美国规范-ATC-40简介

March27,20021R.K.GoelCAPACITY-DEMAND-DIAGRAMMETHODSFORESTIMATINGDEFORMATIONOFINELASTICSYSTEMSAnilK.ChopraandRakeshK.GoelIncollaborationwithDegenkolbEngineersMarch27,20022R.K.GoelATC-40NonlinearStaticProcedure1.DevelopthepushovercurveuNVbPushoverCurveuNVbMarch27,20023R.K.GoelATC-40NonlinearStaticProcedure2.ConvertpushovercurvetocapacitydiagramPushoverCurveuNVbCapacityDiagramD=Γ1φN1uNM1*A=VbMarch27,20024R.K.GoelATC-40NonlinearStaticProcedure3.PlotelasticdesignspectruminA-DformatDA4π2Tn2=DemandDiagramATn,1DTn,2ATnMarch27,20025R.K.GoelATC-40NonlinearStaticProcedure4.PlotthedemanddiagramandcapacitydiagramtogetherIntersectionpointgivesdisplacementdemandAvoidsnonlinearRHA;insteadanalyzeequivalentlinearsystemsAD5%DemandDiagramCapacityDiagramDemandDiagramDemandPointMarch27,20026R.K.GoelATC-40NonlinearStaticProcedure5.Convertdisplacementdemandtoroofdisplacementandcomponentdeformation.6.Comparetolimitingvaluesforspecifiedperformancegoals.March27,20027R.K.GoelObjectives!ExaminetheproceduretodeterminethedeformationofSDFsystemsDoestheiterativeprocedureconverge?Howaccurateistheestimateddeformation?DampingmodificationinATC-40?!DevelopimprovedprocedureBasedoninelasticdesignspectrumGivesdeformationconsistentwithdesignspectrumMarch27,20028R.K.GoelEvaluationMethod!DefineequivalentlinearsystemPeriodbasedonsecantstiffnessEquivalentdampingratio!EstimatedeformationbyATC-40proceduresGroundmotionDesignspectrum!Compareestimateddeformationwith“exact”valuefromnonlinearRHAorreferencevaluefromdesignspectrumMarch27,20029R.K.GoelEquivalentPeriod!Forbilinearsystems!Forelasto-plasticsystemsµTTneq=ααµµ−+=1TTneqmuyuyfDeformationForce111kαkseck()ααµ−+1fyMarch27,200210R.K.GoelEquivalentDamping!Forbilinearsystems!Forelasto-plasticsystems()()()ααµµαµπζ−+−−=1112eq()µµπζ12−=eqDESEDeformationForcefy()ααµ−+1fyumuyMarch27,200211R.K.GoelVariationofPeriodandDampingofEquivalentLinearSystemwithDuctilityMarch27,200212R.K.GoelATC-40Procedure!Dampingmodification!κdependsonStructuralbehavior!TypeA!TypeB!TypeCJudgementζκζζeqeq+=ˆMarch27,200213R.K.GoelATC-40ProcedureA1.Plotthecapacitydiagramand5%-dampedelasticdemanddiagram.2.EstimatedeformationdemandDianddetermineAifromthecapacityspectrum.Initially,assumeDi=D(Tn,ζ=5%).3.Computeµ=Di÷Dy.4.Computeζeq=ζ+κζeq.5.Plottheelasticdemanddiagramforζeq,intersectionwithcapacitydiagramgivesdisplacementDj.6.Checkforconvergence.If(Dj-Di)÷Dj≤TolerancethenD=Dj.Otherwise,setDi=Djandrepeatsteps3to6.March27,200214R.K.GoelExamples:SpecifiedGroundMotionMarch27,200215R.K.GoelATC-40Procedure-AAnalysisofSystem5!Given:Tn=1s,ζ=0.05,fy÷w=Ay÷g=0.10.!Input:1940ElCentroGroundMotion!Find:Dapprox1.Capacityand5%-dampedelasticdemanddiagram2.StartatD=11.3cmMarch27,200216R.K.GoelATC-40Procedure-AAnalysisofSystem53.µ=11.3÷2.56=4.404.ζeq=(2/π)×(µ-1/µ)=0.49=0.45k=0.77ζeq=0.05+0.77×0.45=0.3975.Capacitydiagramintersects39.7%-dampedelasticdemanddiagramat3.73cmMarch27,200217R.K.GoelATC-40Procedure-AAnalysisofSystem56.Error=100×(3.73-11.3)÷3.72=-202.6%5%toleranceRepeatsteps3to6tillconvergenceisachievedDapprox=4.46cmDexact=10.2cmError=-56.1%March27,200218R.K.GoelATC-40Procedure-AAnalysisofSystem5March27,200219R.K.GoelATC-40Procedure-AAnalysisofSystem5!TheATC-40ProcedureAconvergestoadeformationmuchsmallerthanthe“exact”value.!Convergenceisdeceptivebecauseitmayleavetheerroneousimpressionthatcalculateddeformationisaccurate.March27,200220R.K.GoelATC-40Procedure-AAnalysisofSystem6!Given:Tn=1s,ζ=0.05,fy÷w=Ay÷g=0.17.!Input:1940ElCentroGroundMotion!Find:Dapprox!Procedure-AfailstoconvergeMarch27,200221R.K.GoelATC-40Procedure-AAnalysisofSystem6!ATC-40ProcedureAfailstoconverge.!Intersectionpointoscillatesbetween11.7and3.52cm.!Proceduredivergesevenwhenrestartedwithdeformationcloseto“exact”value.March27,200222R.K.GoelExamples:DesignSpectrumMarch27,200223R.K.GoelNewmark-HallElasticDesignSpectrum0.020.050.10.20.51251020500.0020.0050.010.020.050.10.20.512510Tn,sA,gaTa=1/33secbTb=0.125seccTcdTdeTe=10secfTf=33secAccelerationSensitiveVelocitySensitiveDisplacementSensitiveMarch27,200224R.K.GoelATC-40Procedure-AAnalysisofSystem5!Given:Tn=1s,ζ=0.05,fy÷w=Ay÷g=0.45.!Input:Newmark-Hall(1982)designspectrum!Find:Dapprox1.Capacityand5%-dampedelasticdemanddiagram2.StartatD=44.6cmMarch27,200225R.K.GoelATC-40Procedure-AAnalysisofSystem53.µ=44.6÷11.6=4.04.ζeq=(2/π)×(µ-1/µ)=0.48=0.45k=0.77ζeq=0.05+0.77×0.45=0.3975.Capacitydiagramintersects39.7%-dampedelasticdemanddiagramat28.2cmMarch27,200226R.K.GoelATC-40Procedure-AAnalysisofSystem56.Error=100×(28.2-44.6)÷44.6=-58.4%5%toleranceRepeatsteps3to6tillconvergenceisachievedDapprox=30.4cmDexact=44.6cmError=-31.8%March27,200227R.K.GoelATC-40Procedure-AAnalysisofSystem5March27,200228R.K.GoelATC-40Procedure-AAnalysisofSystem5!ATC-40ProcedureAgivesdeformationsmallerthaninelasticdesignspectrum.!Convergenceleavesanerroneousimpressionthatcalculateddeformationisaccurate.March27,200229R.K.GoelATC-40Procedure-AAnalysisofSystem6!Given:Tn=1s,ζ=0