Ductility of Reinforced and Prestressed Concrete Flexural ......Ductility of Reinforced and Prestressed Concrete Flexural Members Brian C. Skogman Structural Engineer Black Veatch

Ductility of Reinforcedand Prestressed Concrete

Flexural Members

Brian C. SkogmanStructural EngineerBlack & VeatchKansas City, Missouri

Maher K. tadrosProfessor of Civil

EngineeringUniversity of NebraskaOmaha, Nebraska

Ronald GrasmickStructural EngineerDana Larson Roubal and

AssociatesOmaha, Nebraska

The current ACI Code' specifies sepa-rate sets of reinforcement limits forconventionally reinforced and pre-stressed concrete. The reinforced con-crete limit is related to the steel arearatio, p, which depends on the definitionof member depth and width. This limitis applicable only to rectangular andflanged sections, with or without com-pression reinforcement.

The limit of reinforcement in pre-stressed concrete is given in terms of thesteel index, u, which is a function of theratio, p. It accounts for the presence ofmild tension and compression rein-forcement, thus allowing for partial pre-stressing. It, too, is applicable only to

rectangular and flanged sections. How-ever, this limit does not default to that ofa conventionally reinforced sectionwhen the area of prestressed steel is setequal to zero. The Code provisions areconfusing if the section is flanged andcontains both prestressed and nonpre-stressed steel, or if the section has morethan one type of concrete as in compos-ite sections.

The purpose of this paper is to exam-ine the background of both limits and todevelop a unified approach that wouldapply to the entire spectrum of struc-tural concrete members. Several rec-ommendations are discussed. These in-clude the 1986 Supplement to the ACI

94

Commentary, 2 the Canadian Code, 3 theCEB-FIP Model Code,' and the work ofNaaman and his associates. 5.6' 7 Based onthese earlier studies, a very simple yetgeneral formula is proposed herein. It iscompatible with the intent of the ACICode, and is valid regardless of the sec-tion shape, reinforcement, and number'of concrete types used in composite ac-tion. Moreover, it allows the engineer tofocus on the factors affecting ductility,which include but are not limited tomaximum tension reinforcement.

Numerical examples are provided toillustrate the proposed formula and tocompare it with other methods. A pro-posal for revision of the ACI Code andCommentary, on the basis of the devel-opments given herein, is presented inAppendix B.

THEORETICALDEVELOPMENT

Various codes require member duc-tility by limiting the maximum amountof flexural reinforcement. One of thebenefits of ductility is large deflectionsand thus warning before failure. Ductil-ity is also important for seismic designand moment redistribution in continu-ous members.

A good indicator of ductility is thesection curvature, which is the secondderivative of deflection. Referring toFig. 1, the section curvature, fir, is de-fined by the relationship:

(1)C

where e,,, is the maximum usable com-pressive strain at the extreme concretefiber and c is the distance from the ex-treme compression fiber to the neutralaxis.

Naaman, Harajli, and Wight6 havediscussed in detail the factors affectingmember ductility. An acceptable degreeof ductility can be achieved by keeping4r greater than or equal to a certain min-

imum value. It is more convenient,however, to work with the nondimen-sional quantity of member rotation, 0,over a given length.

In plastic design, the length overwhich plastic hinging develops is es-sentially an assumed value based onjudgment and experience. $" A com-monly assumed length is the effectivedepth (see Ref. 4). Thus, for memberswith prestressed steel only:

B = f d- i^idx =Ord = "'d-ps ps BmEn, ps

o C

(2a)

For conventionally reinforced mem-bers:

f d- TB,^ J dx dns = BmEn,ns

o C

(2b)

Eqs. (2) clearly show that ductility canbe improved by reducing the neutralaxis depth, c, or by increasing the ulti-

PCI JOURNAL/November-December 1988 95

i— b ^,

e^

Assumed Plasticc Curvature W Rotation a

ecu(o.85 h)

M Mh c B^

0.85h

NA

(a) Cross Section (b) Strain Diagram (c) Assumed length of plastic rotationsegment in the maximum bending zone,not to scale.

Fig. 1. Flexural ductility relationships.

mate concrete strain, e. The latter pa-rameter is recognized by the CEB-FIPModel Code,' but not by the ACI orCanadian Codes. Numerous studieshave shown that E 5 can be increased byconfining the concrete with closed ties.Concrete strength and other factors alsoaffect eau.

