Recommended Practice for the Design of … Journal...Recommended Practice for the Design of Prestressed Concrete Columns and Walls prepared by PCI Committee on Prestressed Concrete

Recommended Practicefor the Design of

Prestressed ConcreteColumns and Walls

prepared by

PCI Committee on PrestressedConcrete Columns

DONALD F. MEINHEITChairman

AHMAD J. DURRANI G. LASZLOtALBERT J. GOUWENS LESLIE D. MARTINGRANT T. HALVORSENMOHAMMED IQBAL ANTOINE E. NAAMAN

GEORGE LASZLO NOEL D. NATHAN*

tDeceased, Former Chairman *Past Chairman

56

CONTENTS

CommitteeStatement .................................58

Preface............... .............................59

Notation............... .............................60

Chapter1 — Definitions ..............................61

Chapter2—Scope ..................................62

Chapter 3 — General Considerations ..................63

Chapter4 — Basic Assumptions ......................64

Chapter 5 — Limiting Dimensions .....................64

Chapter 6 — Effective Dimensions of Walls .............65

Chapter7 — Slenderness Effects ......................66

Chapter 8 — Approximate Evaluation of Slenderness

Effects.................................67

8.1 General8.2 Moment Magnification Factors

Chapter 9 — Permissible Stresses in Concrete and

PrestressingSteel .......................71

Chapter10 — Bearing Stresses ........................72

Chapter11 —Shear ..................................73

Chapter 12 — Reinforcing Details of Prestressed ConcreteColumnsand Walls ......................73

12.1 General Reinforcing Details12.2 End Regions12.3 Limits of Longitudinal Reinforcement12.4 Lateral Reinforcement12.5 Two-Way Prestressing12.6 Special Reinforcement12.7 Minimum Bonded Reinforcement for

Unbonded Prestressing

References............ .............................76

Bibliography.........................................78

Appendix— Design Examples .........................81

PCI JOURNAL/July-August 1988 57

COMMITTEE STATEMENTThese recommendations for pre-

stressed concrete columns and wallsare written in a code format. In themain body of the recommendations,background details and suggestionsfor satisfying the requirements arenot included. Commentaries are in-cluded in selected sections for thepurpose of amplification of intent.There are 12 chapters in this Recom-mended Practice plus sections onnotation, selected references, a bib-liography and sample problems.

References citing research used indeveloping these recommendationsare included for the user desiring tostudy individual topics in greater de-tail. A bibliography listing additionalreferences related to prestressedconcrete column and wall design hasalso been included.An Appendix section contains nu-merical design examples (togetherwith design aids) to show how theprovisions of the report can be ap-plied in practice.

58

PREFACEThe provisions given in these recom-

mendations are intended to cover mini-mum requirements for the design ofprestressed concrete compressionmembers (columns and walls) in whichthe use of prestressing steel is of primeimportance to ensure their stability andstrength.

These recommendations supersede"Recommended Practice for the Design ofPrestressed Concrete Columns andBearing Walls," published in the PCIJOURNAL, V. 21, No. 6, November-De-cember 1976.

COMMENTARYThe development of prestressed con-

crete has led to the use of prestressedcompression elements: columns, wallsand piles. Prestressing a structuralmember designed to carry compressionmay seem contradictory because someof the capacity of the concrete is "usedup" by the application of the prestress-ing force. The effective prestress levelsin columns and walls seldom exceed 10percent of the concrete compressivestrength, and therefore, prestressing hasnegligible effect on the axial loadcarrying capacity. Often, prestressedcompression members, especially wallpanels, support low axial loads and highbending moments. In such cases, pre-

stressing may prove to be beneficial.The use of prestressing strands is muchmore economical than deformed rein-forcing bars in a precasting plant, andfurthermore the ACI Building Codewaives the minimum reinforcement re-quirement for prestressed compressionmembers. Under plant controlled con-ditions, it is less costly to increasemember capacity by increasing concretestrength than to increase capacity withadded reinforcement.

Columns and walls may have dimen-sions governed by architectural or firerating requirements and other condi-tions, such as thermal insulation or con-structability, not dependent on stabilityor stress. In such cases, manufacturersmay elect to prestress the elementsmerely to avoid cracking during trans-portation and erection, or for economyin manufacture. In such circumstances,members so prestressed are not properlyclassed as "prestressed columns."These recommendations (in particular,the minimum prestress of 225 psi) arenot intended to apply to those situations.Design should be based, instead, onACI 318-83, 1,2 which gives minimumsteel requirements.

This recommended practice, preparedby the PCI Committee on PrestressedConcrete Columns, updates the Com-mittee's previous documents.3•4


NOTATIONCm = a factor relating actual moment

diagram to an equivalent uniformmoment diagram

f% = dead loads, or related internalmoments and forces

E, = modulus of elasticity of concrete,psi

El = flexural stiffness of compressionmember

Eg = modulus of elasticity of rein-forcement, psi

f^ = specified compressive strengthof concrete, psi

= square root of specified compres-sive strength of concrete, psi

= compressive strength of concreteat time of initial prestress, psi

./p8 = stress in prestressed reinforce-ment at nominal strength

= moment of inertia of section re-sisting externally applied fac-tored loads

Ig = moment of inertia of gross con-crete section about centroidalaxis, neglecting reinforcement

k = effective length factor for com-

pression memberslu = unsupported height of compres-

sion memberL = live loads, or related internal

moments and forcesM, = factored moment to be used for

design of compression memberMia = value of smaller factored end

moment on compression mem-ber due to the loads that result inno appreciable sidesway, calcu-lated by conventional elasticframe analysis, positive ifmember is bent in single curva-ture, negative if bent in doublecurvature

M2b = value of larger factored end mo-ment on compression memberdue to loads that result in no ap-

preciable sidesway, calculatedby conventional elastic frameanalysis

M20 = value of larger factored end mo-ment on compression memberdue to loads that result in appre-ciable sidesway calculated byconventional elastic frameanalysis

n = ratio of modulus of elasticity ofsteel to modulus of elasticity ofconcrete = E 3 /E,

Pb = nominal axial load strength atbalanced strain conditions

P, = critical load (Euler)Pn = nominal axial load strength at

given eccentricityP o = nominal axial load strength at

zero eccentricityP„ = factored axial load at given ec-

centricity <OP,^r = radius of gyration of cross section13d = absolute value of ratio of maxi-

mum factored dead load momentto maximum factored total loadmoment, always positive

Sb = moment magnification factor forframes braced against sidesway,to reflect effects of member cur-vature between ends of compres-sion member

S S = moment magnification factor forframes not braced against side-sway, to reflect lateral drift re-sulting from lateral and gravityloads

71 = correction factor applied forstiffness accounting for P,,/Poratio

0 = correction factor for stiffness ac-counting for flanges of the crosssection

A = correction factor applied to thegross stiffness of cross section

= strength reduction factor

60

CHAPTER 1 -DEFINITIONS1.1 In addition to the definitions givenin Chapter 2 of ACI 318-83, the supple-mental definitions in Sections 1.2 to 1.6,herein, are for clarification.1.2 Beam-Column — Structural elementsubject to axial compressive loads incombination with flexure.1.3 Column — A vertical member inwhich the ratio of the larger overallcross-sectional dimension to the smalleris equal to or less than 3.0, and in whichthe height is greater than three times theleast lateral dimension.1.4 Flat Wall — A vertical member inwhich the cross-sectional ratio, definedin Section 1.3, is greater than 3.0, andthe section is of constant thickness inthe direction of the smaller dimension.

COMMENTARYThe previous committee report4 de-

fined the vertical members consideredhere as "thin" walls. A hesitation to usethe word flat existed because of its con-notations of expressing smooth, without

projection, horizontal, level or having nocurved surface. It is current industrypractice to speak of flat walls and thisterm will encompass walls that areslightly curved as used for fluid or solidmaterial storage.

1.5 Ribbed Wall — A vertical member inwhich the load is distributed betweenall or part of a flat wall section and amonolithic cast rib(s).1.6 For the purpose of these recommen-dations, the height of columns and wallsis defined as the vertical spanning di-mension and the length (width) of wallsis defined as the horizontal spanningdimension.

COMMENTARYIn developing these recommenda-

tions it was realized that the word"length" applied to a wall would nor-mally be associated with the plan di-mension; thus, the words "height" and"width" seem more appropriate.


