo. 2 850 550 95 375 525 1,000,000

NORTHERN RED OAK

Select Structural 1400 800 110 885 1150 1,400,000No. 1 20-4" thick 1000 575 110 885 925 1,400,000No. 2 2" & wider 975 575 110 885 725 1,300,000

Select Structural Beams and 1600 950 105 885 950 1,300,000No.I Stringers 1350 675 105 885 800 1,300,000No.2 875 425 105 885 500 1,000,000 NELMA

Select Structural Posts and 1500 1000 105 885 1000 1,300,000No.1 Timbers 1200 800 105 885 875 1,300,000No. 2 700 475 105 885 400 1,000,000

RED MAPLE

Select Structural 1300 750 105 615 1100 1,700,000No. 1 2"-4" thick 925 550 105 615 900 1,600,000No. 2 2" & wider 900 525 105 615 700 1,500,000

Select Structural Beams and 1500 875 100 615 900 1,500,000No. 1 Stringers 1250 625 100 615 750 1,500,000No.2 800 400 100 615 475 1,200,000 NELMA

Select Structural Posts and 1400 925 100 615 950 1,500,000No.1 Timbers 1150 750 100 615 825 1,500,000No.2 650 425 100 615 375 1,200,000

z



Parallel Parallel Perpendicular Parallel of GradingSpecies and Size Bending to Grain to Grain to Grain to Grain Elasticity Rules

Commercial Grade Classification Fb Ft F„ F, F. E Agency

RED OAK

Select Structural 1150 675 85 820 1000 1,400,000No. 1 2"-4" thick 825 500 85 820 825 1,300,000No. 2 2" & wider 800 475 85 820 625 1,200,000

Select Structural Beams and 1350 800 80 820 825 1,200,000No. 1 Stringers 1150 550 80 820 700 1,200,000No.2 725 375 80 820 450 1,000,000 NELMA

Select Structural Posts and 1250 850 80 820 875 1,200,000No.I Timbers 1000 675 80 820 775 1,200,000No. 2 575 400 80 820 350 1,000,000

SOUTHERN PINE

Select Structural 2850 1600 100 565 2100 1,800,000 SPIBNo. 1 2!'-40 thick 1850 1050 100 565 1850 1,700,000No. 2 2"-4" wide 1500 825 90 565 1650 1,600,000

Select Structural 2550 1400 90 565 2000 1,800,000No. 1 2"-4" thick 1650 900 90 565 1750 1,700,000No. 2 5"-6" wide 1250 725 90 565 1600 1,600,000

Select Structural 2300 1300 90 565 1900 1,800,000No. 1 2"4" thick 1500 825 90 565 1650 1,700,000No. 2 8" wide 1200 650 90 565 1550 1,600,000

Select Structural 2"--4" thick 2050 1100 90 565 1850 1,800,000No. 1 10" wide 1300 725 90 565 1600 1,700,000No. 2 1050 575 90 565 1500 1,600,000

Select Structural 1900 1050 90 565 1800 1,800,000No. 1 2"--4" thick 1250 675 90 565 1600 1,700,000No. 2 12" wide 975 550 90 565 1450 1,600,000

wTABLE 13.5.1A Tabulated Design Values for Visually Graded Lumber and Timbers (Continued)



Species and Size Bending to Grain to Grain to Grain to Grain Elasticity RulesCommercial Grade Classification Fb F, F,. F~, F. E Agency

SOUTHERN PINE (Dry or Wet Service Conditions)

Dense Select Structural 1750 1200 110 440 1100 1,600,000Select Structural 5" x 5" 1500 1000 110 375 950 1,500,000No. 1 & larger 1350 900 110 375 825 1,500,000 SPIBNo. 2 850 550 100 375 525 1,200,000

SPRUCE-PINE-FIR

Select Structural 2 "-4" thick 1250 675 70 425 1400 1,500,000No. 1/No. 2 2" & wider 875 425 70 425 1100 1,400,000 d

DOSelect Structural Beams and 1100 650 65 425 775 1,300,000No. 1 Stringers 900 450 65 425 625 1,300,000 pNo.2 600 300 65 425 425 1,000,000 NLGA Z

dSelect Structural Posts and 1050 700 65 425 800 1,300,000No.1 Timbers 850 550 65 425 700 1,300,000 toNo. 2 500 325 65 425 500 1,000,000

SPRUCE-PINE-FIR (SOUTH) z

Select Structural 1300 575 70 335 1200 1,300,000No. 1 2"-A" thick 850 400 70 335 1050 1,200,000No. 2 2" & wider 750 325 70 335 975 1,100,000 NELMA

Select Structural Beams and 1050 625 65 335 675 1,200,000No.1 Stringers 900 450 65 335 575 1,200,000 WCLIBNo.2 575 300 65 335 350 1,000,000 NSLB

Select Structural Posts and 1000 675 65 335 700 1,200,000 WWPANo. 1 Timbers 800 550 65 335 625 1,200,000No. 2 350 225 65 335 225 1,000,000

YELLOW POPLAR

Select Structural 1000 575 75 420 900 1,500,000No. 1 2"-4" thick 725 425 75 420 725 1,400,000 NLSBNo. 2 2" & wider 700 400 75 420 575 1,300,000

w

1W

011


1. Design values are taken from the 1991 Edition of the NDS* and are for a 10-year load duration and dry service conditions. Refer to the 1991 NDS*for additional species and grades and for a summary of grading rules agencies and commercial species classifications.

2. Wet Service Factor, Cm. When dimension lumber, 2" to 4" thick is used where moisture content will exceed 19%, design values shall be multiplied bythe following wet service factors:

WET SERVICE FACTORS, CM

Fb F, F" F.j- F. E

0.85* 1.0 0.97 0.67 0.8** 0.9

* when (Fb )(C F)s

1,150 psi, CM = 1.0* * when F, <— 750 psi, CM = 1.0

When timbers 5" by 5" and larger are used where moisture content will exceed 19%, design values shall be multiplied by the following wet service factors(for Southern Pine and Mixed Southern Pine, use tabulated values without further adjustment):


Fb F, F„ F~L F~ E

1.00 1.00 1.00 0.67 0.91 1.00

3. Size Factor, CF . For all species other than Southern Pine and Mixed Southern Pine, tabulated bending, tension, and compression parallel to grain designvalues for dimension lumber 2" to 4" thick shall be multiplied by the following size factors:

SIZE FACTORS, C F

Fb F, F.

ThicknessGrades Width 2"& 3" 4"

2", 3" & 4" 1.5 1.5 1.5 1.15Select 5" 1.4 1.4 1.4 1.1

Structural, 6" 1.3 1.3 1.3 1.1No. 1 & Btr. 8" 1.2 1.3 1.2 1.05

No. 1, No. 2, 10" 1.1 1.2 1.1 1.0No. 3 12" 1.0 1.1 1.0 1.0

14" & wider 0.9 1.0 0.9 0.9


For Southern Pine and Mixed Southern Pine dimension lumber, 2" to 4" thick, appropriate size adjustment factors have been incorporated in tabulated values,with the following exceptions:

For dimension lumber 4" thick, 8" and wider, tabulated bending design values shall be multiplied by the size factor, CF = I.I.

For dimension lumber wider than 12", tabulated bending, tension, and compression parallel to grain design values for 12" wide lumber shall bemultiplied by the size factor, CF = 0.9.

4. Flat Use Factor, G„• Bending design values are based on edgewise use (load applied to narrow face). When dimension lumber 2" to 4" thick is usedflatwise (load applied to wide face), the bending design value shall be multiplied by the following flat use factors:

FLAT USE FACTORS, Cr„

Width

Thickness

2"& 3" 4"

2" & 3" 1.0 ...4" 1.1 1.05" 1.1 1.056" 1.15 1.058" 1.15 1.05

10" & wider 1.2 1.1

5. Repetitive Member Factor, C,. Bending design values for dimension lumber 2" to 4" thick shall be multiplied by the repetitive member factor C. = 1.15,when such members are used as stringers, decking or similar members which are in contact or are spaced not more than 24" on centers, are not less than3 in number and are joined by load distributing elements adequate to support the design load.

6. Shear Stress Factor, C H . Tabulated shear design values parallel to grain, Fv, have been reduced to allow for the occurrence of splits, checks, and shakesand may be multiplied by the shear stress factors given below when the length of split, or size of check or shake isknown and no increase in them is anticipated.When the shear stress factor is applied to Southern Pine or Mixed Southern Pine, a tabulated design value of Fv = 901b/in? shall be used for all grades.Shear stress factors shall be linearly interpolated.

SHEAR STRESS FACTORS, CH

Length of split on Size of shake= inLength of split on wide face wide face of 3" (nominal) 2" (nominal) and

of 2" (nominal) lumber CH and thicker lumber CH thicker lumber CH

no split..................................................2.00112 x wide face....................................... 1.673/4 x wide face .......................................1.501 x wide face......................................... 1.331-1/2 x wide face or more........................1.00

no split......................................................2.001/2 x narrow face ....................................... 1.673/4 x narrow face........................................1.501 x narrow face..........................................1.331-1/2 x narrow face or more........................ 1.00

no shake.................................................... 2.001/6 x narrow face ........................................1.67114 x narrow face........................................1.501/3 x narrow face ........................................1.331/2 x narrow face or more ........................... 1.00

"Shake is measured at the end between lines enclosing the shake and perpendicular to the loaded face.


TABLE 13.5.1B Tabulated Design Values for Mechanically Graded Dimension Lumber

Design Valuesin Pounds per Square Inch (psi)

Tension Compression ModulusParallel Parallel of Grading

Species and Size Bending to Grain to Grain Elasticity RulesCommercial Grade Classification Fb Ft F~ E Agency

MACHINE STRESS RATED (MSR) LUMBER

900f-LOE 900 350 1050 1,000,000 WCLIB, WWPA1200f-1.2E 1200 600 1400 1,200,000 NLGA, SPIB, WCLIB, WWPA1350f-1.3E 1350 750 1600 1,300,000 SPIB, WCLIB, WWPA1450f-1.3E 1450 800 1625 1,300,000 NLGA, WCLIB, WWPA1500f-1.3E 1500 900 1650 1,300,000 SPIB1500f-1.4E 1500 900 1650 1,400,000 NLGA, SPIB, WCLIB, WWPA1650f-1.4E 1650 1020 1700 1,400,000 SPIB1650f-1.5E 1650 1020 1700 1,500,000 NLGA, SPIB, WCLIB, WWPA1800f-1.6E 1800 1175 1750 1,600,000 NLGA, SPIB, WCLIB, WWPA1950f-1.5E 2" & less in thickness 1950 1375 1800 1,500,000 SPIB1950f-1.7E 1950 1375 1800 1,700,000 NLGA, SPIB, WWPA2100f-1.8E 2" & wider 2100 1575 1875 1,800,000 NLGA, SPIB, WCLIB, WWPA2250f-1.6E 2250 1750 1925 1,600,000 SPIB2250f-1.9E 2250 1750 1925 1,900,000 NLGA, SPIB, WWPA2400f-1.7E 2400 1925 1975 1,700,000 SPIB2400f-2.OE 2400 1925 1975 2,000,000 NLGA, SPIB, WCLIB, WWPA2550f-2.1E 2550 2060 2025 2,100,000 NLGA, SPIB, WWPA2700f-2.2E 2700 2150 2100 2,200,000 NLGA, SPIB, WCLIB, WWPA2850f-2.3E 2850 2300 2150 2,300,000 SPIB, WWPA3000f-2.4E 3000 2400 2200 2,400,000 NLGA, SPIB3150f-2.5E 3150 2500 2250 2,500,000 SPIB3300f-2.6E 3300 2650 2325 2,600,000 SPIB

900f-1.2E 900 350 1050 1,200,000 NLGA, WCLIB1200f-1.5E 2" & less in thickness 1200 600 1400 1,500,000 NLGA, WCLIB1350f-1.8E 1350 750 1600 1,800,000 NLGA1500f-1.8E 6" & wider 1500 900 1650 1,800,000 WCLIB1800f-2.1E 1800 1175 1750 2,100,000 NLGA, WCLIB

1. Design values are taken from the 1991 Edition of the NDS ® and are for a 10-year load duration and dry service conditions. Refer tothe 1991 NDS® for additional grades and for a summary of grading rules agencies.

2. Design values for shear parallel to grain and compression perpendicular to grain shall be as specified in Table 13.5. IA for No. 2 visuallygraded dimension lumber of the appropriate species.

3. Use of the wet service factor, shear stress factor, repetitive member factor, and flat use factor shall be as specified in Table 13.5.1Afor visually graded dimension lumber.

tors, C M , given in footnotes to Tables 13.5.1A and13.5.1B.

13.5.5.1.2 Tabulated values for glued laminated tim-ber and structural composite lumber assume that the ma-terial is used under continuously dry conditions where themoisture content in service does not exceed 16%. Whenthe moisture content in service is expected to exceed 16%,tabulated values shall be reduced by the wet service fac-tors, C M, given in the footnotes to Tables 13.5.3A and13.5.3B for glued laminated timber and Tables 13.5.4A

and 13.5.4B for structural composite lumber.

13.5.5.1.3 The moisture content of wood used inexposed bridge applications will normally exceed 19%and tabulated values shall be reduced by the wet servicefactor unless an analysis of regional, geographic, and cli-matological conditions that affect moisture content indi-cate that the in-service moisture content will not exceed19% for sawn lumber and 16% for glued laminated tim-ber and structural composite lumber over the life of thestructure.


TABLE 13.5.2A Tabulated Design Values for Bearing Parallel to Grain

Dry Service Conditions

Sawn Lumber

Wet Service 5" x 5" 2" to 4" GluedSpecies Combination Conditions & Larger Thick Laminated Timber

Douglas Fir-Larch (Dense) 1570 1730 2360 2750

Douglas Fir-Larch 1350 1480 2020 2360Eastern Softwoods 880 — 1340 —Hem-Fir 1110 1220 1670 1940Mixed Southern Pine 1270 1390 1900 —Northern Red Oak 1150 1270 1730 2010Red Maple 1100 1210 1650 1930Red Oak 1010 1110 1520 1770Southern Pine 1320 1450 1970 2300Southern Pine (Dense) 1540 1690 2310 2690Spruce-Pine-Fir 940 1040 1410 1650Spruce-Pine-Fir (South) 810 900 1220 1430Yellow Poplar 890 — 1340 1560

1. Design values are taken from the 1991 Edition of the NDS® . Refer to the 1991 NDS® for additional species.

2. Wet and dry service conditions are as defined in Article 13.5.5.1. The wet service factor has been applied to valuestabulated for wet service conditions and further adjustment by this factor is not required.

13.5.5.2 Load Duration Factor, CD

13.5.5.2.1 Wood can sustain substantially greatermaximum loads for short load durations than for long loaddurations. Tabulated stresses for sawn lumber, glued lam-inated timber, and structural composite lumber are basedon a normal load duration which contemplates that themember is stressed to the maximum stress level, eithercontinuously or cumulatively, for a period of approxi-mately 10 years, and/or stressed to 90% of the maximumdesign level continuously for the remainder of the mem-ber life.

13.5.5.2.2 When the full maximum load is appliedeither cumulatively or continuously for periods other than10 years, tabulated stresses shall be multiplied by the loadduration factor, C D , given in Table 13.5.5A.

13.5.5.2.3 The provisions of this article do not applyto modulus of elasticity or to compression perpendicularto grain, but do apply to mechanical fastenings, except asotherwise noted. The load duration factor for impact doesnot apply to members pressure-impregnated with preser-vative salts to the heavy retentions required for marine ex-posure.

13.5.5.2.4 Increases in tabulated stresses resultingfrom various load duration factors are not cumulative and

the load duration factor for the shortest duration load ina combination of loads shall apply for that load combi-nation. The resulting structural members shall not besmaller than required for a longer duration of loading(refer to the 1991 Edition of the NDS ® for additionalcommentary).

13.5.5.2.5 Modification of design stresses for loadcombinations, as specified in Section 3, are cumulativewith load duration adjustments.

13.5.5.3 Adjustment for Preservative Treatment

Tabulated values apply to untreated wood and to woodthat is preservatively treated in accordance with the re-quirements of AASHTO M 133. Unless otherwise noted,no adjustment of tabulated values is required for preserv-ative treatment.

13.6 BENDING MEMBERS

13.6.1 General

13.6.1.1 The provisions of this article are applicableto straight members and to slightly curved bending mem-bers where the radius of curvature exceeds the span ininches divided by 800. Additional design requirements for


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TABLE 13.5.3A Design Values for Structural Glued Laminated Softwood Timberwith Members Stressed Primarily in Bending (Continued)

1. Design values in this table are for a 10-year load duration and dry service conditions and are based on combinations conforming toAITC 117-93 (Design Standard Specifications for Structural Glued Laminated Timber of Softwood Species), by American Institute of TimberConstruction, and manufactured in accordance with American National Standard ANSI/AITC A190.1-1991 (Structural Glued LaminatedTimber). Refer to AITC 117-93 for additional combinations and design values.

2. The combinations in this table are intended primarily for members stressed in bending due to loads applied perpendicular to the widefaces of the laminations (bending about X-X axis). Design values are tabulated, however, for loading both perpendicular and parallel tothe wide faces of the laminations, and for axial loading. For combinations applicable to members loaded primarily axial or parallel to thewide faces of the laminations, see Table 13.5.3B.

3. Design values in this table are applicable to members having 4 or more laminations. For members having 2 or 3 laminations, see Table13.5.313.

4. The 24F combinations for members 15 and less in depth may not be readily available and the designer should check availability priorto specifying. The 20F combinations are generally available for members 15' and less in depth.

5. The symbols used for species are Douglas Fir-Larch (DF), Hem-Fir (HF), and Southern Pine (SP). N3 refers to No. 3 structural joistsand planks or structural light framing grade.

6. Design values in this column are for bending when the member is loaded such that the compression zone laminations are subjectedto tensile stresses. For more information, see AITC 117-93. The values in this column may be increased 200 psi where end-joint spacingrestrictions are applied to the compression zone when stressed in tension.

7. These combinations are intended for straight or slightly cambered members for dry use and industrial appearance grade, because theymay contain wane. If wane is omitted these restrictions do not apply.

8. These combinations are balanced and are intended for members continuous or cantilevered over supports and provide equal capacityin both positive and negative bending.

9. For bending members greater than 15 in depth, these design values for compression perpendicular to grain are 650 psi on the tensionface.

10. These design values may be increased in accordance with AITC 117-93 when the member conforms with special constructionrequirements therein. For more information, see AITC 117-93.

z

wJ

WJN

TABLE 13.5.3A Design Values for Structural Glued Laminated Softwood Timberwith Members Stressed Primarily in Bending (Continued)

11. For these combinations manufacturers may substitute E-rated Douglas Fir-Larch laminations that are 200,000 psi higher in modulusof elasticity than the specified E-rated Hem-Fir, with no change in design values.

12. Species groups for split ring and shear plate connectors should be determined by associated compression design values perpendicularto grain, Fes , as follows:

Species GroupsF.- for Split Ring and(psi) Shear Plate Connectors

650* A590 or 560 B500 C470 or 375 C315 C255 D

* For F.- = 650 psi for Douglas Fir-South, useGroup B.

13. The values for shear parallel to grain, F_ and Fey, apply to members manufactured using multiple piece laminations with unbondededge joints. For members manufactured using single-piece laminations or using multiple-piece laminations with bonded-edge joints, theshear parallel to grain values in the previous column apply.

14. Wet Service Factor, Cm. When glued laminated timber is used where moisture content will exceed 16%, design values shall bemultiplied by the appropriate wet service factors from the following table:

WET SERVICE FACTORS, CND

Fb F, F, F.- Fc E

0.8 0.8 0.875 0.53 0.73 0.833

TABLE 13.5.3B Design Values for Structural Glued Laminated Softwood Timberwith Members Stressed Primarily in Axial Tension or Compression', 2,8,10


Bending About Y-Y Axis Bending About X-X AxisLoaded Parallel to Wide Loaded Perpendicular to Wide

All Loading Axially Loaded Faces of Laminations Faces of Laminations

ShearTensionParallel Compression Parallel

to Grain Parallel to Grain Bending Shear Parallel to Grain4 Bending to Grain4

4 or MoreLami-

nations(for

Com- Memberspression with 2Perpen- 2 or 4 or 4 or Multiple 4 or Lami- 4 or 2 or

Modulus dicular More More 2 or 3 More 3 2 Piece More 3 2 nations More More

Combi- of to Lami- Lami- Lami- Lami- Lami- Lami- Lami- Lami- Lami- Lami- to 15" Lami- Lami-

nation Elasticity Grain nations nations nations nations nations nations nations)9 nations nations nations deeps nations 6 nations

Symbol Species3 E Fc 1 Ft Fc Fc Fby Fb y Fby F„y Fey Fyy F,,y F

bx Fbx F_

VISUALLY GRADED WESTERN SPECIES

2 DF 1,700,000 5607 1250 1900 1600 1800 1600 1300 75 145 135 125 1700 2000 165

3 DF 1,800,000 650 1450 2300 1850 2100 1850 1550 75 145 135 125 2000 2300 165

5 DF 2,000,000 650 1600 2400 2100 2400 2100 1800 75 145 135 125 2200 2400 165

15 BF 1,400,000 375 7 1050 1350 1300 1500 1350 1100 70 135 130 115 1450 1700 155

16 BF 1,600,000 375 7 1200 1500 1450 1750 1550 1300 70 135 130 115 1600 1900 155

17 BF 1,700,000 500 1400 1750 1700 2000 1850 1550 70 135 130 115 1900 2200 155

VISUALLY GRADED SOUTHERN PINE

47 SP 1,400,000 5607 1200 1900 1150 1750 1550 1300 90 175 165 150 1400 1600 200

48 SP 1,700,000 650 1400 2200 1350 2000 1800 1500 90 175 165 150 1600 1900 200

49 SP 1,170,000 5607 1350 2100 1450 1950 1750 1500 90 175 165 150 1800 2100 200

50 SP 1,900,000 650 1550 2300 1700 2300 2100 1750 90 175 165 150 2100 2400 200

z

wJw

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TABLE 13.5.3B Design Values for Structural Glued Laminated Softwood Timberwith Members Stressed Primarily in Axial Tension or Compression (Continued)

1. Design values in this table are for a 10-year load duration and dry service conditions and are based on combinations conforming toAITC 117-93 (Design Standard Specifications for Structural Glued Laminated Timber of Softwood Species), by American Institute of TimberConstruction, and manufactured in accordance with American National Standard ANSI/AITC A190.1-1991 (Structural Glued LaminatedTimber). Refer to AITC 117-93 for additional combinations and design values.

2. The combinations in this table are intendedprimarily for members loaded either axially or in bending with the loads acting parallelto the wide faces of the laminations (bending about Y-Y axis). Design values for bending due to loads applied perpendicular to the widefaces of the laminations (bending about X-X axis) are also included, although the combinations in Table 13.5.3A are usually better suitedfor this condition of loading.

3. The symbols used for species are Douglas Fir-Larch (DF), Hem-Fir (HF), and Southern Pine (SP).4. The design values in shear parallel to grain are based on members that do not contain wane.5. The design values in bending about the X-X axis in this column are for members up to 15" in depth without tension laminations.6. The design values in bending about the X-X axis in this column are for members having specific tension laminations and apply to

members having 4 or more laminations. When these values are used in design and the member is specified by combination symbol, thedesign should also specify the required bending design value.

