PCI Handbook/Sixth Edition 11–1 CHAPTER 11 GENERAL DESIGN INFORMATION 11.1 Design Information ....................................................................................................... 11–2 11.1.1 Dead Weights of Floors, Ceilings, Roofs, and Walls....................................... 11–2 11.1.2 Recommended Minimum Uniformly Distributed and Concentrated Live Loads................................................................................. 11–3 11.1.3 Beam Design Equations and Diagrams .......................................................... 11–5 11.1.4 Camber (Deflection) and Rotation Coefficients for Prestress Force and Loads ...........................................................................11–23 11.1.5 Moments in Beams with Fixed Ends .............................................................11–25 11.1.6 Torsion Diagrams, Reactions, and Rotations ................................................ 11–26 11.1.7 Moving Load Placement for Maximum Moment and Shear .......................... 11–27 11.1.8 Moments, Shears, and Deflections in Beams with Overhangs ..................... 11–28 11.2 Material Properties ..................................................................................................... 11–29 11.2.1 Table of Concrete Stresses ........................................................................... 11–29 11.2.2 Concrete Modulus of Elasticity as Affected by Unit Weight and Strength .............................................................................. 11–29 11.2.3 Properties and Design Strengths of Prestressing Strand and Wire .............. 11–30 11.2.4 Properties and Design Strengths of Prestressing Bars ................................. 11–31 11.2.5 Typical Stress-Strain Curve, 7-Wire Low-Relaxation Prestressing Strand ...11–32 11.2.6 Transfer and Development Lengths for 7-Wire Uncoated Strand ................. 11–33 11.2.7 Reinforcing Bar Data .....................................................................................11–34 11.2.8 Location of Reinforcement Confined by Stirrups or Ties............................... 11–35 11.2.9 Required Development Lengths for Reinforcing Bars ................................... 11–36 11.2.10 Common Styles of Structural Welded Wire Reinforcement .......................... 11–38 11.2.11 Wire Used in Structural Welded Wire Reinforcement ................................... 11–39 11.2.12 Bar Area Equivalents in a One Foot Wide Section ....................................... 11–40 11.2.13 ACI Required Minimum Reinforcement Areas Per Foot Width of Section .... 11–41 11.3 Standard Bolts, Nuts and Washers ............................................................................ 11–42 11.3.1 Dimensions of Nuts and Bolts ....................................................................... 11–42 11.3.2 Dimensions of Standard Washers ................................................................. 11–44 11.4 Welding Information.................................................................................................... 11–45 11.4.1 Weld Symbols Commonly Used in Precast Construction ............................. 11–45 11.4.2 Typical Welded Joints in Precast Construction ............................................. 11–46 11.4.3 Properties of Weld Groups Treated as Lines ................................................11–47 11.5 Section Properties ...................................................................................................... 11–48 11.5.1 Properties of Geometric Sections.................................................................. 11–48 11.5.2 Plastic Section Moduli and Shape Factors .................................................... 11–53 11.6 Metric Conversion....................................................................................................... 11–54 11.6.1 Metric Calculations and Example .................................................................. 11–54 11.6.2 Conversion from U.S. Customary Units to International System .................. 11–55 11.6.3 Preferred SI Units and U.S. Customary Equivalents.................................... 11–57 First Printing/CD-ROM Edition
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PCI Handbook/Sixth Edition 11–1
CHAPTER 11 GENERAL DESIGN INFORMATION
11.1 Design Information .......................................................................................................11–2
11.1.1 Dead Weights of Floors, Ceilings, Roofs, and Walls.......................................11–2 11.1.2 Recommended Minimum Uniformly Distributed and Concentrated Live Loads.................................................................................11–3 11.1.3 Beam Design Equations and Diagrams ..........................................................11–5 11.1.4 Camber (Deflection) and Rotation Coefficients for Prestress Force and Loads ...........................................................................11–23 11.1.5 Moments in Beams with Fixed Ends .............................................................11–25 11.1.6 Torsion Diagrams, Reactions, and Rotations................................................11–26 11.1.7 Moving Load Placement for Maximum Moment and Shear ..........................11–27 11.1.8 Moments, Shears, and Deflections in Beams with Overhangs .....................11–28
11.2 Material Properties .....................................................................................................11–29
11.2.1 Table of Concrete Stresses...........................................................................11–29 11.2.2 Concrete Modulus of Elasticity as Affected by Unit Weight and Strength ..............................................................................11–29 11.2.3 Properties and Design Strengths of Prestressing Strand and Wire ..............11–30 11.2.4 Properties and Design Strengths of Prestressing Bars.................................11–31 11.2.5 Typical Stress-Strain Curve, 7-Wire Low-Relaxation Prestressing Strand ...11–32 11.2.6 Transfer and Development Lengths for 7-Wire Uncoated Strand.................11–33 11.2.7 Reinforcing Bar Data .....................................................................................11–34 11.2.8 Location of Reinforcement Confined by Stirrups or Ties...............................11–35 11.2.9 Required Development Lengths for Reinforcing Bars...................................11–36 11.2.10 Common Styles of Structural Welded Wire Reinforcement ..........................11–38 11.2.11 Wire Used in Structural Welded Wire Reinforcement ...................................11–39 11.2.12 Bar Area Equivalents in a One Foot Wide Section .......................................11–40 11.2.13 ACI Required Minimum Reinforcement Areas Per Foot Width of Section ....11–41
11.3 Standard Bolts, Nuts and Washers ............................................................................11–42
11.3.1 Dimensions of Nuts and Bolts .......................................................................11–42 11.3.2 Dimensions of Standard Washers.................................................................11–44
11.4.1 Weld Symbols Commonly Used in Precast Construction .............................11–45 11.4.2 Typical Welded Joints in Precast Construction .............................................11–46 11.4.3 Properties of Weld Groups Treated as Lines ................................................11–47
11.6.1 Metric Calculations and Example ..................................................................11–54 11.6.2 Conversion from U.S. Customary Units to International System ..................11–55 11.6.3 Preferred SI Units and U.S. Customary Equivalents....................................11–57
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11–2 PCI Handbook/Sixth Edition
11.1 DESIGN INFORMATION Design Aid 11.1.1 Dead Weights of Floor, Ceilings, Roofs and Wallsa
Component Load (psf) Component Load
(psf) Component Load (psf)
Ceilings Floor Fill Masonry wallsb Acoustical fiber board 1 Cinder concrete, per inch 9 Clay brick wythes: Gypsum board (per Q/K in. thickness) 0.55 Lightweight concrete, per inch 8 4 in. 39 Mechanical duct allowance 4 Sand, per inch 8 8 in. 79 Plaster on tile or concrete 5 Stone concrete, per inch 12 12 in. 115Plaster on wood lath 8 16 in. 155Suspended steel channel system 2 Floors and floor finishes Suspended mtl lath and cem plaster 15 Asphalt block (2 in.) Q/S in. mortar 30Suspended mtl lath and gyp plaster 10 Cement finish (1 in.), on stone concrete fill 32
Hollow concrete masonry unit wythe: Wythe thickness (in.)