CHAPTER 2- SCOPE2.1 These recommendations apply tocolumns and walls prestressed withhigh strength steel meeting the re-quirements for prestressing steels inSection 3.5.5 of ACI 318-83.2.2 All provisions of ACI 318-83 not spe-cifically excluded, and not in conflictwith the provisions of these recommen-dations, are to be considered applicableto prestressed concrete columns andwalls.2.3 The following provisions of ACI318-83 do not apply to prestressed con-crete columns and walls, unless specif-ically noted: Sections 8.4, 8.10.2, 8.10.3,8.10.4, 8.11, 10.3.2, 10.3.3, 10.5, 10.6,10.9.1, 10.9.2 and Chapters 13 and 14.2.4 Design formulas and permissiblestresses included in these recommen-dations are for concrete columns andwalls prestressed with bonded tendons.2.5 Columns and walls containing un-bonded tendons should be designed onthe basis of a rational analysis, or loadtest, in which the ultimate flexuralstrength of the member, including slen-derness effects, is properly taken intoaccount. In all cases where the serviceload is governed by tension, minimumbonded reinforcement in the precom-pressed tensile zone should be providedaccording to Section 12.7 of theserecommendations.

COMMENTARYAvailable research data do not permit

development of simplified empiricalprocedures for the design of columnsand walls with unbonded tendons. De-spite this shortcoming, the Committeebelieves that the use of unbonded ten-dons should not be discouraged. How-ever, design of such members should bebased on rational analysis or load test.

The requirement for minimumbonded reinforcement in Chapter 12 isincluded to prevent the formation, at theservice load level, of a single crack at thecritical sections.

2.6 The provisions of these recommen-dations apply to columns and wallswhich have a minimum average pre-stress, after all losses, of 225 psi on thegross section. Columns and wallsstressed to a lower nominal prestress,used to control cracking and to facilitatehandling, shall have minimum rein-forcement in accordance with Section10.9 of ACI 318-83 for columns and Sec-tions 11.10 or 14.3 of ACI 318-83 forwalls.

COMMENTARYThe requirement of a minimum aver-

age prestress of 225 psi is in conform-ance with Section 18.11.2 of ACI 318-83.The Commentary on Building Code Re-quirements for Reinforced Concrete2(ACI 318-83) also deals with this ques-tion in detail. Gross section propertiesmay be used in lieu of the uncrackedtransformed section properties. Struc-tural members in which prestress isadded primarily for handling conditionsdo not fall within the scope of this re-port.

2.7 When the slenderness ratio, klu/r, isbelow the lower bounds given in Sec-tion 8.1.6, the effects of column or wallslenderness may be neglected. Forthose members with slenderness greaterthan the upper bound in Section 8.1.6,the provision for approximate slender-ness evaluation with these recommen-dations is not allowed.

62

CHAPTER 3- GENERAL CONSIDERATIONS3.1 Prestressed concrete columns andwalls must be designed for all the forcesto which they are subjected and theirbehavior should be considered with re-spect to lateral displacement, end con-ditions, repetitive loading, axial short-ening, effects of creep, shrinkage, tem-perature changes, foundation settle-ment, cracking, construction or handlingloads and required strength.

COMMENTARYThe recommendations for the design

of members subject to axial loads andbending are in conformance with thegeneral requirements of Section 18.2 ofACI 318-83.

3.2 Consideration should also be given,where applicable, to requirements fordurability, fire resistance and, in thecase of walls, for watertightness and in-sulation. Requirements in Section 4.2and Chapter 5 of ACI 318-83 should beconsidered.3.3 Permissible stresses specified inthese recommendations may be ex-ceeded if the design strength of the col-umn or wall member is shown by test orrational analysis to provide theminimum load factors specified in ACI318-83 taking into account the propercapacity reduction factor, (A, and that theperformance will not be otherwise im-paired.

COMMENTARYThe purpose of the capacity reduction

factor is to account in part for: (a) inac-curacies in the methods of calculatingdesign strengths, (b) for variability of thedesign strength, (c) for the importance ofthe member in the structure and (d) forthe type of potential failure — whetherductile or brittle.

When the design strength has beendetermined experimentally, all but the

first of the factors listed above are stillpresent. Therefore, the observed meanstrength should still be reduced by thecapacity reduction factor before com-paring the code capacity with factoredload effects.

3.4 Members should meet the strengthrequirements specified in Chapter 9 ofACI 318-83. Special attention should begiven to load factors of the local juris-diction if different from those in ACI318-83.3.5 Design should be based on strengthand checked for behavior at various ser-vice load conditions that may be criticalduring the life of the structure from thetime the prestress is first applied.3.6 Strength design should be per-formed by rational analysis, consideringequilibrium of forces and compatibilityof strains, and based upon accepted val-ues for the mechanical properties of thesteel and the concrete.3.7 All cross sections should be de-signed for the applied axial compressiveload and the accompanying bendingmoment, with consideration of the slen-derness effects.3.8 Stresses due to prestressing andstress increases due to any change in thecross section should be considered inthe design.3.9 Where grouted tendons are used forprestressed columns or walls, the possi-bility of member buckling between thepoints where the concrete and theprestressing steel are in contact shouldbe considered during and after theprestressing operation and until thegrouting is complete and has achieved75 percent of its strength.3.10 The effect of local buckling of seg-ments of a wall member should be in-vestigated when evaluating the overallstability of the wall.

(see Commentary on next page)


COMMENTARYWall panel segments are generally

attached at discrete points which areintended to make the entire wall act asan integral unit. Local buckling of thewall, or buckling of the segment beforeit is integral with the rest of the wall,should be investigated.

3.11 In earthquake resistant structures, aportion of the steel, either prestressed ornonprestressed, should be bonded tothe concrete so that under design loadconditions, the critical sections willmeet the ductility requirements forseismic design as given in Appendix A,ACI 318-83.

CHAPTER 4- BASIC ASSUMPTIONS

4.1 The strength design of columns andwalls for flexural and axial forces shouldbe based upon the applicable assump-tions given in Sections 10.2, 10.3, 18.2and 18.3 of ACI 318-83, and shouldsatisfy conditions of equilibrium offorces and compatibility of strains.

COMMENTARYThe assumptions in Sections 10.2,

10.3, 18.2 and 18.3 of ACI 318-83 are

well accepted and the recommendationsin this report endorse these assump-tions. Repetition of these assumptions inthis chapter is not considered necessary.General requirements and designguidelines for prestressed concrete,outlined in Chapter 18 of ACI 318-83,should also be followed. Other back-ground information on the requiredstrength calculations can be found inthe bibliography at the end of thisreport.

CHAPTER 5- LIMITING DIMENSIONS5.1 The limiting dimensions for pre-stressed concrete columns and wallsshould be determined by taking into ac-count local and overall stability as wellas requirements for concrete placement,the effectiveness of lateral reinforce-ment (if required), steel protection, fireprotection and insulation.

COMMENTARYThe Committee believes that there is

no need to recommend a minimumthickness for walls or a minimum di-mension for columns. However, whenlateral ties are used in a member, theminimum practical column or wall di-mension for proper development of aclosed tie is about 8 in.

Designers of walls should considerthe practical limitations of fabrication,handling, concrete placement and fireprotection in selecting the thickness of awall panel. The Committee suggests apractical overall minimum wall thick-ness of 3 in.

5.2 Calculation of deflections should bein accordance with Sections 9.5.4.1 and9.5.4.2 of ACI 318-83.

5.3 The dimensions of columns andwalls should be such that, under serviceload conditions, nonstructural elementsattached to columns or walls would notbe damaged by lateral deflection andthe stresses in the concrete do not ex-ceed the stresses in Chapter 9.

64

COMMENTARYIn previous committee reports, provi-

sions were given for checking the lateraldeflections of the prestressed column orwall in order to establish the minimumsection under service load conditions.These provisions for service load de-flection calculations were eliminatedfrom this report because the permissiblestresses listed in Chapter 9 produce es-sentially a redundant calculation ofminimum section dimensions.

5.4 Calculated lateral deflections of pre-stressed concrete compression membersunder factored load should not exceedlu/100.

COMMENTARYA deflection limitation under factored

load was introduced because a P-Deltaanalysis can sometimes indicate largeand unreasonable deflections beforestability failure.

In calculating deflection, the nonlin-ear geometric and material properties of

a prestressed compression membershould be recognized. The nonlineareffect may be aggravated by an eccentricprestressing force and cracking. Guid-ance for calculating deflections can befound in the PCI Design Handbooks orreferences on stability of compressionmembers, 6-10

The Committee believes that deflec-tions should be checked under factoredload particularly in seismic areas wherestructural elements have greater poten-tial of being loaded to their ultimatecapacity and the probability of crackingis higher.

The Committee notes that it is lesslikely that prestressed columns and/orwalls subjected to wind loads wouldhave the section dictated by a deflectioncriterion.

The deflection limit is based on in-formation in a test report on slenderwalls."