7. These design values may be increased in accordance with AITC 117-93when member conforms with special construction requirementstherein. For more information see AITC 117-93.

8. Species groups for split ring and shear plate connectors should be determined by associated compression design values perpendicularto grain, Fcl, as given in Table 13.5.3A.

9. The values for shear parallel to grain, F yy , apply to members manufactured using multiple-piece laminations with unbonded edge joints.For members using single-piece laminations or using multiple-piece laminations with bonded-edge joints the shear parallel to grain valuestabulated in the next three columns apply.

10. Wet Service Factor, CM . When glued laminated timber is used where moisture content will exceed 16%, design values shall bemultiplied by the appropriate wet service factors given in the footnotes to Table 13.5.3A.

TABLE 13.5.4A Representative Tabulated Design Values for Laminated Veneer Lumber'

Design Values in Pounds Per Square Inch (psiy

Compression Perpendicularto Grain Horizontal Shear

F, F,.

Tension Compression Load Direction Load Direction ModulusExtreme Fiber Parallel Parallel of

in Bending to GrainZ to Grain Parallel Perpendicular Parallel Perpendicular Elasticity

Species Grade Fb Ft K to glueline to glueline to glueline to glueline E

Douglas-Fir 2.0E 2800 1750 2725 750 480 285 175 2,000,000

Southern Pine 2.0E 2925 1805 3035 880 525 285 150 2,000,000

1. Design values are representative of species and grades that are commonly available from manufacturers and are for a 10-year load

duration and dry service conditions.2. Tabulated values in tension parallel to grain shall be adjusted by the size factor, CF, given by the following equation:

CF

where: I\\

L = length of tension member in feet;in = parameter for the specific material determined in accordance with the requirements of ASTM D-5456.

3. Wet Service Factor, CM . When laminated veneer lumber is used where moisture content will exceed 16%, design values shall bemultiplied by the following wet service factors:


Fb F, F,. F~l F~ E

0.8 0.8 0.875 0.53 0.73 0.833

z

IwU

WJU

TABLE 13.5.411 Representative Tabulated Design Values for Parallel Strand Lumber'Design Values in Pounds Per Square Inch (psi) '

Compression Perpendicularto Grain Horizontal Shear

FC1 F„

Load Direction Load DirectionTension Compression

Extreme Fiber Parallel Parallel Parallel Perpendicular Parallel Perpendicular Modulus ofin Bending to Grain' to Grain to wide face to wide face to wide face to wide face Elasticity

Species Grade Fb F, R of strand of strand of strand of strand E

Douglas-Fir 2.0E 2900 2400 2900 750 480 290 210 2,000,000

Southern Pine 2.0E 2900 2400 2900 880 525 290 210 2,000,000

1. Design values are representative of species and grades that are commonly available from manufacturers and are for a 10-year loadduration and dry service conditions.

2. Tabulated values in tension parallel to grain shall be adjusted by the size factor, C F , given by the following equation:

3 vm

CF –

(i:)

where:

L = length of tension member in feet;m = parameter for the specific material determined in accordance with the requirements of ASTM D-5456.

3. Wet Service Factor, Cm.When parallel strand lumber is used where moisture content will exceed 16%, design values shall be multipliedby the following wet service factors:

WET SERVICE FACTORS, C.

Fb F, F„ F~1 F~ E

0.8 0.8 0.875 0.53 0.73 0.833


TABLE 13.5.5A Load Duration Factor, Co

Load Duration CD

Permanent 0.902 months (vehicle live load) 1.157 days 1.251 day 1.335 minutes (railing only) 1.65

curved glued laminated timber members shall be as spec-ified in the 1991 Edition of the NDS ®.

13.6.1.2 For simple, continuous, and cantileveredbending members, the span shall be taken as the clear dis-tance between supports plus one-half the required bearinglength at each support.

13.6.1.3 Bending members shall be transverselybraced to prevent lateral displacement and rotation andtransmit lateral forces to the bearings. Transverse bracingshall be provided at the supports for all span lengths andat intermediate locations as required for lateral stabilityand load transfer (Article 13.6.4.4). The depth of trans-verse bracing shall not be less than %4 the depth of thebending member.

13.6.1.4 Support attachments for bending membersshall be of sufficient size and strength to transmit vertical,longitudinal and transverse loads from the superstructureto the substructure in accordance with the requirements ofSection 3.

13.6.1.5 Glued laminated timber and structural com-posite lumber girders shall preferably be cambered a min-imum 3 times the computed dead load deflection., but notless than %2 inch.

13.6.2 Notching

Notching of bending members can severely reducemember capacity and is not recommended. When notch-ing is required for sawn lumber members, design limita-tions and requirements shall be in accordance with theNDS

®, 1991 Edition. Design requirements and limitations

for notching glued laminated timber members shall be asgiven in the "Timber Construction Manual," 1985 Editionby the American Institute of Timber Construction, pub-lished by John Wiley & Sons, New York, New York. De-sign requirements and limitations f'or notching structuralcomposite lumber shall be as specified for glued lami-nated timber.

13.6.3 Modulus of Elasticity

The modulus of elasticity used for stiffness and stabil-ity computations shall be the tabulated modulus of elas-ticity adjusted by the applicable adjustment factor givenin the following equation:

E ' = ECM (13-1)

where:

E' = allowable modulus of elasticity in psi;E = tabulated modulus of elasticity in psi;C M = wet service factor from Article 13.5.5.1.

13.6.4 Bending

13.6.4.1 Allowable Stress

The allowable unit stress in bending shall be the tabu-lated stress adjusted by the applicable adjustment factorsgiven in the following equation:

Fb = FbCMCDCFCVCLCfCfuCr (13-2)

where:

Fb = allowable unit stress in bending in psiF b = tabulated unit stress in bending in psiCM = wet service factor from Article 13.5.5.1C D = load duration factor from Article 13.5.5.2C F = bending size factor for sawn lumber and struc-

tural composite lumber, and for glued laminatedtimber with loads applied parallel to the wideface of the laminations, from Article 13.6.4.2

C v = volume factor for glued laminated timber withloads applied perpendicular to the wide face ofthe laminations, from Article 13.6.4.3

CL = beam stability factor from Article 13.6.4.4.C f = form factor from Article 13.6.4.5Cf„ = flat use factor for sawn lumber from footnotes to

Tables 13.5. and 13.5.C, = repetitive member factor for sawn lumber from

footnotes to Table 13.5. IA.

The volume factor, C,, shall not be applied simultane-ously with the beam stability factor, C L , and the lesser ofthe two factors shall apply in Equation (13-2).

13.6.4.2 Size Factor, CF

13.64.2.1 The tabulated bending stress, for dimen-sion lumber 2 inches to 4 inches thick shall be multipliedby the bending size factor, CF , given in the footnotes toTable 13.5. IA.


13.6.4.2.2 For rectangular sawn lumber bendingmembers 5 inches or thicker and greater than 12 inches indepth, and for glued laminated timber with loads appliedparallel to the wide face of the laminations and greaterthan 12 inches in depth, the tabulated bending stress shallbe multiplied by the size factor, CF, determined from thefollowing relationship:

= (CF

12\1/9

d Jl (13-3)

where d is the member depth in inches.

13.6.4.2.3 For structural composite lumber bendingmembers of any width, the tabulated bending stress shallbe reduced by the size factor, C F , given by the followingequation:

CF = (21/L)"(12/d)" (13-4)

where:

L = length of bending member between points of zeromoment in feet;

d = depth of bending member in inches;m = parameter for the specific material determined in

accordance with the requirements of ASTM D5456.

13.6.4.3 Volume Factor, C,

13.6.4.3.1 The tabulated bending stress for gluedlaminated timber bending members with loads appliedperpendicular to the wide face of the laminations shall beadjusted by the volume factor, Cv , as determined by thefollowing relationship:

Cv = (21/L)"x (12/d)"x (5.125/b)"x <_ 1.0 (13-5)

where:

L = length of bending member between points of zeromoment in feet;

d = depth of bending member in inches;b = width of bending member in inches;x = 20 for Southern pine;x 10 for all other species.

13.6.4.3.2 When multiple piece width layups areused, the width of the bending member used in Equation(13-4) shall be the width of the widest piece used in thelayup.

13.6.4.4 Beam Stability Factor, CL

13.6.4.4.1 Tabulated bending values are applicableto members which are adequately braced. When membersare not adequately braced, the tabulated bending stressshall be modified by the beam stability factor, C L .

13.6.4.4.2 When the depth of a bending memberdoes not exceed its width, or when lateral movement ofthe compression zone is prevented by continuous supportand points of bearing have lateral support to prevent rota-tion, there is no danger of lateral buckling and CL = 1.0.For other conditions, the beam stability factor shall be de-termined in accordance with the following provisions.

13.6.4.4.3 The bending member effective length, l e ,shall be determined from the following relationships forany loading condition:

le = 2.061 when l„/d < 7l e = 1.631„ + 3d when 7 <_ l„/d <_ 14.3l e = 1.841„ when l„/d > 14.3

where:

le = effective length in inches;l„ = unsupported length in inches;d = depth of bending member in inches.

If lateral support is provided to prevent rotation at thepoints of bearing, but no other lateral support is providedthroughout the bending member length, the unsupportedlength, lu , is the distance between points of bearing, or thelength of a cantilever.

If lateral support is provided to prevent rotation andlateral displacement at intermediate points as well as atthe bearings, the unsupported length, 1,,, is the distance be-tween such points of intermediate lateral support.

13.6.4.4.4 The slenderness ratio for bending mem-bers, RB , is determined from the following equation:

R B = ba < 50 (13-6)

where:

RB = bending member slenderness ratio;d = depth of bending member in inches;b = width of bending member in inches.

13.6.4.4.5 The beam stability factor, CL , shall becomputed as follows:


_ 1 + (FbE /Fb) (1 +FbE / F

b ) z _F

b]./F

bCL1.90

_3.61 0.95

(13-7)

FbE =KRE (13-9)

B

where:

Fb = tabulated bending stress adjusted by all ap-plicable adjustment factors given in Equation(13-2) except the volume factor, C,, the beamstability factor, C L , and the flat-use factor, Cf.;

KbE = 0.438 for visually graded sawn lumber 0.609for glued laminated timber, structural com-posite lumber, and machine stress rated lum-ber;

E' = allowable modulus of elasticity in psi as de-termined by Article 13.6.3.

13.6.4.5 Form Factor, C f

For bending members with circular cross sectionsthe tabulated bending stress shall be adjusted by theform factor, Cf = 1.18. A tapered circular section shallbe considered as a bending member of variable crosssection.

13.6.5 Shear Parallel to Grain

13.6.5.1 General

13.6.5.1.1 The provisions of this article apply toshear parallel to grain (horizontal shear) at or near thepoints of vertical support of solid bending members. Referto the 1991 edition of the NDS

®for additional design re-

quirements for other member types.

13.6.5.1.2 The critical shear in wood bending mem-bers is shear parallel to grain. It is unnecessary to verifythe strength of bending members in shear perpendicular tograin.

13.6.5.2 Actual Stress

The actual unit stress in shear parallel to grain due toapplied loading on rectangular members shall be deter-mined by the following equation:

f" = ZV(13-9)

where:

f, = actual unit stress in shear parallel to grain in psi;b = width of bending member in inches;d = depth of bending member in inches;V = vertical shear in pounds, as determined in accor-

dance with the following provisions.

For uniformly distributed loads, such as dead load, themagnitude of vertical shear used in Equation (13-9) shallbe the maximum shear occurring at a distance from thesupport equal to the bending member depth, d. Whenmembers are supported by full bearing on one surface,with loads applied to the opposite surface, all loads withina distance from the supports equal to the bending memberdepth shall be neglected.

For vehicle live loads, the loads shall be placed to pro-duce the maximum vertical shear at a distance from thesupport equal to three times the bending member depth,3d, or at the span quarter point, L/4, whichever is thelesser distance from the support. The distributed live loadshear used in Equation (13-9) shall be determined by thefollowing expression:

VLL = 0.50 [(0.60 VLU) + VLDI (13-10)

where:

V LL = distributed live load vertical shear in pounds;V LU = maximum vertical shear, in pounds, at 3d or

L/4 due to undistributed wheel loads;VLD = maximum vertical shear, in pounds, at 3d or

L/4 due to wheel loads distributed laterally asspecified for moment in Article 3.23.

For undistributed wheel loads, one line of wheels is as-sumed to be carried by one bending member.


The allowable unit stress in shear parallel to grain shallbe the tabulated stress adjusted by the applicable adjust-ment factors given in the following equation:

Fv = F,CMCD (13-11)

where:

F V' = allowable unit stress in shear parallel to grain inpsi;

Fv = tabulated unit stress in shear parallel to grain inpsi;

CM = wet service factor from Article 13.5.5.1;CD = load duration factor from Article 13.5.5.2.


For sawn lumber beams, further adjustment by theshear stress factor may be applicable as described in thefootnotes to Table 13.5. IA.

For structural composite lumber, more restrictive ad-justments to the tabulated shear stress parallel to grainshall be as recommended by the material manufacturer.

13.6.6 Compression Perpendicular to Grain

13.6.6.1 General

When calculating the bearing stress in compressionperpendicular to grain at beam ends, a uniform stress dis-tribution shall be assumed.


The allowable unit stress in compression perpen-dicular to grain shall be the tabulated stress adjusted bythe applicable adjustment factors given in the followingequation:

Fri = F~iCM Cb (13-12)

where:

F,' = allowable unit stress in compression perpendic-ular to grain, in psi;

F, = tabulated unit stress in compression perpendic-ular to grain, in psi;

C M = wet service factor from Article 13.5.5.1;C b = bearing area factor from Article 13.6.6.3.

13.6.6.3 Bearing Area Factor, C b

Tabulated values in compression perpendicular tograin apply to bearings of any length at beam ends, and toall bearings 6 inches or more in length at any other loca-tion. For bearings less than 6 inches in length and notnearer than 3 inches to the end of a member, the tabulatedvalue shall be adjusted by the bearing area factor, C b,given by the following equation:

C lb +0.375(13-13)C

b — lb

where lb is the length of bearing in inches, measured par-allel to the wood grain. For round washers, or other roundbearing areas, the length of bearing shall be the diameterof the bearing area.

The multiplying factors for bearing lengths on smallareas such as plates and washers are given in Table13.6.1A.

TABLE 13.6.1A Values of the Bearing Area Factor, C b ,for Small Bearing Areas

Length ofBearing, lb

(in.) 1/2 1 1-1/2 2 3 4 6 or more

Bearing AreaFactor, Cb 1.75 1.38 1.25 1.19 1.13 1.10 1.00

13.6.7 Bearing on Inclined Surfaces

For bearing on an inclined surface, the allowable unitstress in bearing shall be as given by the following equa-tion:

F'Ft Fctl

(13 -14)a Fg sin 2 0 + F,l cos 2 8

where:

Fe = allowable unit stress for bearing on an inclinedsurface, in psi;

Fg = allowable unit stress in bearing parallel to grainfrom Article 13.7.4;

Fc'l = allowable unit stress in compression perpendic-

ular to the grain from Article 13.6.6;0 = angle in degrees between the direction of load

and the direction of grain.

13.7 COMPRESSION MEMBERS

13.7.1 General

13.7.1.1 The provisions of this article apply tosimple solid columns consisting of a single piece ofsawn lumber, piling, structural composite lumber, orglued laminated timber. Refer to the 1991 Edition of theNDS ® for design requirements for built-up columns,consisting of a number of solid members joined to-gether with mechanical fasteners, and for spacedcolumns consisting of two or more individual memberswith their longitudinal axes parallel, separated andfastened at the ends and at one or more interior points byblocking.

13.7.1.2 The term "column" refers to all types ofcompression members, including members forming partof a truss or other structural components.

13.7.1.3 Column bracing shall be provided wherenecessary to provide lateral stability and resist wind orother lateral forces.


13.7.2 Eccentric Loading or Combined Stresses

Members with eccentric loading or combined stressesshall be designed in accordance with the provisions of theNDS ® , 1991 Edition.

13.7.3 Compression

13.7.3.1 Net Section

The actual unit stress in compression parallel to grain,fe, shall be based on the net section as described in Article13. 1, except that it may be based on the gross section whenthe reduced section does not occur in the critical part of thecolumn length that is most subject to potential buckling.


The allowable unit stress in compression parallel tograin shall not exceed the tabulated stress adjusted by theapplicable adjustment factors given in the following equa-tion:

Fc' = F,C MC DC FC P (13-15)

where:

Fc' = allowable unit stress in compression parallel tograin in psi;

Fe = tabulated unit stress in compression parallel tograin in psi;

C M = wet service factor from Article 13.5.5.1:;C D = load duration factor from Article 13.5.5„2;C F = compression size factor for sawn lumber from

footnotes to Table 13.5.1A;C P = column stability factor from Article 13.7.3.3.

13.7.3.3 Column Stability Factor, CP

13.7.3.3.1 Tabulated values in compression parallelto grain are applicable to members which are adequatelybraced. When members are not adequately braced, thetabulated stress shall be modified by the column stabilityfactor, Cp.

13.7.3.3.2 When a compression member is supportedthroughout its length to prevent lateral displacement in alldirections, C P = 1.0. For other conditions, the column sta-bility factor shall be determined in accordance with thefollowing provisions.

13.7.3.3.3 The effective column length, le, shall bedetermined in accordance with good engineering practice.

Actual column length, 1, may be multiplied by an effectivelength factor to determine the effective column length:

le = Kl (13-16)

where:

le = effective column length in inchesK = effective length factor from Table C-1 of Appen-

dix C= actual column length between points of lateral

support in inches.

13.7.3.3.4 For columns of rectangular cross section,the column slenderness ratio, l,/d, shall be taken as thelarger of the ratios, le ,ldj or le zldz. (See Figure 13.7.1A.)The slenderness ratio shall not exceed 50.

!t and fi . distances between points of lateral support in planes 1 and 2.inches.

d t and d: a cross-sectional dimensions of rectanjular compression mem-ber in planes of lateral support. inches.

FIGURE 13.7.1A

13.7.3.3.5 The column stability factor, C P , shall be asgiven by the following expressions:

_ 1 + F,, I F, ~1 + FEE I Fc,FEE

/ F~CP 2c (2c) 2 c

(13-17)

F,E= KcEEa

(13-18)(le d)


TABLE 13.7.1A Support Condition Coefficients forTapered Columns

SupportCondition

Support Condition Coefficient, a

Large end fixed, small end unsupported 0.70Small end fixed, large end unsupported 0.30Both ends simply supported

Tapered toward one end 0.50Tapered towards both ends 0.70

where:

F* = tabulated stress in compression parallel to grainadjusted by all applicable modification factorsgiven in Equation (13-14) except Cp;

KeE = 0.300 for visually graded sawn lumber; 0.418

for glued laminated timber, structural compos-ite lumber, and machine stress-rated lumber;

c = 0.80 for sawn lumber;0.85 for round piles;0.90 for glued laminated timber and structuralcomposite lumber.

For especially severe service conditions or extraordi-nary hazardous conditions, the use of lower design valuesthan those obtained above may be necessary. Refer to the1991 Edition of the NDS

®.

13.7.3.4 Tapered Columns

13.7.3.4.1 For rectangular columns tapered at one orboth ends, the cross-sectional area shall be based on therepresentative dimension of each tapered face. The repre-sentative dimension, dLep , of each tapered face shall bebased on the support condition coefficient given in Table13.7.1A.

13.7.3.4.2 For support conditions given in Table13.7.1A, the representative dimension, d Lep , of each ta-pered face shall be as given by the following equation:

drep = d rain + (d

max — drain)Ca — 0.15 (1 — drain

)]dmax

(13-19)

where:

drep = representative dimension for a tapered columnface, in inches;

dm;,, = minimum column face dimension, in inches;dmax = maximum column face dimension, in inches;a = coefficient based on support conditions.

13.7.3.4.3 For support conditions other than those inTable 13.7.1A, the representative dimension of each ta-pered face shall be as given by the following equation:

dCep = dmj + 0.33(d,,~ — dmij (13-20)

13.7.3.4.4 For any tapered column, the actual stressin compression parallel to grain, f e , shall not exceed the al-lowable stress determined by Equation (13-14), assumingthe column stability factor Cp = 1.0.

13.7.3.5 Round Columns

The design of a round column shall be based on the de-sign of a square column of the same cross-sectional areawith the same degree of taper.

13.7.4 Bearing Parallel to Grain

13.7.4.1 The actual stress in bearing parallel to grainshall be based on the net area and shall not exceed the tab-ulated stress for bearing parallel to grain adjusted bythe applicable adjustment factor given in the followingequation:

Fg = FgC, (13-21)

where:

Fg = allowable unit stress in bearing parallel to grainin psi;

Fg = tabulated unit stress in bearing parallel to grainfrom Table 13.5.2A, in psi;

CD = load duration factor from Article 13.5.5.2.

13.7.4.2 When the bearing load is at an angle to thegrain, the allowable bearing stress shall be determined byEquation (13-14), using the design values for end-grainbearing parallel to grain and design values in compressionperpendicular to grain.

13.7.4.3 When bearing parallel to grain exceeds 75%of the allowable value determined by Equation (13-21),bearing shall be on a metal plate or on other durable, rigid,homogeneous material of adequate strength and stiffnessto distribute applied loads over the entire bearing area.

13.8 TENSION MEMBERS

13.8.1 Tension Parallel to Grain

The allowable unit stress in tension parallel to grainhall be the tabulated value adjusted by the applicable ad-justment factors given in the following equation:

F,' = FtC MC D CF (13-22)


where:

F; = allowable unit stress in tension parallel to grainin psi;

Ft = tabulated unit stress in tension parallel to grainin psi;

C M = wet service factor from Article 13.5.5.1;C D = load duration factor from Article 13.5.5.2;C F = tension size factor for sawn lumber from foot-

notes to Table 13.5.1A and for structural com-posite lumber from footnotes to Tables 13.5.4Aand 13.5.413.

13.8.2 Tension Perpendicular to Grain

Designs which induce tension perpendicular to thegrain of wood members should not be used. When tensionperpendicular to grain cannot be avoided, mechanical re-inforcement sufficient to resist all such forces should beused. Refer to the 1991 Edition of the NDS ® for additionalinformation.

13.9 MECHANICAL CONNECTIONS

13.9.1 General

13.9.1.1 Except as otherwise required by this speci-fication, mechanical connections and their installationshall conform to the requirements of the NDS

®, 1991 Edi-

tion.

13.9.1.2 Components at mechanical connections, in-cluding the wood members, connecting elements, and fas-teners, shall be proportioned so that the design strengthequals or exceeds the required strength for the loads act-ing on the structure. The strength of the connected woodcomponents shall be evaluated considering the net sec-tion, eccentricity, shear, tension perpendicular to grainand other factors that may reduce component strength.

13.9.2 Corrosion Protection

13.9.2.1 Except as permitted by this section, all steelhardware for wood structures shall be galvanized in ac-cordance with AASHTO M 232 or cadmium plated in ac-cordance with AASHTO M 299.

13.9.2.2 All steel components, timber connectors,and castings, other than malleable iron, shall be galva-nized in accordance with AASHTO M 111.

13.9.2.3 Alternative corrosion protection coatings,such as epoxies, may be used when the demonstrated per-formance of the coating is sufficient to provide adequateprotection for the intended exposure conduction.