Wood furring suspension system 2.5 Ceramic or quarry tile (E/F in.) on Q/S in. bed 16 Ceramic or quarry tile (E/F in.) on 1 in. bed 23 4 6 8 10 12 Coverings, roof and wall Concrete fill finish (per inch thickness) 12 Hardwood flooring, U/K in. 4Asbestos – cement shingles 4 Linoleum or asphalt tile, Q/F in. 1
Density of unit (105 pcf)
Asphalt shingles 2 Marble and mortar on stone-concrete fill 33 No grout 22 24 31 37 43 Cement tiles 16 48 in. o.c. 29 38 47 55 Slate (per inch thickness) 15 40 in. o.c. 30 40 49 57 Clay tile (for mortar add 10 lb.) Solid flat tile on 1 in. mortar base 23 (grout spacing) Book tile, 2 in. 12 Subflooring, E/F in. 3 32 in. o.c. 32 42 52 61 Book tile, 3 in. 20 Terazzo (1 Q/S in.) directly on slab 19 24 in. o.c. 34 46 57 67 Ludowici 10 Terazzo (1 in.) on stone-concrete fill 32 16 in. o.c. 40 53 66 79 Roman 12 Terazzo (1 in.) 2 in. stone concrete 32 Full grout 55 75 95 115 Spanish 19 Wood block (3 in.) on mastic, no fill 10Composition: Wood block (3 in.) on Q/S in. mortar base 16
Density of unit (125 pcf):
Three-ply ready roofing 1 No grout 26 28 36 44 50 Four-ply felt and gravel 5.5 48 in. o.c. 33 44 54 62 Five-ply felt and gravel 6 Floors, wood joist (no plaster) 40 in. o.c. 34 45 56 65 (grout spacing) Copper on tin 1 Double wood floor 32 in. o.c. 36 47 58 68 Corrugated asbestos-cement roofing 4 24 in. o.c. 39 51 63 75 Deck, metal 20 gage 2.5 16 in. o.c. 44 59 73 87 Deck, metal 18 gage 3 Full grout 59 81 102 123Decking, 2 in. wood (Douglas fir) 5
Joist Size (in.)
12 in. spacing
(psf)
16 in. spacing
(psf)
24 in. spacing
(psf) Decking, 3 in. wood (Douglas fir) 8 2 x 6 6 5 5
Density of unit (135 pcf)
Fiberboard, Q/S in. 0.75 2 x 8 6 6 5 No grout 29 30 39 47 54 Gypsum sheating, Q/S in. 2 2 x 10 7 6 6 48 in. o.c. 36 47 57 66 2 x 12 8 7 6 40 in. o.c. 37 48 59 69 (grout spacing) Insulation, roof boards (per in. thickness) 32 in. o.c. 38 50 62 72 Cellular glass 0.7 Frame partitions 24 in. o.c. 41 54 67 78 Fibrous glass 1.1 Movable steel partitions 4 16 in. o.c. 46 61 76 90 Fiberboard 1.5 Wood or steel studs, Q/S gyp board each side 8 Full grout 62 83 105 127 Perlite 0.8 Wood studs, 2 x 4, unplastered 4 Polystyrene foam 0.2 Wood studs, 2 x 4, plastered one side 12 Urethane foam with skin 0.5 Wood studs, 2 x 4, plastered two sides 20
Solid concrete masonry unit wythe: Wythe thickness (in.)
Plywood (per Q/K in. thickness) 0.4 Rigid insulation, Q/S in. 0.75 Frame walls 4 6 8 10 12 Skylight, metal frame, E/K in. wire glass
8 Exterior stud walls: Density of unit (105 pcf) 32 51 69 87 105
Slate, E/AH in. 7 2 x 4 @ 16 in., T/K in. gyp., insulated, E/K in. siding 11 Slate, Q/F in. 10 2 x 6 @ 16 in., T/K in. gyp., insulated, E/K in. siding 12 Density of unit 38 60 81 102 124Waterproofing membranes (125 pcf) Bituminous, gravel-coated 5.5 Exterior stud walls with brick veneer 48 Bituminous, smooth surface 1.5 Windows, glass, frame, and sash 8 Density of unit 41 64 87 110 133 Liquid applied 1 (135 pcf) Single-ply, sheet 0.7 Wood sheathing (per inch thickness) 3 Wood shingles 3
a. Source: “Minimum Design Loads for Buildings and Other Structures,” ASCE 7-02, American Society of Civil Engineers, Reston, VA. b. Weights of masonry include mortar but not plaster. For plaster, add 5 lb/ft2 for each face plasterEdition, Values given represent averages. In
some cases, there is a considerable range of weight for the same construction.
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PCI Handbook/Sixth Edition 11–3
DESIGN INFORMATION Design Aid 11.1.2 Recommended Minimum Uniformly Distributed and Concentrated Live Loadsa
Occupancy or use Uniform load (psf) Concentrated
load (lb) Apartments (see residential) Access floor systems Computer use 100 2,000 Office use 50 2,000 Armories and drill rooms 150 Assembly areas and theaters Fixed seats (fastened to floor) 60 Lobbies 100 Movable seats 100 Platforms (assembly) 100 Stage floors 150 Balconies (exterior) 100 On one- and two-family residences only, and not exceeding 100 ft2 60 Bowling alleys, poolrooms and similar recreational areas 75 Corridors First floor 100 Other floors, same as occupancy served except as indicated Dance halls and ballrooms 100 Decks (patio and roof) Same as area served, or for the type of occupancy accommodated Dining rooms and restaurants 100 Dwellings (see residential) Elevator machine room grating (on area of 4 in.2) 300 Finish light floor plate construction (on area of 1 in.2) 200 Fire escapes 100 On single-family dwellings only 40 Garages (passenger cars only) 50 Note b Truck and buses Note c Grandstands (see stadium and arena bleachers) Gymnasiums, main floors and balconies (see note e) 100 Handrails, guardrails and grab bars Note i Hospitals Corridors above first floor 80 1,000 Operating room, laboratories 60 1,000 Private rooms 40 1,000 Wards 40 1,000 Hotels (see residential) Libraries Corridors above first floor 80 1,000 Reading rooms 60 1,000 Stack rooms (see note d) 150 1,000 Manufacturing Heavy 250 2,000 Light 125 3,000 Marquees and Canopies 75 Office Buildings Corridors above first floor 80
File and computer rooms shall be designed for heavier loads based on anticipated occupancy 2,000
Lobbies and first floor corridors 100 2,000 Offices 50 2,000 See following page for all notes.