5.5 Limits on compression memberslenderness are given in Section 8.1.6 ofthese recommendations.

CHAPTER 6- EFFECTIVEDIMENSIONS OF WALLS

6.1 For walls, the effective width (theportion of the wall to be considered aseffective) for design of members to ac-commodate each concentrated load ormoment should be determined by ra-tional analysis.In lieu of a rational analysis, the effec-tive width should not exceed:

a. The center-to-center distance be-tween loads;

b. The length of the loaded portionplus six times the wall thickness oneither side;

c. The width of the rib (in ribbed wallpanels) plus six times the thicknessof the wall between ribs on either

side of the rib; ord. 0.4 times the actual height of the

wall.The effect of local stresses in the vicin-ity of the applied load should be in-ye stigated.

COMMENTARYThe provisions in Section 6.1 are not

in conformance with Section 14.2 of ACI318-83, where the width of the wall tobe considered as effective for concen-trated loads is the width of the bearingplus four times the wall thickness. Atheory of elasticity solution to the effec-


tive width is given in Ref. 12. Othermore recent analytical studies, based onfinite element analysis, 13 have shownthat larger effective widths can be justi-fied. Likewise, recent research at theUniversity of Texas at Arlington indi-cates that even wider effective widthsare appropriate."

The use of greater effective widthsthan suggested here may result in localoverstressing (crushing) of the wallbelow the concentrated load.

This provision first appeared in theprevious committee report4 and has notproduced deficient designs to theCommittee's knowledge. This success-ful industry experience further justifiesthe liberalization.

6.2 If loading on the wall is uniform, thefull width can be considered effectivefor resisting axial load and moment.

COMMENTARYFull width section properties are

permitted by ACI 318-83 for precastelements subject to flexural loading andare logically extended here to includeaxial load.

6.3 When the noneffective portion of aribbed wall, excluded in Section 6.1c, is

carrying compressive load, the strengthand slenderness of the noneffectiveportion should be determined as for aflat wall without considering any sup-port from nearby ribs. This provisionmay be waived if shown by rationalanalysis or test that the ribs can providelateral support.6.4 The effective width of sandwichpanels should be the same as outlined inSections 6.1, 6.2 and 6.3 of theserecommendations. The effective thick-ness of a sandwich panel may be as-sumed equal to the thickness of theequivalent solid flat wall, provided thesandwich layers are connected by inte-grally cast ribs or adequate mechanicalshear connectors for full composite ac-tion. If the shear connection betweenwythes of a sandwich panel are less thanrequired for full composite action, theeffective thickness of the panel shouldbe taken as the thickness of only onewythe of the panel.

COMMENTARYIn the absence of published literature

or test results, the provisions of masonrycodes" pertinent to bonding and tyingof masonry wall wythes may be used as aguide in establishing adequate me-chanical shear connectors for full com-posite action.

CHAPTER 7-SLENDERNESS EFFECTS7.1 The design of compression membersshould be based on factored forces andmoments determined from an analysis ofthe structure. Such an analysis shouldtake into account the influence of axialloads and variable moments of inertia onmember stiffness and fixed-end mo-ments, the effect of deflection on mo-ments and forces, and the effects of du-ration of loads. The loads induced byprestressing should be considered witha load factor of 1.0.

7.2 In lieu of the procedure described inSection 7.1, the design of compressionmembers described in this recommen-dation may be based on the approximateprocedure for the evaluation of slender-ness presented in Chapter 8.

COMMENTARYThe use of second order (P-Delta)

analysis to evaluate slenderness is rec-ommended. 15-" The analysis is usually

66

done by calculating deflections usingelastic analysis methods, but with fac-tored loads. When using the P-Deltamethod, however, often difficult judg-ments are needed to estimate an appro-priate stiffness (EI). The P-Deltamethod for establishing member stabil-ity effects usually gives satisfactory re-sults in simple cases. However, whenthe loading cases produce loads andmoments that are close to the criticalstiffness value at cracking, the instabil-ity point may be missed by using an in-correct stiffness (EI) with the P-Deltamethod unless stiffness is continuouslyupdated. Therefore, the Committee en-courages the use of more sophisticatedmethods of analysis such as iterativecomputer programs fashioned after theprocedures outlined by Nathan. 18 Com-

mercially available computer programsexist for making the more sophisticatedanalyses.

Likewise, evaluating slenderness ef-fects using the approximate proceduresin ACI 318-83 for columns has shownthat Section 10.11 of ACI 318-83 rendersthe design of some prestressed columnsand walls unconservative. 19 This is par-ticularly true of sections that are un-symmetrical with respect to the axis ofbending, such as double-tee wall mem-bers.

Studies at the University of BritishColumbia by Nathan 18, 20, 21-23 with thePCI Committee on Prestressed Con-crete Columns serving in an advisorycapacity, form the basis of the recom-mendations for approximate evaluationof slenderness in Chapter 8.

CHAPTER 8- APPROXIMATE EVALUATIONOF SLENDERNESS EFFECTS

8.1 General8.1.1 The unsupported height 1,, of acompression member should be taken asthe clear distance between floor slabs,beams, girders, or other elements capa-ble of providing lateral support for themember.

COMMENTARYThe general procedure follows that of

ACI 318-83. Deviations from those pro-cedures will be noted and discussed.The designer must determine whichelements, such as bearing pads betweenstructural members, provide lateralsupport.8.1.2 Where column capitals orhaunches are present, the unsupportedheight should be measured to the lowerextremity of the capital or haunch in theplane considered.8.1.3 The radius of gyration r may betaken equal to 0.30 times the overall di-

mension in the direction in which sta-bility is being considered for rectangu-lar members, and 0.25 times the diame-ter for circular members. For othershapes, r may be computed for the grosssection considering the effective dimen-sions as defined in Chapter 6.

COMMENTARYIn the design of members for axial

load, Section 6.1 defines an effectivewidth for flanged cross sections. Whendesigning flanged members for pure flex-ure, 5 however, it has been customary touse the full width of flange. Thus, it isnot obvious what width should be usedin stability calculations.

The effect of including additionalflange area in these computations is toincrease the critical buckling loadand, therefore, reduce the momentmagnification factor. However, use ofthe effective widths defined in Sections


6.1 and 6.2 may be unduly conservativein certain cases.

If the radius of gyration is based onthe full width of the flanged section, r isgenerally smaller than that based on ef-fective width section properties. Con-sequently, the slenderness ratio will bemore conservative if the full width isused. Use of the full gross cross sectionfor members with small axial load, rela-tive to axial capacity, is usually appro-priate.

8.1.4 For members braced againstsidesway, the effective length factor kmay be taken as 1.0 unless an analysisshows that a lower value maybe used.

COMMENTARYThe commentary for ACI 318-83'

Section 10.11.2 describes equations andcharts that may be considered asanalytical justification fork less than 1.0.

8.1.5 For members not braced againstsidesway, the effective length factor kshould be determined with due consid-eration of the effects of cracking andreinforcement on relative stiffness, andshould be equal to or greater than 1.0.

COMMENTARYThe commentary for ACI 318-832

Section 10.11.2 describes equations andcharts that can be used to account forrestraint at the ends of the compressionmember.

8.1.6 For members braced againstsidesway, the effects of slenderness maybe neglected when kl,^ lr is less than[25 -10 (M, 6 /M, )]. For members notbraced against sidesway, the effects ofslenderness may be neglected whenkl/r is less than 15. For all memberswith kl„/r greater than 150, a rationalanalysis should be performed toevaluate slenderness effects.

COMMENTARYThe lower limits of slenderness stated

are less than those in ACI 318-83. Thereduction in the unbraced case followsthe trend set by the Canadian concretecode24 where all unbraced columns mustconsider slenderness. The approximatemethods in Section 8.2 have been em-pirically fit to slenderness as low as 25.

The analytical work1s used for theserecommendations showed that strengthreduction due to slenderness effects forprestressed columns and walls was sig-nificantly more than the ACI recom-mendations. Analytical studies haveclearly shown that the prestressedmember has greater strength reductionfor slenderness and is more sensitive toslenderness effects than the reinforcedconcrete columns considered by ACI318-83.

The upper limit of slenderness has in-creased from the previous committeereport because the slenderness equa-tions have been empirically fit to in-clude a slenderness of 150.21

8.1.7 For eccentrically prestressedmembers, consideration should begiven to the effect of lateral deflectiondue to prestressing in determining themagnified moment.

COMMENTARYThe eccentric prestressing force may

cause camber which must be taken intoaccount in computing the magnificationfactor.

It is conservative to underestimate theprestress losses due to causes other thanelastic shortening for such calculations.

8.1.8 The evaluation of the slendernesseffects by approximate methods is notrecommended for members having un-bonded prestressing tendons.

COMMENTARYThe Committee has limited informa-

68

tion on the behavior of column members as:having unbonded prestressing.25Therefore, the applicability of the ap-proximate method for this case is not yetverified.

8.1.9 In addition to Sections 8.1.1 to8.1.8 of this recommended practice,Sections 10.11.5 to 10.11.7 of ACI Code318-83 should apply to all designs per-formed by the approximate method.