13.9.2.4 Heat-treated alloy components and fasten-ings shall be protected by an approved alternative protec-tive treatment that does not adversely affect the mechani-cal properties of the material.

13.9.3 Fasteners

13.9.3.1 Fastener design values shall be adjusted bythe applicable adjustment factors for the intended use con-dition.

13.9.3.2 When determining fastener design values,wood shall be assumed to be used under wet-use or ex-posed to weather conditions.

13.9.3.3 Glulam rivets shall not be used in perma-nent structures.

13.9.4 Washers

13.9.4.1 Washers shall be provided under bolt andlag screw heads and under nuts that are in contact withwood. Washers may be omitted under heads of specialtimber bolts or dome-head bolts when the size andstrength of the head is sufficient to develop connectionstrength without excessive wood crushing.

13.9.4.2 Washers shall be of sufficient size andstrength to prevent excessive wood crushing when the fas-tener is tightened. For bolts or rods loaded in tension,washers shall be of sufficient size and strength to developthe tensile strength of the connection without excessivebending or exceeding wood strength in compression per-pendicular to grain.

Section 14

BEARINGS

14.1 SCOPE

This section contains requirements for the design andselection of structural bearings.

The selection and layout of the bearings shall be con-sistent with the proper functioning of the bridge, and shallallow for deformations due to temperature and other timedependent causes.

The loads induced in the bearings and structural mem-bers depend on the stiffnesses of the individual elementsand the tolerances achieved during fabrication and erec-tion. These influences shall be taken into account whencalculating design loads for the elements.

Units used in this section shall be taken as KIP, IN,RAD, °F and Shore Hardness, unless noted.

14.2 DEFINITIONS

Bearing-A structural device that transmits loads whilefacilitating translation and/or rotation.

Bronze Bearing-A bearing in which displacements or ro-tations take place by the slip of a bronze surface againsta mating surface.

Cotton Duck Reinforced Pad (CDP)-A pad made fromclosely spaced layers of elastomer and cotton duck,bonded together during vulcanization.

Disc Bearing-A bearing which accommodates rotationby deformation of a single elastomeric disc, moldedfrom a urethane compound. It may contain a device forpartially confining the disc against lateral expansion.

Double Cylindrical Bearing-A bearing made from twocylindrical bearings placed on top of each other withtheir axes at right angles to each other, in order to pro-vide rotation about any horizontal axis.

Fiberglass Reinforced Pad (FGP)-A pad made from dis-crete layers of elastomer and woven fiberglass, bondedtogether during vulcanization.

Fixed Bearing-A bearing which prevents differentiallongitudinal translation of abutting structure elements.It may or may not provide for differential lateral trans-lation or rotation.

Knuckle Bearing-A bearing in which a concave metalsurface rocks on a convex metal surface to provide ro-tation capability about any horizontal axis.

Longitudinal-The direction associated with the axis ofthe main structural trusses or girders in the bridge.

Metal Rocker or Roller Bearing-A bearing which carriesvertical load by direct contact between two metal sur-faces and which accommodates movement by rollingof one surface with respect to the other.

Movable Bearing-A bearing that facilitates differentialhorizontal translation of abutting structural elements ina longitudinal and/or lateral direction. It may or maynot provide for rotation.

Plain Elastomeric Pad (PEP)-A pad made exclusively ofelastomer.

Pot Bearing-A bearing which carries vertical load bycompression on an elastomeric disc confined in a steelcylinder and which accommodates rotations by defor-mations of the disc.

PTFE Sliding Bearing-A bearing which carries verticalload by contact stresses between a PTFE sheet or wovenfabric and its mating surface, and which permits move-ments by sliding of the PTFE over the mating surface.

Rotation about the Longitudinal Axis-Rotation about anaxis parallel to the longitudinal axis of the bridge.

Rotation about the Transverse Axis-Rotation about anaxis parallel to the transverse axis of the bridge.

RMS-Root mean square.Sliding Bearing-A bearing which accommodates move-

ment by slip of one surface over another.Steel Reinforced Elastomeric Bearing-A bearing made

from alternate laminates of steel and elastomer, bondedtogether during vulcanization.

Translation-Horizontal movement of the bridge in thelongitudinal or transverse direction.

Transverse-The horizontal direction normal to the lon-gitudinal axis of the bridge.

14.3 NOTATIONS

A = Plan area of elastomeric bearing (in')B = length of pad if rotation is about its transverse

axis, or width of pad if rotation is about its longi-tudinal axis (in)

385


c = Design clearance between piston and pot wall(in)

D = Diameter of the projection of the loaded surface ofthe bearing in the horizontal plane (in)

Da = Diameter of disc element (in)DP = Internal pot diameter in pot bearing (in)D l = Diameter of curved surface of rocker or roller unit

(in)

Dz = Diameter of curved surface of mating unit(Dz = - for a flat plate) (in)

d; = Diameter of the j th hole in an elastomeric bearingE = Young's modulus (ksi)E, = Effective modulus in compression of elastomeric

bearing (ksi)E, = Young's modulus for steel (ksi)e = Eccentricity of loading on a bearing (in)F,r = Allowable fatigue stress range for over 2,000,000

cycles (ksi)Fy = Yield strength of the least strong steel at the con-

tact surface (ksi)G = Shear modulus of the elastomer (ksi)Hm = Maximum horizontal load on the bearing or re-

straint considering all appropriate load combina-tions (kip)

h,; = Thickness of i1' elastomeric layer in elastomeric

bearing (in)h, ,a, = Thickness of thickest elastomeric layer in elas-

tomeric bearing (in)h, = Total elastomer thickness in an elastomeric bear-

ing (in)h, = Thickness of steel laminate in steel-laminated

elastomeric bearing (in)I = Moment of inertia (in')L = Length of a rectangular elastomeric bearing (par-

allel to longitudinal bridge axis) (in)Mm = Maximum bending moment (K-in)n = Number of interior layers of elastomerPD Compressive load due to dead load (kip)P

TL = Compressive load due to live plus dead load (kip)PL = Compressive load due to live load (kip)Pm = Maximum compressive load considering all ap-

propriate load combinations (kip)R = Radius of a curved sliding surface (in)Ro = Radial distance from center of bearing to object,

such as an anchor bolt, for which clearance mustbe provided (in)

S = Shape factor of one layer of an elastomericbearing

_ Plan AreaArea of Perimeter Free to Bulge

LW= for rectangular bearings without

2h,m,,, (L + W) holesD

= for circular bearings without holes4hm,aX

t v = Pot wall thickness (in)W = Width of the bearing in the transverse direction

(in)w = Height of piston rim in pot bearing (in)(3 = Effective angle of friction angle in PTFE bear-

ings = tan - ' (HJPD)Do = Maximum service horizontal displacement of the

bridge deck (in)A, = Maximum shear deformation of the elastomer

(in)8 = Instantaneous compressive deflection of bearing

(in)8,,, = Maximum compressive deflection of bearing (in)E = Instantaneous compressive strain of a plain elas-

tomeric padEi = Instantaneous compressive strain in i"' elastomer

layer of a laminated elastomeric bearing0 = Component of maximum service rotation in di-

rection of interest on an elastomeric bearing underload for Article 14.6.5.3

OD = Maximum rotation due to dead load (rad)

eL = Maximum rotation due to live load (rad)e,,,,X = Maximum rotation considering all appropriate

load and deformation combinations about trans-verse axis (rad)

em,z = Maximum rotation considering all appropriateload and deformation combinations about longi-tudinal axis (rad)

em = Maximum design rotation considering all appro-priate load and deformation combinations includ-ing live and dead load, bridge movements, andconstruction tolerances (rad)

µ = Coefficient of frictionQD = Average compressive stress due to dead load

(ksi)v L = Average compressive stress due to live load (ksi)Q

TL = Average compressive stress due to total dead pluslive load (ksi)

Q m = Maximum average compressive stress (ksi)

14.4 MOVEMENTS AND LOADS

Bearings shall be designed to resist loads and accom-modate movements. No damage due to joint or bearingmovement shall be permitted under any appropriate loadand movement combination.


Translational and rotational movements of the bridgeshall be considered in the design of bearings. The se-quence of construction shall be considered and all criticalcombinations of load and movement shall be consideredin the design. Rotations about two horizontal axes and thevertical axis shall be considered. The movements shall in-clude those caused by the loads, deformations and dis-placements caused by creep, shrinkage and thermal ef-fects, and inaccuracies in installation. In all cases, bothinstantaneous and long-term effects shall be considered,but the influence of impact need not be included. The mostadverse combination of movements shall be used for de-sign. All design requirements shall be tabulated in a ratio-nal form such as shown in Figure 14.4.

14.4.1 Design Requirements

The minimum thermal movements shall be computedfrom the extreme temperature defined in Article 3.16 ofDivision I and the estimated setting temperature. Designloads shall be based on the load combinations and loadfactors specified in Section 3 of Division 1.

The design rotation, Om, for bearings such as elasto-meric pads or steel reinforced elastomeric bearings whichdo not achieve hard contact between metal componentsshall be taken as the sum of:

-the dead and live load rotations.-an allowance for uncertainties, which is normallytaken as less than 0.005 rad.

The design rotation, 0,,,, for bearings such as pot bearings,disc bearings and curved sliding surfaces which may de-velop hard contact between metal components shall betaken as the sum of:

-the greater of either the rotations due to all applicablefactored loads or the rotation at the service limit state.-the maximum rotation caused by fabrication and in-stallation tolerances, which shall be taken as 0.01 radunless an approved quality control plan justifies asmaller value.-an allowance for uncertainties, which shall be takenas 0.01 rad unless an approved quality control plan jus-tifies a smaller value.

14.5 GENERAL REQUIREMENTS FORBEARINGS

Bearings may be fixed or movable as required for thebridge design. Movable bearings may include guides tocontrol the direction of translation. Fixed and guided bear-

ings shall have lateral strength adequate to resist all ap-plied loads and restrain unwanted translation.

Combinations of different types of fixed or moveablebearings should not be used at the same expansion joint,bent or pier unless the effects of differing deflection androtational characteristics on the bearings and structure areaccounted for in the design.

14.5.1 Load and Movement Capabilities

The movements and loads to be used in the designof the bearing shall be clearly defined on the contractdrawings.

14.5.2 Characteristics

The bearing chosen for a particular application musthave appropriate load and movement capabilities. Thoselisted in Table 14.5.2-1 may be used as a guide. Figure14.5.2-1 may be used as a guide in defining the differentbearing systems.

The following terminology shall apply to Table 14.5.2-1:

S = SuitableU = UnsuitableL = Suitable for limited applicationsR = May be suitable but requires special considera-

tions or additional elements such as sliders orguideways.

Long. = Longitudinal axisTrans. = Transverse axisVert. = Vertical axis

14.5.3 Forces in the Structure Caused by Restraintof Movement at the Bearing

Horizontal forces and moments induced in the bridgeby restraint of movement at the bearing shall be takeninto account in the design of the bridge and the bear-ings. They shall be determined using the calculatedmovements and the bearing characteristics given inArticle 14.6.

14.5.3.1 Horizontal Force

Horizontal forces may be induced by sliding friction,rolling friction or deformation of a flexible element in thebearing. The force used for design shall be the largest oneapplicable.

Sliding friction force shall be computed as

Hm = µPm (14.5.3.1-1)


Bridge Name or Ref.

Bearing Identification Marl:

Number of bearings required

Seating Material Upper Surface

Lower Surface

Allowable contact pressure

(KSI)

Average

Edge Load

Design load effects (KIP) Vertical max.

perm.

min.

Transverse

Longitudinal

Translation Irreversible Transverse

Longitudinal

Reversible Transverse

Longitudinal

Rotation (RAD) Irreversible Transverse

Longitudinal

Reversible Transverse

Longitudinal

Maximum Bearing dimensions (IN) Upper surface Transverse

Longitudinal

Lower surface Transverse

Longitudinal

Overall height

Tolerable movement of bearing

under transient loads (IN)

Vertical

Transverse

Longitudinal

Allowable resistance to translation under service

load (KIP)

Transverse

Longitudinal

Allowable resistance to rotation under service load

(.IN-KIP)

Transverse

Longitudinal

Type of attachment to structure and substructure Transverse

Longitudinal

FIGURE 14.4


Table 14.5.2-1 Bearing Suitability

Type of Bearing

Movement

Long Trans

Rotation about bridgeaxis indicated

Trans Long Vert

Resistance to Loads

Vert Long Trans

Plain Elastomeric Pad S S S S L L L LFiberglass Reinforced Pad S S S S L L L LCotton Duck Reinforced Pad U U U U U S L LSteel-reinforced Elastomeric Bearing S S S S L S L LPlane Sliding Bearing S S U U S S R RCurved Sliding Spherical Bearing R R S S S S R RCurved Sliding Cylindrical Bearing R R S U U S R RDisc Bearing R R S S L S S RDouble Cylindrical Bearing R R S S U S R RPot Bearing R R S S L S S SRocker Bearing S U S U U S R RKnuckle Bearing U U S U U S S RSingle Roller Bearing S U S U U S U RMultiple Roller Bearing S U U U U S U U

Low FrictionSliding Surface

Cylindrical Bearing

Low FriotionSliding iisurface

Spherical Bearing

L0

Rocker Bearing

2\"\1.,--1on

rric Diek

Pot Bearing RUBBER REINF'ORGEtENTLAYER

Elastomeric Bearing

FIGURE 14.5.2-1 Typical Bearing Components

RUBBER COVER


where:

Hm = maximum horizontal load (kip)µt = coefficient of frictionPm = maximum compressive load (kip)

The force required to deform an elastomeric element shallbe computed as:

Hm = GADS /h, (14.5.3.1-2)

where:

G = shear modulus of the elastomer (ksi)A = plan area of elastomeric element or bearing (in')A s = maximum shear deformation of the elastomer (in)h,t = total elastomer thickness (in)

Rolling forces shall be determined by test.

14.5.3.2 Bending Moment

The bridge substructure and superstructure shall be de-signed for the largest moment, Mm , which can be trans-ferred by the bearing.

For curved sliding bearings without a companion flatsliding surface, M m shall be estimated by:

M m = VP m R (14.5.3.2-1A)

and for curved sliding bearings with a companion flatsliding surface, M. shall be estimated by:

M m = 2µPmR (14.5.3.2-113)

where:

Mm = maximum bending moment (K-in)R = radius of curved sliding surface (in)

For unconfined elastomeric bearings and pads, M m

shall be estimated by:

Mm = (0.5 E,I)6 m/h, (14.5.3.2-2)

where:

I = moment of inertia of plan shape of bearing (in 4)O m = maximum design rotation (rad)E, = effective modulus of elastomeric bearing in com-

pression (ksi)

The load deflection curve of an elastomeric bearing isnonlinear, so E, is load-dependent. However, an accept-able constant approximation is:

E, = 6GS2

(14.5.3.2-3)

where:

G = shear modulus of elastomer (ksi)S = shape factor"

14.6 SPECIAL DESIGN PROVISIONS FORBEARINGS

The stress increases permitted for certain load combi-nations by Table 3.22.1A of this specification shall notapply in the design of bearings.

14.6.1 Metal Rocker and Roller Bearings

14.6.1.1 General Design Considerations

The rotation axis of the bearing shall be aligned withthe axis about which the largest rotations of the supportedmember occur. Provision shall be made to ensure that thebearing alignment does not change during the life of thebridge. Multiple roller bearings shall be connected bygearing to ensure that individual rollers remain parallel toeach other and at their original spacing.

Metal rocker and roller bearings shall be detailed sothat they can be easily inspected and maintained.

14.6.1.2 Materials

Rocker and roller bearings shall be made of stainlesssteel conforming to ASTM A 240, or of structural steelconforming to AASHTO M 169 (ASTM A 108), M 102(ASTM A 668), or M 270 (ASTM A 709) Grades 36,50 or 50W. Material properties of M 169 (ASTM A 108),M 102 (ASTM A 668), and M 270 (ASTM A 709) steelare given in Tables 10.2A and 10.213.

14.6.1.3 Geometric Requirements

The dimensions of the bearing shall be chosen takinginto account both the contact stresses and the movementof the contact point due to rolling.

Each individual curved contact surface shall have aconstant radius. Bearings with more than one curved sur-face shall be symmetric about a line joining the centers oftheir two curved surfaces.

Bearings shall be designed to be stable. If the bearinghas two separate cylindrical faces, each of which rolls ona flat plate, stability may be achieved by making the dis-tance between the two contact lines no greater than thesum of the radii of the two cylindrical surfaces.

14.6.1.4 Contact Stresses

The maximum compressive load, P m , shall satisfy:

• for cylindrical surfaces:

F Z

Pm <8 WD,

L2(14.6.1.4-1)

(1-D i /D 2 E S


• for spherical surfaces:2 3

P,,, !_ 40D,

EY2 (14.6.1.4-2)5

where:

D, = the diameter of rocker or roller surface (in), andD 2 = the diameter of the mating surface (in). D 2 shall

be taken as:• positive if the curvatures have the same sign• infinite if the mating surface is flat

F, = specified minimum yield strength of the leaststrong steel at the contact surface (ksi)

E, = Young's modulus for steel (ksi)W = Width of the bearing (in)

14.6.2 PTFE Sliding Surfaces

PTFE, polytetrafluorethylene, may be used in slidingsurfaces of bridge bearings to accommodate translation orrotation. All PTFE surfaces other than guides shall satisfythe requirements of this section. Curved PTFE surfacesshall also satisfy Article 14.6.3.

14.6.2.1 PTFE Surface

The PTFE surface shall be made from pure virginPTFE resin satisfying the requirements of ASTM D 4894or D 4895. It shall be fabricated as unfilled sheet, filledsheet or fabric woven from PTFE and other fibers.

Unfilled sheets shall be made from PTFE resin alone.Filled sheets shall be made from PTFE resin uniformlyblended with glass fibers or other chemically inert filler.The maximum filler content shall be 15%.

Sheet PTFE may contain dimples to act as reservoirsfor lubricant. Their diameter shall not exceed 0.32-in atthe surface of the PTFE and their depth shall be not lessthan .08-inch and not more than half the thickness of thePTFE. The reservoirs shall be uniformly distributed overthe surface area and shall cover more than 20% but lessthan 30% of it. Lubricant shall be silicone grease whichsatisfies military specification MIL-S-8660.

Woven fiber PTFE shall be made from pure PTFEfibers. Reinforced woven fiber PTFE shall be made byinterweaving high strength fibers, such as glass, with thePTFE in such a way that the reinforcing fibers do not ap-pear on the sliding face of the finished fabric.

14.6.2.2 Mating Surface

The PTFE shall be used in conjunction with a mating sur-face. Flat mating surfaces shall be stainless steel and curvedmating surfaces shall be stainless steel or anodized aluminium.Flat surfaces shall be a minimum #8 mirror finish Type 304stainless steel and shall conform to ASTM A 167/A 264.

Curved metallic surfaces shall not exceed 16 micro in RMS.Other surface finishes may be employed if the coefficient offriction is substantiated by test results. The mating surfaceshall be large enough to cover the PTFE at all times.

14.6.2.3 Minimum Thickness Requirements

14.6.2.3.1 PTFE

For all applications, the thickness of the PTFE shall beat least 1

/16 inch after compression. Recessed sheet PTFEshall be at least 3

/16 inch thick when the maximum dimen-sion of the PTFE is less than or equal to 24 inches, and1/4 inch when the maximum dimension of the PTFE isgreater than 24 inches. Woven fabric PTFE which is me-chanically interlocked over a metallic substrate shall havea minimum thickness of 1

/16 inch and a maximum thick-ness of 1

/8 inch over the highest point of the substrate.

14.6.2.3.2 Stainless Steel Mating Surfaces

The thickness of the stainless steel mating surface shallbe at least '/16 inch when the maximum dimension of thesurface is less than or equal to 12 inches and 1

/8 inch whenthe maximum dimension is larger than 12 inches.

Backing plate requirements are specified in Article14.6.2.6.2.

14.6.2.4 Contact Pressure

The maximum contact stress, Qm, between the PTFEand the mating surface shall be determined with the max-imum compressive load, Pm , using the nominal area.

The average contact stress shall be computed by divid-ing the load by the projection of the contact area onto aplane perpendicular to the direction of the load. The contactstress at the edge shall be computed by taking into accountthe maximum moment, Mm , transferred by the bearing as-suming a linear distribution of stress across the PTFE.

Stresses shall not exceed those given in Table 14.6.2.4-1.Permissible stresses for intermediate filler contentsshall be obtained by linear interpolation within Table14.6.2.4-1.

14.6.2.5 Coefficient of Friction

The design coefficient of friction of the PTFE slidingsurface shall be determined from Table 14.6.2.5-1. Inter-mediate values may be determined by interpolation. Thecoefficient of friction shall be determined by using thestress level associated with the maximum compressiveload, Pm . Lesser values of the coefficient of friction maybe used if verified by tests.

Where friction is required to resist applied loads, thedesign coefficient of friction under dynamic loading maybe taken as not more than 10% of the value listed in Table14.6.2.5-1 for the bearing stress and PTFE type.


TABLE 14.6.2.4-1 Limits on Contact Stress for PTFE

Ave. Contact Stress (KSI) Edge Contact Stress (KSI)

Material Dead Load All Loads Dead Load All Loads

Unconfined PTFE:Unfilled sheets 1.5 2.5 2.0 3.0Filled sheets-These figures 3.0 4.5 3.5 5.5

are for maximum filler contentConfined sheet PTFE 3.0 4.5 3.5 5.5Woven PTFE over a metallic 3.0 4.5 3.5 5.5

substrateReinforced woven PTFE over 4.0 5.5 4.5 7.0

a metallic substrate

TABLE 14.6.2.5-1 Design Coefficients of Friction

Coefficient of Friction

Type of PTFE Pressure (psi) 500 1000 2000 >3000

Temperature (°F)

Dimpled Lubricated 68 0.04 0.03 0.025 0.02-13 0.06 0.045 0.04 0.03-49 0.10 0.075 0.06 0.05

Unfilled or Dimpled 68 0.08 0.07 0.05 0.03Unlubricated -13 0.20 0.18 0.13 0.10

-49 0.20 0.18 0.13 0.10Filled 68 0.24 0.17 0.09 0.06

-13 0.44 0.32 0.25 0.20-49 0.65 0.55 0.45 0.35

Woven 68 0.08 0.07 0.06 0.045-13 0.20 0.18 0.13 0.10-49 0.20 0.18 0.13 0.10

The coefficients of friction in Table 14.6.2.5-1 arebased on a #8 mirror finish mating surface. Coefficients offriction for rougher surface finishes must be establishedby test results in accordance with Division II, Section 18.

14.6.2.6 Attachment

14.6.2.6.1 PTFE

Sheet PTFE confined in a recess in a rigid metal backingplate for one half its thickness may be bonded or unbonded.

Sheet PTFE which is not confined shall be bonded byan approved method to a metal surface or an elastomericlayer with a Shore A durometer hardness of at least 90.Woven PTFE on a metallic substrate shall be attached tothe metallic substrate by mechanical interlocking whichcan resist a shear force no less than 0.10 times the appliedcompressive force.

14.6.2.62 Mating Surface

The mating surface for flat sliding shall be attached toa backing plate by welding in such a way that it remainsflat and in full contact with its backing plate throughoutits service life. The weld shall be detailed to form an ef-fective moisture seal around the entire perimeter of the

mating surface so that interface corrosion cannot occur.The attachment shall be capable of resisting the maximumfriction force which can be developed by the bearingunder service loads. The welds used for the attachmentshall be clear of the contact and sliding area of the PTFEsurface.

