Shanghai-Lecture1-Estimating知識資料Seismic知識資料Demands知識資料for知識資料Performance-Based知識資料Engineering知識資料of知識資料Buildings

EstimatingSeismicDemandsforPerformance-BasedEngineeringofBuildingsAnilK.ChopraUniversityofCalifornia,BerkeleyTongjiUniversityShanghai,ChinaJune20-21,2011EstimatingSeismicDemands

MajorShiftinProfessionFromElasticanalysisforreducedforces,e.g.,buildingcodesToExplicitrecognitionofinelasticeffects ATC-40(1996) FEMA-356(2000) ASCE41-06(2007)Chooseheight-wisedistributionoflateralforcesDeveloppushovercurve:Plotofbaseshearv’sroofdisplacementNonlinearStaticProcedure(NSP)DeterminetargetroofdisplacementDetermineseismicdemandsfrompushoveranalysisComparetolimitingvaluesforperformancegoalNonlinearStaticProcedure(NSP)OrganizationofPresentationNonlinearstaticprocedure:currentpracticeModalPushoverAnalysisEstimatingDeformationofSDFSystemsCurrentpracticeImprovedmethodsPARTI

NONLINEARSTATICPROCEDURES

CurrentPractice

6

ELFandRSAdistributionsintendedtoconsiderhighermoderesponses

Height-wiseDistributionofLateralForces:FEMA-356&ASCE41-06

hjFEMA-356&ASCE41-06ForceDistributionsEachforcedistributionpushesallfloorsinsamedirectionPushoverCurvesUsing

FEMA-356ForceDistributions

EssentiallyelasticresponseFEMAforcedistributionsdonotpredictincreasingdriftsinupperstoriesELFandRSAdistributionsareinadequateStoryDrifts:BostonBuildingsSignificantinelasticresponseFEMAforcedistributionsdonotpredictdriftconcentrationinupperstoriesELFandRSAdistributionsareinadequateStoryDrifts:SeattleBuildingsStronglyinelasticresponseFEMAforcedistributionsdonotpredictdriftpatterninupperstoriesELFandRSAdistributionsareinadequateStoryDrifts:L.A.Buildings

FEMAforcesunderestimateorfailtoidentifyplasticrotationsinupperstoriesPlasticRotations:SeattleBuildings

FEMAforcesunderestimateorfailtoidentifyplasticrotationsinupperstoriesPlasticRotations:L.A.BuildingsImprovedNonlinearStaticProcedure

GoalsRetaintheconceptualsimplicityandcomputationalattractivenessofcurrentNSPObtainmuchimprovedestimateofseismicdemandsPARTII

MODALPUSHOVERANALYSIS

BasicconceptStep-by-stepsummaryEvaluateaccuracyofMPACompareresultsfromMPAwiththosefromFEMA-356forcedistributionsModalPushoverAnalysis(MPA)OutlineEquationsofmotion:SolvedirectlythesecoupledequationsSpatial(height-wise)distributionofforcesResponseHistoryAnalysis

Symmetric-planBuildingspeff(t)ModalExpansionofForceDistributionNine-StorySACBuildingNine-storySACbuildingNaturalVibrationPeriodsandModesNine-storySACbuildingModalExpansionofForces,s

Estimatepeak“modal”responseofstructuretobyPushoveranalysisforforcedistributionuptoroofdisplacementCombinepeak“modal”responses (SRSSorCQC)ModalPushoverAnalysis(MPA)ModalPushoverAnalysis(MPA)ForElasticBuildingsMPAisidenticaltoRSAForInelasticBuildingsMPAismotivatedbytheweakmodalcouplingofresponsetoComputenaturalperiodsTnandmodes8-StoryRC-SMRFBuildingSummaryofMPA

Eight-StoryRC-SMRFBuilding

Forthenthmode,developpushovercurveusingforcedistribution“Modal”ForceDistributions“Modal”PushoverCurvesSummaryofMPA

BaseShear/WeightRoofDriftRatio,%IdealizepushovercurveasatrilinearcurveSummaryofMPA

Convertidealizedpushovercurvetoforce-deformationrelationfornth-“mode”inelasticSDFsystemSummaryofMPA

ComputepeakdeformationDnofthenth-“mode”inelasticSDFsystembyNonlinearresponsehistoryanalysis,orInelasticdesignspectrum,orEmpiricalequationsSummaryofMPA

6.

Calculatepeakroofdisplacement,nth-“mode”:7.Frompushoverdatabase,extractvaluesofdesiredresponses

atroofdisplacement8.Repeatsteps3-7forafew“modes”9.Computenth-”mode”dynamicresponse:10.Determinetotaldemand:SummaryofMPA

4-,8-,12-,and20-storyRC-SMRFbuildingsPeriod:1.09,1.67,1.96,and2.56secStructuralSystems&ModelingStructuralDesignCodesIBC2003:LosAngeles,R=8ASCE7-2002ACI318-2002GroundMotions78groundmotionsScaledtomatchA(T1)Seismichazardspectrum:Exceedanceprobability2%in50yearsMPAversusNL-RHA:StoryDriftsFirst“mode”isadequatefor4-storybuildingMPAversusNL-RHA:StoryDriftsFortallerbuildings,1st“mode”isinadequateIncludingmore“modes”improvesresultsNeglectmodalcoupling;showntobeweakCombinepeak“modal”responsesusingSRSSorCQCrulesThisapproximationisthebasisforRSAofelasticsystemsApproximationsinMPAProcedureRelativeAccuracyofRSAandMPARSAMPAElasticSystemsInelasticSystemsCompareRSAtoRHACompareMPAtononlinearRHABaselineerrorAdditionalerrors?RSA(ElasticSystems)vs.MPA(InelasticSystems)

