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EVALUATIONOFMPA

TALLBUILDINGS,TWOCOMPONENTSOFGROUNDMOTIONTongjiUniversity,Shanghai,ChinaJune20-21,2011AnilK.ChopraUniversityofCalifornia,BerkeleyStructuralSystemsTwobuildingsinSanFrancisco:48-and62-story.Lateralresistingsystemsductileconcretecorewalltwochannel-shapedwallsconnectedtorectangularwallsbycouplingbeamsFloors:8”post-tensionedslabsspanningbetweenthecoreandperimeterconcretecolumnsSchematicPlans&Elevations

362-StoryBuildingOutriggercolumnsincreasetheaspectratioandstiffnessintheshortdirection.OutriggercolumnsconnectedtothecorewithBRBsat28thand51stfloors.Tunedliquidmassdamperattheroof./GroundMotionsRecordsfromnineearthquakes,magnitude7.3to7.9.ScaledtomatchA(T1)fromuniformhazardspectrumfor2%probabilityofexceedancein50years.MedianResponseSpectrav’sUniformHazardSpectrum48-storybuilding62-storybuildingHazardspectrumMediana-dirMedianb-dirHazardspectrumMediana-dirMedianb-dirEquationsofmotion:SolvedirectlythesecoupledequationsbynonlinearRHA;avoidedinMPA.SpatialdistributionofforcessResponseHistoryAnalysis

TwoHorizontalComponentsofGroundMotionspeff(t)7ModalExpansionofForceDistribution,8ModalExpansionofForces,9ModalPushoverAnalysis(MPA)Estimatepeak“modal”responseofstructureto

byPushoveranalysisforforcedistributionuptoroofdisplacementCombinepeak“modal”responses(SRSSorCQC).Combinepeakresponsestotwohorizontalcomponentsofgroundmotion(usingSRSS).10ModalContributionsSymmetric-planbuildingsTorsionalmodesdonotrespondResultsformodalpairsHighermodecontributionstofloordisplacementsaresmallFloorDisplacementsFloorFloor12ModalContributionsHighermodecontributionstostorydriftsaresignificantStoryDriftsStoryStoryEvaluationofMPAThefirstpairoflateral“modes”isadequateinestimatingfloordisplacements,butisinadequateforestimatingstorydriftsFloorDisplacementsFloorFloor14EvaluationofMPAWiththesecondpairoflateral“modes”included,storydriftsestimatedbyMPAaremuchbetter,andresemblenonlinearRHAresults.StoryDriftsStoryStoryModifiedMPAandPracticalMPAMMPATreatbuildingaslinearlyelasticincomputingresponsecontributionsof“modes”higherthanfirstthree“modes”.PMPAEstimatedeformationofthenth-modeinelasticSDFsystemfromelasticspectrumandempiricalequationforinelasticdeformationratio.EvaluationofMMPAandPMPAFloorDisplacementsStoryDriftsFloorFloorStoryStoryEvaluationofMMPAandPMPASeismicdemandsestimatedbyMMPAandMPAareclose;validtotreatbuildingaslinearlyelasticinestimatinghigher-modecontributionstoseismicdemands.PMPAprovidesalargerestimateofseismicdemandscomparedtoMPAbecauseisoverestimated.

18StoryStoryRSA(elasticsystems)v’sPMPA(inelasticsystems)StoryStoryStoryDriftRatio,%19RSA(elasticsystems)v’sPMPA(inelasticsystems)RSAunderestimatesstorydriftsofelasticsystemsbyupto20%and22%fortheCW48andCW62buildings,respectively.Additionalerrorsintroducedbyneglectingmodalcouplingandcyclicstiffnessdegradation,andbyestimatingusingempiricalequationsinPMPAforinelasticsystemsaresmall.UCNCEE_201020ShearforcesforcoreshearwallShearforcesandendrotationsforthecouplingbeamsEvaluationofPMPA:OtherResponseQuantitiesStoryStoryFloorExtremeSeismicHazardGroundmotionspreviouslyscaledtorepresentA(T1)fromuniformhazardspectrumfor2%probabilityofexceedancein50years.Scaledagainbyfactorsof3.0forCW48building,and2.0forCW62buildingtotestMPAforextremegroundmotions.21UCNCEE_201022EvaluationofPMPAforExtremeSeismicHazard:PushoverCurvesReferencedisplacement/height,%Baseshear/weight23RSA(elasticsystems)v’sPMPA(inelasticsystems)StoryStoryStoryStoryStoryDriftRatio,%24ShearforcesforcoreshearwallEvaluationofPMPA:ShearForcesforCoreShearWall

StoryStory25ConclusionsThePMPAprocedurefornonlinearsystemsisalmostasaccurateasRSAisforlinearsy

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