The neutral axis depth, c, may be re-duced by increasing the concrete com-pressive strength, adding compressionreinforcement, or by decreasing the ten-sile force. The last factor corresponds tothe ACI Code provisions for maximumreinforcement limits.

The ACI Code maximum reinforce-ment limit for prestressed concrete isbased on keeping the strain in the pre-stressing steel equal to or greater thanthe yield strain (see Ref. 12). Other as-sumptions implied in the ACI Codeformulas for maximum reinforcementare: decompression steel strain =0.00585 and e, = 0.003.

Using these quantities, a corre-sponding value of dP8 lc may be ob-tained from Fig. 1(b). Substitution intoEq. (2a) yields:

Bmiu,pS = 0.00715 (3a)

The ACI Code provisions for rein-forced concrete are based on limiting

the steel area to 0.75 of the theoreticalbalanced failure area. For Grade 60 steelplaced in rectangular sections, the cor-responding rotation is:

0.003 + e_ = 0.0068 (3b)emit,== 0.75

For Grade 40 steel, which is not com-mon anymore, Burin, ,,$ = 0.0058. Forflanged sections, limiting the area oftensile reinforcement to 0.75 of the bal-anced area does not correspond to afixed minimum curvature or rotationlimit. If the width of the compressionzone is nonuniform, 0.75 of the area inthe compression zone does not corre-spond to 0.75 of the neutral axis depth. Amore consistent approach is to limit theneutral axis depth to 0.75 of the bal-anced depth for all section shapes.13This will be further clarified by Exam-ple 2.

It can be seen from Eqs. (3) that °miniscomparable for both construction types.For the general case of a cross sectioncontaining significant quantities of bothtypes of steel, i.e., partially prestressedsections, it would be convenient to haveone equation instead of applying Eqs.(2) and (3) separately. A unified and con-servative equation may be obtained bysetting the ductility limit in terms of the

96

full member depth, h, rather than theeffective depths dp. and d,,. Thus, Eqs.(2) become:

C

h , a ecu (4)

where a is equal to d, /(h B„,,,,, ,) andd, l(h Bmi„, ,,․ ) for prestressed and con-ventionally reinforced members, re-spectively.

Examination of numerous practicalapplications has revealed that takingd,lh = 0.85 is a reasonable assumption.Therefore, the corresponding value of ais 0.85/0.00715 = 118.9, say 120 for sim-plicity. For a = 120, the correspondingvalue of d,, /h is 0.0068(120) = 0.816,which is an acceptable ratio for conven-tionally reinforced sections. Thus:

c _- 120 ecu (5)h

Eq. (5) is proposed for use as a mini-mum ductility requirement in place ofthe maximum reinforcement limitsgiven in the ACI Code. It contains thetwo most important parameters that in-fluence ductility, namely, the neutralaxis depth and the ultimate concretestrain.

The use of total member depth, h,rather than an effective depth in theductility criterion can be justified asfollows:

1. In members containing both pre-stressed and nonprestressed steel, theeffective depth has no single definition,while the total depth, h, is a well knownquantity.

2. The effective depth is a product ofthe design process. It is possible tocomplete the strength design of partiallyprestressed sections, for example, with-out any need for its calculation.

3. At sections of maximum bendingmoment, where it is critical to checkductility, the tensile stress resultant isgenerally farther from the compressionface than 0.85h for prestressed concreteand 0.816h for reinforced concrete.

Thus, Eq. (5) is more conservative thanthe ACI Code limits for the great major-ity of practical cases.

4. In plastic analysis, the length ofsegment for calculating rotation issomewhat arbitrary.

5. The Canadian Code uses this con-cept for its prestressed concrete ductil-ity provisions.

COMPARISON WITHOTHER METHODS

As shown earlier, the proposed for-mula was developed to give results con-sistent with the 1983 ACI Code. The1986 Supplement to the ACI 318-83Commentary provides an alternativemethod for calculating the maximumreinforcement index of prestressedmembers:

0.85 -- 0.36 ,8, (6)vg

For noncomposite sections, Eq. (6) isequivalent to the maximum reinforce-ment limit given in the 1983 Code. Set-ting dP3 = 0.85h and e,.0 = 0.003 in pro-posed Eq. (5) yields:

= -- 0.42 (7)dps

which is equivalent to Eq. (6).In addition to being compatible with

the intent of the ACI Code limits, pro-posed Eq. (5) is easy to use and offersconsistent results for the entire spec-trum of structural concrete (see the Pro-posed Commentary Revisions in Ap-pendix B).

