ATeE!1Seismic evaluation and retrofitof concrete buildingsVolume 1aTe Applied Technology Council", .......\.. 0 TN . _ ~ . ~ CALIFORNIA SEISMIC SAFETY COMMISSIONo .Proposition122 SeismicRetrofit PracticesImprovement ProgramReport sse 96-01.,,. t'L 4. J..:U":l:.~ A'Ic,S((ATC-4DSeismic Evaluation and Retrofitof Concrete BuildingsVolume 1byAPPLIED TECHNOLOGY COUNCIL555. Twin Dolphin Drive, Suite 550Redwood City,California 94065Funded bySEISMIC SAFETY COMMISSIONState of CaliforniaProducts 1.2 and 1.3of the Proposition 122Seismic Retrofit Practices Improvement Programi,..5,000 Not APplicableSa Rocl< 2,500 2,000Soft Roclx/Lwxt/Jx]V). The capacitycurveis generally constructed to representthe first mode response of thestructurebased on theassumptionthat thefundamental mode of vibration is thepredominant response of thestructure.This is generallyvalid for buildings withfundamental periods of vibration up toabout one second. ,>...':4. Sameas Level 3 until first yielding, Foreach increment beyond yielding, adjust theforces to be consistent with the changingdeflected shape.5.. Similar to 3 and 4 above, but include theeffects of the higher modes of vibration indetermining yielding in individualstructural elements while plotting thecapacity curve for the building in terms offirst mode lateral forces anddisplacements. The higher mode effectsmay be determined by doing higher modepushover analyses (i.e., loads may beprogressively applied in proportion to amode shapeother than the fundamentalmodeshapeto determine itsinelasticbehavior.) For the higher modes thestructure is being both pushed and pulledconcurrently to maintain themode shape.4. Calculate member forces for the requiredcombinations of verticaland lateral load.5. Adjust the lateral force level so that some (or groupof.elements)is stressed toj_Within 10 percent of Its memberstrength. . Ts7. For each spectral accelerationon the 5 %damped spectrum, S85%, calculate thecorresponding spectral displacement, Sd5%, asSd5%=S85%(I'/21Cl.8. For each T(OT displacement dpi),ijygs, thensolve for the spectral reductionvalue, SRA,using equation8-9 with api' substitutedforIlpi,If T>Ts then solve for the spectral reductionChapter 8, Nonlinear Static Analysis procedures(((((r((((((((((SEiSMIC EVALUATBON AND RETROFIT OF COIl\tHtRETE BU!LDINGS'"-- Capacity spectrumDemand Curves for ~ a f f=5%, 10%, 15%, 20%, 25% and 30%Spectra! Displacement, inchesFigure 8-54. capacity spectra Procedure rc:Afterstep 2value, SRv, using equation 8-10 withapi'substitutedfor a.9. For each T(or displacement dpi), plot the pointwhere Sa=SRXSa5% and Sd=SRxSd5% whereSRx=SRA if Tg'S1and SRx=SRv ifT>Ts10. Draw a line connecting theSa7Sd pointsplotted in Step 9. Theintersection of thislinewith thecapacity spectrum is the demanddisp lacement.8.2.2.1.4 Calculating Performance PointUsing Procedure C. This procedure has beendeveloped to providea graphical solution usinghand methods.It has been found to often bereasonably close to the performance point on thefirsttry. The following stepsare involved:1. Developthe 5 percent damped responsespectrum appropriateforthe site using theprocedures provided in Chapter 4.2. Draw the 5 percent dampedresponse spectrumanddraw a familyof reduced spectra on thesamechart, as illustrated in Figure 8-34. It isconvenient if the spectra plotted correspondtoeffective damping values ( ~ e f f ) ranging from 5percent to the maximum value allowed for thebuilding's structural behavior type. Themaximum~ e f f for TypeA construction is 40percent,Type B construction is 29 percent andType C construction is 20 percent.Chapter8,Nonlinear static Analysis proceduresDemand Curves for ~ e f f=5%, 10%, 15%, 20%, 25%and 30%Spectral Displacement, inchesFigure 8-S5. capacity spectra procedurelie" AfterstepS3. Transform the capacity curve intoa capacityspectrum as described in Section 8.2.2.1.1.using equations 8-1, 8-2, 8-3 and 8-4, and plotit on thesamechart as thefamily of demandspectra, as illustrated in Figure 8-35.4. Developa bilinear representation