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11–4 PCI Handbook/Sixth Edition
DESIGN INFORMATION Design Aid 11.1.2 Recommended Minimum Uniformly Distributed and Concentrated Live Loadsa (Cont.)
Occupancy or use Uniform load (psf) Concentrated
load (lb) Penal institutions Cell Blocks 40 Corridors 100 Residential Dwellings (one- and two-family) Habitable attics and sleeping areas 30 Uninhabitable attics with storage 20 Uninhabitable attics without storage 10 All other areas except balconies 40 Hotels and multifamily houses Private rooms and corridors serving them 40 Public rooms and corridors serving them 100 Reviewing stands, grandstands and bleachers (see Note e) 100 Roofs Note j Schools Classrooms 40 1,000 Corridors above first floor 80 1,000 First floor corridors 100 1,000 Scuttles, skylight ribs, and accessible ceilings 200 Sidewalks, vehicular driveways, and yards, subject to trucking (see Note f, g) 250 8,000 Stadiums and arenas Bleachers (see Note e) 100 Fixed seats, fastened to floor (see Note e) 60 Stairs and exitways 100 Note h Storage areas above ceilings 20 Heavy 250 Light 125 Storage warehouses (shall be designed for heavier loads if required for
anticipated storage)
Stores Retail First floor 100 1,000 Upper floors 75 1,000 Wholesale, all floors 125 1,000 Vehicle barriers Note i Walkways and elevated platforms (other than exitways) 60 Yards and terraces, pedestrians 100 a. Source: “Minimum Design Loads for Buildings and Other Structures,” ASCE 7-02, American Society of Civil Engineers, Reston, VA. b. Floors in garages or portions of buildings used for the storage of motor vehicles shall be designed for the uniformly distributed live loads
of Design Aid 11.1.2 or the following concen trated load: (1) for passenger cars accommodating not more than nine passengers 3,000 lb. acting on an area of 20 in.2; and (2) mechanical parking structures without slab or deck, passenger car only, 1,500 lb/wheel.
c. Garages accommodating trucks and buses shall be designed in accordance with an approved method which contains provisions for truck and bus loadings.
d. The weight of books and shelving shall be computed using an assumed density of 65 pcf and converted to a uniformly distributed load;this load shall be used if it exceeds 150 pcf.
e. In addition to the vertical live loads, horizontal swaying forces parallel and normal to the length of seats shall be included in the designaccording to the requirements of ANSI/NFPA 102.
f. Other uniform loads in accordance with an approved method which contains provisions for truck loadings shall also be considered whereappropriate.
g. The concentrated wheel load shall be applied on an area of 20 in.2. h. Minimum concentrated load on stair treads on area of 4 in.2 is 300 lb. i. See ASCE 7-02, Section 4.4. j. See ASCE 7-02, Sections 4.3 and 4.9.
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PCI Handbook/Sixth Edition 11–5
DESIGN INFORMATION Design Aid 11.1.3 Beam Design Equations and Diagrams
This visual index assists in quickly locating the desired beam equations. The top row shows the support type, and the left column shows the load. For example, to find the equations for a beam fixed on both ends with a uniform load, go down from Column 4 and right on Row B. Locate 4B on upper right corner (page 11–17).
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11–6 PCI Handbook/Sixth Edition
DESIGN INFORMATION Design Aid 11.1.3 Beam Design Equations and Diagrams (Cont.) 1A
1A.1 SIMPLE BEAM – CONCENTRATED LOAD AT CENTER
R = V ........................................................= P2
Mmax (at point of load)...............................= P4
Mx (when <x2
) .....................................= Px2
∆max (at point of load) ...............................= 3P
R1 = V1 (max when a < b).........................= Pb
R2 = V2 (max when a > b).........................= Pa
Mmax (at point of load)...............................= Pab
Mx (when x < a) ........................................= Pbx
∆max a(a 2b)at x when a b
3⎛ ⎞+= >⎜ ⎟⎜ ⎟⎝ ⎠
....... = Pab(a 2b) 3a(a 2b)27El
+ +
∆a (at point of load)...................................= 2 2Pa b
3El
∆x (when x < a).........................................= 2 2 2Pbx ( b x )6El
− −
1A.3 SIMPLE BEAM – TWO EQUAL CONCENTRATED LOADS SYMMETRICALLY PLACED R = V........................................................= P Mmax (between loads) ...............................= Pa Mx (when x < a) ........................................= Px
∆x (when x < a).........................................= 2 2Px (3 a 3a x )6El
− −
∆x [when x > a and < ( − a )]...................= 2 2Pa (3 x 3x a )6El
− −
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PCI Handbook/Sixth Edition 11–7
DESIGN INFORMATION Design Aid 11.1.3 Beam Design Equations and Diagrams (Cont.) 1A,1B
1A.4 SIMPLE BEAM – TWO UNEQUAL CONCENTRATED LOADS UNSYMMETRICALLY PLACED
R1 = V1 .....................................................= 1 2P ( a) P b− +
R2 = V2 .....................................................= 1 2P a P ( b)+ −
Vx [when x > a and < ( b− )] ...................= R1 – P1 M1 (max when R1 < P1) ............................= R1a M2 (max when R2 < P2) ............................= R2b Mx (when x < a) ........................................= R1x Mx [when x > a and < ( b− )]...................= R1x – P1(x – a)
1B.1 SIMPLE BEAM – UNIFORMLY DISTRIBUTED LOAD
R = V ........................................................= w2
Vx .............................................................= w x2
5A.1 CANTILEVER BEAM – CONCENTRATED LOAD AT FREE END R = V .........................................................= P Mmax (at fixed end).....................................= P Mx..............................................................= Px
∆x...............................................................= 3 2 3P (2 3 x x )6El
− +
5A.2 CANTILEVER BEAM – CONCENTRATED LOAD AT ANY POINT R = V .........................................................= P Mmax (at fixed end).....................................= Pb Mx (when x > a) .........................................= P(x – a)
∆max (at free end).......................................= 2Pb (3 b)
6El−
∆a (at point of load)....................................= 3Pb
3El
∆x (when x < a)..........................................= 2Pb (3 3x b)
6El− −
∆x (when x > a)..........................................= 2P( x) (3b x)
6El− − +
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11–20 PCI Handbook/Sixth Edition
DESIGN INFORMATION Design Aid 11.1.3 Beam Design Equations and Diagrams (Cont.) 5B,5C,5D
5B.1 CANTILEVER BEAM – UNIFORMLY DISTRIBUTED LOAD R = V ..........................................= w Vx ...............................................= wx
5E.1 CANTILEVER BEAM – MOMENT APPLIED AT FREE END R = V ...............................................= O Mx....................................................= Mo
fpuAps, kips 2.43 3.11 3.83 4.55 5.34 6.27 7.23 7.55 11.78 14.05 a. The Q/S in. special strand has a larger actual diameter than the Q/S in. regular strand. The table values take this difference into account.