Naaman's proposed formula:

= -- 0.425 (8)de

where

Ade = nJ +,d ns Ansfv dns (9)A,Jw + A.J,

PCI JOURNAL/November-December 1988 97

Table 1. Reinforcement limits for conventionally reinforced and prestressed concretesections by currently available methods.

REINFORCEMENT LIMITS`Maximum for Under-Reinforced Maximum for Moment Negative Moment Redistribution

Sections Redistribution In percentAll cases: All cases: All cases:

Proposed c 5120eh cu h 580ecu I (F)20111- J120ecu

(1) Reinforced ConcreteACI Section 10.3 ACI Section 8.4 ACI Section 8.4(a) Rectangular Sections (p-pp)50.5pb 20(1-P-IY JIPmax50.75p +p , I8

b

b

wherep =0. 85p 87ksi

• 1 +fy)b (87ks

(b) T-Sectionsb f'

Pmax S o. 75( b+Pt) +pY fs\ J ywhere

0.85 f 'c(b- bw)hfp f fybwd

As, maxP max =bd

ACI 318-83 (2) Prestressed ConcreteACI Section 18.8.1 ACI Section 18.10.4.3 ACI Section 18.10.4.1Code (a) Rectangular Sections (a) Rectangular Sections (a) Rectangular Sectionsm+ dP m-m)50.36p1

smp+df m-m-)50.24)t mp+d m-m')

where 201- 036,1A 5 t5 Ans tym P = bdps f 1c m=

A^frns c

(b) T Sections (b) T Sections (b) T Sectionso,+ mw -w-w )50.36p 1 mpw+dns(w -mw)50.24p1

pmpw+mw-mw)^.

where mp w , mw and mw are 201 0.36kcomputed as for mp ,m and m'except that b shall be the webwidth, and reinforcement areashall be that required to developcompressive strength of webonly.

Symbols not defined here are given in the Notation section.

is close to Eq. (7), which is a specialform of the proposed limit, Eq. (5). Thisis a good approach if the designer doesnot mind the work required to calculatede . The authors prefer to use total mem-ber depth, h, instead of de, for theaforementioned reasons.

The Canadian Code 3 endorses thefollowing expression as a ductility limitfor prestressed concrete members:

h -- 0.36 (12)If dP8 < 0.8h, the Canadian Commen-

tary 3 recommends that Eq. (10) be re-placed by the following limit:

d^C] < 0.6 (11)

p8

If e,u = 0.003, the proposed limit, Eq.

98

Table 1 (cont.). Reinforcement limits for conventionally reinforced and prestressedconcrete sections by currently available methods.

REINFORCEMENT LIMITSMaximum for Under-Reinforced Maximum for Moment Negative Moment Redistribution

Sections Redistribution in percent(1) Reinforced Concrete

Same as 1983 Code. Same as 1983 Code. Same as 1983 Code.(2) Prestressed ConcreteACI 318

1986 Section 18.8.1 Commentary Section 18.10.4 Commentary Section 18.10.4 CommentarySupplement Same as 1983 Code, or Same as 1983 Code, or Same as 1983 Code, or

to alternatively: alternatively: alternatively:Commentary 0.85-s 0.3611 0.85-e 0.24 P ( (o.aba-11

ps)]ps ps 201L1 - 1 0.36111All cases: All cases: All cases:

de 50.42 -5028 20(1-2.36a-)JNaaman where

Apfpsdp+Asfydsde - Apfps+Asfy

(1) Reinforced ConcreteSection 10.3.3 Not specified (1) Section 8.4

Canadian c 5 87ksid (30-50a)52087ksi+fyA23.3 (2) Prestressed Concrete1984 Section 18.8.1 Not specified (2) Section 18.11.2

h 50.5 (30-50x)520

(5), reduces to:

0.36 (12)h

Thus, the Canadian Code has a duc-tility limit similar in form to the oneproposed herein.