14.6.3 Bearings with Curved Sliding Surfaces

Bearings with curved sliding surfaces shall consist oftwo metal parts with matching curved surfaces and a lowfriction sliding interface. The curved surfaces shall beeither cylindrical or spherical. The material properties,characteristics, and frictional properties of the slidinginterface shall satisfy the requirements of either Article14.6.2 or Article 14.6.7.


The radius of the curved surface shall be large enoughto assure that the maximum average bearing stress, o r., onthe horizontal projected area of the bearing at the maxi-mum load, Pm, shall satisfy the average stress require-ments of Article 14.6.2.4 or Article 14.6.7.3. The maxi-mum average bearing stress shall be taken as


o For cylindrical bearings and

P.6m - (14.6.3.1-1)

DW

• For spherical bearings

4P6

m= 1LDm

(14.6.3.1-2)

where

D = diameter of the projection of the loaded surfaceof the bearing in the horizontal plane (in)

W = length of the cylinder (in)

The two surfaces of a sliding interface shall have equal radii.

14.6.3.2 Resistance to Lateral Load

In bearings which are required to resist horizontalloads, either an external restraint system shall be pro-vided, or for a cylindrical sliding surface the horizontalload shall be limited to

H,,, < 2RWOrPTrE sin(`Y - R - 6m) sin

R(14.6.3.2-1)

and for a spherical surface the horizontal load shall satisfy

Hn, < 7rR2 QPTRE sin 2 (T - (3 - 6m) sin (3 (14.6.3.2-2)

Where

R = tan_iH

P m (14.6.3.2-3)D

9n,SURFACE AREAAVAILABLE TO CARRYCOMPRESSION ,

T=sin-i(2R)

(14.6.3.2-4)

and:

H e = maximum horizontal load.L = projected length of the sliding surface perpen-

dicular to the rotation axis.PD = compressive load due to permanent loads.R = radius of the curved sliding surface.w = length of the cylindrical surface.

R = angle between the vertical and applied loads.6 m = maximum design rotation angle. See Article

14.4.1.Q

PTFE = maximum average contact stress permitted onthe PTFE by Table 14.6.2.4-1.

T = subtended semi-angle of the curved surface.

14.6.4 Pot Bearings

14.6.4.1 General

Where pot bearings are provided with a PTFE slider toprovide for both rotation and horizontal movement, suchsliding surfaces and any guidance systems shall be designedin accordance with the appropriate Articles 14.6.2 and 14.6.9.

The rotational elements of pot bearing shall satisfy therequirements of this section. They shall consist of at leasta pot, a piston, an elastomeric disc, and sealing rings.

For the purpose of establishing the forces and defor-mations imposed on a pot bearing, the axis of rotationshall be taken as lying in the horizontal plane at mid-height of the elastomeric disc.

EQUAL LLENGTHS

L

FIGURE 14.6.3.2-1


The minimum vertical load on a pot bearing should notbe less than 20% of the vertical design load.

14.6.4.2 Materials

The elastomeric disc shall be made from a compoundbased on virgin natural rubber or virgin neoprene. Itsnominal hardness shall lie between 50 and 60 on the ShoreÀ' scale.

The pot and piston shall be made from structuralsteel conforming to AASHTO M 270 (ASTM A 709)Grades 36, 50 or 50W, or from stainless steel conform-ing to ASTM A 240. The finish of surfaces in contactwith the elastomeric pad shall be smoother than 63micro-in rms.

Sealing rings satisfying Articles 14.6.4.5.1 and14.6.4.5.2 shall be made from brass conforming to ASTMB 36 (half hard) for rings of rectangular cross-section,and Federal Specification QQB626, Composition 2, forrings of circular cross-section.


The depth of the elastomeric disc, h r , shall satisfy

h r ? 3.33D p 9 m (14.6.4.3-1)

where

Dp = internal diameter of the pot (in)O m = maximum design rotation specified in Article

14.4.1 (rad)

The dimensions of the components shall satisfy the fol-lowing requirements under the least favorable combina-tion of maximum displacements and rotations:

• the pot shall be deep enough to permit the seal andpiston rim to remain in full contact with the verticalface of the pot wall.

• contact or binding between metal components willnot prevent further displacement or rotation.

14.6.4.4 Elastomeric Disc

The maximum average stress on the elastomer shallnot exceed 3.5 ksi. To facilitate rotation, the top and bot-tom surfaces of the elastomer shall be treated with a lu-bricant which is not detrimental to the elastomer, or thinPTFE discs may be used on the top and bottom of the elas-tomer.

14.6.4.5 Sealing Rings

A seal shall be used between the pot and the piston. Theseals shall be adequate to prevent escape of elastomer

under compressive load and simultaneously appliedcyclic rotations. The seals shall also be adequate to pre-vent escape of elastomer under compressive load and si-multaneously applied static rotation.

Brass rings satisfying the requirements of either Arti-cle 14.6.4.5.1 or 14.6.4.5.2 may be used to satisfy theabove requirements. The Engineer may approve othersealing systems on the basis of experimental evidence.

14.6.4.5.1 Rings with rectangular cross-sections

Three rings shall be used. Each ring shall be circular inplan, but shall be cut at one point around its circumfer-ence. The faces of the cut shall be on a plane at 45° to thevertical and to the tangent of the circumference. The ringsshall be oriented so that the cuts on each of the three ringsare equally spaced around the circumference of the pot.

The width of each ring shall be equal to or greater thanthe larger of 0.02 D, or 1

/4 inch, but it shall not exceed 3/4

inch. The depth of each shall be equal to or greater than0.2 times the width.

14.64.5.2 Rings with circular cross-sections

One circular closed ring shall be used with an outsidediameter of D P. It shall have a cross-sectional diameter notless than the larger of 0.0175 D p or 5

/16 inch.

14.6.4.6 Pot

The pot shall consist at least of a wall and base. All com-ponents shall be designed to act as a single structural unit.

The minimum thickness of the base shall exceed 0.06Dp and 3/4 inch when bearing directly against concrete orgrout, and shall exceed 0.04 Dp and 1/2 inch when bearingdirectly on steel girders or load distribution plates.

The pot walls shall be thick enough to resist all theforces induced in them. In lieu of a more precise analysis,this requirement may be satisfied for unguided sliding potbearings by using a minimum wall thickness such that

Dt

W> P a (14.6.4.6-1)

1.25Fym

and tw ? 3 /4 "

where

ta, = pot wall thickness (in)

Qm = maximum average compressive stress (ksi)F, = yield strength of the steel (ksi)

14.6.4.7 Piston

The piston shall have the same plan shape as the insideof the pot. Its thickness shall be adequate to resist the


loads imposed on it, but shall not be less than 6.0% of theinside diameter of the pot, DP , except at the rim.

The diameter of the piston rim shall be the inside di-ameter of the pot less a clearance, c. The clearance, c, shallbe as small as possible in order to prevent escape of theelastomer, but not less than 0.02 inch. If the surface of thepiston rim is cylindrical, the clearance shall satisfy

c >! O n, w -DPO_

)(14.6.4.7-1)

where

DP = internal diameter of pot (in)w = height of piston rim (in)0m = design rotation specified in Article 14.4.1 (rad)

14.6.4.8 Lateral Loads

Pot bearings which are subjected to lateral loads shallbe proportioned so that the thickness, t, of the pot wall andthe pot base shall satisfy

t>40H m 0,,,

(14.6.4.8-1)FY

For pot bearings which transfer lateral load through thepiston

w >2,5H m

(14.6.4.8-2)D p Fy

and w >_ W?

where w is the rim thickness of the piston which is in con-tact with the pot wall.

14.6.5 Steel Reinforced Elastomeric Bearings-Method B

14.6.5.1 General

Steel reinforced eastomeric bearings shall consist ofalternate layers of steel reinforcement and elastomer,bonded together. Tapered elastomer layers shall not beused. All internal layers of elastomer shall be of the samethickness. The top and bottom cover layers shall be nothicker than 70% of the internal layers. In addition to anyinternal reinforcement, bearings may have external steelload plates bonded to the upper or lower elastomer layersor both.

14.6.5.2 Material Properties

The elastomer shall have a shear modulus between0.08 and 0.175 ksi and a nominal hardness between 50and 60 on the Shore A scale.

The shear modulus of the elastomer at 73°F shall beused as the basis for design. If the elastomer is specifiedexplicitly by its shear modulus, then that value shall beused in design and the other properties shall be obtainedfrom Table 14.6.5.2-1. If the material is specified by itshardness, the shear modulus shall be taken as the leastfavorable value from the range for that hardness given inTable 14.6.5.2-1. Intermediate values shall in all cases beobtained by interpolation.

For the purposes of bearing design, all bridge sitesshall be classified as being in temperature Zones A, B, C,D or E. Characteristics for each zone are given in Table14.6.5.2-2. In the absence of more precise information,Figure 14.6.5.2-2 may be used as a guide in selecting thezone required for a given region.

Bearings shall be made from AASHTO low tempera-ture grades of elastomer as defined in Section 18 of Divi-sion II. The minimum grade of elastomer required foreach low temperature zone is specified in Table14.6.5.2-2.

Any of the three design options listed below may beused:

specify the elastomer with the minimum low tem-perature grade indicated in Table 14.6.5.2-2 and de-termine the shear force transmitted by the bearing asspecified in Article 14.5.3.1.specify the elastomer with the minimum low tem-perature grade for use when special force provisionsare incorporated in the design and provide a low fric-tion sliding surface, in which case the special forceprovision is that the bridge components shall be de-signed to withstand twice the design shear forcespecified in Article 14.5.3.1, orspecify the elastomer with the minimum low tem-perature grade for use when special force provisionsare incorporated in the design, but do not provide alow friction sliding surface, in which case the com-ponents of the bridge shall be designed to resist fourtimes the design shear force as specified in Article14.5.3.1.

Table 14.6.5.2-1 Elastomer Properties At DifferentHardnesses

Hardness (Shore 'A') 50 60 70

Shear modulus at 73T (psi) 95-130 130-200 200-300Creep deflection at 25 yrsInstantaneous deflection

25% 35% 45%


Table 14.6.5.2-2 Low Temperature Zones and Elastomer Grades

Low Temperature Zone A B C D E

50 year low temperature (°F) 0 -20 -30 -45 all othersMax. no. of days below 32°F 3 7 14 N/A N/ALow temp. elastomer grade 0 2 3 4 5

without special provisionsLow temp. elastomer grade 0 0 2 3 5

with special provisions

FIGURE 14.6.5.2-1 Map of Low Temperature Zones

14.6.5.3 Design Requirements 14.6.5.3.2 Compressive Stress

14.6.5.3.1 ScopeIn any bearing layer, the average compressive stress

(ksi) shall satisfy the following:Bearings designed by the provisions of this section

shall be subsequently tested in accordance with the re- • for bearings subject to shear deformationquirements for steel reinforced elastomeric bearings ofArticle 18.7 of Division II of this Specification. Steel re- 6TL 1.6 ksiinforced elastomeric bearings may also be designed under 6TL 1.66 GS (14.6.5.3.2-1)the provisions of Article 14.6.6. 6L 0.66 GS

1600

1400

Q 1200

1000

> 800NQ)

L 600EU 400

200

00 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7

Compressive strain (%) Compressive strain (%)

FIGURE 14.6.5.3.3-1 Load Deflection Behavior of Elastomeric Bearings

1600

1400

.a 1200

1000v~

800.N

n 600EU 400

200

0


• for bearings fixed against shear deformation h, = total elastomeric thickness (in)0, = maximum service shear deformation of the

QTL < 1.75 ksi6TL < 2.00 GS (14.6.5.3.2-2)

elastomer (in)

6L 1.00 GS14.6.5.3.5 Combined Compression and Rotation

where

QL = average compressive stress due to the live load(ksi)

6TL = Average compressive stress due to total deadplus live load (ksi)

G = shear modulus of elastomer (ksi)S = shape factor of the thickest layer of the bearing

14.6.5.3.3 Compressive Deflection

Deflections due to total load and to live load alone shallbe considered separately. A maximum relative deflectionof % inch across a joint is preferred.

Instantaneous deflection shall be calculated as follows:

8 = lE,h« (14.6.5.3.3-1)

where:

E; = instantaneous compressive strain in the it" elas-

tomer layer of a laminated elastomeric bearinghrt = thickness of

itnelastomeric layer in elastomeric

bearing (in)

Values for e, shall be determined from test results or byrational analysis. The effects of creep of the elastomershall be added to the instantaneous deflection when con-sidering long-term deflections. They should be computedfrom information relevant to the elastomeric compoundused. In the absence of material-specific data, the valuesgiven in Article 14.6.5.2 shall be used. In the absence ofinformation specific to the particular bearing to be used,Figure 14.6.5.3.3-1 may be used.

14.65.3.4 Shear

The horizontal movement of the bridge superstructure,Ao, shall be taken as the maximum possible displacementcaused by creep, shrinkage, post-tensioning, combinedwith thermal effects computed in accordance with thisSpecification. The maximum shear deformation of thebearing, A s , shall be taken as Ao, modified to account forthe pier flexibility and construction procedures. If a lowfriction sliding surface is installed, A s need not be takenlarger than the deformation corresponding to first slip.

The bearing shall be designed so that

hn >_ 20 s (14.6.5.3.4-1)

where

Rotations shall be taken as the maximum possible dif-ference in slope between the top and bottom surfaces ofthe bearing. They shall include the effects of initial lack-of-parallelism and subsequent girder end rotation due toimposed loads and movements. Bearings shall be de-signed so that uplift does not occur under any combina-tion of loads and corresponding rotation.

All rectangular bearings shall satisfy

2

6TL ? LOGS(B_ )(B (14.6.5.3.5-1)n h i

A rectangular bearing subject to shear deformation shallalso satisfy Equation (14.6.5.3.5-2); those fixed againstshear deformation shall also satisfy Equation (14.6.5.3.5-3).

6TL -1.875GS 1- 0.200Om )( B)2) (14.6.5.3.5-2)n h j

)2)

6TL_ 2.250GS 1-0.167( 0`°)(B (14.6.5.3.5-3)

n h i

where

B = length of pad if rotation is about its transverseaxis, or width of pad if rotation is about its lon-gitudinal axis (in)

G = shear modulus of elastomer (ksi)hr; = thickness of the

ittilayer of elastomer (in)

n = number of interior layers of elastomer, where in-terior layers are defined as those layers whichare bonded on each face. Exterior layers are de-fined as those layers which are bonded only onone face. When the thickness of an exterior layerof elastomer is more than one-half the thicknessof an interior layer, the parameter, n, may be in-creased by one-half for each such exterior layer.

S = shape factor of the thickest layer of the bearinge

m = component of maximum service rotation in di-rection of interest (rad)

CrTL = average compressive stress due to the total

dead plus live load (ksi)

All circular bearings shall satisfy

z6TL > 0.75GS~Ori )~ D (14.6.5.3.5-4)

n _)


A circular bearing subject to shear deformation shall alsosatisfy Equation (14.6.5.3.5-5); those fixed against sheardeformation shall also satisfy Equation (14.6.5.3.5-6).

la TL <2.5GS 1-0.15\ / (en I(D

)2)

(14.6.5.3.5-5),

)2)

aTL < 3.OGS~I - 0.125 On )( D (14.6.5.3.5-6)n

where

D = diameter of pad (in)

14.65.3.6 Stability

Bearings shall be proportioned to avoid instability. If

the bearing is stable for all allowable loads in this speci-fication and no further consideration of stability is required.

For rectangular bearings not satisfying Equation(14.6.5.3.6-1), an additional check involving 6 TL shall bemade in accordance with Equation (14.6.5.3.6-2) or 3. Anegative or infinite limit from Equation (14.6.5.3.6-3) indi-cates that the bearing is stable and is not dependent on a TL .

• if the bridge deck is free to translate horizontally

G2.67

S(S + 2)(1 + L/4W)

(14.6.5.3.6-2)

• if the bridge deck is not free to translate horizontally

GaTL < 1.92(hrt /L) _ 2.67

CS 1+2L/w S(S+2)(1+L/4W)

(14.6.5.3.6-3)

If L is greater than W for a rectangular bearing, stabil-ity shall be checked by the above formulas with L and Winterchanged.

For circular bearings, stability may be evaluated by usingthe equations for a square bearing with W = L = 0.8 D.

14.6.5.3.7 Reinforcement

The thickness of the reinforcement, h s , shall satisfy therequirements

hs >3.OhrF~aTL

(14.6.5.3.7-1)Y

and

h, >2.Oh

r m,, G Ls (14.6.5.3..7-2)

F,

where

hs = thickness of steel laminate (in)F sr = allowable fatigue stress range for over 2,000,000

cycles (ksi)

If holes exist in the reinforcement, the minimum thick-ness shall be increased by a factor of 2(gross width)/(netwidth).

14.6.6 Elastomeric Pads and Steel ReinforcedElastomeric Bearings-Method A

14.6.6.1 General

This section of the specification covers the design ofplain elastomeric pads, PEP, pads reinforced with discretelayers of fiberglass, FGP, and pads reinforced with closelyspaced layers of cotton duck, CDP and steel reinforcedelastomeric bearings. Layer thicknesses in FGP may bedifferent from one another. For steel reinforced elas-tomeric bearings designed in accordance with the provi-sions of this section, internal layers shall be of the samethickness and cover layers shall be no more than 70% ofthe thickness of internal layers.

14.6.6.2 Material Properties

The materials shall satisfy the requirements of Article14.6.5.2, except that the shear modulus shall lie between0.080 and 0.250 ksi and the nominal hardness shall lie be-tween 50 and 70 on the Shore À' scale. This excep-tion shall not apply to steel reinforced elastomeric bear-ings designed in accordance with the provisions of thisarticle.

14.6.6.3 Design Requirements

14.6.6.3.1 Scope

Plain elastomeric pads, fiberglass reinforced pads andcotton duck reinforced pads shall be designed in accor-dance with the provisions of this article. Steel reinforcedelastomeric bearings designed in accordance with theprovisions of this article shall qualify for the test require-ments appropriate for elastomeric pads.

The provisions for FGP apply only to pads where thefiberglass is placed in double layers 1/8 inch apart.

The physical properties of neoprene and natural rubberused in these bearings shall conform to the followingASTM requirements, with modifications as noted:

3.84 (h rt /L) <

SVI + 2 L/w

2.67S(S + 2)(1 + L/4w)

(14.6.5.3.6-1)

6TT. <3.84(h,/L) _

~S 1+2L/W


Neoprene: D4014Natural Rubber: D4014

Modifications:

(1) The Shore A Durometer hardness shall lie withinthe limits specified in Article 14.6.6.2.(2) Samples for compression set tests shall be pre-pared using a Type 2 die.

14.66.3.2 Compressive Stress

The average compressive stress, QTL , in any layer shallsatisfy

• for PEP, QTL < 0.80 ksi, and QTL <_ 0.55GS• for FGP, QTL :5 0.80 ksi, and QTL <- 1.OOGS• for CDP, QTL <_ 1.50 ksi

In FGP, the value of S used shall be that for the great-est distance between the mid-point of double reinforce-ment layers at the top and bottom of the elastomer layer.

For steel reinforced elastomeric bearings designed inaccordance with the provisions of this article QTL C 1.00ksi, and o-TL <_ 1.0 GS where the value of S used shall bethat for the thickest layer of the bearing. These stress lim-its may be increased by 10% where shear deformation isprevented.

14.66.3.3 Compressive Deflection

The provisions of Article 14.6.5.3.3 shall apply. Ap-propriate data for PEP, FGP and CDP may be used to es-timate their deflections. In the absence of such data, thecompressive deflection of PEP and FGP may be estimatedat 3 and 1.5 times the deflection estimated for steel rein-forced bearings of the same shape factor in Article14.6.5.3.3, respectively.

CDP are typically very stiff in compression and theprovisions of this article may be considered as satisfied onthe basis of past experience, and no calculations need bedone, provided the provisions of Article 14.6.6.3.2 are met.

14.6.6.3.4 Shear

The horizontal bridge movement shall be computed inaccordance with Article 14.4. The maximum shear defor-mation of the pad, A,, shall be taken as the horizontalbridge movement, reduced to account for the pier flexi-bility and modified for construction procedures. If a lowfriction sliding surface is used, A s need not be taken largerthan the deformation corresponding to first slip.

The pad shall be designed as follows:

h n ? 2A5 for PEP, FGP and steel reinforced elastomericbearings

hrt >! 100 s for CDP (14.6.6.3.4-1)

14.6.6.3.5 Rotation

The rotation about each axis shall be taken as the max-imum possible rotation between the top and bottom of thepad caused by initial lack of parallelism and girder end ro-tation.

14.6.6.3.5a PEP and CDP

The shape factor of CDP shall be defined as 100 for usein Equations (14.6.6.3.5a-1) and (14.6.6.3.5a-2). Theyshall satisfy:

• for rectangular pads

2

aTL ? 0.5GS~h 0 m ,x orrt

l2

6TL ? 0.5GSI h 10m , z (14.6.6.3.5a-1)rt

• for circular pads

12

6TL ? 0.375GSI D

rt J0m (14.6.6.3.5a-2)

14.663.5b FGP and Steel Reinforced ElastomericBearings

They shall satisfy:

• for rectangular pads or bearings

(h,j1a'TL ? 0.5GS L 1

0m'xor

/ n

2

6TL >_ 0.5GS(h0n 'z

(14.6.6.3.5b-1)

• for circular pads or bearings

2

61Z >_ 0.375GS(h, ) 0n (14.6.6.3.5b-2)

where

n = number of interior layers of elastomer, where in-terior layers are defined as those layers whichare bonded on each face. Exterior layers are de-fined as those layers which are bonded only onone face. When the thickness of an exterior layerof elastomer is more than one-half the thickness

400 HIGHWAY BRIDGES 14.6.6.3.5b

of an interior layer, the parameter, n, may be in-creased by one-half for each such exterior layer.

h ri = thickness of the itb layer of elastomer (in)

14.6.6.3.6 Stability

To ensure stability, the total thickness of pad shall notexceed the least of L/3, W/3, or D/4.

14.6.6.3.7 Reinforcement

The reinforcement in FGP shall be fiberglass with afailure strength in each direction of at least 2.2 hri K/in ofwidth. For the purpose of this article, if the layers of elas-tomer are of different thickness, h; shall be taken as themean thickness of the two layers of the elastomer bondedto the reinforcement. If the fiberglass reinforcement con-tains holes, its strength shall be increased over the mini-mum value specified above by two times the gross widthdivided by net width.

Reinforcement for steel reinforced elastomeric bear-ings designed in accordance with the provisions ofthis article shall conform to the requirements of Article14.6.5.3.7.

14.6.6.4 Resistance to Deformation

The shear force on the structure induced by deforma-tion of the elastomer shall be based on a G value not lessthan that of the elastomer at 73°F. Effects of relaxationshall be ignored.

If the design shear force, Hm, due to pad deformationexceeds one-fifth of the minimum vertical force, the padshall be secured against horizontal movement.

The pad shall not be permitted to sustain uplift forces.

14.6.7 Bronze or Copper Alloy Sliding Surfaces

Bronze or Copper Alloy may be used in

flat sliding surfaces to accommodate translationalmovements,curved sliding surfaces to accommodate translationand limited rotation,pins or cylinders for shaft bushings of rocker bear-ings or other bearings with large rotations.