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PCI Handbook/Sixth Edition 11–31
MATERIAL PROPERTIES PRESTRESSING STEEL
Design Aid 11.2.4 Properties and Design Strengths of Prestressing Bars
For design purposes, the following assumptions are satisfactory:
Es = 29,000 ksi
fy = 0.95fpu
a. Verify availability before specifying.
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11–32 PCI Handbook/Sixth Edition
MATERIAL PROPERTIES PRESTRESSING STEEL
Design Aid 11.2.5 Typical Stress-Strain Curve, 7-Wire Low-Relaxation Prestressing Strand
Note: approximate strain at rupture is 0.05 to 0.07 in./in. These curves can be approximated by the following equations: 250 ksi strand: 270 ksi strand: ps 0.0076ε ≤ : ps psf 28,500 (ksi)= ε ps 0.0086ε ≤ : ps psf 28,500 (ksi)= ε
ps 0.0076ε > : psps
0.04f 250 (ksi)0.0064
= −ε −
ps 0.0086ε > : psps
0.04f 270 (ksi)0.007
= −ε −
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PCI Handbook/Sixth Edition 11–33
MATERIAL PROPERTIES PRESTRESSING STEEL
Design Aid 11.2.6 Transfer and Development Lengths for 7-Wire Uncoated Strand
The ACI 318-02 (Section 12.9.1) equation for required development length may be rewritten as: d = se b ps se b(f / 3)d (f f )d+ −
where: d = required development length, in. fse = effective prestress, ksi fps = stress in prestressing steel at nominal strength, ksi db = nominal diameter of strand, in. The first term in the equation is the transfer length and the second term is the additional length required for the stress increase (fps – fse) corresponding to the nominal strength.
Transfer and development lengtha in inches fse = 150 ksi fse = 160 ksi fse = 170 ksi
Development Length Development Length Development Length
a. The development length values given in the table must be doubled where bonding of the strand does not extend to the member end and
the member is designed such that tension in the precompressed tensile zone is produced under service loads (see ACI 318-02, Section 12.9.3).
b. The Q/S in. special (Q/S S) strand has a larger nominal diameter than the Q/S in. regular (Q/S) strand. The table values for transfer and development length reflect this difference in diameters.
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11–34 PCI Handbook/Sixth Edition
MATERIAL PROPERTIES REINFORCING BARS
Design Aid 11.2.7 Reinforcing Bar Data
ASTM STANDARD REINFORCING BARS NOMINAL DIMENSIONS BAR SIZEa
DESIGNATION DIAMETER AREA WEIGHT OR MASS U.S. CUSTOMARY SI in. mm in.2 mm2 lb/ft kg/m
a. Many mills will mark and supply bars only with metric (SI) designation, which is a soft conversion. Soft conversion means that the metric
(SI) bars have exactly the same dimensions and properties as the equivalent U.S. customary designation.
STANDARD HOOKS STIRRUP AND TIE-HOOKS
180° 90° 90° 135° BAR SIZE D
A OR G J A OR G D
A OR G A OR G H U.S. SI U.S. SI U.S. SI U.S. SI U.S. SI U.S. SI U.S. SI U.S. SI U.S. SI #3 #10 2Q/F 60 5 125 3 80 6 150 1Q/S 40 4 105 4 105 2Q/S 65 #4 #13 3 80 6 150 4 105 8 200 2 50 4Q/S 115 4Q/S 115 3 80 #5 #16 3E/F 95 7 175 5 130 10 250 2Q/S 65 6 155 5Q/S 140 3E/F 95 #6 #19 4Q/S 115 8 200 6 155 1–0 300 4Q/S 115 1–0 305 8 205 4Q/S 115 #7 #22 5Q/F
a. ASTM A767 requires that bars bent cold prior to hot dip galvanizing must be fabricated to a minimum bend diameter equal to 7 in. for #7
bar and 8 in. for #8 bar.
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PCI Handbook/Sixth Edition 11–35
MATERIAL PROPERTIES REINFORCING BARS
Design Aid 11.2.8 Location of Reinforcement Confined by Stirrups or Ties
Z Dimension (in.)
Stirrup or Tie Size
#3 #4 #5
#4 U/K 1Q/AH 1Q/F
#5 U/K 1Q/K 1T/AH
#6 QT/AH 1E/AH 1E/K
#7 1 1E/AH 1U/AH
#8 1Q/AH 1Q/F 1U/AH
#9 1Q/AH 1T/AH 1Q/S
#10 1Q/K 1T/AH 1Q/S
Mai
n R
einf
orce
men
t Siz
e
#11 1E/AH 1E/K 1O/AH To determine location of main reinforcement, add specified cover to the “z” dimension from above table.