The Canadian Code also provides thefollowing equation for calculating theductility limit of conventionally rein-forced concrete members:

C 87 ksi(13)

d 87ksi +f„

where d is the depth to the centroid ofthe tensile reinforcement. Eq. (13) does,however, have a form that is suitable forcross sections of any shape. Eqs. (10)and (13) permit a greater amount of re-inforcement than both the ACI Codeand the proposed formula [Eq. (5)].

The CEB-FIP Model Code 4 uses thefollowing formula to determine member

ductility:

eadm = Ecud (14)C

where 0ad,,, is an admissible plastic rota-tion. Eqs. (2a) and (2b) have the sameform as Eq. (14). The effective depth d isnot clearly defined in Ref. 4 and a mini-mum value for 0adm is not given. Thus, acomplete comparison with proposed Eq.(5) is not possible.

A summary of currently availablemethods for calculating the reinforce-ment limits for under-reinforced sec-tions, moment redistribution, and per-centage of negative moment that may beredistributed is given in Table 1. It isseen that the proposed method requiresthe least computational work and hasthe widest scope of application..

On the following pages, two numeri-cal examples are given to illustrate theproposed method for determining duc-tility requirements in a concrete section.

PCI JOURNAL/November-December 1988 99

NUMERICAL EXAMPLES

To illustrate the proposed method fordetermining ductility requirements in aconcrete section, two numerical exam-ples are given. The first example coversa prestressed concrete beam containingboth prestressed and nonprestressed

EXAMPLE 1A modified version of the beam given

in Example 4.2.6 of the PCI DesignHandbook, L4 shown in Fig. 2, is consid-ered. The proposed approach and fourother methods will be used to investi-gate if the tension reinforcement meetsthe ductility requirements.

Given: f, (precast) = 5 ksi (34.5 MPa)fc' (topping) = 3 ksi (20.7 MPa)Reinforcement is 10 - r in. (12.7 mm)diameter 270 ksi (1862 MPa) low relaxa-tion prestressed strands.Azs = 1.836 in. 2 (1185 mm2)f3e = 162 ksi (1117 MPa)

= 60 ksi (413.7 MPa)An8 = 2 – #8 = 1.58 in. 2 (1019 mm2)A 3 = 2 – #9 = 2.0 in. 2 (1290 mm2)

Solution: From the flexural analysis (seefor example Ref. 15):c = 6.57 in. (166.9 mm)a = 5.51 in. (140 mm)

reinforcement while the second exam-ple considers a conventionally rein-forced concrete beam. The results ofthe proposed design approach are com-pared with four other methods of cal-culation.

,6, average = 0.839= 253.61 ksi (1749 MPa)

fg = 60 ksi (413.7 MPa)

1. Proposed methodFrom Eq. (5):c = 6.57 = 0.253h 26

< 120 (0.003) = 0.36 (ok)Percent of limit used =100(0.253)/0.36 = 70.3 percent

2. 1983 ACI Code methodThe 1983 Code does not apply to this

case unless certain assumptions aremade. These include definition of thevarious steel indexes and of an averageconcrete strength.

3. 1986 Supplement to the ACI318-83 Commentary

Fig. 2. Partially prestressed beam used in Example 1.

100

From Eq. (6):

0.85( P., ) = 0.85 (--23 4)

= 0.200

< 0.36 (0.8/39) = 0.302 (ok)Percent of limit used = 66.2 percent

4. Naaman's methodFrom Eq. (9):de _ 1.836 (253.61) (23.4) + 1.58 (60) (24)

1.836 (253.61) + 1.58 (60)= 23.5 in. (597 mm)

Inserting de into Eq. (8) gives:C = 6.57 = 0.279 < 0.425 (ok)de 23.5Percent of limit used = 65.6 percent

EXAMPLE 2The ductility requirements for the

reinforced concrete beam shown inFig. 3 will be investigated by five meth-ods. Answers will be expressed in termsof the percent of A, .., used so that themethods can be accurately compared.

1. Proposed methodFrom Eq. (5):

h) max = 120 (0.003) = 0.36

5. Canadian CodeFrom Eq. (10):c = 6.57 = 0.253 < 0.5 (ok)h 26

Percent of limit used = 50.6 percentThis example illustrates the extreme

simplicity of the proposed method. Also,the method shows it to be the most con-servative. Method 3 overcomes a defi-ciency and the 1983 ACI Code and is arational and simple approach. However,it is not applicable to conventionallyreinforced sections. Method 4 is identi-cal to Method 3 except that a slightlydifferent depth of steel is used. TheCanadian Code is as simple as Method 1but it is the least conservative of all.

c,,,ax = 0.36 (20) = 7.20 in. (183 mm)a„zax _ x(31 cmax = 0.85 (7.20) = 6.12 in.