8.2 Moment Magnification Factors8.2.1 Members subject to axial load andflexure should be designed using thefactored axial load P,, from a conven-tional frame analysis and a magnifiedfactored moment M, defined by:

MC = SbM2b + SSM23 (8.1)

C" > 1.0 (8.2)s6 1 – Pul p P,

COMMENTARY

El = Ecl9/X

(8.5)(1 +/3d)

X=i18,3.0 (8.6)

71 = 2.5 + 1.6 (8.7)

6 70

For cross sections without a compres-sion flange:

0 = (kl 7r) – 0.05 (8.8)

For cross sections with a compressionflange:

B(kl5r) – 0.09 (8.9)

1 _- 1.0 (8.3)S$ 1–,P../oEPC

and

`

_ r2EI

2PC (klu)

COMMENTARYThe general procedure for determin-

ing the design bending moment in anaxially compressed member follows ACI318-83. A detailed description of theterms and the commentary pertaining tothese provisions are not repeated herebut can be found in ACI 318-83 and itscommentary. 12 Subscripts "b" and "s"represent braced and sway (unbraced)frames, respectively. For sway framesthe effect of story stability must bechecked. The 8, computed is for the en-tire story based on the use of 1P„IIP,.

8.2.2 In lieu of detailed analytical cal-culations, EI in Eq. (8.4) may be taken

Provisions for calculating EI havechanged significantly since the previouspublication of this recommended prac-tice. 4 Development of the EI equation isbased on analytical studies conductedby Nathan. 1 ' The equation for EI is abest fit of analytical results for pre-stressed concrete columns and wallpanels. The equations are intended toapply to members where the averageprestress is equal to or greater than 0.50Jr,.

In the commentary to ACI 318-83, it isnoted that the EI values were derivedfor columns with relatively large ratiosof P. /P o and for column loads above thebalance point of the interaction diagram(Pb). In a prestressed member, particu-larly in a lightly reinforced wall panelwith a wide compression flange, it isknown that these members have evenhigher \ allies of P,,IP„ than reinforcedconcrete columns. Because the normaldesign range values of P,,/Po in a pre-stressed column are considerably lowerthan those for the reinforced concrete


100 f^r71= 2.5+P^/PQ 80/

6 ^ r1 70 60

40 lfor P, equation: $0

El = E I,/X 4^1 +(3d

20700

10 fY

8 ^S^ EEE6

(a) Compression flange 4O=--0.09 0.09

Fig. 8.1 2P„/Po

10080 fe/

60 ^,S

40

SO

20 i

10\fPi^ 7^S8

^6

(b) No compression flange 4-------

0 ke^r - 0.05

Fig. 8.2 2 0.02 .04 .06 .08 .10 .14 .20 .30 .40 .50P„/Po

Coefficients, A, for modified El70

column, the need to modify the ACI 318provision existed. The difference in EIfor the prestressed column and thereinforced column were significantenough to develop unique EI equationsfor the prestressed column.

In order to retain the form of theequations used in ACI 318-83, it wasnecessary to include the effect of thestrength reduction factor 4) and thelong-term load factor 13d into Eqs. (8.7),(8.8) and (8.9) because Eqs. (8.2) [or Eq.(8.3)1 and (8.5) did not properly accountfor their influence. The 0 and jed factorswere included in X because the mo-ment-curvature diagram for a pre-stressed column or wall is significantlydifferent than the typical reinforcedconcrete column that was used to de-velop the ACI stiffness equations.

Nathan's 1985 paper' s provides addi-tional discussion of this matter.

Design aids for determining A areshown in Figs. 8.1 and 8.2.8.2.3 For members braced against side-sway and without transverse loads be-tween supports, C m in Eq. (8.2) may betaken as:

C m = 0.7 + 0.3 (Mlb /M2b) > 0.4 (8.10)

For all other cases, C m should be takenas 1.0.

COMMENTARYAnalytical studies by Nathan 19 have

indicated that the above expression is abetter fit for the bending moment dis-tribution coefficient in Eq. (8.2) thanthat in ACI 318-83 Eq. (10-12).

CHAPTER 9- PERMISSIBLE STRESSES INCONCRETE AND PRESTRESSING STEEL

9.1 Procedures for investigating stressesat transfer of prestress, at service load, atany other loading condition during han-dling, or under service conditions dur-ing the life of the member should bebased on the design assumptions givenin Section 18.3 of ACI 318-83.9.2 Computed flexural stresses in a pre-stressed compression member shouldnot exceed the limits in ACI 318-83Section 18.4.1 for transfer and Section18.4.2a and b for service loads. Section18.4.2c is not applicable. If exposedsurfaces are to remain free of discerniblecracks, the allowable tensile stresses innormal weight concrete should not ex-ceed5 f,.

COMMENTARYStresses in the prestressed column or

wall are not allowed to exceed the limi-tations specified in Sections 18.4.1 and18.4.2a and b of ACI 318-83 nor is the

waiver clause of ACI 318-83 Section18.4.3 permitted. Slender prestressedcolumns and walls can be sensitive toinitial crookedness and cracking andsince ACI 318-83 does not specificallyaddress these items, the rigid restric-tions on stress limitations in the con-crete are recommended by the Com-mittee.

Permissible stress limitations must becompared to stresses caused by load in-cluding the effects of secondary bendingmoment. Service load stress calculationsare based on elastic behavior; therefore,the cross section must remain essen-tially uncracked and linearly elastic. Anincrease in allowable stresses due towind or any incidental load is not al-lowed.

If lightweight aggregate concrete isused, the allowable stress should bemodified with the factors in ACI 318-83Section 11.2.1.2.


9.3 Permissible stresses in Section 9.2 COMMENTARYd f h dl'should not be exceede or an mg,

transportation or erection. If themember is designed to carry tensionwithout cracking under service condi-tions, the member should not be al-lowed to crack under handling, trans-portation or erection.

Handling and storage conditions mustnot be conducive to causing permanent,nonrecoverable deformations.

9.4 Permissible stresses in the pre-stressing steel should be in accordancewith Section 18.5 of ACI 318-83.

CHAPTER 10- BEARING STRESSES10.1 In calculating bearing stresses, theaverage prestress in the vicinity of theloaded area at the time of loading shouldbe taken into consideration in additionto the design bearing stresses under theloaded area.

COMMENTARYThe contact area between supporting

and supported structural elementsshould be checked to ascertain that localcrushing of concrete does not occur.When the contact area occurs at the topof a prestressed column, or especiallyalong the top of a flat prestressed wallpanel, the possibility of local crushing inthe vertical (supporting) element ishigher than in the horizontal (sup-ported) element because of the addi-tional stresses caused by the transfer ofthe prestressing tendon force.

10.2 The design compressive bearingstrength of concrete should be in accor-dance with Section 10.15.1 of ACI318-83 and the PCI Design Handbook,Third Edition.

COMMENTARYBearing strength calculated using ACI

318-83 deals only with the load appliedperpendicular to the bearing supportsurface, while the PCI Design Hand-book5 includes loads applied parallel tothe support surface.

10.3 When the bearing strength is ex-ceeded in a member, reinforcementshould be provided in accordance withrecommendations in the PCI DesignHandbook, Third Edition.

10.4 Panels or columns should be rein-forced for horizontal tensile forces,nominally perpendicular to the direc-tion of the concentrated gravity load,with an additional area of steel in ac-cordance with the PCI Design Hand-book, Third Edition.

COMMENTARYAxial tension caused by restrained

shrinkage should be accounted for byplacing reinforcement in the direction ofthe tensile force and/or perpendicular tothe potential crack. This additionalreinforcement is particularly importantto avoid accidental spalling and crackingat the ends of thin stemmed members.

10.5 Post-tensioning anchorages shouldbe reinforced in accordance with ACI318-83 Section 18.13. Reinforcementrequired to resist stresses in the con-crete due to prestressing strands or ten-don anchorages should be additive tothe reinforcement required for the de-sign loads in Section 10.3.

COMMENTARYReinforcement in the concentrated

load areas of a member is intended to

72

resist bursting, horizontal splitting and be impaired.spalling forces.26

10.6 Concentrated loads should not belocated at or in the vicinity of post-ten-sioning anchorages, unless it is shownanalytically or experimentally that theperformance of the anchorage will not

COMMENTARYThis provision emphasizes the neces-

sity of considering external load inaddition to the high localized stressesfrom the effect of the anchorage.

CHAPTER 11 - SHEAR

11.1 The nominal shear strength of pre-stressed columns and walls should bebased on provisions in Sections 11.1,11.2, 11.4, 11.5, 11.10 and 11.11 of ACI318-83.