of thecapacity spectrum as described inSection 8.2.2.1.1and illustrated in Figure8-9.Select theinitial point api, dpi at the furthestpoint out on the capacity spectrum or at theintersection withthe 5 percent dampedspectrum, whichever is less. A displacementslightly larger than that calculated usingtheequal displacement approximation (say1.5 times larger) may alsobe a reasonableestimatefortheinitial dpi. See Figure8-36foran illustration of this step.5. Determine theratios dpi/d, and [(api/a-) -l]/[(dpi/dy) - 1]. Notethat thesecond term isthe ratio of the post yield stiffnessto the ini tialstiffness.Commentary: Figure8-37provides someexamples of the physical significance of theratiosdpi/dy and [(aprlay) - l]/[(dpi/d.v) - 1]. Thefigureshows example bilinear representationsof capacity spectra along withthecorresponding ratios.SEISMIC EVALUATION AND RETROFIT OF CONCRETE BUILDINGS.(J(c('(:(Demand Curves for 13eft = 5%, 10%, 15%, 20%, 25%and 30%Table 8-5. EFFective Damping, fJeFF, in percent-(structural Behavior Type A('INate: Area A, '" Area ~ I(CDCBilinear representation (.2ofCapacity spactnim(iii10 10 12 16 21 30 37 40 a-(Q) BpIiii8 11 14 18 23 31 37 40(Co)SyCo)-::t6 13 16 20 25 33 37 40iii(a-t,;4 16 19 23 28 34 37 40 Q)(' e-m3 16 19-. 23 27 33 36 39(2 16 19 22 25 29 31 33dyc:fp1(Spectral Displacement, inches1.5 13 16 - 18 20 23 24 241.25 11 12 13 15 16 17 18(Figure 8-56. capacityspectraprocedure "e"AFterstep 4Table 8-6. EFFective Damping, fJeFF, in percent-Based on the ratiosobtained in step 5, enterstructural Behavior Type B6.either Table8-5, 8-6, or 8-7,depending on thebuilding's structural behavior type, (see(Table8-4 for definition of structural behavior 10 9 10 12 16 23 27 29(types)and find the effective damping value,8 9 11 13 17 24 27 29(Q .-12 15 19 25 27 29perro6 10Commentary: Thef3eff term can also be4 11 14 17 21 25 27 29calculated using theformula given in equation3 12 14 17 21 25 27 298-8.However, for the. purposes of thisgraphical procedure, it may be easier to2 12 14 16 19 22 24 25calculatef3eff using the above tables, which are1.5 11 12 14 15 17 18 18based on the slopes of the two legs of the 1.25 9 10 10 11 12 13 13bilinear representation of the capacityspectrum. The values given in Tables 8-5, 8-6Table 8-7. EFFective Damping, fJen, in percent-and 8-7 are derivedfromequation 8-8. Thestructural Behavior Type Cequation and the tables give the same results.7. Refer to Figure8-38. Extend the initialstiffnessline, labeled Line 1 in the figure, upto intersect the 5 percent damped curve. Also,10 7 7 9 10- 14 17 20drawa line, labeled Line 2 in the figure,. from8 7 8 9 11 15 18 20the origin to point api, dpi).6 7 9 10 12 16 18 208. Refer to Figure 8-39. Draw a line, labeledLine3 in the figure, from the intersection point4 8 9 11 13 16 18 20of Line1 and the 5 percent damped response 3 9 10 11 13 16 17 19spectrumto" the intersection point of Line2 and2 9 10 11 12 14 15 16(the reduced spectrum which corresponds to the1.5 8 9 9 10 11 11 11(3eff determined in step 6. Note that the figure is1.25 7 7 8 8 9 '9 9 Idrawn for aj3eff of approximately 24 percent.(8-28Chapter S, Nonlinear static Analysis proceduresI(SEISMIC EVALUATU:JN AND RETROFiT OF CONCRETE BUILDINGS~ Capacity spectrumBilinear representationof Capacity spectrumQ)c.s-;"-BpiCDiiie2y(JI0:=("iiil-t)CD0-enDemand Curves for13eft =5%,10%,15%,20%,25% and 30%0:L...5:!. =z.o~ I elyi!r3!!. -1_i!r __ =0.3~ely -,d, dpl~ - 1a.,-d--=0.5...::e!. -11---+--1-_ dyFigure 8-37. Example Slope Ratios.Spectral Displacement, inchesDemand Curves for ~ a f f=5%,10%,15%,20%,25% and 30%Figure 8-40. capacity Spectrum procedureCAFterstep 9Demand Curves for ~ a f f=5%, 10%, 15%, 20%, 25% and 30%SpectralDisplacement, inchesFigure 8-39. capacity spectrum procedure CAFterstep s9. Refer to Figure 8-40.The point where Line 3intersects thecapacity spectrum istaken astheestimated performance point ap2, dp2 point.Commentary: In the case of a compositesawtooth" capacityspectrum, constructedfrom a family of capacity spectrum curves, thebilinear representation should be based on theindividual capacity spectrum curve that makesup the portion of thecompositecapacityspectrum where Line 3 intersects withthecomposite capacity spectrum (i.e., the pointapi, dpi). .10. If displacement dp2 iswithin 5percent ofdisplacement dpl, then the pointap2, dp2 is theperformance point (or in more general terms,if displacementdp(i+ 1) is within 5 percent ofdisplacementdpi, then the pointap(i+l), dp(i + l ) isthe performance point. If thedisplacementsarenot within thespecified tolerance, thenproceed tostep11.Commentary: VVlzen the exactperformance point iscritical for theacceptability, then the 5 percent toleranceshould be adhered to, and additional iterationsshould be performed. If the exact performancepoint is not critical for the acceptability, thenadditional iterationsare probably'll\:

++-- - -- -1\"/

rI'----;'--lPerformance point

"

..... at Sd = 3.4inches-- - 1--r--..'I'----1/:....... ['...1r-. I---t--. ........../Ir-........r--.....r--r--,:---.... r-. t--, I--I"- ---r--I--- I II-I--. '---V,--,VIII

1'\ CA =0.44,Cv =O.P'JJelf = 5%,10%,151\ 1"-/and 20%//-,-, //r-,..+-''S:aj:s...CDLateral DeformationFigure 9-7. Alternative IdealizedLoad-DeFormationRelation For a component.. Point Eis a point defining the maximumdeformationcapacity. Deformations beyondthis limit are not permitted because gravityload can nolonger be sustained. Insomecases, initial failureat C will "result in loss ofgravity load resistance, in whichcase E is apoint having deformation equal to that at C "and zero resistance. In other cases,deformations beyond C willbe permitted eventhough thelateral load resistance is greatlyreduced or even zero-valued.Many currently available computerprograms can onlydirectlymodel a simple9-22bilinear load-deformation relation. For thisreason, it is acceptable torepresent the load-deformation relationby lines connecting pointsA-B-C, provided response is not permitted toextend beyond C.Alternatively, it may be possible anddesirable touse more-detailed /000-deformation relations such as that illustratedin Figure 9-7. This relation has the followingfeatures:.. The initial slope ofthelateral 1000-displacement relation represents behaviorbefore cracking. In using such a relation, theengineer should bear in mind that some initialcracking may have occurred because ofrestrained shrinkage and unknown loads... Lateral load resistance in some componentsmay degrade in a more controlled manner thanshown in Figure 9-6. Therate of degradationwithincreasing lateral deformation depends onthe action being modeled and thenumber ofloading cycles.In general, this aspect ofbehavior should be established on thebasis oftest data.Components subject to degrading during cyclicloading, such as shear-controlled beams,columns,and piers, show a loss of resistance between pointsB and C. (Refer to the discussion of Figure 9-11inSection 9.5.4.1.) Degrading behavior must bemodeled.Commentary: Degradation is different fromductile yielding. Components that yield'are able tomaintain their strength over several cycles butcannot accept additional load.Degradingcomponents donot maintain their strength; someoftheload carried by a degrading component onone cycle must be carried by different componentsonsubsequent cycles: Overall building responsecould be altered if enoughelements or componentsexperience this effective loss of strength.Consequently, widespread degradation must bemodeled. .Degrading components are generally force-controlled, although some components may beableChapter 9, Modelintl RUles((((c((((SEISMIC EVALUATION AND RETROFIT OF CONCRETE BUILDING!';--9.5.2_2 ConcreteEvaluation of concretematerial propertiesshould involve determination of compressive9.5.2. 