(155 mm)An max _ 0.85(4) [(76 - 12)4 + 12(6.12)]

60= 18.67 in. 2 (12,045 mm2)

Percent of limit used:100(9.36)/18.67 = 50.1 percent

2. 1983 ACI Code methodAe= 0.85(4) (76 - 12)4

60

Ill76"

f'c =4 ksif=60ksi

12"

y• • •

A 5 =6-#11 • •=9.36 in2

Fig. 3. Conventionally reinforced beam used in Example 2.

16.1"

Ans

4"

20"

PCI JOURNAL/November-December 1988 101

A,= 14.51 in. 2 (9361 mm2)The area of steel corresponding to

balanced strain conditions for a 12 in.wide rectangular section is:Ath = 0.0285(12)16.1

= 5.51 in. 2 (3555 mm2)An,, max =0.75(A +A0)

= 15.02 in. 2 (9690 mm2)Percent of limit used = 62.3 percent

3. Modified 1983 ACI Code methodThe authors and others 13 recommend

that c be limited to 0.75cb for the pur-pose of maintaining the same minimumsection curvature requirements as forrectangular sections.Cmax = O.7S Cb

=0.75 (_E"` ldEcu + Eu)

= 0 0.003.75 0.003+0.0021) 1.1

= 7.10 in. (180 mm)amax = 181 Cmax = 0.85 (7.10)

= 6.04 in. (153 mm)A, max - 0.85(4) [(76 - 12)4 + 12(6.04)]60

= 18.61 in. 2 (12,006 mm2)Percent of limit used = 50.3 percent

4. Naaman's methodFrom Eq. (8):

Cma^.= 0.425de = 0.425 (16.1)= 6.84 in. (174 mm)

9, cmax"= 0.85 (6.84)= 5.81 in. (148 mm)

0.85(4) [(76 - 12)4 + 12(5.81)]A max = 60= 18.46 in. 2 (11,910 mm2)

Percent of limit used = 50.7 percent

5. Canadian CodeFrom Eq. (13):

_ f 87 ksi87 ksi + f5 d

_ ( 87 u16.187+60)= 9.53 in. (242 mm)

a,,, = /31 cmax = 0.85 (9.53)= 8.10 in. (206 mm)

0.85(4) [(76 - 12)4 + 12(8.10)]A ns, max = 6O= 20.01 in. 2 (12,913 mm2)

Percent of limit used = 46.8 percent

This example shows that all themethods, except Method 2, give com-parable results. Method 2 contains a de-ficiency in its treatment of nonrectan-gular sections and should be modified asindicated by Method 3. Methods 1 and 4are the only two approaches applicableto both reinforced and prestressed con-crete. Method 1 is the simplest of allfour methods.

102

CONCLUSIONS1. The following ductility limit is

recommended for both prestressed andconventionally reinforced concreteflexural members:

--- 120 Ecu (5)

where c is the neutral axis depth at ulti-mate flexure and h is the total memberdepth.

2. The proposed limit is simpler andmore rational than the current ACI Codelimits, and bridges the gap between theconventionally reinforced and pre-stressed concrete provisions. It is shownto be more conservative than the ACICode limits for prestressed concretewhen dig > 0.85h and for reinforced

concrete when d,za > 0.816h, which cov-ers the great majority of practical cases.In addition, it is more reasonable thanthe ACI Code limit for nonrectangularconventionally reinforced concrete sec-tions, and it allows for adjustments in e,,„from the typical value of 0.003 if con-crete confinement or other conditionsjustify it.

3. The proposal by Naaman is an ac-ceptable alternative to the proposedlimit. It has the advantage of using an"effective depth" to the center of thetensile stress resultant at ultimate flex-ure. However, computation of thatdepth is an extra step that may not beneeded for other purposes. Also, no pro-vision is given for a possible increase inthe value of eau.

PCI JOURNAL/November-December 1988 103

REFERENCES

1. ACI Committee 318, "Building CodeRequirements for Reinforced Concrete(ACI 318-83)," American Concrete In-stitute, Detroit, Michigan, 1983.