COMMENTARYPrestressed columns should be de-

signed for shear in the same manner asprestressed beams, i.e., by ignoring theinfluence of axial load.

Perpendicular to the plane of a flatprestressed wall, shear should be con-sidered as for slabs and footings. Shearforces parallel to the plane of a flat pre-stressed wall should be consideredunder the provisions for shear walls.

For the rare case of two-way pre-stressed walls, the design for shear inthe plane of the wall may be based onsuperimposing the effects of the verticaland horizontal prestressing. An approxi-mate method can be found in Section

11.3.2 of the 1976 committee recom-mendations.4

Specific recommendations for con-sidering the effects of torsion on a pre-stressed compression member have notbeen thoroughly researched. Combinedshear and torsion of prestressed mem-bers 27 is not covered by ACI 318-83 butshear and torsion design for flexuralmembers is considered in the ThirdEdition of the PCI Design Handbook.5The Committee knows of no researchrelating to the behavior of prestressedcolumns subject to torsional loads or thatspecific problems with torsion in a col-umn presents a common design situa-tion.

If combined axial load, shear and tor-sion exist in a prestressed column, theCommittee recommends designing themember as a prestressed concrete beam.Suggested design procedures for shearand torsion can be found in the PCI De-sign Handbook.

CHAPTER 12- REINFORCING DETAILS OFPRESTRESSED CONCRETE COLUMNS AND WALLS

12.1 General Reinforcing Details12.1.1 Structural details of prestressedand nonprestressed reinforcementshould conform to Chapter 7 of ACI318-83 except as modified by these pro-visions.

12.2 End Regions12.2.1 Reinforcement in the end anchor-age zone of the member should be inaccordance with Section 18.13 of ACI318-83.12.2.2 End anchorage zone reinforce-


ment is not required in post-tensionedconstruction if the average bearingstress beneath the anchor is less than 0.5

COMMENTARYThese provisions are generally ap-

plicable to post-tensioned concrete con-struction. Bearing stresses of less thanhalf of the concrete strength directly be-neath the anchor plate of post-tension-ing tendons do not need supplementalreinforcement to resist bursting orspalling forces induced by the tension.Concentrated bearing stresses of thismagnitude have a negligible effect onuntied reinforced concrete columns.

12.3 Limits of LongitudinalReinforcement12.3.1 All prestressed columns and wallsmeeting the requirements of Section18.11 of ACI 318-83 may be designed asprestressed members.

12.3.2 Prestressed flat wall panels andribbed wall panels may have the mini-mum reinforcement requirements ofACI 318-83, Section 14.3, waived.

12.4 Lateral Reinforcement12.4.1 Lateral reinforcement require-ments for prestressed columns shouldconform to ACI 318-83 Section 18.11.2.2except Section 18.11.2.2a may bewaived for prestressed columns.

COMMENTARYThe previous edition of this recom-

mended practice 4 required that axialload capacity be multiplied by 0.85when lateral ties were not provided in aprestressed column. Recent research14•28has shown no justification for this re-duction. Ties do not lead to a significantincrease in column capacity at peakloads, do not necessarily limit columndeflections at peak loads, and do notconsistently influence the ability to

sustain deformations on the descendingbranch of the load-deflection curve.These conclusions apply to columnswhen stability, rather than material be-havior, governs load capacity.

Lateral reinforcement should be con-sidered for relatively short, stocky col-umns where axial load is high, andwhere member shear force is significant.

12.4.2 Lateral reinforcement in the formof rectangular continuous spiral rein-forcement may be substituted for indi-vidual lateral ties if the spiral has an areaequivalent to that of ties spaced in ac-cordance with ACI 318-83 Section18.11.2.2b and 18.11.2.2c.

COMMENTARYPrestressed piles use continuous

square spirals as ties and the typicalspacing exceeds that of round spirals.

12.4.3 Lateral reinforcement require-ments for prestressed ribbed wallsmeeting the requirements of Section12.3.1 may have the lateral reinforce-ment requirement waived if the nominalcapacity is multiplied by 0.85.

COMMENTARYRibbed wall panels often use the

thickened rib as a column. This type ofwall panel is frequently designed with alarge slenderness and eccentricity. Thefact that lateral ties are not typicallyused in wall panels is cause for makingthe factor of safety higher than normal.ACI 318-83 Section 18.11.2.3 has al-ready waived the minimum reinforce-ment requirement in Section 14.3 for aflat wall but does not indicate thiswaiver applies to ribbed walls.

If the rib in a ribbed wall panel isused as a column, the designer shoulddetail the rib as for a column. However,when the entire panel is considered as acompression member, the lateral rein-forcement requirement may be waived

74

if the nominal axial capacity is multi-plied by 0.85. This multiplying factoreffectively increases the factor of safetyas for an unreinforced concrete wall.

Minimum lateral reinforcement maybe needed to improve ductility if shearand torsion are sufficient to causecracking of the ribbed wall.

12.5 Two-Way Prestressing12.5.1 Where two-way prestressing isused in walls, no additional horizontalreinforcement is required if the hori-zontal prestress, after losses, is at least150 psi.

12.6 Special Reinforcement12.6.1 Prestressed flat wall panelsshould have perimeter deformed barreinforcement near the panel free edgesparallel to the direction of the axial pre-stress. Anchorage for this deformed barreinforcement should extend a mini-mum of 24 in. perpendicular to the pre-stress direction at the longitudinal panelends. These extensions should be con-sidered for the deformed bar reinforce-ment only and not as providing rein-forcement in the anchorage zone.12.6.2 The stipulation in Section 12.6.1may be waived if prestressing steel isplaced along the sides within 0.75 of thewall thickness from the edge; exceptthat in such a case, confinement steel, inthe form of mesh or cross-reinforcementtransverse to the prestressing steel,should be evenly distributed over a 24

in. length at each longitudinal end of theedge tendons.

COMMENTARYThis reinforcement has been found to

be necessary to control cracking duringhandling and transportation, and to helpwith end block stresses. When the pre-stressing steel is placed near the longi-tudinal panel edges, confinement steelis required over a 2 ft length at each endof the tendon to guard against longi-tudinal splitting.

12.6.3 Reinforcement should be pro-vided in the end anchorage zoneperpendicular to the prestressing steelof all flat type wall panels unless experi-ence has shown this reinforcement canbe eliminated.

COMMENTARYIn order to control cracking parallel to

the prestressing in the end anchoragezone, a minimum area of steel should beuniformly distributed in the transferlength of each layer of prestressingsteel.29

12.7 Minimum BondedReinforcement for UnbondedPrestressing12.7.1 Minimum area of bonded rein-forcement for members with unbondedtendons should be in accordance withACI 318-83 Section 18.9.


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88. Zia, P., and Andrew, J. R., "UltimateStrength of Rectangular PrestressedConcrete Columns Under Concentricand Eccentric Loadings," North CarolinaState University, Raleigh, September1967.

89. Zia, P., Andrew, J. R., and Chawla, M. S.,"Prestressed Concrete Columns UnderConcentric and Eccentric Loadings,"North Carolina State University, Raleigh,July 1969.

90. Zia, P., and Guillermo, E. C., "CombinedBending and Axial Load in PrestressedConcrete Columns," PCI JOURNAL, V.12, No. 3, June 1967, pp. 52-59, Discus-sion by Laszlo, G., Nathan, N. D., andAuthors, PCI JOURNAL, V. 12, No. 6,December 1967, pp. 77-88.

91. Zia, P., and Moreadith, F. L., "UltimateLoad Capacity of Prestressed ConcreteColumns," ACI Journal, Proceedings, V.63, No. 7, July 1966, pp. 767-788.

92. Elias, Hani E., and Durrani, A. J., "Con-finement of Prestressed Concrete Col-umns," PCI JOURNAL, V. 33, No. 3,May-June 1988, pp. 122-141.

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

80

APPENDIX - DESIGN EXAMPLESThe following two design examples

show how some of the provisions con-tained in the report can be applied. Thefirst example treats slenderness effectsfor precast prestressed ribbed wallpanels and precast prestressed columns.

EXAMPLE 1This design example considers slen-

derness effects using moment magnifi-cation for precast prestressed ribbedwall panels and precast prestressed col-umns.Given: The structure shown is theinterior portion of a long building that isisolated from the remaining structure byexpansion joints, creating an unbraced(sway) frame.

A structural frame analysis gives thefollowing service load data:

Each wall panel D

Axial load (kips) 14.4Top bending moment

(kip-ft) 9.6Bottom bending moment

(kip-ft) 4.2

*I lange of tee wall panel in compre:

Each column D L W

Axial load (kips) 115.2 57.6 0Top bending moment

(kip-ft)t 0 0 0Bottom bending moment

(kip-ft) 0 0 3.0

tPinned

60'

all panels16'

LperbayLT— shear resistance

The second example covers the designof slender wall panels.