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11–36 PCI Handbook/Sixth Edition
MATERIAL PROPERTIES REINFORCING BARS
Design Aid 11.2.9 Required Development Lengthsa for Reinforcing Bars (Grade 60)
Tension Development Length:
d = b
c
d2400
f ′; min. 12 in. (#6 and smaller)
d = b
c
d3000
f ′; min. 12 in. (#7 and larger)
(Note: for Grade 40 bars, replace 2400 and 3000 with 1600 and 2000, respectively.) Multiply d values by : (a) 1.3 for lightweight concrete (b) 1.3 for “top bars” (c) 1.5 for epoxy coated bars with cover < 3db or
clear spacing < 6db, otherwise multiply by 1.2 (Note: Product of factors (b) and (c) need not exceed
1.7) (d) 1.5 for bars with less than minimum stirrups or
ties, clear spacing less than 2db or clear cover less than db.
(e) As (required)/As (provided) for excess reinforce-ment unless development of fy is specially required. This multiplier is not to be applied to lap splices per ACI 318-02, Section R12.15.1.
Compression Development Length:
d = b
c
1200df ′
; min. 18db and 8 in.
(Note: For Grade 40 bars, replace 1200 with 800 and 18 with 12) Multiply d values by: (a) As(required)/As (provided) for excess reinforcement (b) 0.75 for adequate spiral or tie enclosure (see ACI 318-02, Section 12.3.3b) Compression Splice Lap Length: Lap length = 30db; min. 12 in. The values of cf ′ used in these equations shall not exceed 100 psi (see Section 12.1.2, ACI 318-02)
a. Source: Manual of Standard Practice – Structural Welded Wire Reinforcement, Wire Reinforcement Institute, 1992, Findlay, Ohio. b. Commonly available in 8 ft x 12 ft or 8 ft x 15 ft sheets. c. These items may be carried in sheets by various manufacturers in certain parts of the U.S. and Canada. d. Exact W-number size for 2 gage is 5.4.
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PCI Handbook/Sixth Edition 11–39
MATERIAL PROPERTIES STRUCTURAL WELDED WIRE REINFORCEMENT (WWR)
Design Aid 11.2.11 Wires Used in Structural Welded Wire Reinforcementa
Area – in.2 per ft of width Wire Size Number Center to Center Spacing, in.
a. Source: Manual of Standard Practice—Structural Welded Wire Reinforcement, Wire Reinforcement Institute, 1992, Findlay, Ohio. b. ASTM A 82, Available fy = 65,000 psi to 80,000 psi in 2500 psi increments. c. ASTM A 496, Available fy = 70,000 psi to 80,000 psi in 2500 psi increments.
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11–40 PCI Handbook/Sixth Edition
MATERIAL PROPERTIES BAR AREA EQUIVALENTS
Design Aid 11.2.12 Bar Area Equivalents in a One Foot Wide Section
Bar Reinforcing Bar Size (Nominal Diameter – in.) Area
Spacing c/c (in.)
#3 (0.375)
#4 (0.500)
#5 (0.625)
#6 (0.750)
#7 (0.875)
#8 (1.000)
#9 (1.128)
#10 (1.270)
#11 (1.410) Range
2 0.66 1.20 1.86 2.64 3.60 4.74 Exceeds min. bar clear 2Q/S 0.53 0.96 1.49 2.11 2.88 3.79 4.80 spacing of db 3 0.44 0.80 1.24 1.76 2.40 3.16 4.00 5.08 6.24
Area Range ≤ 0.25 sq in. 0.25 to 0.50 sq in. 0.50 to 0.75 sq in.
NOTE: Check minimum requirements for temperature and shrinkage steel.
How to use this design aid. Given a design (or minimum temperature/shrinkage) reinforcement are required per foot, enter the design aid along right column or bottom row. Select one of the bar area ranges from that given sq in./ft, and follow the range band upward and/or to the left. Select the combina-tion of bar size and spacing satisfying the design and spacing requirements for the section.
Example. A design that requires reinforcement at 0.62 in.2/ft, with bar size restricted to No. 7 or smaller. Enter the design aid in the 0.50 to 0.75 sq in. range located along the bottom row. Follow the shaded band up to the top of the table. Select one of the following combinations: one layer of No.4 at about 3.5 in. o.c., No. 5 at 6 in. o.c., No. 6 at 8.5 in. o.c., or No. 7 at 11.5 in. o.c. Similar spacing(s) could be determined for two reinforcement layers, if desired.
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PCI Handbook/Sixth Edition 11–41
MATERIALS PROPERTIES Design Aid 11.2.13 ACI Required Minimum Reinforcement Areas Per Foot Width of Section
Member Thickness or Vertical Height – h (in.) Element/Category As/Agross
Notes: a. Ratio is reinforcement area to gross concrete area. b. Minimum controls for fy > 77 ksi. c. For deformed bars not larger than #5, with a specified yield strength not less than 60,000 psi,or for welded wire reinforcement (plain or
deformed) not larger than W31 or D31. d. For other deformed bars. e. Refer to ACI 318-02, Section 16.4.2.
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11–42 PCI Handbook/Sixth Edition
11.3 STANDARD BOLTS, NUTS AND WASHERS Design Aid 11.3.1 Dimensions of Nuts and Bolts
Bolt Heads
Bolt head dimensions, rounded to nearest Q/AH inch, are in accordance with ANSI B18.2.1 – 1972 (Square and Hex) and ANSI 18.5 – 1971 (Countersunk)
Standard Dimensions for Bolt Heads
Square Hex Heavy Hex Countersunk Dia. of Bolt D Width
11.4 WELDING INFORMATION Design Aid 11.4.1 Weld Symbols Commonly Used in Precast Construction
Basic Welding Symbols and Their Meanings Elements of a Typical Weld Symbol
Location / Position of Symbol Supplemental Symbols
Type of Weld Arrow Side Other Side Both Sides Field Weld Weld All Around
Finishing Contours
Fillet Weld
Plug or Slot Weld
Not Applicable
Square
Side Designation
V
Bevel
Maximum Detailed Fillet Weld Sizes at Edges
Flare-Bevel
Groove Welds
Flare-V
End Returns
Stud Weld
No arrow or other side significance to the stud weld symbol.
For other basic and supplemental weld symbol and process information, refer to
ANSI/AWS A2.4 References a. AWS, Standard Symbols for Welding, Brazing and Nondestruction Examination, ANSI/AWS A2.4-86, American Welding Society, Miami,
Florida, 1986. b. AWS, Structural Welding Code – Steel, ANSI/AWS D1.1:2000, 17th Edition, American Welding Society, Miami, Florida, 2000. c. AISC, Load & Resistance Factor Design, – Manual of Steel Construction, Third Edition, American Institute of Steel Construction,
Chicago, Illinois, 2001.