2. ACI Committee 318, "Commentary onBuilding Code Requirements for Rein-forced Concrete (ACI 318-83)," (ACI318R-83), American Concrete Institute,Detroit, Michigan, 1983, 155 pp. See alsothe 1986 Supplement.

3. CSA Standard CAN3-A23.3-M84, "De-sign of Concrete Structures for Buildingswith Explanatory Notes," CanadianStandards Association, Rexdale (To-ronto), Canada, 1984.

4. CEB-FIP, Model Code for ConcreteStructures, 1978, Comite Euro-Interna-tional du Beton, 6 Rue Lauriston, F-75116, Paris, France.

5. Harajli, M. H., and Naaman, A. E.,"Evaluation of the Ultimate Steel Stressin Partially Prestressed Flexural Mem-bers," PCI JOURNAL, V. 30, No. 5,September-October 1985, pp. 54-81. Seealso discussion by A. H. Mattock andAuthors, V. 31, No. 4, pp. 126-129.

6. Naaman, A. E., Harajli, M. H., and Wight,J. K., "Analysis of Ductility in PartiallyPrestressed Concrete Flexural Mem-bers," PCI JOURNAL, V. 31, No. 3,May-June 1986, pp. 64-87.

7. Proposal to ACI-ASCE Committee 423,Prestressed Concrete, on changes in theCode provisions for prestressed and par-tially prestressed concrete. Proposal wassubmitted by A. E. Naaman on March 8,1987.

8. Mattock, A. H., "Rotational Capacity of

Hinging Region in Reinforced ConcreteBeams," Proceedings, InternationalSymposium on Flexural Mechanics ofReinforced Concrete, Miami, Florida,1964, pp. 143-181; see also PCA BulletinD101.

9. Sawyer, A. H., "Design of Concrete forTwo Failure States," Proceedings, Inter-national Symposium on Flexural Me-chanics of Reinforced Concrete, Miami,Florida, 1964, pp. 405-431.

10. Corley, W. G., "Rotational Capacity ofReinforced Concrete Beams," Proceed-ings, ASCE, Structural Division, V. 92,No. ST5, October 1966, pp. 121-146; seealso PCA Bulletin D108.

11. Park, R., and Thompson, K. J., "CyclicLoad Tests on Prestressed and PartiallyPrestressed Beam-Column Joints," PCIJOURNAL, V. 22, No. 5, September-Oc-tober 1977, pp. 84-111.

12. Mattock, A. H., "Modification of ACICode Equation for Stress in Bonded Pre-stressed Reinforcement at Flexural Ul-timate," ACI Journal, V. 81, No. 4, July-August 1984, pp. 331-339.

13. Wang, C. K., and Salmon, C. G., Rein-forced Concrete Design, 4th Edition,Harper & Row, New York, N.Y., 1985, pp.301-302.

14. PCI Design Handbook, Third Edition,Prestressed Concrete Institute, Chicago,Illinois, 1985.

15. Skogman, B. C., Tadros, M. K., andGrasmick, R., "Flexural Strength of Pre-stressed Concrete Members," PCIJOURNAL, V. 33, No. 5, September-October 1988, pp. 96-123.

104

APPENDIX A - NOTATIONThe symbols listed below supplement 318-83 Code and Commentary (see Refs.

and supercede those given in the ACI 1 and 2).

A„$ = area of nonprestressed tension ed tension reinforcementreinforcement h = overall thickness of member

c = distance from extreme com- Ecu = maximum usable compressivepression fiber to neutral axis strain at extreme concrete

cb = distance from extreme com- fiber, normally taken equal topression fiber to neutral axis 0.003 unless higher values canunder balanced strain condi- be justifiedtions e, = yield strain of mild reinforce-

d = depth to centroid of tensile mentreinforcement, Eq. (13) °min = minimum required rotation of

d = effective depth of member, a member, additional sub-Eq. (14) scripts ns and ps refer to con-

de = equivalent effective depth, ventionally reinforced andEq. (9) fully prestressed members,

d„,, dp8 = distance from extreme com- respectivelypression fiber to centroid of pmar = 0.75 pbnonprestressed and prestress- Ji = section curvature, Eq. (1)

PCI JOURNAL/November-December 1988 105

APPENDIX B - PROPOSED ACI 318-83 CODEAND COMMENTARY REVISIONS

Proposed Code RevisionsIt is proposed that the following nota-

tion be changed.Section 8.0: Add:c = distance from extreme compres-

sion fiber to neutral axish = overall thickness of memberE,.u = maximum usable compressive

strain at extreme concrete fiber,normally taken equal to 0.003 un-less higher values can be justified

Section 10.0: Add definitions for c, h,and Ecu.Section 18.0: Delete op, o., cow, and w,p,and add definitions for c and Ec,,.