Reference to the PCI Design Hand-book, PCI Column Committee report orACI Code are given in the right handmargin alongside the calculations.

Wall panel properties (from PCI DesignHandbook, Third Edition):A = 401 in. 2 ; I = 20,985 in.' p. 2-17

_ 20,985 7.23 in.r 4014)P0 = 1165 kips; 4) = 0.7Po = 1165/0.7 = 1664 kips p. 2-5

Note that loading is uniform on wallpanel. Therefore, full section is effec-tive. 6.2f,' = 5000 psi, E, = 4,300,000 psiColumn properties (from PCI DesignHandbook, Third Edition):A = 576 in. 2 ; I = 27,648 in.'

27,648r = 6.93 in. p. 2-55

5764)P0 = 1325 kips; 0 = 0.7Po = 1325/0.7 = 1893 kips p. 2-48f,' = 5000 psi, E, = 4,300,000 psi

Problem: Find the magnified momentsfor the wall panels and columns andcheck loads against design capacity.

Solution: Use following procedure.Wall Panel:• Case 1 (Dead + Live Loads) Gravity

ACI 318-83 9.2.1

60'

1-24 x 24 P/S column each bay

8DT24 wall panelsslab isolation joint around column

L W

7.2 0

4.8 0

2.1 17.0*

Sion


P,, = 1.4(14.4) + 1.7(7.2) = 32.4 kips Cm = 0.7 + 0.3 (9.5/21.6)M2 (top) = 1.4(9.6) + 1.7(4.8) = 0.83

= 21.6 kip-ftM , (bottom) = 1.4(4.2) + 1.7(2.1) Calculate Euler buckling load [Eq.

= 9.5 kip-ft (8.4)]: 8.2.1

Larger end moment (M2 ) occurs at top o Pc = it2EI

wall panel. Therefore, use M2 to deter- (klu)2mine fad. a .2 (649,195)

_ Factored dead load moment,8d 8.2.2

_

[(1.0)(16)(12)]2Factored total moment

1.4(9.6) = 173.8 kips=

1.4(9.6) + 1.7(4.8)Determine 0 at magnitude of factored

= 0.62axial load: ACI 318-83

(9.3.2)Calculate magnified moment: = 0.7 at P, = 0.1 f, A9

Since axial loads on this structural frame = 0.1 (5.0)(401)are symmetrical and do not contribute to = 200 kipssidesway, the value of k can be taken as1.0 and 83 M2 = 0. 8.2.1 =0.9atPu=0

klu _ (1.0)(16)(12) = 0.9 - 0.2 (32.4/200) = 0.87r 7.23 Calculate moment magnifying factor

= 26.6 > 25 - 10 (Mlb /M25 ) 8.1.6 [Eq . (8.2)]: 8.2.1Therefore, consider slenderness.Pu lP, = 32.4/1664 = 0.02 sb = 1- 1.0

From Fig. 8.1 or Eqs. (8.6), (8.7) and(8.9): 8.2.2 __ 0.83A= 7) 0 > 3.0 1-32.4/0.87(173.8)

1.6^ = 2.5 + = 1.06

Pu/Po Calculate magnified moment [Eq. (8.1)]:

= 2.5+ 1.6 8.2.10.02 MI = db M2b + 38M28

= 82.5 > 70 (use n = 70)= 1.06(21.6) + 0

0 = 35 - 0.09 = 22.8 kip-ftklu/r

• Case 2 (Dead + Live + Wind Loads)= 35 - 0.09 AC 1318-83

26.6 9.2.2= 1.23 Wind load contributes to sidesway.

X = 70(1.23) = 85.8 Since the bending moment at the top is

Calculate stiffness [Eq.ss [ q. (8.5)1: 8.2.2not affected by wind, the only momentsthat can be magnified by sidesway are

El = E,I,/X the bottom moments.1 + /3d P = 0.75 [1.4(14.4) + 1.7(7.2) + 1.7(0)]4300(20,985)/85.8 = 24.3 kips

1 + 0.62 Bottom moments:= 649,195 kip-in. 2 M25 = 0.75 [1.4(4.2) + 1.7(2.1)]

Calculate coefficient for end moment = 7.1 kip-fteffect [Eq. (8.10)]: 8.2.3 M2s = 0.75 [1.7(17)]C m = 0.7 + 0.3 (Mlb/M2b) 0.4 = 21.7 kip-ft

82

or

= 0.9(14.4) + 1.3(0)

= 13.0 kips

M2b = 0.9(4.2)

= 3.8 kip-ft

M23 = 1.3(17)

= 22.1 kip-ft

To find large end moment at bottom,calculate sustained load factor:

/3 db = 0.62 (see earlier calculation) 8.2.2

Ads- 0

Determine unbraced effective lengthfactor using Jackson-Moreland align-ment chart. Fixity at base of wall panel(lJA ) is approximately equal to the ratioof length of panel above to below floor:

8.1.5

q'A = 16/3 = 5.3

For top of column that was assumed aspinned:

qjR = 10 (max)

k = 2.6

kl u/r = 2.6(16)(12)/7.23 8.1.6

= 69 > 15

Therefore, consider slenderness

Ps/Po = 24.3/1664= 0.015

From Fig. 8.1 or Eqs. (8.6), (8.7) and (8.9):

X=29 8.2.2

Calculate stiffness for braced loads[Eq. (8.5)]: 8.2.2

(F.I) b = E,I0IX

I + Ndb

_ 4300(20,985)/291+0.62

= 1,920,721 kip-in.2

Calculate coefficient for end momenteffect (braced): 8.2.3

C m = 0.83 (see earlier calculation)

Calculate Euler buckling load (bracedcase) [Eq. (8.4)]: 8.2.1

(Pc) 1r2EIb =

(kblw)2

7r2 (1.92n_721 )

[(1)(16)(12)]`= 514 kips

Determine 0 for axial load (braced case):

= 0.9 - 0.2(24.3/200) ACI 318-83= 0.88 9.3.2

Calculate moment magnification factor- braced case moments[Eq.(8.2)]: 8.2.1

8 _ C.

° 1 - P„/ 4)P.

0.831 - 24.3/0.88(514)

= 0.88 (use 1.0) 8.2.1

Calculate stiffness for sidesway loads[Eq. (8.5)]:

(EI) s = E,I0/A

8.2.11 + Rds

_ (4300)(20,985)/291+0

= 3,111,569 kip-in.2

Coefficient for end moment effects -sidesway case 8.2.3

Cm = 1.0

Calculate Euler buckling load - side-sway case [Eq. (8.4)]: 8.2.1

(Pa ). = 7r2EI

(k.plu)2

_ 172 (3,111,569)[(2.6)(16)(12)] 2

= 123.2 kips

Determine 0 for sidesway case axialload.Base 0 on I P,{ and I (0.1)A gf .

ACI 318-839.3.2

Calculate moment magnification factor- sidesway case [Eq. (8.3)] : 8.2.1

11- lPul4 1PC

Note: 8, for wall panel needs P. and P. forcolumn. Hold 8, calculation for columninformation.


Column• Case 1 (Dead + Live Loads) GravityPa = 1.4(115.2) + 1.7(57.6) ACI 318-83

= 259.2 kips 9.2.1M2 = 0

M, = 0/3a = 0 8.2.2

'fake k = 1.0, i.e., no bending momentsto magnify.

kl,,/r = (1.0)(16)(12)/6.93= 27.7 > 25 - 10 (M 1 /M2 ) 8.1.6

Since kl/r is close to the limit to neglectslenderness, ignore slenderness forCase 1 loading.

• Case 2 (Dead + Live + Wind Loads)ACI 318-83

9.2.2

P„ = 0 . 75[1.4(115.2)+ 1.7(57.6)+ 1.7(0)]

= 194.4 kips

M26 = 0.75 [1.4(0) + 1.7(0) + 1.7(0)]=0

M2s = 0.75 [1.4(0) + 1.7(0) + 1.7(3.0)]= 3.83 kip-ft

or

PP = 0.9(115.2) + 1.3(0)= 103.7 kips

M2b = 0.9(0) + 1.3(0)=0

M2s = 0.9(0) + 1.3(3.0)= 3.9 kip-ft

Determine effective length usingalignment chart. Base fixity taken to besufficient for: 8.1.5

(Irbase = 1.0; ([i0,, = 10.0 (pinned)

k = 1.9 (see alignment chart)

kl.a/r = 1.9(16)(12)/6.93=52.6>15 8.1.6

Therefore, consider slenderness.