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11–46 PCI Handbook/Sixth Edition
WELDING INFORMATION Design Aid 11.4.2 Typical Welded Joints in Precast Construction
Fillet Weld
Fillet Weld
2 in. of T/AH fillet weld on 6 in. centers, each side
Q/F in. fillet weld, 6 in. long, each side
Plug Weld Flare Bevel with Fillet Weld
1 in. Ø plug welds x Q/S in. deep at 4 in. on-center Flare bevel weld of tube to plate followed by Q/F in. fillet weld reinforcing
Bevel with Fillet Weld Square Weld with Fillet
Q/F in. bevel weld with T/AH in. fillet weld reinforcing, one side
E/K in. square weld with Q/S in. fillet weld reinforcing, both sides
Stud Weld
Reinforcing Bar Welds
6 - Q/S in. Ø studs spaced at 3 in. on-center in one line
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PCI Handbook/Sixth Edition 11–47
WELDING INFORMATION Design Aid 11.4.3 Properties of Weld Groups Treated as Lines (tw = 1)
Section b = width; d = depth
Distance to centroid
Section modulus xI / y
Polar moment of inertia IP, about center of gravity
(1) S =
2d6
Ip = 3d
12
(2)
S = 2d
3 Ip =
2 2d(3b d )6
+
(3)
S = bd Ip = 2 2b(3d b )6
+
(4)
2dy2(b d)
=+
2bx2(b d)
=+
Stop = 24bd d
6+
Sbott = 2d (4b d)6(2b d)
++
Ip =
4 2 2(b d) 6b d12(b d)
+ −+
(5)
2bx2b d
=+
S = 2dbd
6+
Ip =
3 2 3 48b 6bd d b12 2b d
+ + −+
(6)
2dyb 2d
=+
Stop =
22bd d3+
Sbott = 2d (2b d)3(b d)
++
Ip =
3 2 3 4b 6b d 8d d12 2d b
+ + −+
(7)
S = 2dbd
3+ Ip =
3(b d)6
+
(8)
2dyb 2d
=+
Stop =
22bd d3+
Sbott = 2d (2b d)3(b d)
++
Ip =
3 3 4b 8d d12 b 2d+ −
+
(9)
S = 2dbd
3+ Ip =
3 2 3b 3bd d6
+ +
(10)
S = 2rπ Ip = 32 rπ
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11–48 PCI Handbook/Sixth Edition
11.5 SECTION PROPERTIES Design Aid 11.5.1 Properties of Geometric Sectionsa
SQUARE
Axis of Moments Through Center
A = d2
c = d2
I = 4d
12
S = 3d6
r = d 0.288675d12
=
RECTANGLE
Axis of Moments on Diagonal
A = bd
c = 2 2
bd
b d+
I = 3 3
2 2b d
6(b d )+
S = 2 2
2 2
b d
6 b d+
r = 2 2
bd
6(b d )+
SQUARE Axis of Moments on Base
A = d2 c = d
I = 4d
3
S = 3d
3
r = d 0.577350d3
=
RECTANGLE
Axis of Moments Any Line Through Center of Gravity
A = bd
c = bsina dcosa2+
I = 2 2 2 2bd(b sin a d cos a)
12+
S = 2 2 2 2bd(b sin a d cos a)
6(bsina dcosa)++
r = 2 2 2 2b sin a d cos a
12+
SQUARE Axis of Moments on Diagonal
A = d2
c = d 0.707107d2
=
I = 4d
12
S = 3
3d 0.117851d6 2
=
r = d 0.288675d12
=
HOLLOW RECTANGLE
Axis of Moments Through Center
A = bd – b1d1
c = d2
I = 3 3
1 1bd b d12−
S = 3 3
1 1bd b d6d−
r = 3 3
1 1bd b d12A
−
RECTANGLE Axis of Moments Through
Center
A = bd
c = d2
I = 3bd
12
S = 2bd
6
r = d 0.288675d12
=
EQUAL RECTANGLES
Axis of Moments Through Center of Gravity
A = b(d – d1)
c = d2
I = 3 3
1b(d d )12
−
S = 3 3
1b(d d )6d
−
r = 3 3
1
1
d d12(d d )
−−
a. Source: “Manual of Steel Construction, Allowable Stress Design,” Ninth Edition, American Institute of Steel Construction, Chicago, IL, 1989.
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SECTION PROPERTIES Design Aid 11.5.1 Properties of Geometric Sections (Cont.)
RECTANGLE
Axis of Moments on Base
A = bd
c = d2
I = 3bd
3
S = 2bd
3
r = d 0.577350d3
=
UNEQUAL RECTANGLES
Axis of Moments Through Center of Gravity
A = bt + b1t1
c = 2
1 1 1bt b t (d t )A
+ −Q/S Q/S
I = 33
2 21 11 1 1
b tbt bty b t y12 12
+ + +
S = 11
I ISc c
=
r = IA
TRIANGLE Axis of Moments Through
Center of Gravity
A = bd2
c = 2d3
I = 3bd
36
S = 2bd
24
r = d18
HALF CIRCLE
Axis Through Moments of Center of Gravity
A = 2R
2π
c = 4R 13
⎛ ⎞−⎜ ⎟π⎝ ⎠
I = 4 8R8 9π⎛ ⎞−⎜ ⎟π⎝ ⎠
S = 3 2R (9 64)
24 (3 4)⎡ ⎤ ⎡ ⎤π −⎢ ⎥ ⎢ ⎥
π −⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦
r = 29 64R6
π −π
TRIANGLE
Axis of Moments on Base
A = bd2
c = d
I = 3bd
12
S = 2bd
12
r = d6
PARTIAL CIRCLE
Axis of Moments Through Circle Center
NOTE: Angles in Radians
I = 4
2 2 311
yR (R y )8 2
π + −
22 2 2 1 1
1 1yR y R y R sin
4 R−⎛ ⎞− − +⎜ ⎟
⎝ ⎠
A = 2
2 21 1
R y R y2
π − −
2 1 1yR sin
R− ⎛ ⎞− ⎜ ⎟⎝ ⎠
c = 2 2 3 / 2
12(R y )/ A
3−
TRAPEZOID
Axis of Moments Through Center of Gravity
A = 1d(b b )2+
c = 1
1
d(2b b )3(b b )
++
I = 3 2 2
1 1
1
d (b 4bb b )36(b b )
+ ++
S = 2 2 2
1 1
1
d (b 4bb b )12(2b b )
+ ++
r = 2 2
1 11
d x 2(b 4bb b )6(b b )
+ ++
PARABOLA
A = 4 ab
3
m = 2 a5
I1 = 316 a b175
I2 = 34 ab15
I3 = 332 a b105
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11–50 PCI Handbook/Sixth Edition
SECTION PROPERTIES Design Aid 11.5.1 Properties of Geometric Sections (Cont.)