14.6.7.1 Materials

Bronze sliding surfaces or castings shall conform toAASHTO M 107 (ASTM B 22) and shall be made of AlloyC90500, C91100 or C86300 unless otherwise specified.The mating surface shall be structural steel which has a

Rockwell hardness value at least 100 points greater thanthat of the bronze.

Copper alloy 913 or 911 or copper alloy plates,AASHTO M 108 (ASTM B 100), shall be used unless oth-erwise specified.

14.6.7.2 Coefficient of Friction

The design coefficient of friction shall be determinedby applying an appropriate safety factor to the measuredcoefficient of friction obtained using a rational test proce-dure. In lieu of such test data, the design coefficient offriction may be taken as 0.1 for self-lubricating bronzecomponents and 0.4 for other types.

14.6.7.3 Limits on Load and Geometry

The nominal bearing stress due to combined dead andlive load shall be no greater than 2.0 ksi.

14.6.7.4 Clearances and Mating Surface

The mating surface shall be steel which is accuratelymachined to match the geometry of the bronze surface andprovide uniform bearing and contact.

14.6.8 Disc Bearings

14.6.8.1 General

For the purposes of establishing the forces and defor-mations imposed on a disc bearing, the axis of rotationmay be taken as lying in the horizontal plane at mid-height of the disc. The urethane disc shall be held in placeby a positive location device.

The disc bearing shall be designed for the design rota-tion, 0,,,, defined in Article 14.4.1.

14.6.8.2 Materials

The elastomeric disc shall be made from a compoundbased on polyether urethane, using only virgin materials.The hardness shall lie between 45 and 65 on the Shore Dscale.

The metal components of the bearing shall be madefrom structural steel conforming to AASHTO M 270(ASTM A 709) Grades 36, 50, or 50W, or from stainlesssteel conforming to ASTM A 240.

14.6.8.3 Overall Geometric Requirements

The dimensions of the components shall be such thathard contact between metal components which prevents


further displacement or rotation will not occur under theleast favorable combination of design displacements androtations.

14.6.8.4 Elastomeric Disc

The elastomeric disc shall be held in location by a pos-itive locator device. The disc shall be designed so that

• its instantaneous deflection under total load does notexceed 10% of the thickness of the unstressed disc,and the additional deflection due to creep does notexceed 8% of the thickness of the unstressed disc;

• the average compressive stress due to the maximumload, Pm , on the disc does not exceed 5.0 ksi. If theouter surface of the disc is not vertical, the stress shallbe computed using the smallest plan area of the disc.

If a PTFE slider is used

• the stresses on the PTFE slider do not exceed 75%of the allowable values for average and edge stressesgiven in Article 14.6.2. The effect of moments in-duced by the urethane disc shall be included in thestress analysis.

14.6.8.5 Shear Resisting Mechanism

In fixed and guided bearings, a shear-resisting mecha-nism shall be provided to transmit horizontal forces betweenthe upper and lower steel plates. It shall be capable of re-sisting a horizontal force in any direction equal to the largerof the design shear force and 10% of the design vertical load.

The horizontal design clearance between the upper andlower components of the shear-restricting mechanism shallnot exceed the value for guide bars given in Article 14.6.9.

14.6.9.2 Design Loads

The guide or restraint shall be designed using the max-imum load combinations for the larger of

• the horizontal design load, or• 10% of the maximum vertical load acting on all the

bearings at the bent divided by the number of guidedbearings at the bent.

14.6.9.3 Materials

For steel bearings, the guide or restraint shall be madefrom steel conforming to AASHTO M 270 (ASTM A 709)Grades 36, 50 or 50W, or stainless steel conforming toASTM A 240. The guide for aluminum bearings may alsobe aluminum.

The low-friction interface material shall be approvedby the Engineer.


Guides shall be parallel, long enough to accommodatethe full design displacement of the bearing in the slidingdirection, and shall permit a minimum Of 1/32-inch and amaximum of 1/16-inch free slip in the restrained direction.Guides shall be designed to avoid binding under all designloads and displacements, including rotations.

14.6.9.5 Design Basis

14.69.5.1 Load Location

The horizontal load acting on the guide or restraintshall be assumed to act at the centroid of the low-frictioninterface material. Design of the connection between theguide or restraint and the body of the bearing system shalltake into account both shear and overturning moment.

14.6.8.6 Steel Plates14.6.9.5.2 Contact Stress

The thickness of the upper and lower steel plates shallnot be less than 0.045 Dd if the plate is in direct contactwith a steel girder or distribution plate, or 0.06 D d if itbears directly on grout or concrete.

14.6.9 Guides and Restraints

The contact stress on the low-friction material shall notexceed that recommended by the manufacturer. For PTFE,the stresses due to the maximum loads, Pm and Hm, shallnot exceed those given in Table 14.6.2.4.1 under sustainedloading or 1.25 times those stresses for short-term loading.

14.6.9.6 Attachment of Low-Friction Material14.6.9.1 General

Guides may be used to prevent movement in one di-rection. Restraints may be used to permit only limitedmovement in one or more directions. Guides and restraintsshall have a low-friction material at their sliding contactsurfaces.

The low-friction material shall be attached by at leasttwo of the following three methods:

mechanical fasteningbondingmechanical interlocking with a metal substrate.


14.6.10 Other Bearing Systems

Bearing systems made from components not describedin Articles 14.6.1 through 14.6.8 may also be used, subjectto the approval of the Engineer. Such bearings shall be ad-equate to resist the forces and deformations imposed onthem without material distress and without inducing defor-mations large enough to threaten their proper functioning.

The dimensions of the bearing shall be chosen to pro-vide for adequate movements at all times. The materialsused shall have sufficient strength, stiffness, and resis-tance to creep and decay to ensure the proper functioningof the bearing throughout the design life of the bridge.

The Engineer shall determine the tests which the bearingmust satisfy. The tests shall be designed to demonstrate anypotential weakness in the system under individual compres-sion, shear or rotational loading or combinations thereof.Testing under sustained or cyclic loading shall be required.

14.7 LOAD PLATES AND ANCHORAGE FORBEARINGS

14.7.1 Plates for Load Distribution

The bearing, together with any additional plates, shallbe designed so that

• the combined system is stiff enough to prevent dis-tortions of the bearing which would impair its properfunctioning;

• the stresses imposed on the supporting structure sat-isfy the limits specified by the Engineer. Allowablestresses on concrete and grout beds shall be assumedto be based on the maximum compressive load, Pm ,on the bearing;

• the bearing can be replaced within the jacking heightlimits specified by the Engineer without damage to thebearing, distribution plates or supporting structure. Ifno limit is given, a height of 3/8 inch shall be used.

Computations of the strength of steel components andbeam stiffener requirements of steel girders shall be madein conformance with Section 10 of Division I of thesespecifications.

In lieu of a more precise analysis, the load from a bear-ing fully supported by a grout bed may be assumed tospread out at a slope of 1.5:1, horizontal to vertical, fromthe edge of the smallest element of the bearing which car-ries the compressive load.

14.7.2 Tapered Plates

If, under full dead load at the mean annual temperaturefor the bridge site, the inclination of the underside of thegirder to the horizontal exceeds 0.01 rad, a tapered plateshall be used in order to provide a level load surface to beplaced on the bearing.

14.7.3 Anchorage

All load distribution plates and all bearings with exter-nal steel plates shall be positively secured to their supportsby bolting or welding.

All girders shall be positively located on their support-ing bearings by a connection which can resist the horizon-tal forces which may be imposed on it. Separation of bear-ing components shall not be permitted. A connection,adequate to resist the least favorable combination of loads,shall be installed wherever necessary to prevent separation.

14.8 CORROSION PROTECTION

All exposed steel parts of bearings not made from stain-less steel shall be protected against corrosion by zinc me-tallization, hot-dip galvanizing or a paint system approvedby the Engineer. A combination of zinc metallization orhot-dip galvanizing and a paint system may be used.

Section 15

STEEL TUNNEL LINER PLATES

15.1 GENERAL AND NOTATIONS

15.1.1 General

15.1.1.1 These criteria cover the design of cold-formed panel steel tunnel liner plates. The minimumthickness shall be as determined by design in accordancewith Articles 15.2, 3, 4, 5, and 6 and the construction shallconform to Section 26—Division II. The supporting ca-pacity of a nonrigid tunnel lining such as a steel liner plateresults from its ability to deflect under load, so that siderestraint developed by the lateral resistance of the soilconstrains further deflection. Deflection thus tends toequalize radial pressures and to load the tunnel liner as acompression ring.

15.1.1.2 The load to be carried by the tunnel liner isa function of the type of soil. In a granular soil, with littleor no cohesion, the load is a function of the angle of in-ternal friction of the soil and the diameter of the tunnelbeing constructed. In cohesive soils such as clays and siltyclays the load to be carried by the tunnel liner is depen-dent on the shearing strength of the soil above the roof ofthe tunnel.

15.1.1.3 A subsurface exploration program and ap-propriate soil tests should be performed at each installa-tion before undertaking a design.

15.1.1.4 Nothing included in this section shall be in-terpreted as prohibiting the use of new developmentswhere usefulness can be substantiated.

15.1.2 Notations

A = cross-sectional area of liner plates (Article15.3.4)

C d = coefficient for tunnel liner, used in Marston'sformula (Article 15.2.4)

D = horizontal diameter or span of the tunnel (Arti-cle 15.2.4)

D = pipe diameter (Article 15.3.3)

D, = critical pipe diameter (Article 15.3.4)E = modulus of elasticity (Article 15.3.3)FS = factor of safety for buckling (Article 15.3.4)f, = buckling stress (Article 15.3.4)f„ = minimum specified tensile strength (Article

15.3.4)H = height of soil over the top of the tunnel (Article

15.2.4)I = moment of inertia (Article 15.3.3)k = parameter dependent on the value of the friction

angle (Article 15.3.4)P = external load on tunnel liner (Article 15.2. 1)Pd = vertical load at the level of the top of the tunnel

liner due to dead load (Article 15.2. 1)P, = vertical load at the level of the top of the tunnel

liner due to live load (Article 15.2. 1)r = radius of gyration (Article 15.3.4)T = thrust per unit length (Article 15.3.4)W = total (moist) unit weight of soil (Article

15.2.4)4 = friction angle of soil (Article 15.3.4.1)

15.2 LOADS

15.2.1 External load on a circular tunnel liner made upof tunnel liner plates may be predicted by various meth-ods including actual tests. In cases where more precisemethods of analysis are not employed, the external load Pcan be predicted by the following:

(a) If the grouting pressure is greater than the com-puted external load, the external load P on the tunnelliner shall be the grouting pressure.(b) In general the external load can be computed bythe formula:

P = P, + Pd (15-1)

where:

P = the external load on the tunnel liner;

P, = the vertical load at the level of the top of thetunnel liner due to live loads;

403

404 HIGHWAY BRIDGES

P d = the vertical load at the level of the top of the 15.3 DESIGNtunnel liner due to dead load.

15.3.1 Criteria

15.2.1

15.2.2 For an H 20 load, values of P, are approximatelythe following:

H(ft) 4 5 6 7 8 9 10P, (1b per sq ft) 375 260 190 140 110 90 75

15.2.3 Values of P d may be calculated using Marston'sformula for load or any other suitable method.

15.2.4 In the absence of adequate borings and soil tests,the full overburden height should be the basis for P d in thetunnel liner plate design.

The following is one form of Marston's formula:

P d = Cd WD (15-2)

where:

Cd = coefficient for tunnel liner, Figure 15.2.3A;W = total (moist) unit weight of soil;D = horizontal diameter or span of the tunnel;H = height of soil over the top of the tunnel.

The following criteria must be considered in the designof liner plates:

(a) Joint strength.(b) Minimum stiffness for installation.(c) Critical buckling of liner plate wall.(d) Deflection or flattening of tunnel section.

15.3.2 Joint Strength

15.3.2.1 The seam strength of liner plates must besufficient to withstand the thrust developed from the totalload supported by the liner plate. This thrust, T, in poundsper linear foot is:

T = PD/2 (15-3)

where P = load as defined in Article 15.2, and D =diameter or span in feet.

12

CO 10CL

Cn

0

CO

0 4

edata ar

0 1 2 3

Values of coefficient C d

FIGURE 15.2.3A Diagram for Coefficient C d for Tunnels in Soil (~ = Friction Angle)


15.3.2.2 The ultimate design longitudinal seam For diameters less than D., the ring compression stress

strengths are: at which buckling becomes critical is:

TABLE 15.3.2.2

Ultimate Seam Strength of Liner PlatesPlate Thickness Ultimate Strength,

(in.) (kips/ft)

2 Flange 4 Flange

0.075 20.00.105 30.0 26.00.135 47.0 43.00.164 55.0 50.00.179 62.0 54.00.209 87.0 67.00.239 92.0 81.00.313 115.00.375 119.0

15.3.2.3 The thrust, T, multiplied by the safety fac-tor, should not exceed the ultimate seam strength.

15.3.3 Minimum Stiffness for Installation

15.3.3.1 The liner plate ring shall have enough rigid-ity to resist the unbalanced loads of normal construction:grouting pressure, local slough-ins, and miscellaneousconcentrated loads.

The minimum stiffness required for these loads can beexpressed for convenience by the formula below. It mustbe recognized, however, that the limiting values given hereare only recommended minima. Actual job conditions mayrequire higher values (greater effective stiffness). Final de-termination on this factor should be based on intimateknowledge of the project and practical experience.

15.3.3.2 The minimum stiffness for installation is de-termined by the formula:

Minimum stiffness = EI/D2 (15-4)

where:

D = diameter in inches;E = modulus of elasticity, psi (29 X 106);I = moment of inertia, inches to the fourth power per

inch;For 2-Flange (EI/DZ ) = 50 minimum;For 4-Flange (EI/DZ ) = 111 minimum;

15.3.4 Critical Buckling of Liner Plate Wall

15.3.4.1 Wall buckling stresses are determined fromthe following formulae:

f°fu–[48EX(kr )

a ]inpsi (15-5)

For diameters greater than D,:

( 2E)z in psi (15-6)

where:

D c _ (rfk) 24E/fu = critical pipe (15-7)diameters in inches;

fU = minimum specified tensile strength in pounds persquare inch;

f, = buckling stress in pounds per square inch, not toexceed minimum specified yield strength;

D = pipe diameter in inches;r = radius of gyration of section in inches per foot;E = modulus of elasticity in pounds per square

inch.

k will vary from 0.22 for soils with (~ > 15 to 0.44 forsoils (~ < 15.

15.3.4.2 Design for buckling is accomplished by lim-iting the ring compression thrust T to the buckling stressmultiplied by the effective cross-sectional area of the linerplate divided by the factor of safety.

T= F~

(15-8)

where:

T = thrust per linear foot from Article 15.3.2;A = effective cross-sectional area of liner plate in

square inches per foot;FS = factor of safety for buckling.

15.3.5 Deflection or Flattening

15.3.5.1 Deflection of a tunnel depends significantlyon the amount of over-excavation of the bore and is af-fected by delay in backpacking or inadequate backpack-ing. The magnitude of deflection is not primarily a func-tion of soil modulus or the liner plate properties, so itcannot be computed with usual deflection formulae.

15.3.5.2 Where the tunnel clearances are important,the designer should oversize the structure to provide for anormal deflection. Good construction methods shouldresult in deflections of not more than 3% of the normaldiameter.


15.4 CHEMICAL AND MECHANICALREQUIREMENTS

15.4.1 Chemical Composition

Base metal shall conform to ASTM A 569.

15.4.2 Minimum Mechanical Properties of FlatPlate Before Cold Forming

Tensile strength = 42,000 psiYield strength = 28,000 psiElongation, 2 inches = 30 percent

15.4.3 Dimensions and Tolerances

Nominal plate dimensions shall provide the sectionproperties shown in Article 15.5. Thickness tolerancesshall conform to Paragraph 14 of AASHTO M 167.

15.5 SECTION PROPERTIES

The section properties per inch of plate width, based onthe average of one ring of linear plates, shall conform tothe following:

TABLE 153A Section Properties for Four-FlangeLiner Plate

GageThickness

(in.)Area

(in. 2/in.)

EffectiveArea

(in. 2/in.)

Momentof Inertia(in./in.)

12 0.105 0.133 0.067 0.04211 0.1196 0.152 0.076 0.04910 0.135 0.170 0.085 0.055

8 0.164 0.209 0.105 0.0707 0.179 0.227 0.114 0.0755 0.209 0.264 0.132 0.0873 0.239 0.300 0.150 0.120

1/4 0.250 0.309 0.155 0.1015/16 0.3125 0.386 0.193 0.1233/8 0.375 0.460 0.230 0.143

TABLE 15.5B Section Properties for Two-FlangeLiner Plate

Thickness(in.)

EffectiveArea

(in. 2/in.)

Momentof Inertia(in. 4/in.)

0.075 0.096 0.0340.105 0.135 0.0490.135 0.174 0.0640.164 0.213 0.0790.179 0.233 0.0870.209 0.272 0.1030.239 0.312 0.118

15.6 COATINGS

Steel tunnel liner plates shall be of heavier gage orthickness or protected by coatings or other means whenrequired for resistance to abrasion or corrosion.

15.7 BOLTS

15.7.1 Bolts and nuts used with lapped seams shall benot less than %8 inch in diameter. The bolts shall conformto the specifications of ASTM A 449 for plate thicknessequal to or greater than 0.209 inches and A 307 for platethickness less than 0.209 inches. The nut shall conform toASTM A 307, Grade A.

15.7.2 Circumferential seam bolts shall be A 307 or bet-ter for all plate thicknesses.

15.7.3 Bolts and nuts used with four flanged plates shallbe not less than %2 inch in diameter for plate thicknessesto and including 0.179 inches and not less than %8 inch indiameter for plates of greater thickness. The bolts and nutsshall be quick acting coarse thread and shall conform toASTM A 307, Grade A.

15.8 SAFETY FACTORS

Longitudinal test seam strength = 3Pipe wall buckling = 2

Section 16

SOIL-REINFORCED CONCRETE STRUCTUREINTERACTION SYSTEMS

16.1 GENERAL

16.1.1 Scope

Specifications in this Section govern the design ofburied reinforced concrete structures. A buried reinforcedconcrete element becomes part of a composite systemcomprising the reinforced concrete section and the soilenvelope, both of which contribute to the structural be-havior of the system.

16.1.2 Notations

A = effective tension area of concrete surrounding theflexural tension reinforcement and hav-ing thesame centroid as that reinforcement, divided bythe number of bars or wires, sq in.; when the flex-ural reinforcement consists of several bar sizes orwire the number of bars or wires shall be com-puted as the total area of reinforcement dividedby the area of the largest bar or wire used (Arti-cles 16.6.4 and 16.7.4)

AP

= total active lateral pressure acting on pipe, lbs/ft(Article 16.4.5 and Figure 16.4C)

A, = tension reinforcement area on width b, in. 2 /ft(Articles 16.4.6.6, 16.6.4.7, 16.7.4.7, and 16.8.5.7)

As ; = area of total inner cage reinforcement required inlength b, ing /ft (Article 16.4.6.6)

A,® = area of total outer cage reinforcement required inlength b, in g/ft (Article 16.4.6.6)

A ir = stirrup reinforcement area to resist radial ten-sion forces on width b, in. 2/ft in each line ofstirrups at circumferential spacing s (Article16.4.6)

A,, = required area of stirrups for shear reinforcement,in? (Article 16.4.6.6.6.2)

A,,, = steel area required for an individual circumferen-tial wire for flexure at a splice or at the point ofmaximum moment for quadrant mat reinforce-ment, in g (Article 16.4.7)

b = width of section which resists M, N, V—Usually

b = 12 inches (Article 16.4.6)B, = out-to-out horizontal span of pipe or box, ft (Ar-

ticles 16.4.4, 16.4.5, 16.6.4, and 16.7.4.)

Ba = horizontal width of trench at top of pipe or box, ft(Articles 16.4.4, 16.6.4, and 16.7.4.)

B f = bedding factor (Article 16.4.5)

Bfe = earth load bedding factorB ELL = live load bedding factor

B, = crack control coefficient for effect of cover andspacing of reinforcement (Article 16.4.6)

B' = out-to-out vertical rise of pipe, ft (Figure 16AC)C, = load coefficient for embankment installations

(Article 16.4.5)Ca = load coefficient for trench installations (Article

16.4.4)CA = constant corresponding to the shape of pipe (Ar-

ticle 16.4.5)CN = parameter which is a function of the distribution

of the vertical load and the vertical reaction (Ar-ticle 16.4.5)

Ct = crack control coefficient for type of reinforce-ment (Article 16.4.6)

d = distance from compression face to centroid oftension reinforcement, in. (Articles 16.4.6.6,16.6.4.7, 16.7.4.7, and 16.8.5.7)

dc = thickness of concrete cover measured from ex-treme tension fiber to center of bar or wire locatedclosest thereto (Articles 16.6.4.7, 16.7.4.7, and16.8.5.7)

D = D-load of pipe, three-edge bearing test load ex-pressed in pounds per linear foot per foot of spanto produce a 0.01-inch crack (Article 16.4.5)

D t = inside diameter of pipe, in.f, = service load stress in reinforcing steel for crack

control (Articles 16.6.4.7, 16.7.4.7, and 16.8.5.7)f, = maximum allowable strength of stirrup material,

lbs/in. 2 (Article 16.4.6.6.6)fy = specified yield strength of reinforcement, lbs/in. 2

(Article 16.4.6)

407


F, = factor for effect of curvature on diagonal tension(shear) strength in curved components (Article16.4.6.6.5)

Fir = factor for adjusting crack control relative to aver-age maximum crack width of 0.01 inch when F,,= 1.0 (Article 16.4.6.6.4)

Fd = factor for crack depth effect resulting in increasein diagonal tension (shear) strength with decreas-ing d (Article 16.4.6.6.5)

F, = soil-structure interaction factor (Articles 16.4.4,16.6.4, and 16.7.4)

Fel = soil structure interaction factor for embankmentinstallations (Articles 16.4.4, 16.6.4, and 16.7.4)

Fez = soil-structure interaction factor for trenchinstallations (Articles 16.4.4, 16.6.4, and16.7.4)

FrP = factor for process and local materials that af-fect the radial tension strength of pipe (Article16.4.6)

F, = factor for pipe size effect on radial tensionstrength (Article 16.4.6.6.3.1)

F,,P = factor for process and local materials that affectthe shear strength of pipe (Article 16.4.6.6.5)

FN = coefficient for effect of thrust on shear strength(Article 16.4.6.6.5)

f, = design compressive strength of concrete, lbs/in. z

(Articles 16.4.6, 16.6.2, and 16.7.2)h = overall thickness of member (wall thickness), in.