1 GeneralThe material models should consider allavailable information, including building plans,original calculations and design criteria, siteobservations, testing, andrecords of typicalmaterials andconstruction practices prevalent atthetime of construction. Chapter 5describesprocedures for identifying material properties.Default assumptions may berequired incertaincases where information is unavailable.Commentary: Successful application of themethodology requires good information about thebuilding. In general, material properties should beestablished by inspection and testing.Material Models 9.5.2is reached, itmay beacceptable toexclude itfrom the modelaltogether.The point at whichdegrading occurs is notentirely predictable; itmaydepend ondetailing, memberproportions, and therelativemagnitudes ofmoment, shear, andaxial force. Withreference toFigure 9-6,Figure 9-11, and Table9-4, a roughapproach isto assume that thecomponent will be fullydegraded at a ductility demand of 4. Fullydegraded properties can be represented bylateralload resistance equal to about20% of theundegraded strength. Anintermediate partiallydegraded state, assigned at a ductility demand of2, may alsobe assumed. Conclusionsbased onthese analyses should be appropriate totheroughnature of analysis assumptions.to degrade slightly andstill withstand additionaldeformations. In force-controlled primarycomponents, inelasticityis not allowed, sodeformationbeyondpoint B in Figure9-6 isunacceptable. Thisgenerally markstheendof reliable behavior and,consequently, theend ofmeaningful analysis.However, if thecomponent can be designated as secondary(seeChapter 11), analysis may proceed, as long as thedegrading behavior is accountedfor, i.e., as longas the component's forcesare redistributed toother elements.In a nonlinear static analysis such as apushover, degrading is represented by a"shedding" of loadfrom critical componentswithout the application of additional load. Ifavailable computer programs are unable torepresent this effect directly, degradationcan hesimulated with a series of analyses.In the firstanalysis, forcesareapplied until criticalcomponents reacha deformation level at whichthey would be expected to degrade. For the secondanalysis, the critical components are assignedfullyor partiallydegraded strengthand stiffnesslessthan their original properties, and this secondmodel is loaded to a pointat which additionaldegradation is expected. A third model withdegraded properties is analyzed, etc. The series ofmodels and analyses yields a series of capacitycurves; each curveis applicable over a range ofdisplacements. Takentogether, the applicableparts of each curve forman effective capacitycurve forthe degrading structure(Examplebuilding studiesinVolume 2illustratethisapproach). Alternatively, in accordance withSection 9.3.1, if a component is expected to befullydegraded longbefore the performance pointChapter 9, ModelingRulesSEISMIC EVA'LUATION AND RETROFIT IF CONCRETE BUILDINGS(strength,modulus of elasticity, aggregatedensity,and variability.Commentary:Compressive strength may begauged by using thedestructive and nondestructivemethods identified inChapter 5. Alternatively,concrete strength may be projectedfrom early-agevalues1:Jy using conventional relations(ACI 1986).Note that some dataindicate that the strength.increase for air-cured concrete(as opposed to..outdoor exposure) may cease at the age of aboutone year (Wood 1991). The projection of concretestrength should be accepted only where- concretedesign strength is known and quality control isbelieved to have beengood, or where dataareavailable onconcrete strength at thetime ofconstruction.In addition, a visual inspection of thestructure should verify that concrete qualityappears reasonably uniform and that deterioration.has not occurred. Themodulus of elasticity may begaugedfrom nondestructive or destructive tests.Alternatively,' it may be gauged indirectly fromcompression strength and densityinformation byusing conventional relations from ACI 318.Transverse reinforcement may be taken toenhance the strain capacity and compressivestrength of concrete. Except wheremore-detailedmodels areused, compressive strain capacity maybedefined by Equation 9-1 and compressivestrength may be defined by Equation 9-2.