20-storyRC-SMRFBuildingFEMAvs.MPA:StoryDrifts

4-story,RC-SMRFBuildingFEMAvs.MPA:StoryDrifts

20-story,RC-SMRFBuildingASCE41-06NSPbasedonfirstmode,restrictiveifhighermodeeffectsaresignificant.ModalPushoverAnalysisBasedonStructuralDynamicsTheoryRetainsconceptualsimplicityofstandardNSPRequirescomputationaleffortcomparabletostandardNSPGivesmuchimprovedresultsModalPushoverAnalysis:AdvantagesWithoutadditioncomplexityorcomputationaleffort,MPAestimatesseismicdemandsmuchmoreaccuratelythanFEMAproceduresFurtherSimplificationofMPA

ModifiedModalPushoverAnalysis(MMPA)LosAngeles9-storyBuildingConsiderationofinelasticbehaviorEssentialin1st-modepushoveranalysisNotasimportantforestimatinghigher-modedemandsMMPAbasedonthisapproximationTreatbuildingaslinearlyelasticinestimatinghigher-”mode”contributionsModifiedModalPushoverAnalysis(MMPA)MPA:PracticalApplicationRoofdisplacementrequiredforeachpushoveranalysis(MPAandFEMA)EstimatedfromDeformationofnth-”mode”inelasticSDFsystemfromInelasticdesignspectrumEmpiricalequationsforinelasticdeformationratio

PARTIII

DEFORMATIONOFINELASTICSDFSYSTEMS

CurrentPractice1. PlotelasticdesignspectruminA-DformatATC-40CapacitySpectrumMethod

toEstimateD:2. Plotthedemanddiagramandcapacitydiagramtogether.Intersectionpointgivesdeformationdemand.ATC-40CapacitySpectrumMethodATC-40CapacitySpectrumMethodAnalysisofequivalentlinearsystemsIterativeproceduredoesnotalwaysconvergeEvenifitconverges,deformationmaybeinaccurateEvaluationofATC-40ProcedureDiscrepancyinATC-40ProcedureFEMA440MethodtoEstimateDHasrectifiedbothflawsoftheATC-40methodLackofconvergenceinsomecasesLargeerrorsinmanycasesImprovedproceduresforequivalentlinearizationofinelasticsystemsBenefitofEquivalentLinearizationDetour?DeformationofinelasticsystemsavailablefromInelasticdesignspectrumEquationsforinelasticdeformationratioInelasticDesignSpectraClassicalGraphical:Capacity-Demand-Diagram MethodD

fromInelasticDesignSpectrumCapacity-Demand-DiagramMethodAttractivegraphicalfeatureofFEMA440EquivalentLinearSystemorATC-40CapacitySpectrumMethodcanberetainedwithouttheequivalentlinearizationdetour.AchievedintheCDDMethodbyusingtheinelasticdesignspectrumtodefinedemand.InelasticdesignspectrumplottedinA-DformatDeformationfromspectrum:PlotAyv’sDforconstantmInelasticDemandDiagramPlotcapacityanddemanddiagramsinA-DformatYieldingbranchofcapacitydiagramintersectsthedemanddiagramforseveralmThedeformationisgivenbytheoneintersectionpointwherem

fromthetwodiagramsmatchesCapacity-Demand-DiagramMethod

Capacity-Demand-DiagramMethod

PARTIV

DEFORMATIONOFINELASTICSDFSYSTEMS

ImprovedMethods61ImprovedMethodstoEstimateDASCE41-06EquivalentLinearizationMethodASCE41-06ImprovementsforC1andC2EquationsforinelasticdeformationratioconsideringallhysteresisfeaturesInelasticDeformationRatio:EmpiricalEquations

Post-yieldstiffness:Yield-strengthreductionfactor:Ductilityfactor:BilinearSystems:Definitions

Systemswithknownductility

:

Systemswithknownstrength:InelasticDeformationRatio

LimitingvaluesapplytoallexcitationsandsystemsLimitingValuesofum/uo

Nineensembles,170groundmotionsLMSR,LMLR,SMSR,SMLR(4x20)Fourcombinationsoflarge(M=6.6-6.9)orsmall(M=5.8-6.5)magnitudeandsmall(R=13-30km)orlarge(R=30-60km)distanceNEHRPSiteClassesB,C,orD(3x20)M=6.0-7.4R<120kmNear-Fault(2x15)FaultnormalcomponentsFaultparallelcomponentsM=6.2-6.9R<9kmGroundMotionEnsembles

MedianCR-Tnplots,similarforLMSR,LMLR,SMSR,andSMLRensemblesC

-TnplotsarealsosimilarInfluenceofEarthquakeMagnitudeandDistance

MedianC

-TnandCR-TnplotssimilarforsiteclassesB,C,andD.ClosetoLMSR,althoughspectradifferInfluenceofNEHRPSiteClass

MedianResponseSpectrum:LMSREnsemble

MedianResponseSpectrum:LMSREnsemble

Spectralshapesofnear-faultmotionsaremuchdifferentthanfar-faultmotions

MedianResponseSpectrum

Inacceleration-sensitiveregion,CR-Tnplotsdifferfornear-andfar-faultmotionsSimilarwhenCR

isplottedagainstTn/TcCR

forNear-FaultGroundMotionsDeformationofelasticsystemfromelasticdesignspectrumNeedequationforC

forstructureswithknown

NeedequationforCR

forstructureswithknown

fy

orRyEstimatingDeformationofInelasticSystems

Numericalcoefficients:a,b,c,dFunctionofRyandTnTcSatisfieslimitsLRatTn

=0and1atTn

=

EmpiricalEquationforCR

Sameequationandcoefficientsfornear-andfar-faultmotionsEmpiricalEquationforCR

Sameequationandcoefficients,independent