(Articles 16.4.6.6,16.6.4.7,16.7.4.7, and 16.8.5.7)H = height of fill above top of pipe or box, ft (Articles

16.4.4, 16.4.5, 16.6.4, and 16.7.4)HAF = horizontal arching factor (Figure 16.4A)i = coefficient for effect of axial force at service load

stress, fs (Articles 16.4.6.6.4, 16.6.4.7, 16.7.4.7,and 16.8.5.7)

j = coefficient for moment arm at service load stress,fs (Articles 16.4.6.6.4, 16.6.4.7, 16.7.4.7, and16.8.5.7)

K = ratio of the active unit lateral soil pressure to unitvertical soil pressure-Rankine's coefficient ofactive earth pressure (Figures 16AB-D)

Ld = development length of reinforcing wire or bar, in(Article 16.4.7)

Mn, = factored moment acting on length b as modifiedfor effects of compressive or tensile thrust, in-lbs/ft (Article 16.4.6.6.5)

Ms = moment acting on cross section of width, b, ser-vice load conditions, in-lbs/ft (Taken as absolutevalue in design equations, always +) (Articles16.4.6.6.4, 16.6.4.7, 16.7.4.7, and 16.8.5.7)

M„ = factored moment acting on cross section of widthb, in.-lbs/ft (Article 16.4.6.6.6.1)

n = number of layers of reinforcement in a cage—1or 2 (Article 16.4.6.6.4)

N, = axial thrust acting on cross section of width b,service load condition (+ when compressive, —when tensile), lbs/ft (Articles 16.4.6.6.4, 16.6.4.7,16.7.4.7, and 16.8.5.7)

N„ = factored axial thrust acting on cross section ofwidth b, lbs/ft (Article 16.4.6)

p = projection ratio (Article 16.4.5.2.1)p ' = negative projection ratio (Figure 16.4A and Table

16.4A)PL = PL denotes the prism load (weight of the column

of earth) over the pipe's outside diameter, lbs/ft(Figure 16.4.A)

q = ratio of the total lateral pressure to the total verti-cal load (Article 16.4.5)

r s = radius of the inside reinforcement, in. (Article16.4.6.6.3.1)

rsd = settlement ratio (Article 16.4.5.2.1)S = spacing of reinforcement wire or bar, in. (Article

16.4.6.6.4)s,, = circumferential spacing of stirrups, in. (Article

16.4.6.6.6)se = spacing of circumferential reinforcement, in. (Ar-

ticle 16.4.6.6.4)S i = internal horizontal span of pipe, in. (Articles

16.4.6.6 and 16.4.5.1)tb = clear cover over reinforcement, in. (Article

16.4.6.6.4)Vb = basic shear strength of critical section, lbs/ft

where M,,,,/(V„ d) = 3.0 (Article 16.4.6.6.5)V, = nominal shear strength provided by width b of

concrete cross section, lbs/ft (Article 16.4.6.6.6)V„ = factored shear force acting on cross section of

width b, lbs/ft (Article 16.4.6.6.5)V„c = factored shear force at critical section, lbs/ft

where M,,,,/(V„ d) = 3.0 (Article 16.4.6.6.5)VAF = vertical arching factor (Article 16.4.4.2.1.1)w = unit weight of soil, lbs/ft' (Article 16.4.4)WE = total earth load on pipe or box, lbs/ft (Articles

16.4.4, 16.4.5, 16.6.4, and 16.7.4)Wf = fluid load in the pipe as determined according to

Article 16.4.4.2.2, lbs/ftWL = total live load on pipe or box, lbs/ft (Articles

16.4.4 and 16.4.5)WT = total load, earth and live, on pipe or box, lbs/ft

(Articles 16.4.4 and 16.4.5)x = parameter which is a function of the area of the

vertical projection of the pipe over which lateralpressure is effective (Article 16.4.5)

µ = coefficient of internal friction of the soil (Fig-ure 16.4B)

= coefficient of friction between backfill and trenchwalls (Figure 16.4B)

t = central angle of pipe subtended by assumed dis-tribution of external reactive force (Figure 16.41 7)


p = ratio of reinforcement area to concrete area (Ar-ticle 16.4.6)

~f = strength reduction factor for flexure (Article16.4.6.6.1)

~r = strength reduction factor for radial tension (Arti-cle 16.4.6.6.3.1)

4 v = strength reduction factors for shear (Article16.4.6.6.5)

16.1.3 Loads

Design loads shall be determined by the forces actingon the structure. For earth loads, see Article 3.20. For liveloads see Articles 3.4 through 3.8 and Articles 3.11 and3.12. For loading combinations see Article 3.22.

16.1.4 Design

Design may be based on working stress or ultimatestrength principles. The design criteria shall includestructural aspects (e.g. flexure, thrust, shear), handlingand installation, and crack control. Footing design forcast-in-place boxes and arches shall be in conformitywith Article 4.4.

16.1.5 Materials

The materials shall conform to the AASHTO materialsspecifications referenced herein.

16.1.6 Soil

Structural performance is dependent on soil structureinteraction. The type and anticipated behavior of the ma-terial beneath the structure, adjacent to the structure, andover the structure must be considered.


Where abrasive or corrosive conditions exist, suitableprotective measures shall be considered.

16.1.8 End Structures

Structures may require special consideration whereerosion may occur. Skewed alignment may require specialend wall designs.


The construction and installation shall conform to Sec-tion 27, Division 11.

16.2 SERVICE LOAD DESIGN

16.2.1 For soil-reinforced concrete structure interactionsystems designed with reference to service loads and al-lowable stresses, the service load stresses shall not exceedthe values shown in Article 8.15 except as modified herein.

16.2.2 For precast reinforced concrete circular pipe,elliptical pipe, and arch pipe, the results of three edge-bearing tests made in accordance with AASHTO mate-rials specifications may be used in lieu of service loaddesign.

16.3 LOAD FACTOR DESIGN

16.3.1 Soil-reinforced concrete structure interactionsystems shall be designed to have design strengths of allsections at least equal to the required strengths calculatedfor the factored loads as stipulated in Article 3.22, exceptas modified herein.

16.3.2 For precast reinforced concrete circular pipe, el-liptical pipe, and arch pipe, the results of three edge-bear-ing tests made in accordance with AASHTO materialsspecifications may be used in lieu of load factor design.

16.4 REINFORCED CONCRETE PIPE

16.4.1 Application

This Specification is intended for use in design for pre-cast reinforced concrete circular pipe, elliptical pipe, andarch pipe. Standard dimensions are shown in AASHTOmaterial specifications M 170, M 206, M 207, and M 242.Design wall thicknesses other than the standard wall di-mensions may be used, provided the design complies withall applicable requirements of Section 16.

16.4.2 Materials

16.4.2.1 Concrete

Concrete shall conform to Article 8.2 except that eval-uation of f,' may be based on cores.


Reinforcement shall meet the requirements of Articles8.3.1 through 8.3.3 only, and shall conform to one of thefollowing AASHTO material specifications M 31, M 32,M 55, M 221, or M 255. For smooth wire and smooth


TABLE 16.4A Standard Embankment Installation Soils and Minimum Compaction Requirements

Haunch andInstallation Type Bedding Thickness Outer Bedding Lower Side

Type 1 B~/24" (600 mm) minimum, not less than 95% SW 90% SW, 95% ML,3" (75 mm). If rock foundation, use B,/ 12" or(300 mm) minimum, not less than 6" 100% CL(150 mm).

Type 2 B,/24" (600 mm) minimum, not less than 90% SW 85% SW, 90% ML,(See Note 3.) 3 "

(75 mm). If rock foundation, use B,/ 12" or or(300 mm) minimum, not less than 6" 95% ML 95% CL(150 mm).

Type 3 Bc /24" (600 mm) minimum, not less than 85% SW, 90% ML, or 85% SW, 90% ML,(See Note 3.) 3 " (75 mm). If rock foundation, use B,/ 12" 95% CL or

(300 mm) minimum, not less than 6" 95% CL(150 mm).

Type 4 No bedding required, except if rock No compaction required, No compaction required,foundation, use B,/ 12" (300 mm) minimum, except if CL, use except if CL, usenot less than 6" (150 mm). 85% CL 85% CL

NOTES:1. Compaction and soil symbols -i.e. "95% SW" refer to SW soil material with a minimum standard proctor compaction of 95%.

See Table 16AC for equivalent modified proctor values.2. Soil in the outer bedding, haunch, and lower side zones, except within B,/3 from the pipe springline, shall be compacted to at least the same

compaction as the majority of soil in the overfill zone.3. Only Type 2 and 3 installations are available for horizontal elliptical, vertical elliptical and arch pipe.4. SUBTRENCHES4.1 A subtrench is defined as a trench with its top below finished grade by more than O.1H or, for roadways, its top is at an elevation lower than

V (0.3 m) below the bottom of the pavement base material.4.2 The minimum width of a subtrench shall be 1.33 Be , or wider if required for adequate space to attain the specified compaction in the haunch

and bedding zones.4.3 For subtrenches with walls of natural soil, any portion of the lower side zone in the subtrench wall shall be at least as firm as an equivalent

soil placed to the compaction requirements specified for the lower side zone and as firm as the majority of soil in the overfill zone, or shall beremoved and replaced with soil compacted to the specified level.

welded wire fabric, a yield stress of 65,000 psi and for de-formed welded wire fabric, a yield stress of 70,000 psimay be used.

16.4.2.3 Concrete Cover for Reinforcement

The minimum concrete cover for the reinforcement inprecast concrete pipe shall be 1 inch in pipe having a wallthickness of 2%z inches or greater and %4 inch in pipe hav-ing a wall thickness of less than 2%2 inches.

16.4.3 Installations

16.4.3.1 Standard Installations

Standard Embankment Installations are presented inFigure 16AB and Standard Trench Installations are pre-sented in Figure 16AC; these figures define soil areas andcritical dimensions. Generic soil types, minimum com-paction requirements, and minimum bedding thicknessesare listed in Table 16.4A for four Standard EmbankmentInstallation Types and in Table 16AB for four StandardTrench Installation Types.

16.4.3.2 Soils

The AASHTO Soil Classifications and the USCSSoil Classifications equivalent to the generic soil typesin the Standard Installations are presented in Table16AC.

16.4.4 Design


Design shall conform to applicable sections of thesespecifications except as provided otherwise in this arti-cle. For design loads, see Article 16.1.3; for standard in-stallation, see Article 16.4.3.1; and for bedding condi-tions, see Section 27, Division II—Construction and theSoil-Structure Interaction Modifications that follow.Live loads, WL , shall be included as part of the total load,WT , and shall be distributed through the earth cover asspecified in Article 6.4, except that the 2-foot minimumin the first paragraph of Article 6.4 does not apply. Othermethods for determining total load and pressure distrib-ution may be used, if they are based on successful design


TABLE 16AB Standard Trench Installation Soils and Minimum Compaction Requirements

Haunch andInstallation Type Bedding Thickness Outer Bedding Lower Side

Type 1 B,/24" (600 mm) minimum, not less than 95% SW 90% SW, 95% ML,3" (75 mm). If rock foundation, use B,/ 12" 100% CL, or(300 mm) minimum, not less than 6" natural soils of

(150 mm). equal firmness

Type 2 B,/24" (600 mm) minimum, not less than 90% SW 85% SW, 90% ML,

(See Note 3.) 3" (75 mm). If rock foundation, use B,/ 12" or 95% CL, or natural

(300 mm) minimum, not less than 6" 95% ML soils of equal

(150 mm). firmness

Type 3 B,/24" (600 mm) minimum, not less than 85% SW, 90% ML, or 85% SW, 90% ML,(See Note 3.) 3" (75 mm). If rock foundation, use B,/ 12" 95% CL 95% CL, or natural

(300 mm) minimum, not less than 6" soils of equal(150 mm). firmness

Type 4 No bedding required, except if rock No compaction required, 85% SW, 90% MLfoundation, use B c / 12" (300 mm) minimum, except if CL, use 95% CL, or naturalnot less than 6" (150 mm). 85% CL soils of equal

firmness

NOTES:1. Compaction and soil symbols -i.e. "95% SW"-refers to SW soil material with minimum standard Proctor compaction of 95%.

See Table 16.4C for equivalent modified Proctor values.2. The trench top elevation shall be no lower than O.1H below finished grade or, for roadways, its top shall be no lower than an elevation of

l' (0.3 m) below the bottom of the pavement base material.3. Only Type 2 and 3 installations are available for horizontal elliptical, vertical elliptical and arch pipe.4. Soil in bedding and haunch zones shall be compacted to at least the same compaction as specified for the majority of soil in the backfill zone.5. The trench width shall be wider than shown if required for adequate space to attain the specified compaction in the haunch and bedding

zones.6. For trench walls that are within 10 degrees of vertical, the compaction or firmness of the soil in the trench walls and lower side zone need

not be considered.7. For trench walls with greater than 10-degree slopes that consist of embankment, the lower side shall be compacted to at least the same

compaction as specified for the soil in the backfill zone.

practice or tests that reflect the appropriate design con-ditions.

16.4.4.2 Loads

16.4.4.2.1 Earth Loads and Pressure Distribution

The effects of soil-structure interaction shall be takeninto account and shall be based on the design earth cover,sidefill compaction, and bedding characteristics of thepipe-soil installations.

16.4.4.2.11 Standard Installations

For the Standard Installations given in Article 16.4.3.1,the earth load, WE, may be determined by multiplying theprism load (weight of the column of earth) over the pipesoutside diameter by the soil-structure interaction factor,Fe, for the specified installation type.

WE = Fe wB,H (16-1)

Standard Installations for both embankments and trenchesshall be designed for positive projection, embankment

loading conditions where Fe = VAF given, in Figure16AA for each Type of Standard Installation.

For Standard Installations the earth pressure distribu-tion shall be the Heger pressure distribution shown in Fig-ure 16.4A for each type of Standard Installation.

The unit weight of soil used to calculate earth load shallbe the estimated unit weight for the soils specified for thepipe-soil installation and shall not be less than 110 lbs/cu ft.

16.4.4.2.1.2 Nonstandard Installations

When nonstandard installations are used, the earth loadand pressure distribution shall be determined by an ap-propriate soil-structure interaction analysis.

16.4.4.2.2 Pipe Fluid Weight

The weight of fluid, Wf , in the pipe shall be consideredin design based on a fluid weight of 62.4 lbs/ft3 , unlessotherwise specified. For Standard Installations, the fluidweight shall be supported by vertical earth pressure thatis assumed to have the same distribution over the lowerpart of the pipe as given in Figure 16AA for earth load.


TABLE 16AC Equivalent USCS and AASHTO Soil Classifications For SIDD Soil Designations

Representative Soil Types Percent CompactionSIDD Soil USCS AASHTO Standard Proctor Modified ProctorGravelly Sand SW, SP Al, A3 100 95

(SW) GW, GP 95 9090 8585 8080 7561 59

Sandy Silt (ML) GM, SM, ML A2, A4 100 95Also GC, SC 95 90

with less than 20% 90 85passing No. 200 sieve 85 80

80 7549 46

Silty Clay (CL) GL, MH, GC, SC A5, A6 100 9095 8590 8085 7580 7045 40

CH A7 100 9095 8590 8045 40

16.4.4.2.3 Live Loads

Live loads shall be either the AASHTO HS-Series orthe AASHTO Interstate Design truck loads. Live loadsshall be distributed through the earth cover as specified inArticle 6.4, except that the 2-foot minimum in the firstparagraph of Article 6.4 does not apply. For Standard In-stallations the live load on the pipe shall be assumed tohave a uniform vertical distribution across the top of thepipe and the same distribution across the bottom of thepipe as given in Figure 16AA for earth load.

16.4.4.3 Minimum Fill

For unpaved areas and under flexible pavements,the minimum fill over precast reinforced concrete pipeshall be 1 foot or %8 of the diameter or rise, whichever isgreater. Under rigid pavements, the distance between thetop of the pipe and the bottom of the pavement slab shallbe a minimum of 9 inches of compacted granular fill.

16.4.4.4 Design Methods

The structural design requirements of installed precastreinforced concrete pipe may be determined by either theIndirect or Direct Method.

16.4.5 Indirect Design Method Based on PipeStrength and Load-Carrying Capacity

16.4.5.1 Loads

The design load-carrying capacity of a reinforced con-crete pipe must equal the design load determined for thepipe as installed, or

D=[12][WE+WF+ WL

]

(16-2)S l

Bfe

BELL

where

D = D-load of the pipe (three edge-bearing test loadexpressed in pounds per linear foot per foot ofdiameter) to produce a 0.01-inch crack. ForType 1 installations, D-load as calculatedabove shall be modified by multiplying by aninstallation factor of 1.10;

Si = internal diameter or horizontal span of the pipein inches;

B f = bedding factor, see Article 16.4.5.2;B

F, = earth load bedding factor;B

FLL = live load bedding factor;


A6 A6

HAF b6 Dm= 1 b HAF

A5 A5

C e A4uc

)A4

f

h2 A2

ht 2 Al 2

~ J~ I- vh2

uh1VAF

lwu& im Type VAP HAF Al A2 A3 A4 AS A6 a b c e f u v

1 135 0.45 0.62 0.73 135 0.19 0.08 0.16 1.40 0.40 0.1E OA OAS 0.80 0.80

2 1A0 0.40 OAS OM 1.40 0.15 OM 0.17 1.45 0.40 0.19 0.10 0.05 0.82 0.70

3 1.40 037 LOS 035 1.40 0.10 0.10 0.11 1.45 076 020 0.12 OM OAS 0.60

4 1.45 0,30 1AS OM L45'T 0.00 0.11 0.19 1.45 0.30 023 OAO - 1 0.90

NOTES:

1. VAF and HAF are vertical and horizontal arching factors. These coefficients represent nondimensional total vertical and horizontal loads on the pipe,respectively. The actual total vertical and horizontal loads are (VAF) X (PL) and (HAF) X (PL), respectively, where PL is the prism load.

2. Coefficients Al through A6 represent the integration of nondimensional vertical and horizontal components of soil pressure under the indicatedportions of the component pressure diagrams (i.e., the area under the component pressure diagrams). The pressures are assumed to vary either para-bolically or linearly, as shown, with the nondimensional magnitudes at governing points represented by h,, h 2, uh,, vhl , a and b. Nondimensional hor-izontal and vertical dimensions of component pressure regions are defined by c, d, e, uc, vd, and f coefficients.

3. d is calculated as (0.5 c-e)hi is calculated as (1.5A1) / (c) (I + u)h2 is calculated as (1.5 A2) / [(d) (1 + v) + (2e)].

FIGURE 16.4A Heger Pressure Distribution and Arching Factors


STANDARD EMBANKMENT INSTALLATIONS

Overfill - SW. ML. or CL

H

Be Be (Min.)

B c /6 (10- _

Haunch - See Table 17.4A

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -1I Lower Side - See Table 17.4A

Bedding - See Table 17.4A iBC/3

Middle Beddingloosely placed

Outer Bedding uncompacted beddingmaterial and

Compaction each ~— Foundation except for Type 4

side, somerequirements

as haunch

FIGURE 16AB

STANDARD TRENCH INSTALLATIONS

'.: . i)verfdl - SW, ML, or CL

M

Be /6 (Min.)Be Be (Min.)

Excavation line asrequired

-- -Haunch - See Table 17.413

"1 /- Lower Side - See Table 17.413

Bedding - See Table 17.4B

Outer Beddingmaterfol and

compaction eachside. some

requirementsas haunch

Bc~3 Middle Beddingloosely placed

Foundation 3/ uncompacted bedding

except for Type 4

FIGURE 16.4C


WT = W E + W L ;W T = total load on the pipe as determined according

to Article 16.4.4;W E = earth load on the pipe as determined according

to Article 16.4.4;Wp = fluid load in the pipe as determined according

to Article 16.4.4.2.2;WL = live load on the pipe as determined according

to Article 16.4.4.

16.4.5.1.1 Ultimate D-load

The required D-load at which the pipe develops its ul-timate strength in a three-edge-bearing test is the designD-load (at 0.01-inch crack) multiplied by a strength fac-tor that is specified in AASHTO materials specificationsM 170 or M 242 (ASTM C 76 or C 655) for circular pipe,M 206 (ASTM C 506) for arch pipe and M 207 (ASTM C507) for elliptical pipe.

16.4.5.2 Bedding Factor

The bedding factor, B f, is the ratio of the supportingstrength of buried pipe to the strength of the pipe deter-mined in the three-edge-bearing test. The supportingstrength of buried pipe depends on the type of StandardInstallation. See Figures 16.4B and 16.4C for circular pipeand Figures 16.41) and 16.4E for other arch and ellipticalshapes. The Tables 16AA and 16AB apply to circular,arch and elliptical shapes.

16.4.5.2.1 Earth Load Bedding Factor for CircularPipe

Earth load bedding factors, B fe , for circular pipe arepresented in Table 16.4E.

16.4.5.2.2 Earth Load Bedding Factor for Arch andElliptical Pipe

The bedding factor for installations of arch and ellip-tical pipe, Figures 16AD and 16AE, is

B fe = CA (16-3)C N –xq

Values for CA and C N are listed in Table 16.4D.

CA = a constant corresponding to the shape of thepipe;

CN = a parameter which is a function of the distribu-tion of the vertical load and vertical reaction;

x = a parameter which is a function of the area of thevertical projection of the pipe over which lateralpressure is effective;

q = the ratio of the total lateral pressure to the totalvertical fill load.

16.4.5.2.3 Live Load Bedding Factor

The bedding factors for live load, W L, for both circularpipe and arch and elliptical pipe are given in Table 16.5F.If B fe is less than B ELL , use B fe instead of BFLL

for the live

load bedding factor.

Design values for CA, C N, and x are found in Table16AD. The value of q is determined by the followingequations:

Arch and Horizontal Elliptical Pipe

q=.23 p 1+.35p L)I (16-4)

Vertical Elliptical Pipe

q=.48Fe I1+.73p H I (16-5)

where

p = projection ratio, ratio of the vertical distancebetween the outside top of the pipe and theground or bedding surface to the outside ver-tical height of the pipe.

16.4.5.2.4 Intermediate Trench Widths

For intermediate trench widths, the bedding factor maybe estimated by interpolation between the narrow trenchand transition width bedding factors.

16.4.6 Direct Design Method for Precast ReinforcedConcrete Circular Pipe

16.4.6.1 Application

This Specification is intended for use in direct designof precast reinforced concrete circular pipe, and is basedon design of pipe wall for effects of loads and pressuredistribution for installed conditions. Standard dimensionsare shown in AASHTO M 170. Design wall thicknessesother than the standard wall dimension may be used pro-vided the design complies with all applicable require-ments of Section 16.

16.4.6.2 General

Design shall conform to applicable sections of thesespecifications, except as provided otherwise in this article.


Overfill - SW. ML, or CL

Overfill - SW, ML, or CL

-Y- Nounch -Spring Line See Table 16.4B~'~

I ][ 'Lower side -See Table 16.48

Bedding -See Table 16.48J~ —Middle BeddingOuter Bedding loosely placedmaterials and Bc 3 uncompacted bedding

compaction eachside, some LEGEND:requirementsas haunch Be Outside Diameter

/ HBockfill cover above

FoundationJ top of pipe

HORIZONTAL ELLIPTICAL PIPE

Houn InSpring Line See fable 16.48~•drw ,n, Lower Side

cR k& See Table 16.46t3~:L~Y4• ;, t:

Bedding -See Table 16.48 Middle BeddingOuter Bedding loosely placedmaterials and uncompocted bedding

compaction eachside, some LEGEND:

requirements Be Outside Diameteras haunch

Foundation H = Bockfill cover abovetop of pipe

VERTICAL ELLIPTICAL PIPE

Overfill - SW, ML, or CL

Spring LineHoun hSee lgoble 16.46ower Side -ee Table 16.48

Bedding -See Table 18.48 J Middle B e dOuter Bedding loosely placedmaterials and uncompocted bedding

compaction eachside, some LEGEND:

requirements Be Outside Diameteras haunch r•— Foundation H s Bockfill cover above

top of pipe

ARCH PIPEFIGURE 16AD french Beddings, Miscellaneous Shapes

The total load on the pipe shall be determined accord-ing to Article 16.4.4 and Table 3.22. IA.