It is proposed that the following sen-tences be added at the ends of Sections8.4.1, 8.4.3, and 10.3.3:"8.4.1 -. . . Alternatively, the percentchange may be taken as follows:

c

20 1 – percent120 Ecu

8.4.3 — . . . Alternatively, the sectionmust be designed so that (c/h) is notgreater than 80 Ecu.10.3.3 -. . . Alternatively, this ductilityrequirement may be satisfied if (clh) isnot greater than 120 Ecu."

It is proposed that Sections 18.8.1,18.8.2, 18.10.4.1, and 18.10.4.3 bechanged to read as follows:"18.8.1 — Amount of prestressed andnonprestressed reinforcement used forcomputation of moment strength of amember, except as provided in Section18.8.2, shall meet the following ductilitycriterion: (clh) _- 120Ecu.18.8.2 — When the criterion of Section18.8.1 is not met, the design momentstrength shall not exceed the momentstrength based on the compression por-tion of the moment couple.18.10.4.1 — Where bonded reinforce-ment is provided at supports in accor-

dance with Section 18.9.2, negativemoments calculated by elastic theory forany assumed loading arrangement mayeach be increased or decreased by notmore than:

c

20 1 – 120 Ecu percent

18.10.4.3 — Redistribution of negativemoments shall be made only when thesection at which moment is reduced isdesigned such that (clh) < 80E,u."

Proposed Commentary RevisionsIt is proposed that the following

changes be made. Insert the followingparagraph at the end of Section 8.4:

"The adoption of an alternativeductility limit in Section 10.3.3 re-quired a corresponding change inSections 8.4.1 and 8.4.3."Insert the following paragraph at the

end of Section 10.3.3:"A discussion of the development

of the alternative ductility criterionis given in Ref. A.*The new criterion offers the following

advantages:(a) It is a unified approach for the en-

tire spectrum of structural members,from conventionally reinforced to fullyprestressed.

(b) It is relatively easy to use as thequantities c and h are products of thestandard design process.

(c) The limit is valid for composite andnoncomposite sections of general shape.

(d) It is more conservative than theprior limit when d < 0.816h, which cov-ers the most common cases in practice.

(e) It offers designers a clearer pictureof the factors influencing ductility, such

*Ref. A is the same as this paper.

106

as increasing e,,„ by confining concretein compression, or decreasing c by in-creasing concrete compressive strength.

(f) It offers a consistent approach tothe calculation of curvature ductilities inall section shapes. The limits in prioreditions of the code did not always offerconsistent curvature ductilities forflanged sections, as compared with rect-angular sections."

Revise Section 18.8.1 to read as fol-lows:"18.8.1 — A new ductility limit wasadopted for this edition of the code. Thenew criterion is equivalent to the earlierone for noncomposite rectangular andflanged sections when e, u = 0.003 and dp= 0.85h. It is more conservative whend> 0.85h, which covers the great ma-jority of flexural members used in prac-tice. The prior steel indexes were con-fusing for nonrectangular sections andnot capable of providing the correctductility value for composite sections.

Additional information and advantagesof this approach can be found in Section10.3.3."

In Section 18.10.4, delete the secondand third paragraphs and insert the fol-lowing paragraph after the first para-graph:"The adoption of a new ductility limit inSection 18.8.1 of the code required acorresponding change in the allowablepercent of moment redistribution andductility criterion for Sections 18.10.4.1and 18.10.4.3, respectively. The amountof redistribution allowed depends onthe ability of the critical sections to de-form inelastically by a sufficient amount.Serviceability under service loads istaken care of by the limiting stresses ofSection 18.4. The choice of 80 ecu as thelimiting ductility value, for which re-distribution of moments is allowed, is inagreement with the requirements forconventionally reinforced concretestated in Section 8.4.3."

NOTE: Discussion of this article is invited. Please submityour comments to PCI Headquarters by August 1, 1989.

PCI JOURNAL/November-December 1988 107