PJI PO = 194.4/1893= 0.10

From Fig. 8.2 or Eqs. (8.6), (8.7) and(8.8):X = 8.6 8.2.2

Calculate stiffness for sidesway loads[Eq. (8.5)]: 8.2.2

(EI), = EcIg/X

1 +/3d_ 4300(27,648)/8.6

1+0

= 13,824,500 kip-in.2

Calculate coefficient for end momenteffect- sidesway case: 8.2.3Cm = 1.0

Calculate Euler buckling load - side-sway case [Eq. (8.4)1: 8.2.1

(P^)S = ar2El

(1-1 \

_ v.2 (13 824500)[(1.9)(16)(12)]2

= 1025 kips

Calculate moment magnification factors:8.2.1

8b = 1.0

1S S =

1-

Assuming eight wall panels:

I (Pa ), = 8(24.3) + 194.4= 388.9 kips

I (Pa ), = 8(123.2) + 1025= 2010.6 kips

Determine 0 for sidesway case:ACI 318-83

9.3.2= 0.9 - 0.2 (1 Pa/I.0.1 A af, )

= 0.9 - 0.2 {388.9/(0.1)(5)[8(401)+ 576] }

= 0.86

Calculate moment magnification factors:8.2.1

6s(wali) = 5s(column)

1

1-1Pn/4 P,

1

1 - 388.9/0.86(2010.6)= 1.29

84

Summary of bending moments and magnification factors.

Case 1 Case 2

Building M28 M2, M2b, M2s

component 5 6 (kip-ft) S,. (kip-ft) (kip-1i) SS (kip-ft)

Wall panel 1.06 21.6 0 () I .0 7.1 1.29 21.71.0 3.8 1.29 22.1

Column 1.0 0 1.0 0 1.0 0 1.29 3.81.0 0 1.29 3.9

Summary of magnified moments (M, = SbM25 +S 3M2s ) and axial loads.

Case I Case 2

Pu .11, P Jl,.Buildingcomponent (kips) (kip-ft) (kip) (kip-ft)

32.4 22.8 a) 24.3 35.1Wall panel or

(h) 13.0 32.3

259.2 0 (a) 194.4 4.9Column or

(b) 103.7 5.0

A summary of the bending moments andmagnification factors of the wall panel/column system for Cases 1 and 2 isshown in the table above. Similarly, asummary of the magnified moments and

axial loads for Cases 1 and 2 is alsoshown.See interaction diagrams for comparisonof applied loads to design capacity.The selected members are satisfactory.

PCI JOURNALJJuIy-August 1988 85

Wall Panel 100^1=2.5+ Pl PoCase1 80 P!^

6<—i70 60

for Pc equation:40

SOWall PanelEo ls/X Case 2 4,

EI = t+p, x20 f^

10 ^P ^^S

8 DSO

6

(a) Compression flange4

8 35 0.09 k r

Fig. 8.12 P/Pa

100

80

60 ` ?S

40

20 Pi>S

^Pw

Column_____

8

6

(b) No compression flange 4

0=0.05

Fig.8.2 20.02 .04 .06 .08 .10 .14 .20 .30 .40 .50

P„/Po

Coefficients, A, for modified El

86

8 • .0"5.75" îT

2" hlBDT21 only }

Jk=4,-0"L 3.75"

V' = 5000 psi, normal weightstrand = 1/2" dia., t = 270 ksi

Markhin.

tIn.

No.strd.

Full Interaction Curve Data

Partially DevelopedStrand Force

Fully DevelopedStrand Force

d.P. 4,P, 5M,,, 4rMo 4,P,,, 4eM,,, 4DM,,

8DT12 12 2 4 826 549 107 41 509 120 71

80T13 13 3 4 1111 799 130 47 767 145 83

80T16 16 2 4 939 592 175 55 553 193 95

80T17 17 3 4 1224 839 209 61 800 230 107

8DT20 20 2 4 1052 637 254 68 598 277 120

80T21 21 3 6 1324 853 301 91 812 327 159

80T24 24 2 4 1165 684 344 82 644 371 145

Partially developedstrand

N ^ V) nQ ^N00 Co QÎ O

Case 1 ' tiaCase a '

Cose2b

0 20 40 60 80 100 120 140 160

4M, ft-kips per unit

80

60

7a d$a

0 40

Y

20

Fully developed '

strand ' ' '

N MI Î o ^N '

F- F- ^-0 I m1

Ctm fCase1 m° a

Case2 'I I / i--- — lCase 2 b

0 20 40 60 80 100 120 140 160

4M, ft-kips per unit

80

60

C

$ ° 40as

20

Partial interaction curve for prestressed double tee wall panels

PCI JOURNAL/July-August 1988

87

Criteria1. Minimum prestress = 225 psi2. All strand assumed 1/2 in. diameter,

f u = 270 ksi3. durves shown for partial development of

strand near member end, where fps f.4. Horizontal portion of curve is the maximum

for tied columns = 0.800P05. 0=0.9forOP.=0

= 0.7 for ØP0 > 0.10fcA9Varies from 0.9 to 0.7 for points between

NotationOPr, = Design axial strength¢M„ = Design flexural strengthOP0 = Design axial strength at zero ecentricityA 9 = Gross area of the columnS = Moment magnifier (Sect. 10.11, ACI 318-83)

v

x + x

Y ice- 2-1/2" typ.(Assumed fordesign)

2400

2100

1800

1500

a

1200a`

900

600

300Case 1

Case 2b^

24 x 24• 8 strands

BoOo

Ôt> °O

a

\

f

AS

Partial .%development

Ca e 2a ^Fulldevelopment

0 100 200 300 400 500 600 700

(M rn , ft-kips

Design strength interaction curves for precast, prestressed concrete columns

88

OA k 4a 4a k _ J a

50.0 1.010.0

50.010.0 100.0 10.0 100.0

5.0 5.050.030.0- 5.0

50.030.0

3.0 0.9 3.0 20.0- 4.0 20.02.0- -2.0

10.0 3.09.0- 7

10.09.0

1.0 0.8 1.0 8.0- 26• -" //g: 8.06.00.9 0.9 - _ /0.80.7

0.80.7

-5.0 / 5.0

0.6 -0.7 -0.6 4.0- ?20 4.00.5 0.5 3.0 / 3.0

0.3- -0.3- 2.0- c^% 2.00.6 Goy/ 1.5

/0.2 0.21.0- 1.0

0.1- -0.1

0 0.5 0 0 1.0 0

(a) (b)

Braced frames Unbraced frames

= If connection is rigid, ratio of SK of compression members to _K of flexural members ina plane. For typical precast connections usually assumed as pinned in analyses, I maybe taken as 10. Lower values may be used if justified by analysis. For example, d' atfootings may be equal to KK b as calculated in Sect. 3.8.3.

k = effective length factor

Alignment charts for determining effective length factors

PCI JOURNAUJuly-August 1988 89

EXAMPLE 2This example covers the design of slen-der wall panels.Given: Precast prestressed wall panelsenclose a single story building.The following design parameters relateto the proportioning of the prestressedwall panel.— Roof dead load = 0.3 kips per ft of

wall— Roof live load = 0.25 kips per ft of

wall— Eccentricity (e) of load at top of wall

= 6 in.—Structural frame assumed braced:

k=1— Concrete strength: f,' = 5000 psi— Concrete modulus: E, = 4.3 x 10 6 psi— Wall prestress: f9 = 250 psi ('/is in. di-

ameter 270 kip strand at 12 in. oncenter)

— Lateral loads:Seismic: Zone 2Wind: Basic 80 miles per hr;Exposure B; Enclosed

Wall panel properties: 6 x 12 in. widesection properties.A,= 6x12=72in.2Ig = 12(6) 3/12 = 216 in.'r = J216/72= 1.73 or 8.1.3[0.3x6= 1.80 in.]Panel weight = (6/12)(150)

=75psf=Wp

Panel has an outward initial bow of 1/2 in.(assumed fabrication tolerance).

Problem: Find the magnified momentsin the wall panel using a second orderdeflection analysis and by the momentmagnification procedure. Check thepanel for deflection and cracking.

Determine governing loadingLateral load (use Uniform BuildingCode)— Wind suction:

q, = 17psfp = CeCegsI

= 0.8 x1.2x17x1= 16.32 psf _- 17 psf

— Seismic:Fp = Z I C9W9

= 3/8xIx0.3x75= 8.44 psf

Wind load governs: 17 psf > 8.44 psf

Analysis:— Check effective width of panel 6.1

• Center to center spacing of loads =36 in.

• Load width plus 6 x thickness eachside 6 + 6(6) + 6(6) = 78 in.

• 0.4 x wall height0.4(22.5)(12) = 34.9 in. (controls)

Use 36 in. as effective width. Do all cal-culations based on 12 in. wide section.