The pressure distribution on the pipe from appliedloads and bedding reaction shall be determined from asoil-structure analysis or shall be a rational approxima-tion. Acceptable pressure distribution diagrams are theHeger Pressure Distribution (see Figure 16.4A) for usewith the Standard Installations: the Olander/ModifiedOlander Radial Pressure Distribution (see Figure 16.4F);or the Paris/Manual Uniform Pressure Distribution (seeFigure 16.4F).

For use with the Heger Pressure Distribution, fourTypes of Standard Embankment Installations, soil types,and compaction requirements are depicted in Figures16.4B and 16.4E and Tables 16AA and 16.4B.

Table 16AC relates to the Standard Installation desig-nated soils to the AASHTO and Unified Soil Classifica-tion System categories.

For other bedding conditions, see Section 27, DivisionII—Construction.

Other methods for determining total load and pres-sure distribution may be used, if based on successful de-


Overfill` - SW, ML, or CL•: : ,

;:•::•<: ?•,pa........ ,...

Overfill - SW ML 'p CL

....

8c/6(Min,) 8Bc/6(Min. Be Bc(Min.)

Haunch -See Table 16.4A

Spring tine Lower Side - Spring Line-.... Y.. ` -.. See Table 16.4A ~

417

_.Houncn -See Table 16.4A

Lower Side -See Table 16.4A

IBedding - See Table 16.4A Middle Bedding

Outer Bedding loosely placedmaterials and uncompacted bedding

compoction each Bc f 3side, some

requirements Foundationas haunch /— LEGEND:Be Outside DiameterH = Bockfill cover above

top of pipe

HORIZONTAL ELLIPTICAL PIPE

Bedding - See Table 16.4A-J' — Middle Bedding

Outer Bedding loosely placedmaterials and Be uncompacted bedding

compaction eachside, so e

requvemen~s LEGEND:as haunch Foundation

Be Outside DiameterH = Bockfill cover above

top of pipe

VERTICAL ELLIPTICAL PIPE

Overfill - SW, ML. or CL

~ I" ~,,ouncn

S

ee T -See Table 16.4Alower Side -

Spring Line --~ See Table 16,4A

Bedding - See Table 16.4AJ

Middle BeddingOuter Bedding loosely placedmaterials and Bc/3 uncompacted bedding

compaction eachside, some LEGEND:requirements Foundolionas haunch Be Outside Diameter

H = Bockfill cover abovetop of pipe

ARCH PIPEFIGURE 16.4E Embankment Beddings, Miscellaneous Shapes

sign practice or tests that reflect the appropriate designcondition.

16.4.6.3 Strength-Reduction Factors

Strength-reduction factors for load factor designof plant made reinforced concrete pipe may be takenas 1.0 for flexure and 0.9 for shear and radial tension.For Type 1 installations, the strength-reduction factorshall be 0.9 for flexure and 0.82 for shear and radialtension.

16.4.6.4 Process and Material Factors

Process and material factors, F,. P for radial tension andF,,P for shear strength for load factor design of plant madereinforced concrete pipe are conservatively taken as 1.0.Higher values may be used if substantiated by appropriatetest data approved by the Engineer.

16.4.6.5 Orientation Angle

When quadrant mats, stirrups and/or elliptical cagesare used, the pipe installation requires a specific orienta-


TABLE 16AD Design Values of Parameters inBedding Factor Equation

Pipe ShapeValues Type ofof CA Bedding

Valuesof C,v

ProjectionRatio

Valuesof X

HorizontalEllipti-cal andArch 1.337 Type 2 0.630 0.9 0.421

0.7 0.369Type 3 0.763 0.5 0.268

0.3 0.148

VerticalElliptical Type 2 0.516 0.9 0.718

0.7 0.6391.021 Type 3 0.615 0.5 0.457

0.3 0.238

tion. Designs shall be based on the possibility of a rotationmisorientation during installation by an Orientation Angleof 10° in either direction.


16.4.6.6.1 Reinforcement for Flexural Strength

As = (gof

d - N u

- g[&f

d ) 2 - Nu(

20f

d - h)- 2 Mu])/(fy)

(16-6)

where g = 0.85 bf~b = 12 in.

16.4.6.6.2 Minimum Reinforcement

For inside face of pipe

A si = b (S i +h)'/(fy ) (16-7)

where b = 12 in.

For outside face of pipe

A s , = 0.60 2)(S,+h)2/(fy~

(16-8)

where b = 12 in.

For elliptical reinforcement in circular pipe and forpipe 33-inch diameter and smaller with a single cage ofreinforcement in the middle third of the pipe wall, rein-forcement shall not be less than A, where:

As=2(

b )(Si + h) 2 / (fy / (16-9)

12

where b = 12 in.

where

h = wall thickness in inches;S i = internal diameter or horizontal span of pipe in

inches.

In no case shall the minimum reinforcement be lessthan 0.07 square inches per linear foot.

164.6.63 Maximum Flexural ReinforcementWithout Stirrups

16.4.6.6.3.1 Limited by Radial Tension

Inside AS max = ( 12 )(I 6rs F~ fC (Ir-) F. )/(fy )Of

(16-10)

where

As max = maximum flexural reinforcement area withoutstirrups in in.2/ft

b = 12 in.F, = 1 + 0.00833 (72 - S i)

For 12 in. :5 Si < 72 in.

Frp = 1.0 unless a higher value substantiated by testdata is approved by the Engineer;

Fit(1 )2

+0.8026,000

For 72 in. < S i < 144 in.Fn = 0.8 for S i > 144 in,rs = radius of the inside reinforcement in inches.

16.4.6.6.3.2 Limited by Concrete Compression

A, max5.5x104g1$fd

_0.75N (f) (16-11)s([ (87,000+fy) ° y

where

g' = bfe 10.85-0.05(f , 1

,4, 000)

1,000

g'ma = 0.85bfc and gm' -in = 0.65 bfc

16.4.6.6.4 Crack Width Control (Service LoadDesign)

M s +Ns l d h ) ~ ~Fir = Bi \ 2 - C,bh2

V r'30, 0000 fdA s ij

(16-12)


TABLE 16.4E Bedding Factors For Circular Pipe

Pipe Diameter, in. Type 1 Type 2

Standard Installations

Type 3 Type 4

12 4.4 3.2 2.5 1.7

24 4.2 3.0 2.4 1.7

36 4.0 2.9 2.3 1.7

72 3.8 2.8 2.2 1.7

144 3.6 2.8 2.2 1.7

NOTE.1. For pipe diameters other than listed, embankment condition bedding factors, Bf,

can be obtained by interpolation.2. Bedding factors are based on soils being placed with the minimum compaction specified in Tables 16.4A and 16.4B for each Standard

Installation.

F,, = crack control factor, see Note c;M, = bending moment, service load;N, = thrust (positive when compressive), service load.

Crack control is assumed to be 1 inch from theclosest tension reinforcement, even if the cover over thereinforcement is greater or less than 1 in. The crackcontrol factor F, r in Equation (16-12) indicates the prob-ability that a crack of a specified maximum width willoccur.

When F,, = 1.0, the reinforcement area, A,, will pro-duce an average crack maximum width of 0.01 inch. ForF,, values less than 1.0, the probability of a 0.01 inch crackis reduced. For Fir values greater than 1.0, the probabilityof a crack greater than 0.01 inch is increased.

If the service load thrust, N, is tensile rather than com-pressive (this may occur in pipes subject to intermittenthydrostatic pressure), use the quantity (1.1M,-0.6N,d)(with tensile N, taken negative) in place of the quantity([M s + NS (d - h/2)1/ji) in Equation (16-12).

j = 0.74 + 0.1 e/d;

jmax = 0.9;

1i = j

e

MS he = N +d-

2

, in.s

if e/d < 1.15 crack control will not govern

TABLE 16AF Bedding Factors, B LL , For HS 20 Live Loadings

Pipe Diameter, in.

Fill Height, Ft 12 24 36 48 60 72 84 96 108 120 144

0.5 2.2 1.7 1.4 1.3 1.3 1.1 1.1 1.1 1.1 1.1 1.1

1.0 2.2 2.2 1.7 1.5 1.4 1.3 1.3 1.3 1.1 1.1 1.1

1.5 2.2 2.2 2.1 1.8 1.5 1.4 1.4 1.3 1.3 1.3 1.1

2.0 2.2 2.2 2.2 2.0 1.8 1.5 1.5 1.4 1.4 1.3 1.3

2.5 2.2 2.2 2.2 2.2 2.0 1.8 1.7 1.5 1.4 1.4 1.3

3.0 2.2 2.2 2.2 2.2 2.2 2.2 1.8 1.7 1.5 1.5 1.4

3.5 2.2 2.2 2.2 2.2 2.2 2.2 1.9 1.8 1.7 1.5 1.4

4.0 2.2 2.2 2.2 2.2 2.2 2.2 2.1 1.9 1.8 1.7 1.5

4.5 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.0 1.9 1.8 1.7

5.0 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.0 1.9 1.8

5.5 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.0 1.9

6.0 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.1 2.0

6.5 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2

NOTE: For pipe diameters other than listed, B LL values can be obtained by interpolation


FIGURE 16AF Suggested Design Pressure DistributionAround a Buried Concrete Pipe for Analysis by Direct Design

ESSENTIAL FFAflAqES OF TYMS OF INSTALLATION

GROUND SURFACE

x x

ac BC

Bd

a,TRENCH JACKED OR

TUNNELED

TOP OF EMBANKMENT

Bd Bc

x x x

COMPRESSIBLE\ MATERIAL

/ i al B c

ngvBc

Bc B c

POSITIVE PROJECTING \ \INDUCED TRENCH

EMBANKMENT

NEGATIVE PROJECTINGEMBANKMENT

FIGURE 16AG Essential Features of Types of Installation


TOP OF EMBANKMENT

Bo

H

PB C

FIGURE 16.411 General Relationship of Vertical Earth Load and Lateral Pressure


tb = clear cover over reinforcement in inchesh = wall thickness of pipe in inches;

B l = t b se /2n

where

se = spacing of circumferential reinforcement, in.n = 1, when tension reinforcement is a single layer.n = 2, when tension reinforcement is made of multi-

ple layers.

C, = Crack Control Coefficient

Type of Reinforcement C,

1. Smooth wire or plain bars 1.02. Welded smooth wire fabric, 8 in. (200 mm)maximum spacing of longitudinals 1.53. Welded deformed wire fabric, deformed wire,deformed bars, or any reinforcement with stirrupsanchored thereto 1.9

Notes: Higher values for C, may be used if substantiatedby test data and approved by the Engineer.

16.4.6.6.5 Shear Strength

The area of reinforcement, AS , determined in Article16.4.6.6.1 or 16.4.6.6.4 must be checked for shearstrength adequacy, so that the basic shear strength, Vb , isgreater than the factored shear force, V„,, at the criticalsection located where M,,,,/V„d = 3.0. r F 1

Vb = b~vdFvp f~(1.1 + 63p) L

F

FN J (16-13)

where

Vb = shear strength of section where M,,,,N d = 3.0;F vp = 1.0 unless a higher value substantiated by

test data is approved by the Engineer;

ASP = —

bd

PmaX = 0.02;f, ma x = 7,000 psi;

1.6Fd = 0.8 — dmax Fd = 1.3 for pipe with two cages, or a single el-

liptical cagemax Fd = 1.4 for pipe through 36-inch diameter with a

single circular cage

dF, = 1 ± 2r

(+) tension on the inside of the pipe(—) tension on the outside of the pipe;

For compressive thrust (+N„)

N„FN

= 1 + 2 000bh

where b = 12 in.

For tensile thrust (—N„)

N~FN

= 1 + 500bh

where b = 12 in.

Mnu =M„—N„L(4h—d)~LL 8

If Vb is less than V„c, radial stirrups must be provided.See Article 16.4.6.6.6.

16.4.6.6.6 Radial Stirrups

16.4.6.6.6.1 Radial Tension Stirrups

l . l s„ ( M„ — 0.45 N„O r d)Avg _ (16-14)

fj,( ,d

where

A,,r = required area of stirrup reinforcement forradial tension;

S, = circumferential spacing of stirrups (s„ max =

0.75(~ rd);

f„ = maximum allowable strength of stirrup ma-terial (f.,, = f,,, or anchorage strength,whichever is less).

16.4.6662 Shear Stirrups

A,,=l wl"

[ V„ F, — V j + A,,T (16-15)f,sOv

d

where

A„s = required area of stirrups for shear reinforcement;V„ = factored shear force at section;

4V bV, -MM

nu

+ 1Vu d

V, max = 2(~,bd f,'s

vmax = 0.75(~vdf„ max = fy or anchorage strength, whichever is less

16.4.6.6.6.3 DIVISION I—DESIGN 423

16.4.6.6.6.3 Stirrup Reinforcement Anchorage

16.4.6.6.6.3.1 Radial Tension Stirrup Anchorage

When stirrups are used to resist radial tension, theyshall be anchored around each circumferential of the in-side cage to develop the design strength of the stirrup, andthey shall also be anchored around the outside cage, orembedded sufficiently in the compression side to developthe design strength of the stirrup.

16.4.6.6.6.3.2 Shear Stirrup Anchorage

When stirrups are not required for radial tension but re-quired for shear, their longitudinal spacing shall be suchthat they are anchored around each or every other tensioncircumferential. Such spacings shall not exceed 6 inches(150 mm).

16.4.6.6.6.3.3 Stirrup Embedment

Stirrups intended to resist forces in the invert andcrown regions shall be anchored sufficiently in the oppo-site side of the pipe wall to develop the design strength ofthe stirrup.

16.4.6.6.6.3.4 Other Provisions

Article 8.27, Development of Shear Reinforcement,does not apply to pipe designed according to provisions ofArticle 16.4.5.

16.4.7 Development of Quadrant MatReinforcement

16.4.7.1 When quadrant mat reinforcement is used,the area of the main cage shall be no less than 25% of thearea required at the point of maximum moment.

16.4.7.2 In lieu of Article 16.4.7.1, a more detailedanalysis may be made.

16.4.7.2.1 For quadrant mat reinforcement consist-ing of welded smooth wire fabric, the outermost longi-tudinals on each end of the circumferentials shall beembedded: (a) past the point where the quadrant rein-forcement is no longer required by the orientation angleplus the greater of 12 circumferential wire diameters or3/4 of the wall thickness of the pipe, and (b) past the pointof maximum flexural stress by the orientation angle plusthe development length, Ld .

L d = 0.27A.rfy

(16-19)s NIC

The mat shall contain no less than 2 longitudinals at adistance 1 in greater than that determined by the orienta-tion angle from either side of the point requiring the max-imum flexural reinforcement.

The point of embedment of the outermost longitudinalsof the mat shall be at least a distance determined by theorientation angle past the point where the continuing re-inforcement is no less than double the area required forflexure.

16.4.7.2.2 For quadrant mat reinforcement consist-ing of deformed bars, deformed wire, or welded wire fab-ric: (a) circumferentials shall extend past the point wherethey are no longer required by the orientation angle plusthe greater of 12 wire diameters or 3/4 of the wall thicknessof the pipe. (b) circumferentials shall extend on either sideof the point of maximum flexural stress not less than theorientation angle plus the development length. L d requiredby Equation (16-19), and (c) circumferentials shall extendat least a distance determined by the orientation angle pastthe point where the continuing reinforcement is no lessthan double the area required by flexure.

16.5 REINFORCED CONCRETE ARCH, CAST-IN-PLACE

16.5.1 Application

This specification is intended for use in the design ofcast-in-place reinforced concrete arches with the arch bar-rel monolithic with each footing. A separate reinforcedconcrete invert may be required where the structure issubject to scour.

16.5.2 Materials

16.5.2.1 Concrete

Concrete shall conform to Article 8.2.


Reinforcement shall meet the requirements of Article8.3.

16.5.3 Design


Design shall conform to these specifications except asprovided otherwise in this Section. For design loads andloading conditions, see Article 3.2. For reinforced con-crete design requirements see Section 8.



The minimum fill over reinforced concrete arches shallbe 12 inches or Span/8.


Strength-reduction factors for load factor design ofcast-in-place arches may be taken as 0.90 for flexure and0.85 for shear.

16.5.3.4 Splices of Reinforcement

Reinforcement shall be in conformity with Art-icle 8.32.1.1. If lap splicing is used, laps shall be stag-gered with a minimum of 1 foot measured along the cir-cumference of the arch. Ties shall be provided connect-ing the intrados and extrados reinforcement. Ties shallbe at 12-inch maximum spacing, in both longitudinaland circumferential directions, except as modified byshear.

16.5.3.5 Footing Design

Design shall include consideration of differential hor-izontal and vertical movements and footing rotations.Footing design shall conform to Article 4.4.

16.6 REINFORCED CONCRETE BOX,CAST-IN-PLACE

16.6.1 Application

This specification is intended for use in the design ofcast-in-place reinforced concrete box culverts.

16.6.2 Materials

16.6.2.1 Concrete

Concrete shall conform to Article 8.2 except that eval-uation of f,' may be based on test beams.


Reinforcement shall meet the requirements of Article8.3 except that for welded wire fabric a yield strength of65,000 psi may be used. For wire fabric, the spacing oflongitudinal wires shall be a maximum of 8 inches.

16.6.3 Concrete Cover for Reinforcement

The minimum concrete cover for reinforcement shallconform to Article 8.22. The top slab shall be considereda bridge slab for concrete cover considerations.

16.6.4 Design


Designs shall conform to applicable sections of thesespecifications except as provided otherwise in this article.For design loads and loading conditions see Section 3. Fordistribution of concentrated loads through earth for cul-verts with less than 2 feet of cover, see Article 3.24.3,Case B, and for requirements for bottom distribution re-inforcement in top slabs of such culverts see Article3.24. 10. For distribution of wheel loads to culverts with 2feet or more of cover see Article 6.4. For reinforced con-crete design requirements, see Section 8.

Be I.

TRENCH CONDITION

Backfill

Existing

CompactedGround or Fill

FillMaterial

Leveling Course —~Fine Granular

Fill Material 2" min.

CONCRETE BOX SECTIONS

FIGURE 16.6A

EMBANKMENT CONDITION


16.6.4.2 Modification of Earth Loads for Soil 16.6.4.5 Span LengthStructure Interaction

The effects of soil structure interaction shall be takeninto account and shall be based on the design earth cover,sidefill compaction, and bedding characteristics. Theseparameters may be determined by a soil-structure interac-tion analysis of the system. The loads given in Article 6.2may be used, if they are multiplied by a soil-structure in-teraction factor, Fe, that accounts for the type and condi-tions of installation as defined in Figure 16.6A, so that thetotal earth load, WE on the box section is

WE = FewB eH (16-16)

F e may be determined by the Marston-Spangler Theory ofearth loads, as follows

166.4.2.1 Embankment Installations

HFe , = 1 + 0.20

Be(16-17)

F e , need not be greater than 1.15 for installations withcompacted fill at the sides of the box section, and need notbe greater than 1.4 for installations with uncompacted fillat the sides of the box section.

1664.2.2 Trench Installations

CdBdFee

HBe(16-18)

Values of Cd can be obtained from Figure 16AB for nor-mally encountered soils. The maximum value of F ee neednot exceed Fei .

The soil-structure interaction factor, F e , is not applica-ble if the Service Load Design Method is used.

16.6.4.3 Distribution of Concentrated LoadEffects to Bottom Slab

The width of top slab strip used for distribution of con-centrated wheel loads may be increased by twice the boxheight and used for the distribution of loads to the bottomslab.

16.6.4.4 Distribution of Concentrated Loads inSkewed Culverts

Wheel loads on skewed culverts shall be distributedusing the same provisions as given for culverts with mainreinforcement parallel to traffic.

For span length, see Article 8.8, except when mono-lithic haunches included at 45° are considered in the de-sign, negative moment reinforcement in walls and slabsmay be proportioned based on the bending moment at theintersection of haunch and the uniform depth member.


Strength-reduction factors for load factor design maybe taken at 0.9 for combined flexure and thrust and as 0.85for shear.

16.6.4.7 Crack Control

The maximum service load stress in the reinforcingsteel for crack control shall be

fS — 155< 0.6 fy ksi (16-19)

P d~A

~(3

_—C1+ 0.7

d

d

R = approximate ratio of distance from neutral axisto location of crack width at the concrete surfacedivided by distance from neutral axis to centroidof tensile reinforcing

de = distance measured from extreme tension fiber tocenter of the closest bar or wire in inches. Forcalculation purposes, the thickness of clear con-crete cover used to compute de shall not be takengreater than 2 inches.

The service load stress should be computed consideringthe effects of both bending moment and thrust using:

fS— M S +NS(d—h/2)

(16-20)( A S jid)

where

f, = stress in reinforcement under service loadconditions, psi

e = M,/N, + d—h/2e/d min. = 1.15

i = 1/(1—od/e)j = 0.74 + 0.1(e/d) <— 0.9


16.6.4.8 Minimum Reinforcement

Minimum reinforcement shall be provided in accor-dance with Article 8.17.1 at all cross sections subject toflexural tension, including the inside face of walls.Shrinkage and temperature reinforcement shall be pro-vided near the inside surfaces of walls and slabs in accor-dance with Article 8.20.

16.7 REINFORCED CONCRETE BOX,PRECAST

16.7.1 Application

This specification is intended for use in design for pre-cast reinforced concrete box sections. Boxes may be man-ufactured using conventional structural concrete andforms (formed) or with dry concrete and vibrating formpipe-making methods (machine made). Standard dimen-sions are shown in AASHTO materials specifications M259 and M 273.

16.7.2 Materials

16.7.2.1 Concrete

Concrete shall conform to Article 8.2 except that eval-uation of f,' may be based on cores.


Reinforcement shall meet the requirements of Article8.3 except that for welded wire fabric a yield strength of65,000 psi may be used. For wire fabric, the spacing oflongitudinal wires shall be a maximum of 8 inches.


The minimum concrete cover for reinforcementin boxes reinforced with wire fabric shall be three timesthe wire diameter but not less than 1 inch. For boxescovered by less than 2 feet of fill, the minimum coverfor reinforcement in the top of the slab shall be 2inches.

16.7.4 Design


Design shall conform to applicable sections of thesespecifications except as provided otherwise in this article.For design loads and loading conditions see Section 3. Fordistribution of wheel loads to culvert slabs under less than

2 feet of cover see Article 3.24.3, Case B, and for require-ments for bottom reinforcement in top slabs of such cul-verts see Article 3.24. 10. For distribution of wheel loads toculvert slabs with 2 feet or more of cover, see Article 6.4.

For reinforced concrete design requirements see Sec-tion 8. For span length see Article 8.8, except as noted inArticle 16.7.4.6.

16.7.4.2 Modification of Earth Loads forSoil-Structure Interaction

The effects of soil-structure interaction shall be takeninto account and shall be based on the design earth cover,sidefill compaction, and bedding characteristics. Theseparameters may be determined by a soil-structure interac-tion analysis of the system. The loads given in Article 6.2may be used, if they are multiplied by a soil-structure in-teraction factor, F e, that accounts for the type and condi-tions of installation as defined in Figure 16.6A, so that thetotal earth load, WE, on the box section is:

WE = F ewB e H (16-21)

Fe may be determined by the Marston-Spangler Theory ofearth loads as follows:

167.4.2.1 Embankment Installations:

Fey = 1 + 0.20B

(16-22)

Fe, need not be greater than 1.15 for installations withcompacted fill at the sides of the box section, and need notbe greater than 1.4 for installations with uncompacted fillat the sides of the box section.