CIRCLE
Axis of Moments Through Center
A = 2
2d R4
π = π
c = d R2
=
I = 4 4d R
64 4π π=
S = 3 3d R
32 4π π=
r = d R4 2
=
HALF PARABOLA
A = 2 ab3
m = 2 a5
n = 3 b8
I1 = 38 a b175
I2 = 319 ab480
I3 = 316 a b105
I4 = 32 ab15
HOLLOW CIRCLE
Axis of Moments Through Center
A = 2 2
1(d d )4
π −
c = d2
I = 4 4
1(d d )64
π −
S = 4 4
1(d d )32d
π −
r = 2 2
1d d4−
COMPLEMENT OF HALF
PARABOLA
A = 1 ab3
m = 7 a10
n = 3 b4
I1 = 337 a b2100
I2 = 31 ab80
PARABOLIC FILLET
IN RIGHT ANGLE
a = t2 2
b = t2
A = 21 t6
m = n = 4 t5
I1 = I2 = 411 t2100
*ELLIPTIC COMPLEMENT
* See note on next page
A = ab 14π⎛ ⎞−⎜ ⎟
⎝ ⎠
m = a
6 14π⎛ ⎞−⎜ ⎟
⎝ ⎠
n = b
6 14π⎛ ⎞−⎜ ⎟
⎝ ⎠
I1 = 3 1 1a b3 16 36 1
4
⎛ ⎞⎜ ⎟π⎜ ⎟− −⎜ ⎟π⎛ ⎞−⎜ ⎟⎜ ⎟
⎝ ⎠⎝ ⎠
I2 = 3 1 1ab3 16 36 1
4
⎛ ⎞⎜ ⎟π⎜ ⎟− −⎜ ⎟π⎛ ⎞−⎜ ⎟⎜ ⎟
⎝ ⎠⎝ ⎠
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PCI Handbook/Sixth Edition 11–51
SECTION PROPERTIES Design Aid 11.5.1 Properties of Geometric Sections (Cont.)
*HALF ELLIPSE
A = 1 ab2
π
m = 4a3π
I1 = 3 8a b8 9π⎛ ⎞−⎜ ⎟π⎝ ⎠
I2 = 31 ab8
π
I3 = 31 a b8
π
REGULAR POLYGON
n = number of sides
φ = 180n
a = 2 212 R R−
R = a2sinφ
R1 = a2 tanφ
A = 21 na cot4
φ
= 2 21
1 nR sin2 nR tan2
φ = φ
I1 = I2 =2 2A(6R a )
24−
= 2 21A(12R a )
48+
r1 = r2 =2 26R a24
−
= 2
112R a48
+
*QUARTER ELLIPSE
A = 1 ab4
π
m = 4a3π
n = 4b3π
I1 = 3 4a b16 9π⎛ ⎞−⎜ ⎟π⎝ ⎠
I2 = 3 4ab16 9π⎛ ⎞−⎜ ⎟π⎝ ⎠
I3 = 31 a b16
π
I4 = 31 ab16
π
BEAMS AND CHANNELS I3 = 2 2
x yI sin I cosφ + φ
I4 = 2 2x yI cos I sinφ + φ
fb = x y
y xM sin cosI I
⎛ ⎞⎜ φ + φ⎟⎜ ⎟⎝ ⎠
Where M is bending moment due to force F.
* To obtain properties of half circles, quarter circle and circular complement, substitute a = b = R.
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11–52 PCI Handbook/Sixth Edition
SECTION PROPERTIES Design Aid 11.5.1 Properties of Geometric Sections (Cont.)
ANGLE
AXIS OF MOMENTS THROUGH CENTER OF GRAVITY
Z-Z is Axis of Minimum I
tan2θ = y x
2kI I−
A = t(b – c) x = 2b ct
2(b c)++
y = 2d at
2(b c)++
K = product of inertia about X-X & Y-Y
= abcdt4(b c)
±+
Ix = 3 3 31 [t(d y) by a(y t) ]3
− + − −
Iy = 3 3 31 [t(b x) dx c(x t) ]3
− + − −
Iz = 2 2x yI sin I cos K sin2θ + θ + θ
Iw = 2 2x yI cos I sin K sin2θ + θ + θ
K is negative when heel of angle, with respect to center of gravity, is in first or third quadrant, positive when in second or fourth quadrant.
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SECTION PROPERTIES Design Aid 11.5.2 Plastic Section Moduli and Shape Factors
For TS shapes, refer to AISC-LRFD Manual, Third Edition for Zs values.
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11–54 PCI Handbook/Sixth Edition
11.6 METRIC CONVERSION Design Aid 11.6.1 Metric Calculations and Example
“Hard” SI (metric) Calculations for Precast Concrete
Design Aid 11.4.1 shows direct conversion from inch-lb. (U.S. customary) to SI units. Calculations made in SI units are usually rounded to even numbers. These are known as “hard” metric calculations. The metric version of the Code is 318M-02. Some of the common SI units used are: Concrete Strength: 20 MPa is approximately equivalent to 3000 psi 35 MPa is approximately equivalent to 5000 psi Concrete weight (or mass): Normal weight concrete may be assumed to weigh 2400 kg/m3 (149.8 pcf). Lightweight concrete may be assumed to weigh 1900 kg/m3 (118.6 pcf). Reinforcement: Most U. S. reinforcing bar manufacturers mark bars with metric designations, although the actual sizes have not changed (see Design Aid 11.2.7). Grade 420 reinforcing bar (fy = 420 MPa) is equivalent to Grade 60 reinforcing bar. Prestressing Strand: Strand diameters and areas are rounded to the nearest mm, e.g., 13 mm is equivalent to Q/S in. diam-eter, area = 99 mm2. Relationships in SI
Structural engineering calculations in SI units involve forces which include gravitational effects, rather than just weights, or mass. Thus one kilogram (kg) of mass converts to 9.8 newtons (N) of force. For example, a 50 mm thick concrete topping 1 meter wide weighs (50/1000)m × 1m × 2400 kg/m3 = 120 kg/m. It exerts 120 × 9.8 = 1176 N/m or 1.18 kN/ m of force.
