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TSINGHUASCIENCEANDTECHNOLOGYISSN1007021420/21pp124130Volume11,Number1,February2006PushOverAnalysisoftheSeismicBehaviorofaConcreteFilledRectangularTubularFrameStructureNIEJianguoWyS,QINKaiU,XIAOYanoû†DepartmentofCivilEngineering,TsinghuaUniversity,Beijing100084,China†DepartmentofCivilEngineering,UniversityofSouthernCalifornia,LosAngeles,CA90089,USAAbstractToinvestigatetheseismicbehaviorofconcretefilledrectangularsteeltubeCFRTstructures,apushoveranalysisofa10storymomentresistingframeMRFcomposedofCFRTcolumnsandsteelbeamswasconducted.Theresultsshowthatpushoveranalysisissensitivetothelateralloadpatterns,sotheuseofatleasttwoloadpatternsthatareexpectedtoboundtheinertiaforcedistributionsisrecommended.TheMφcurvesandNMinteractionsurfacesoftheCFRTcolumnscalculatedeitherbyHansformulaeorbytheUSCRCprogramreinforcedconcreteprogramputforwardbyUniversityofSouthernCalifoniaaresuitableforfuturepushoveranalysesofCFRTstructures.TheP∆effectaffectstheMRFseismicbehaviorseriously,andsoshouldbetakenintoaccountinMRFseismicanalysis.Inaddition,threekindsofRCstructureswereanalyzedtoallowacomparisonoftheearthquakeresistancebehaviorofCFRTstructuresandRCstructures.TheresultsshowthattheductilityandseismicperformanceofCFRTstructuresaresuperiortothoseofRCstructures.Consequently,CFRTstructuresarerecommendedinseismicregions.KeywordsconcretefilledrectangularsteeltubepushoveranalysiscapacitycurvereinforcedconcreteIntroductionOverthepasttwentyyearsthestaticpushoverprocedurehasbeenpresentedanddevelopedbyseveralauthors,includingSaiidiandSozen1,FajfarandGaspersic2,Braccietal.3,amongstothers.Thismethodisalsodescribedandrecommendedasatoolfordesignandassessmentpurposesfortheseismicrehabilitationofexistingbuildings4.Thepurposeofpushoveranalysisistoevaluatetheexpectedperformanceofastructuralsystembyestimatingitsstrengthanddeformationdemandsindesignearthquakesbymeansofastaticinelasticanalysis,andbycomparingthesedemandstoavailablecapacitiesattheperformancelevels.Pushoveranalysisisbasicallyanonlinearstaticanalysisthatisperformedbyimposinganassumeddistributionoflateralloadsovertheheightofastructureandincreasingthelateralloadsmonotonicallyfromzerototheultimatelevelcorrespondingtotheincipientcollapseofthestructure.Thegravityloadremainsconstantduringtheanalysis.Pushoveranalysisisveryusefulinestimatingthefollowingcharacteristicsofastructure1thecapacityofthestructureasrepresentedbythebaseshearversustopdisplacementgraph2themaximumrotationandductilityofcriticalmembers3thedistributionofplastichingesattheultimateloadand4thedistributionofdamageinthestructure,asexpressedintheformoflocaldamageindicesattheultimateload.Althoughpushoveranalysesofreinforced﹡Received20040630revised20041107SupportedbytheOverseasYouthCooperativeFoundationoftheNationalNaturalScienceFoundationofChinaNo.50128807﹡﹡Towhomcorrespondenceshouldbeaddressed.Emailniejgmail.tsinghua.edu.cnTel861062772457NIEJianguoWySetalPushOverAnalysisoftheSeismicBehaviorof125concreteRCstructuresandsteelstructureshavebeencarriedoutbymanyresearchersanddesigners,atpresentpushoveranalysesfortheconcretefilledsteeltubeCFTstructuresarerarelyreportedintheliterature.CFTcolumnshavebecomeincreasinglypopularinstructuralapplications.Thisispartlyduetotheirexcellentearthquakeresistantpropertiessuchashighstrength,highductility,andlargeenergyabsorptioncapacity5.Atpresent,theoreticalanalysisofthesestructuresfocusesmostlyonthestaticbehavioroftheCFTmembers,suchthattheseismicresponsesoftheCFTstructureshavebeenrarelystudied.SomeresearchontheseismicbehaviorofCFTstructuresis,however,documentedintheliterature.TheelastoplastictimehistoryanalysisofCFTstructureshasbeendiscussedbyLietal.6Theirresultsshowthatnoirreparabledamageoccursinstructuresunderintenseearthquakeloading,whichdemonstratesthatCFTstructuresexcelinseismicperformance.Theseismicbehaviorsoffourkindsof5storyframestructuresthatarecomposedofCFTandofRCcolumnshavebeenstudiedbyHuangetal.7TheSAP2000programwasusedinthetimehistoryanalysesforcalculatingtheseismicresponsesofthestructures.ThedynamicbehaviorandearthquakeresponseoftheCFTandRCstructureswereanalyzed.TheauthorsconcludethattheearthquakeresistancebehaviorofCFTstructuresisexcellentcomparedtothatofRCstructures.Experimentalinvestigationofa2span,3storymodelofaCFTframehasbeencarriedoutunderverticalstableloadsandlateralcyclicloadsbyLietal.8BasedontheCFTframemodelexperiment,anonlinearfiniteelementanalysiswascompleted9.Thecalculatedresultscoincidedwiththetestresults,providingapracticalmethodfortheseismicdesignofCFTframes.AlthoughtheseismicbehaviorofCFTframestructureshasbeeninvestigatedbymanyresearchersinrecentyears,thedifferentelastoplasticanalysismethodsareconfinedbytheirrationality,applicability,andefficiency.Thesemethodsneedtobemodifiedregardingaspectsoftheirmechanicalmodels,hystereticcharacteristics,andcalculationefficiency,andmoreexperimentalresearchstillneedstobecarriedouttochecktheaccuracyoftheseanalysismethods.Althoughconcretefilledsteelrectangulartubularcolumnsareinferiortoconcretefilledsteelcirculartubularcolumnsintermsofbearingcapacity,theyaresuperiorinmanyotheraspects,suchasbeamcolumnconnectionconstructability,stability,andfireresistance.Therefore,theyareincreasinglyusedforhighrisebuildingsinmanycountriesallaroundtheworld.However,applicationofconcretefilledrectangularsteeltubeCFRTstructuresisstillrestrictedbecauseofthelackofengineeringinformationontheoverallseismicbehaviorofCFRTstructures.Forthepurposeofinvestigatingtheseismicresponsesundersevereearthquakeconditions,apushoveranalysisofa10storyCFRTstructurehasbeencarriedoutandisreportedinthispaper.1PushOverAnalysisA10storymomentresistingframestructurethatiscomposedofconcretefilledrectangularsteeltubecolumnsandsteelbeamswasstudied.Theplan,elevation,andtypicalcrosssectionsofstructuralmembersoftheCFRTFig.1Plan,elevation,andtypicalcrosssectionsofstructuralmembersoftheCFRTstructuremmTsinghuaScienceandTechnology,February2006,111124130126structureareshowninFig.1.TheSAP2000programisusedforthepushoveranalysisoftheCFRTstructure.Thefloorsofthebuildingare100mmdeep,andaremodeledasshellelementsinSAP2000.ThedimensionsandmaterialpropertiesofthestructuralmembersareshowninTable1.InSAP2000theCFRTcolumnsandsteelbeamsaremodeledasframeelements.Table1DimensionsandmaterialpropertiesofthestruturalmembersoftheCFRTstructureStoryNo.SteelbeamsmmCFRTcolumnsmm1,2700300132470020370030013247001846692300132070018710692300132070016MaterialpropertyQ345Q345C401.1HingepropertiesInframestructuresplastichingesusuallyformattheendsofbeamsandcolumnsunderearthquakeaction.Forbeamelements,plastichingesaremostlycausedbyuniaxialbendingmoments,whereasforcolumnelements,plastichingesaremostlycausedbyaxialloadsandbiaxialbendingmoments.Therefore,inpushoveranalysisdifferenttypesofplastichingesshouldbeappliedforthebeamelementsandthecolumnelementsseparately.InSAP2000,theM3hingeisusedtosimulatetheplastichingecausedbyuniaxialmoment,souserdefinedM3hingesareappliedtothesteelbeamsinthismodel.Tocalculatemomentrotationcurvesofthesteelbeams,thefollowingassumptionsareadopted1aclassicalbilinearisotropichardeningmodelisappliedtorepresentthestressstrainbehaviorofthesteelbeamand2planesectionsremainplane.ThetypicalMφcurveforthesteelbeamsisshowninFig.2.Fig.2Mφcurveofsteelbeamsinthe1st3rdstoriesSimilarly,thePMMhingeisusedbySAP2000tosimulatetheplastichingecausedbyaxialloadandbiaxialbendingmoments.UserdefinedPMMhingesarethereforeappliedtotheCFRTcolumnsinthismodel.TheMφcurvesandNMinteractionsurfacesoftheCFRTcolumnsarecalculatedusingbothHansformulae10andtheUSCRCprogramRCprogramputforwardbyUniversityofSouthernCalifornia,forthepurposeofcomparison.ThetypicalN−MinteractionsurfaceandMφcurveoftheCFRTcolumnsareshowninFig.3.Fig.3NMinteractionsurfaceandMφcurveofCFRTcolumnsinthe1stand2ndstories1.2LateralloadpatternsThelateralloadpatternsareintendedtorepresentthedistributionofinertiaforcesinadesignearthquake11.Itisclearthatthedistributionofinertiaforceswillvarywiththeseverityoftheearthquakei.e.,theextentofinelasticdeformationsandwithtimeduringanearthquake.Sincenosingleloadpatterncancapturethevariationsinthelocaldemandsexpectedinadesignearthquake,twolateralloadpatternsthatareexpectedtoboundtheinertiaforcedistributionsareusedinthispushoveranalysis.OneisaninvertedtriangularlateralloadpatterncalculatedbythebaseshearmethodtheotheristhedesignlateralloadpatterncalculatedusingSAP2000includinghighermodeeffects.TheNIEJianguoWySetalPushOverAnalysisoftheSeismicBehaviorof127horizontalloadsareappliedintheXdirectionandYdirectioninturnforthepurposeofinvestigatingtheseismicbehaviorofthewholestructure.AsDongetal.mentionedinRef.12,theP∆effectseriouslyaffectsthestabilityofanunbracedframe.Therefore,pushoveranalyseswithandwithoutaccountingfortheP∆effectarecarriedoutinordertoinvestigatetheP∆effectontheseismicbehavioroftheCFRTstructure.1.3ResultsTheresultsofthepushoveranalysiscanbeusedtoestimatethepotentialductilityofthestructure,toevaluateitslateralloadresistantcapacity,andtoidentifythefailuremechanism.ItisthusimportanttoanalyzethepushoverresultstoobtaintheseismicbehavioroftheCFRTstructure.1.3.1LoaddeformationrelationshipThecapacityofthestructureasrepresentedbythebaseshearversustopdisplacementgraphisveryusefulinestimatingtheseismicbehaviorofastructureinapushoveranalysis.ThecapacitycurvesobtainedinthepushoveranalysesareshowninFig.4,fromwhichwefindthatforthecasesAccelXYHanP−,AccelXYUSCRCP−,EQXYHanP−,EQXYUSCRCP−,andEQXYHanPtheterminationiscausedbyexceedingthetargettopdisplacement1.6m,whileforthecasesAccelXYHanP,AccelXYUSCRCP,andEQXYUSC,RCPtheterminationiscausedbytheformationofaplasticmechanismforthewholestructure.TheinitialstiffnessvaluesandyieldbaseshearsofthecasesusingAccelXYlateralloadpatternsarehigherthanthecasesusingEQXYlateralloadpatterns.Therefore,theconclusioncanbedrawnthatthepushoveranalysisresultsaresensitivetolateralloadpatterns.Moreover,thetrendsofthecapacitycurvesintheXdirectionandintheYdirectionaresimilar,asshowninFig.4.Consequently,theseismicbehaviorofthewholestructurecanbeevaluatedbyoneofthedirectionsforthiscase.AsshowninFig.4,thecapacitycurvesarealmostthesameintheelasticregiondespitethedifferentMφcurvesandNMinteractionsurfacesoftheCFRTcolumns.ThepostyieldstiffnessvaluesforcasesusingMφandNMcurvescalculatedbyHansformulaearehigherthanthosecalculatedbyUSCRCprogram,butthedifferencesaresmallcomparedtootherparameters.Figure4alsoshowsthattheultimatebaseshearsdecreaseremarkablyinthepushoveranalysesasaresultoftheP∆effect.Similarly,thepostyieldstiffnessdecreasesforthesamereason.Therefore,wecandrawaconclusionthattheP∆effectaffectstheseismicbehaviorofthemomentresistingframeseriouslyandconsequently,theeffectshouldbetakenintoaccountinanyfutureMRFseismicanalyses.Fig.4CapacitycurvesofdifferentpushovercasesoftheCFRTstructureNotesEQXYrepresentscasesusingtheinvertedtriangularlateralloadpatterncalculatedbythebaseshearmethod,AccelXYrepresentscasesusingthedesignlateralloadpatterncalculatedusingSAP2000includinghighermodeeffectsHanrepresentscasesusingtheMφandNMcurvescalculatedbyHansformulae,USCRCrepresentscasesusingtheMφandNMcurvescalculatedusingtheUSCRCprogramP−representscaseswithoutconsideringtheP∆effect,PrepresentscasesincludingtheP∆effect.1.3.2FinalinterstorydriftsTheinterstorydriftsatthemomentofterminationinthepushoveranalysesareshowninFig.5.ThesedataareusefulinpredictingtheweakstoriesoftheCFRTstructure.FromFig.5,weobservethattheinterstorydriftsofthe1st3rdstoriesareremarkablyhigherthan
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