16.7.4.2.2 Trench Installations:

FCdB'J

(16-23)FeeHB e

Values of C d can be obtained from Figure 16AB for nor-mally encountered soils. The maximum value of F e e neednot exceed Fe ,.

The soil-structure interaction factor F e, is not applica-ble if the Service Load Design Method is used.

16.7.4.3 Distribution of Concentrated LoadEffects in Sides and Bottoms

The width of the top slab strip used for distribution ofconcentrated wheel loads shall also be used for determi-nation of bending moments, shears, and thrusts in thesides and bottoms.



Wheel loads on skewed culverts shall be distributedusing the same provisions as given for culverts with mainreinforcement parallel to traffic.

16.7.4.5 Span Length

When monolithic haunches inclined at 45° are takeninto account, negative reinforcement in walls and slabsmay be proportioned based on the bending moment atthe intersection of haunch and uniform depth member.


Strength-reduction factors for load factor design of ma-chine-made boxes may be taken as 1.0 for moment and 0.9for shear.

cle 8.20 do not apply to precast concrete box sections,except if units of unusual length (over 16 ft) are fabri-cated, the minimum longitudinal reinforcement forshrinkage and temperature should be as provided in Ar-ticle 8.20.

16.8 PRECAST REINFORCED CONCRETETHREE-SIDED STRUCTURES

16.8.1 Application

This specification is intended for use in design for pre-cast reinforced concrete three-sided structures supportedon a concrete footing foundation. Units may be manufac-tured using conventional structural concrete and forms(formed) or machine made using low slump concrete andvibrating forms.

16.8.2 Materials

16.8.2.1 Concrete16.7.4.7 Crack Control

The maximum service load stress in the reinforcingsteel for crack control shall be:

98ksi (16-24)s 3

dA


fs s (16-25)( A S jid)

where

f5 = stress in reinforcement under service loadconditions, psi

e = M,/Ns + d—h/2e/d min. = 1.15

i = 1/(1—(jd/e)j = 0.74 + 0.1(e/d) < 0.9


The primary flexural reinforcement in the direction ofthe span shall provide a ratio of reinforcement area togross concrete area at least equal to 0.002. Such mini-mum reinforcement shall be provided at all cross sec-tions subject to flexural tension, at the inside face ofwalls, and in each direction at the top of slabs of box sec-tions with less than 2 feet of fill. The provisions of Arti -

Concrete shall conform to Article 8.2 except that eval-uation of f ' may also be based on cores.


Reinforcement shall meet the requirements of Art-icle 8.3 except that for welded wire fabric a yieldstrength of 65,000 psi may be used. For wire fabric, thespacing of longitudinal wires shall be a maximum of8 inches. Circumferential welded wire fabric spacingshall not exceed a 4-inch maximum and 2-inch mini-mum. Prestressing if used, shall be in accordance withSection 9.


The minimum concrete cover for reinforcementin precast three-sided structures reinforced with weldedwire fabric shall be three times the wire diameter butnot less than 1 inch. For precast three-sided structures cov-ered by less than 2 feet of fill, the minimum cover for thereinforcement in the top of the top slab shall be 2 inches.

16.8.4 Geometric Properties

The shape of the precast three-sided structures mayvary in span, rise, wall thickness, haunch dimensions andcurvature. Specific geometric properties shall be specifiedby the manufacturer. Wall thicknesses, however, shall bea minimum of 8 inches for spans under 24 feet and 10inches for 24-foot spans and larger.


16.8.5 Design intersection of the haunch and uniform depthmember.


Designs shall conform to applicable sections, of thesespecifications except as provided otherwise in this article.For design loads and loading conditions see Section 3. Fordistribution of wheel loads to culvert surfaces under lessthan 2 feet of cover see Article 3.24.3, Case B. For re-quirements for bottom reinforcement in top slabs of suchculverts see Article 3.24.10. For distribution of wheelloads to culvert surfaces with 2 feet or more of cover, seeArticle 6.4.

For reinforced concrete design requirements see Sec-tion 8 and for prestress concrete design requirements seeSection 9. For span length see Article 8. 8, except as notedin Article 16.8.5.5. Design analysis shall be based on apinned (hinged) connection at the footing and take into ac-count footing movement, see Article 16.8.5. 10.

16.8.5.2 Distribution of Concentrated LoadEffects in Sides

The width of the top slab strip used for distribution ofconcentrated wheel loads shall also be used for determina-tion of bending moments, shears, and thrusts in the sides.


Wheel loads on skewed culverts shall be distributedusing the same provisions as given for culverts with mainreinforcement parallel to traffic. For culvert elements withskews greater than 15°, the effect of the skew shall be con-sidered in analysis.

16.8.5.4 Shear Transfer in Transverse JointsBetween Culvert Sections

Each precast three-sided structure is analyzed indepen-dently with no shear or stress transfer assumed betweensections. As no shear transfer is assumed between sections,distribution width for a wheel load must be limited to theunit width. Flat top structures with shallow cover may ex-perience differential deflection of adjacent units which cancause pavement cracking if a shear key is not utilized.

16.8.5.5 Span Length

When monolithic haunches inclined at 45° are takeninto account, negative reinforcement in walls and slabsmay be proportioned based on the bending moment at the

16.8.5.6 Strength-Reduction Factor

These structures shall be designed by load factordesign and the maximum strength-reduction factorsshall be 0.95 for combined flexure and thrust and 0.9for shear. See Section 8 and Section 9 for factors usedfor cast-in-place and prestressed components, respectively.

16.8.5.7 Crack Control

The maximum service load stress in the reinforcingsteel for crack control shall be:

98 ksif, = 3 d

A(16-26)


fs_ M s + N S (d – h/2)

(16-27)(A s jid)

where

fs = stress in reinforcement under service loadconditions, psi

e = M,/Ns + d–h/2e/d min. = 1.15

i = 1/(1–(jd/e)j = 0.74 + 0.1(e/d) < 0.9


The primary flexural reinforcement in the direction ofthe span shall provide a ratio of reinforcement area togross concrete area at least equal to 0.002. Such minimumreinforcement shall be provided at all cross sections sub-ject to flexural tension, at the inside face of walls, and ineach direction at the top of slabs of three-sided sectionswith less than 2 feet of fill. The provisions of Article 8.20do not apply to precast three-sided structures.

16.8.5.9 Deflection Control

Live load deflection of the top section in three-sidedstructures shall not exceed %boo of the span, except for sec-tions in urban areas used in part by pedestrians, the ratioshall not exceed %000.


16.8.5.10 Footing Design paction requirement of 90% standard proctor densityshould be achieved to prevent roadway settlement adja-

Design shall include consideration of differential hor- cent to the structure. A higher backfill compaction densityizontal and vertical movements and footing rotations. may be required on structures utilizing a soil-structure in-Footing design shall conform to Article 4.4. teraction system.

16.8.5.11 Structure Backfill

Different backfill may be required depending on de-sign assumptions. However, a minimum backfill com -

16.8.5.12 Scour Protection

Consideration should be given to scour susceptibility.Footing protection should be designed accordingly.

Section 17

SOIL-THERMOPLASTIC PIPE INTERACTION SYSTEMS

17.1 GENERAL

17.1.1 Scope

The specifications of this section are intended for thestructural design of plastic pipes. It must be recognizedthat a buried plastic pipe is a composite structure made upof the plastic ring and the soil envelope, and that both ma-terials play a vital part in the structural design of plasticpipe.

17.1.2 Notations

A = area of pipe wall in square inches/foot (Articles17.2.1 and 17.3.1)

B = water buoyancy factor (Articles 17.2.2 and17.3.2)

c = distance from inside surface to neutral axis (Arti-cles 17.2.2, 17.3.2, and 17.4.2)

D e = effective diameter = ID + 2cE = modulus of elasticity of pipe material (Articles

17.2.2 and 17.3.2)FF = flexibility factor (Articles 17.2.3 and 17.3.3)fa = allowable stress-specified minimum tensile

strength divided by safety factor (Article17.2.1)

fir = critical buckling stress (Articles 17.2.2 and17.3.2)

f„ = specified minimum tensile strength (Articles17.2.1, 17.3.1, and 17.3.2)

I = average moment of inertia, per unit length, ofcross section of the pipe wall (Articles 17.2.2,17.2.3, and 17.3.3)

ID = inside diameter (Articles 17.2.2, 17.3.2, and17.4.2)

M, = soil modulus (Articles 17.2.2, 17.3.2)OD = outside diameter (Article 17.4.2)P = design load (Article 17.1.4)SF = safety factor (Article 17.2.1)T = thrust (Article 17.1.4)TL = thrust, load factor (Article 17.3.1)T, = thrust, service load (Article 17.2.1)0 = capacity modification factor (Article 17.3. 1)

17.1.3 Loads

Design load, P, shall be the pressure acting on the struc-ture. For earth pressures see Article 3.20. For live load seeArticles 3.4 to 3.7, 3.11, 3.12, and 6.4, except that thewords "When the depth of fill is 2 feet or more" in Article6.4.1 need not be considered. For loading combinationssee Article 3.22.

17.1.4 Design

17.1.4.1 The thrust in the wall shall be checked bytwo criteria. Each considers the mutual function of theplastic wall and the soil envelope surrounding it. The cri-teria are:

(a) Wall area(b) Buckling stress

17.1.4.2 The thrust in the wall is:

DT = P X

2(17-1)

where:

P = design load, in pounds per square foot;D =diameter in feet;T = thrust, in pounds per foot.

17.1.4.3 Handling and installation strength shall besufficient to withstand impact forces when shipping andplacing the pipe.

17.1.5 Materials

The materials shall conform to the AASHTO andASTM specifications referenced herein.

17.1.6 Soil Design

17.1.6.1 Soil Parameters

The performance of a flexible culvert is dependent onsoil structure interaction and soil stiffness.

431


The following must be considered:(a) Soils:(1) The type and anticipated behavior of the founda-tion soil must be considered; i.e., stability for beddingand settlement under load.(2) The type, compacted density, and strength proper-ties of the envelope immediately adjacent to the pipemust be established.

Good side fill is obtained from a granular materialwith little or no plasticity and free of organic material,i.e., AASHTO classification groups A-1, A-2, and A-3,compacted to a minimum 90% of standard densitybased on AASHTO T 99 (ASTM D 698).(3) The density of the embankment material above thepipe must be determined. See Article 6.2.(b) Dimensions of envelopeThe general recommended criteria for lateral limits ofthe culvert envelope are as follows:(1) Trench installations—the minimum trench widthshall provide sufficient space between the pipe and thetrench wall to ensure sufficient working room to prop-erly and safely place and compact backfill material. Asa guide, the minimum trench width should not be lessthan the greater of the pipe diameter plus 16.0 inches,or the pipe diameter times 1.5 plus 12.0 inches. The useof specially designed equipment may enable satisfac-tory installation and embedment even in narrowertrenches.(2) Embankment installations—the minimum widthof the soil envelope shall be sufficient to ensure lateralrestraint for the buried structure. The combined widthof the soil envelope and embankment beyond shall beadequate to support all the loads on the pipe. As aguide, the width of the soil envelope on each side of thepipe should be the pipe diameter or 2.0 feet, whicheveris less.(3) The minimum upper limit of the soil envelope is 1foot above the culvert.


Extra thickness may be required for resistance to abra-sion. For highly abrasive conditions, a special design maybe required.


When multiple lines of pipes greater than 48 inchesin diameter are used, they shall be spaced so that the sidesof the pipe shall be no closer than one-half diameter or3 feet, whichever is less, to permit adequate compactionof backfill material. For diameters up to and including48 inches, the minimum clear spacing shall not be lessthan 2 feet.

17.1.9 End Treatment

Protection of end slopes may require special consider-ation where backwater conditions may occur, or whereerosion and uplift could be a problem. Culvert ends con-stitute a major run-off-the road hazard if not properly de-signed. Safety treatment, such as structurally adequategrating that conforms to the embankment slope, extensionof culvert length beyond the point of hazard, or provisionof guardrails, is among the alternatives to be considered.End walls on skewed alignment require a special design.


The construction and installation shall conform to Sec-tion 26, Division IL

17.2 SERVICE LOAD DESIGN

Service Load Design is a working stress method, as tra-ditionally used for culvert design.

17.2.1 Wall Area

A = Tjfa

where:

A = required wall area in square inches per foot;T, = thrust, service load in pounds per foot;fa = allowable stress, specified minimum tensile

strength, pounds per square inch, divided bysafety factor, f„/SF. (For, SF, see Article17.4.1.2.)

17.2.2 Buckling

Walls within the required wall area, A, shall be checkedfor possible buckling. If the allowable buckling stress,f,~ SF, is less than fa, the required area must be recalculatedusing f,, SF in lieu of fa . The formula for buckling is:

B = water buoyancy factor or= 1-0.33h w/h;

hW = height of water surface above top of pipe;h = height of ground surface above top of pipe;E = Long term (50-year) modulus of elasticity of the

plastic in pounds per square inch;M, = soil modulus in pounds per square inch;

= 1700 for side fills meeting Article 17.1.6;f,, = critical buckling stress in pounds per square inch;

f r = 9.24 (RIA) BM, EI/0.149R3

where:


R = effective radius in inches= c + ID/2;

A = actual area of pipe wall in square inches/foot.


Handling and installation rigidity is measured by aflexibility factor, FF, determined by the formula:

FF = flexibility factor in inches per pound;De = effective diameter in inches;E = initial modulus of elasticity of the pipe material

in pounds per square inch;I = average moment of inertia per unit length of

cross section of the pipe wall in inches to the 4thpower per inch.

17.3 LOAD FACTOR DESIGN

Load Factor Design is an alternative method of designbased on ultimate strength principles.

17.3.1 Wall Area

A = TL/(~fu

where:

A = required area of pipe wall in square inches perfoot;

TL = thrust, load factor in pounds per foot;fU = specified minimum tensile strength in pounds

per square inch;= capacity modification factor.

17.3.2 Buckling

If f, is less than fu , A must be recalculated using f, inlieu of f,,. The formula for buckling is:

f,, = 9.24 (R/A) BM, E1/0. 149R3

where:

B = water buoyancy factor or= I — 0.33h,/h;

hW = height of water surface above top of pipe;h = height of ground surface above top of pipe;E = Long term (50-year) modulus of elasticity of the

plastic in pounds per square inch;M, = soil modulus in pounds per square inch

= 1,700 for side fills meeting Article 12.1.6;fir = critical buckling stress in pounds per square

inch;R = effective radius in inches

= c + ID/2;A = actual area of pipe wall in square inches/foot.


Handling rigidity is measured by a flexibility factor,FF, determined by the formula:

FF = D,2/EI

where:

FF = flexibility factor in inches per pound;De = effective diameter in inches;E = initial modulus of elasticity of the pipe material

in pounds per square inch;I = average moment of inertia per unit length of

cross section of the pipe wall in inches to the 4thpower per inch.

17.4 PLASTIC PIPE

17.4.1 General

17.4.1.1 Plastic pipe maybe smooth wall, corrugatedor externally ribbed and may be manufactured of poly-ethylene (PE) or poly (vinyl chloride) (PVC). The mater-ial specifications are:

Polyethylene (PE)Smooth Wall —ASTM F 714 Polyethylene (PE)

Plastic Pipe (SDR-PR) Based onOutside Diameter

Corrugated —AASHTO M 294 CorrugatedPolyethylene Pipe, 12 to 36 in.Diameter

Ribbed —ASTM F 894 Polyethylene (PE)Large-Diameter Profile WallSewer and Drain Pipe

Poly (Vinyl Chloride)(PVC)Smooth Wall —AASHTO M 278 Class PS 46

Polyvinyl Chloride (PVC)Pipe, ASTM F 679 Poly (VinylChloride) (PVC) Large-Diame-ter Plastic Gravity Sewer Pipeand Fittings

Ribbed —AASHTO M 304 Poly (VinylChloride) (PVC) Ribbed DrainPipe and Fittings and Based on

FF = De/EI

where:


Controlled Inside DiameterASTM F 794 Poly (Vinyl Chlo-ride) (PVC) Large-DiameterRibbed Gravity Sewer Pipe andFittings Based on Controlled In-side Diameter

17.4.1.2 Service Load Design-safety factor, SF:

Wall area = 2.0Buckling = 2.0

17.4.1.3 Load Factor Design-capacity modifica-tion factor, 4:

PE, (~ = 1.0PVC, q~ = 1.0

17.4.1.4 Flexibility Factor:

PE, FF = 9.5 X 10-2

PVC, FF = 9.5 X 10- 2

Note: PE and PVC are thermoplastics and, therefore,subject to reduction in stiffness as temperature is in-creased.


The minimum cover for design loads shall be ID/8 butnot less than 12 inches. (The minimum cover shall bemeasured from the top of a rigid pavement or the bottomof a flexible pavement.) For construction requirements,see Article 26.5, Division II.

17.4.1.6 Maximum Strain

The allowable deflection of installed plastic pipe maybe limited by the extreme fiber tensile strain of the pipewall. Calculation of the tension strain in a pipe signifi-cantly deflected after installment can be checked againstthe allowable long-term strain for the material in Article17.4.3. Compression thrust is deducted from deflectionbending stress to obtain net tension action. The allowablelong-term strains shown in Article 17.4.3 should not bereached in pipes designed and constructed in accordancewith this specification.

17.4.1.7 Local Buckling

The manufacturers of corrugated and ribbed pipeshould demonstrate the adequacy of their pipes againstlocal buckling when designed and constructed in accor-dance with this specification.


The values given in the following tables are limitingvalues and do not describe actual PE or PVC pipe products.Section properties for specific PE or PVC pipe products areavailable from individual pipe manufacturers and can becompared against the following values for compliance.

17.4.2.1 PE Corrugated Pipes (AASHTO M 294, MPG-95)

Nominal Min. Max. Min. Min. Min.Size I.D. O.D. A C I(in.) (in.) (in.) (in. 2/ft) (in.) (in."/in.)

12 11.8 14.7 1.50 0.35 0.02415 14.8 18.0 1.91 0.45 0.05318 17.7 21.5 2.34 0.50 0.06224 23.6 28.7 3.14 0.65 0.11630 29.5 36.4 3.92 0.75 0.16336 35.5 42.5 4.50 0.90 0.22242 * 41.5 48.0 4.69 1.11 0.54348' 47.5 55.0 5.15 1.15 0.543

For 42" and 48-pipe, the wall thickness should be designed using thelong term tensile strength provision (900 psi) until new design cri-teria are established.

17.4.2.2 PE Ribbed Pipes (ASTM F 894)

Min. I(in.°/in.)

Nominal Min. Max. Min. Min. Cell CellSize I.D. O.D. A C Class Class(in.) (in.) (in.) (in./ft) (in.) 334433C 335434C

18 17.8 21.0 2.96 0.344 0.052 0.03821 20.8 24.2 4.15 0.409 0.070 0.05124 23.8 27.2 4.66 0.429 0.081 0.05927 26.75 30.3 5.91 0.520 0.125 0.09130 29.75 33.5 5.91 0.520 0.125 0.09133 32.75 37.2 6.99 0.594 0.161 0.13236 35.75 40.3 8.08 0.640 0.202 0.16542 41.75 47.1 7.81 0.714 0.277 0.22748 47.75 53.1 8.82 0.786 0.338 0.277

17.4.2.3 Profile Wall PVC Pipes (AASHTO M 304)

Min. 1(in.

4/in.)

Nominal Min. Max. Min. Min. Cell CellSize I.D. O.D. A C Class Class(in.) (in.) (in.) (in.'/ft) (in.) 12454C 12364C

12 11.7 13.6 1.20 0.15 0.004 0.00315 14.3 16.5 1.30 0.17 0.006 0.00518 17.5 20.0 1.60 0.18 0.009 0.00821 20.6 23.0 1.80 0.21 0.012 0.01124 23.4 26.0 1.95 0.23 0.016 0.01530 29.4 32.8 2.30 0.27 0.024 0.02036 35.3 39.5 2.60 0.31 0.035 0.03142 41.3 46.0 2.90 0.34 0.047 0.04348 47.3 52.0 3.16 0.37 0.061 0.056


17.4.3 Chemical and Mechanical Requirements

The polyethylene (PE) and poly (vinyl chloride) (PVC)materials described herein have stress/strain relationshipsthat are nonlinear and time dependent. Minimum 50-yeartensile strengths are derived from hydrostatic design basesand indicate a minimum 50-year life expectancy undercontinuous application of that tensile stress. Minimum 50-year moduli do not indicate a softening of the pipe mater-ial but is an expression of the time dependent relation be-tween stress and strain. For each short-term increment ofdeflection, whenever it occurs, the response will reflect theinitial modulus. Both short- and long-term properties areshown. Except for buckling for which long-term propertiesare required, the judgment of the Engineer shall determinewhich is appropriate for the application. Initial and longterm relate to conditions of loading, not age of the instal-lation. Response to live loads will reflect the initial modu-lus, regardless of the age of the installation.

17.4.3.1 Polyethylene

17.4.3.1.1 Smooth wall PE pipe requirements—ASTM F 714


InitialMinimum Minimum

Tensile Mod.Strength of Elast.

(psi) (psi)

3,000 110,000

Minimum cell class, ASTM D 3350, 335434CAllowable long-term strain = 5%

17.4.3.1.2 Corrugated PE pipe requirements—AASHTO M 294:

perties for Design

50-YearMinimum Minimum


(psi) (psi)

900 22,000

Minimum cell class, ASTM D 3350, 3354000, withadditional environmental stress crack resistance evalua-tion according to SP-NCTL test as per recommendationsin NCHRP Report 429.

Allowable long-term strain = 5%

17.4.3.1.3 Ribbed PE pipe requirements—ASTMF 894


Initial 50 -YearMinimum Minimum Minimum Minimum

Tensile Mod. Tensile Mod.Strength of Elast. Strength of Elast.

(psi) (psi) (psi) (psi)

3,000 80,000 1,125 20,000


OR:



(psi) (psi) (psi) (psi)3,000 110,000 1,440 22,000


17.4.3.2 Poly (Vinyl Chloride) (PVC)

17.4.3.2.1 Smooth wall PVC pipe requirements—AASHTO M 278, ASTM F 679:





7,000 400,000 3,700 140,000


OR:




6,000 440,000 2,600 158,400

Minimum cell class, ASTM D 1784,12364CAllowable long-term strain = 3.5%

50-YearMinimum Minimum


(psi) (psi)

1,440 22,000

Mechanical Pro



(psi) (psi)

3,000 110,000


17.4.3.2.2 Ribbed PVC pipe requirements— OR:AASHTO M 304




6,000 440,000 2,600 158,400

Minimum cell class, ASTM D 1784,12364CAllowable long-term strain = 3.5%

Minimum cell class, ASTM D 1784,12454CAllowable long-term strain = 5%

Minimum Pr



(psi) (psi)

7,000 400,000

operties for Design

50 -YearMinimum Minimum


(psi) (psi)

3,700 140,000

2

Documents

partial sand

integral bent

component

cover plate

maximum resultant

aisc engineering

extreme compression

overload design