Pressure or stress is expressed in pascals (P). 1P = 1N/m2. It is more common to work in megapascals (MPa). 1 MPa =1N/mm2. Bending moments are expressed in newton-meters (N-m) or kilonewton-meters (kN-m).
Design Aid 11.6.2 lists quantities that are fre-quently encountered in the design of precast concrete as well as in general structural engineering practice. Most U.S. Government agencies that require SI unit dimensioning of contract documents will also require consistent use of the listed SI units given in the table. The equivalent U.S. customary units listed are those traditionally used by the design professions in the U.S.
Conversion of frequently encountered concrete stress coefficients used in ACI 318-02 and the PCI Handbook are tabulated in Design Aid 11.6.4.
Example Use of Eq. 18-3 from 318M-02 (Similar to Example 4.2.2.3) Given: Double tee similar to PCI standard 8DT24+2 Concrete: Precast cf ′ = 35 MPa Topping cf ′ = 20 MPa Reinforcement: 12-13 mm dia. 1860 MPa low relaxation strands (6 ea. stem). Area per strand = 99 mm2 Aps = 12(99) = 1188 mm2 As = 2 – #19 = 568 mm2 fy = 420 MPa Problem: Find the design flexural strength of the composite section using Eq. 18-3 from ACI 318M-02.
METRIC CONVERSION Design Aid 11.6.2 Conversion from U.S. Customary Units to International System (SI)
To convert from
to multiply by
Length inch (in.) millimeter (mm) 25.4 inch (in.) meter (m) 0.0254 foot (ft) meter (m) 0.3048 yard (yd) meter (m) 0.9144 mile (mi)
kilometer (km) 1.6093
Area square foot (ft2) square meter (m2) 0.09290 square inch (in.2) square millimeter (mm2) 645.2 square inch (in.2) square meter (m2) 0.0006452 square yard (yd2) square meter (m2) 0.8361 acre (A) hectare (ha) = 10,000 m2 0.4047 square mile
square kilometer 2.590
Volume cubic inch (in.3) cubic meter (m3) 0.00001639 cubic foot (ft3) cubic meter (m3) 0.02832 cubic yard (yd3) cubic meter (m3) 0.7646 gallon (gal) Can. liquida liter 4.546 gallon (gal) Can. liquida cubic meter (m3) 0.004546 gallon (gal) U.S. liquida liter 3.785 gallon (gal) U.S. liquida
cubic meter (m3) 0.003785
Force kip kilogram (kgf) 453.6 kip newton (N) 4448.0 pound (lb) kilogram (kgf) 0.4536 pound (lb)
newton (N) 4.448
Pressure or Stress kips/square inch (ksi) megapascal (MPa)b 6.895 pound/square foot (psf) kilopascal (kPa)b 0.04788 pound/square inch (psi) kilopascal (kPa)b 6.895 pound/square inch (psi) megapascal (MPa)b 0.006895 pound/square foot (psf)
kilogram/square meter (kgf/m2) 4.882
Mass pound (avdp) kilogram (kg) 0.4536 ton (short, 2000 lb) kilogram (kg) 907.2 ton (short, 2000 lb) tonne (t) 0.9072 grain kilogram (kg) 0.00006480 tonne (t) kilogram (kg) 1000
a. One U.S. gallon equals 0.8321 Canadian gallon. b. A pascal equals one newton/square meter; 1 Pa = 1 N/m2. Note: To convert from SI units to U.S. customary units (except for temperature), divide by the factors given in this table.
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11–56 PCI Handbook/Sixth Edition
METRIC CONVERSION Design Aid 11.6.2 Conversion from U.S. Customary Units to International System (SI) (Cont.)
To convert from
to multiply by
Mass (weight) per Length kip/linear foot (klf) kilogram/meter (kg/m) 1488 pound/linear foot (plf) kilogram/meter (kg/m) 1.488 pound/linear foot (plf)
newton/meter (N/m) 14.593
Mass per volume (density) pound/cubic foot (pcf) kilogram/cubic meter (kg/m3) 16.02 pound/cubic yard (pcy)
kilogram/cubic meter (kg/m3) 0.5933
Bending Moment or Torque pound-inch (lb-in.) newton-meter 0.1130 pound-foot (lb-ft) newton-meter 1.356 kip-foot (kip-ft)
Other Section modulus (in.3) mm3 16,387 Moment of inertia (in.4) mm4 416,231 Coefficient of heat transfer (Btu/ft2/h/°F) W/m2/°C 5.678 Modulus of elasticity (psi) MPa 0.006895 Thermal conductivity (Btu/in./ft2/h/°F) Wm/m2/°C 0.1442 Thermal expansion in./in./°F mm/m2/°C 1.800 Area/length (in.2/ft) mm2/m 2116.80
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METRIC CONVERSION Design Aid 11.6.3 Preferred SI Units and U.S. Customary Equivalents
Quantity SI U.S. customary
Area, cross section mm2 in.2 Area, plan dimension mm2 ft2 Bending moment kN-m kip-ft Coefficient of thermal expansion mm/(mm-°C) in./in./°F Deflection mm in. Density, linear kg/m lb/ft, kip/ft Density, area kg/m2 lb/ft2, kip/ft2 Density, mass kg/m3 lb/ft3, kip/ft3 Force kN lb, kip Force, per unit length kN/m lb/ft, kip/ft Force, per unit area kN/m2 lb/ft2, kip/ft2 Length, cross section mm in. Length, plan dimension mm ft Mass kg lb, kip Modulus of elasticity MPa psi, ksi Moment of inertia 106 mm4 in.4 Section modulus 106 mm3 in.3 Stress MPa psi, ksi Temperature °C °F Torque kN-m lb-ft, kip-ft
Design Aid 11.6.4 Concrete stress coefficents
U.S. customary coefficient SI coefficient U.S. customary