(Pwa t ) o = [2 + (22.5/2)175= 994 psf (use 1.0 kip)

(half of panel weight causingP - 0 moment)

— Load factors:• Case 1—U,= 1.4D+ 1.7L

BEARING WIDTHOF 6"ON WALL

ROOF JOIST AT 3 FT. O.C.2-0

6"THICK GIRDERS

PANELS22-6 8F1. WIDE

COLUMNS

,SLAB-ON-GRADE

90

f

0Pw PD+P`N e=g" ,pDtP^)e (PD +Pj+Pw)eow M wiND MroTAL

z /o

o otN

BOW= _ _

)_

0.5^ DZ3

7"____ ________DEFLECTEDSHAPE

PD EFFECT

• Case 2 — UZ = 0.75(1.4D + 1.7L +1.7W)

• Case 3 — U3 = 0.9D + 1.3WNote that earthquake load does not con-trol.

Case 1Top of wall:

P„1 = 1.4(0.3) + 1.4(2 x 75)

+ 1.7(0.25)1000

= 1.055 kips

Mug = 1.4(0.3)(6) + 1.7(0.25)(6)= 5.070 kip-in.2

Midheight of wall:

Put = 1.4(0.3) + 1.4(1.0) + 1.7(0.25)= 2.245 kips

Mu, = [1.4(0.3) + 1.7(0.25)16/2 +[1.4(0.3) + 1.4(1.0) + 1.7(0.25)10.5

= 3.657 kip-in.2Note that the first bracketed term de-notes eccentricity moment while thesecond bracketed term denotes bowingmoment.

Case 2Top of wall:

P., 2 = 0.75(1.055)= 0.791 kips

M..2 = 0.75(5.070)= 3.803 kip-in.

Midheight of wall:

Put = 0.75(2.245)= 1.684 kips

Mug = 0.75 [3.657 +

117x80.017(22.5)z12 ^1

= 19.202 kip-in.

Note that the last term denotes windmoment.

Case 3Top of wall:

P„3 = 0.9 0.3+ 2x75

1000

= 0.405 kips

M,,3 = 0.9(0.3 x 6)= 1.620 kip-in.

Midheight of wall:

= 0.9(0.3 + 1.0)= 1.170 kips

M = 0.9 [(0.3)(6/2) + (1 + 0.3)0.5, +

1.3 0. 017(22 . 5) 2 12

8

= 18.177 kip-in.

in which the first and second termswithin the first bracket denote Pe andP A bow moments, respectively.

A summary of the loading at the top andmidheight of the wall for Cases 1, 2 and3 is given on the next page.


Loading summary

Top Midheight

P,, Mu Pu M,,Case kips kip-in. kips kip-in.

Case 1 1.055 5.070 2.245 3.657Case 2 0.791 3.803 1.684 19.202Case 3 0.405 1.620 1.170 18.177

Calculate sustained load factors: 8.2.2Case 1 at midheight:

1.4(0.3)(6/2) + 1.4(0.3 + 1.0)(0.5)ad1 _ 3.657

= 0.593

Case 2 at midheight:

Nd2 =0.75 1 (I.1)(().,3)(6/2) , (1.4)(0.3+ 1.0'iO.5)

19.202= 0.085

Case 3 at midheight:

-0.9[0.3(6/2) + 1.3(0.5)]Qd3 - 18.177

= 0.077Note: It is conservative to use the largest13 d especially since panel stiffnesschanges significantly when panelcracks.

Solution using P - 0 procedure (secondorder analysis)Calculate 4):

0= 0.7at0.1f.A9= 0.1(5)(72) = 36 kips

0= 0.9atP„=04) = 0.9- 0.2 (P„ /P0. 1 )

For Case 2:0 = 0.9 - 0.2 (1.684/36) = 0.89

El = 1+/3d

_ 0.89(4300)(216)1+0.593

= 518,915 kip-in.2

Deflection at midspan (Case 2)1. Due to Pe:

_ ML 2 _ 0.75(2.535)(270)216 EI 16(518,915)

= 0.0167 in.2

2. Due to P A,.:- 5ML 2 - 5(0.75)(1.123)(270)2

48 EI 48(518,915)= 0.123 in.2

3. Due to wind:5 ML 2 5(0.75)(21.946)(270)2- 48 EI 48(518,915)

= 0.2409 in.2

Summation of deflections (I0):0.0167 + 0.0123 + 0.2409 = 0.2699 in.

4. Deflection due to P - 0 moment atmidspan:

P O' L 2

8EI

0.75[(1.4)(1.3) + 1.7(0.25)](270) 2 0'8(518,915)

0.0296 0'

Iteration 1:0 = 0.0296(0.27) = 0.0080 in.

= 0.2699 + 0.0080 = 0.2779 in.

Iteration 2:A = 0.0296(0.278) = 0.0082 in.

= 0.2699 + 0.0082 = 0.2781 in.

Iteration 3:0 = 0.0296(0.278) = 0.0082 in.A' = 0.2699 + 0.0082 = 0.2781 in.Note: The A' of the last two iterationsare convergent.

92

Mu at midspan (Case 2)Mu = 19.202 + 1.684(0.278)

= 19.670 kip-in.Design loads for P - A analysis (at mid-span):P = 1.684 kipsMu = 19.670 kip-in.

Solution using moment magnificationprocedureLoading Case 2 controls at midspan:P„ 2 = 1.684 kipsM u g = 19.202 kip-in.13d = 0.593 (conservative)kl„/r = 1.0(270)/1.73

= 156 > 150 (ok)Note that k = 1 is conservative and r =1.8 by Section 8.1.3).

4P0 = 205 kips(see PCI Design Handbook, Fig. 2.6.5)P. = 205/0.7 = 292.86 kipsPu /P0 = 1.684/292.86 = 0.0058Determine EI: 8.2.2

EI = EÌ9/X Eq. (8.5)1 + Pd

A_ 71 0>3.0 Eq. (8.6)

= 2.5 + 1.6 Eq. (8.7)

Pu/Po

=2.5+1.6

1.684/292.8

= 280.7

Amax = 70 (use q = 70)

0 = k^ 7r - 0.05 Eq. (8.8)

= 27 - 0.05

156

= 0.123

A = 70(0.123) = 8.62 > 3.0

(see Fig. 8.2)

A`2nn191 FVR R9EI=

-1+0.593

= 67,639 kip-in.2

Determine magnified moment: 8.2.1

PC (klE z Eq. (8.4)

_ ar e (67,639)

(1.0 x 270)2

= 9.16 kips

= 0.89 (earlier calculation)

• Moment magnification factor: Eq. (8.2)

Cm- ° I - Pu/4P,

C m = 1.0 8.2.3

= 1.0

1 - 1.684/0.89(9.16)

= 1.26

M, = 8 b MZb Eq. (8.1)

= 1.26(19.202)

= 24.201 kip-in.

• Check axial load and bending momenton interaction diagram.

Second Momentorder magni-

analysis fication

Axial load(kips) 1.684 1.684

Bending moment(kip-in.) 19.670 24.201(kip-ft) 1.64 2.02

(ok) (ok)

Factored moment deflection check: 5.4EI = 67,639 ksiNote: This is the stiffness at ultimate.Panel is most likely cracked or nearcracking.M„ = 24.20 kip-in. per ft widthDeflection due to magnified moment:

5MUL2

48 EI5(24.20)(270) 2

48(67,639)

= 2.71 in. (L,/99 > L„/100 max)

Deflection is very close to limit (say ok).


Curves based on minimum prestress of 250 psi

= 5000 psiV , = 270 ksi

Partially developed strand10

8v _o

6kips per foot

4

2

0 4 8 12 16 20 24 28

ft-kips per foot

Fully developed strand 101

8 Id to mILI

____o

II

dbP. 6 _ _kips per foot p

N

4 -

IISecond Order t nMomentMa ificati n

P-O Analysis I.68— N I --

II— —

_____

II

0 't 4 8 12 16 20 24 28

— 4)M,,, ft-kips per foot

Partial interaction curve for prestressed solid wall panels

F nteraction Curve Data

DevelopedI Force

Fully DevelopedStrand Force

. 1. 6 6. 2.

. 6. 8 13. 9.

. 11 11 23. 17.

.4 17,5 145 37.2 26.7

94

16100 ,fe

n = 2.5 + P„/Po 80 0 2

6<, s70 60

40for P. equation: Sp

EI EÎs/^ '^`^/r

\^S_

^ pp

8 DSO

6

(a) Compression flange4

8 We7'

Fig. 8.1 2 P /Po

100 ____80 ^P

60 ?S

\ SO

20 /^

\ ^S^Pw

10

8\ ^S

6': EEE

(b) No compression flange 4

e —005kC^r

20.02 .04 .06 .08 .10 .14 .20 .30 .40 .50

Fig. 8.2 PiP.

Coefficients, A, for modified El


Documents

Recommended Practice for the Design of … Journal...Recommended Practice for the Design of Prestressed Concrete Columns and Walls prepared by PCI Committee on Prestressed Concrete