TSINGHUASCIENCEANDTECHNOLOGYISSN1007-021420/21pp124-130Volume11,Number1,February2006Push-OverAnalysisoftheSeismicBehaviorofaConcrete-FilledRectangularTubularFrameStructure*NIEJianguo(WyS)*,QINKai(U:),XIAOYan(o)DepartmentofCivilEngineering,TsinghuaUniversity,Beijing100084,China；DepartmentofCivilEngineering,UniversityofSouthernCalifornia,LosAngeles,CA90089,USAAbstract:Toinvestigatetheseismicbehaviorofconcrete-filledrectangularsteeltube(CFRT)structures,apush-overanalysisofa10-storymomentresistingframe(MRF)composedofCFRTcolumnsandsteelbeamswasconducted.Theresultsshowthatpush-overanalysisissensitivetothelateralloadpatterns,sotheuseofatleasttwoloadpatternsthatareexpectedtoboundtheinertiaforcedistributionsisrecom-mended.The-Mcurvesand-NMinteractionsurfacesoftheCFRTcolumnscalculatedeitherbyHansformulaeorbytheUSC-RCprogram(reinforcedconcreteprogramputforwardbyUniversityofSouthernCalifonia)aresuitableforfuturepush-overanalysesofCFRTstructures.The-PeffectaffectstheMRFseismicbehaviorseriously,andsoshouldbetakenintoaccountinMRFseismicanalysis.Inaddition,threekindsofRCstructureswereanalyzedtoallowacomparisonoftheearthquakeresistancebehaviorofCFRTstructuresandRCstructures.TheresultsshowthattheductilityandseismicperformanceofCFRTstruc-turesaresuperiortothoseofRCstructures.Consequently,CFRTstructuresarerecommendedinseismicregions.Keywords:concrete-filledrectangularsteeltube；push-overanalysis；capacitycurve；reinforcedconcreteIntroductionOverthepasttwentyyearsthestaticpush-overproce-durehasbeenpresentedanddevelopedbyseveralau-thors,includingSaiidiandSozen1,FajfarandGasper-sic2,Braccietal.3,amongstothers.Thismethodisalsodescribedandrecommendedasatoolfordesignandassessmentpurposesfortheseismicrehabilitationofexistingbuildings4.Thepurposeofpush-overanalysisistoevaluatetheexpectedperformanceofastructuralsystembyestimatingitsstrengthanddefor-mationdemandsindesignearthquakesbymeansofastaticinelasticanalysis,andbycomparingthesede-mandstoavailablecapacitiesattheperformancelevels.Push-overanalysisisbasicallyanonlinearstaticanalysisthatisperformedbyimposinganassumeddis-tributionoflateralloadsovertheheightofastructureandincreasingthelateralloadsmonotonicallyfromzerototheultimatelevelcorrespondingtotheincipientcollapseofthestructure.Thegravityloadremainscon-stantduringtheanalysis.Push-overanalysisisveryusefulinestimatingthefollowingcharacteristicsofastructure:1)thecapacityofthestructureasrepresentedbythebaseshearversustopdisplacementgraph；2)themaximumrotationandductilityofcriticalmembers；3)thedistributionofplastichingesattheultimateload；and4)thedistributionofdamageinthestructure,asexpressedintheformoflocaldamageindicesattheul-timateload.Althoughpush-overanalysesofreinforcedReceived:2004-06-30；revised:2004-11-07SupportedbytheOverseasYouthCooperativeFoundationoftheNationalNaturalScienceFoundationofChina(No.50128807)Towhomcorrespondenceshouldbeaddressed.E-mail:；Tel:86-10-62772457NIEJianguo(WyS)etalPush-OverAnalysisoftheSeismicBehaviorof125concrete(RC)structuresandsteelstructureshavebeencarriedoutbymanyresearchersanddesigners,atpresentpush-overanalysesfortheconcrete-filledsteeltube(CFT)structuresarerarelyreportedintheliterature.CFTcolumnshavebecomeincreasinglypopularinstructuralapplications.Thisispartlyduetotheirex-cellentearthquakeresistantpropertiessuchashighstrength,highductility,andlargeenergyabsorptioncapacity5.Atpresent,theoreticalanalysisofthesestructuresfocusesmostlyonthestaticbehavioroftheCFTmembers,suchthattheseismicresponsesoftheCFTstructureshavebeenrarelystudied.Somere-searchontheseismicbehaviorofCFTstructuresis,however,documentedintheliterature.Theelasto-plastictime-historyanalysisofCFTstructureshasbeendiscussedbyLietal.6Theirresultsshowthatnoirreparabledamageoccursinstructuresunderin-tenseearthquakeloading,whichdemonstratesthatCFTstructuresexcelinseismicperformance.Theseismicbehaviorsoffourkindsof5-storyframestructuresthatarecomposedofCFTandofRCcol-umnshavebeenstudiedbyHuangetal.7TheSAP2000programwasusedinthetime-historyanalysesforcalculatingtheseismicresponsesofthestructures.Thedynamicbehaviorandearthquakere-sponseoftheCFTandRCstructureswereanalyzed.TheauthorsconcludethattheearthquakeresistancebehaviorofCFTstructuresisexcellentcomparedtothatofRCstructures.Experimentalinvestigationofa2-span,3-storymodelofaCFTframehasbeencar-riedoutunderverticalstableloadsandlateralcyclicloadsbyLietal.8BasedontheCFTframemodelexperiment,anonlinearfiniteelementanalysiswascompleted9.Thecalculatedresultscoincidedwiththetestresults,providingapracticalmethodfortheseismicdesignofCFTframes.AlthoughtheseismicbehaviorofCFTframestructureshasbeeninvesti-gatedbymanyresearchersinrecentyears,thediffer-entelasto-plasticanalysismethodsareconfinedbytheirrationality,applicability,andefficiency.Thesemethodsneedtobemodifiedregardingaspectsoftheirmechanicalmodels,hystereticcharacteristics,andcalculationefficiency,andmoreexperimentalre-searchstillneedstobecarriedouttochecktheaccu-racyoftheseanalysismethods.Althoughconcrete-filledsteelrectangulartubularcolumnsareinferiortoconcrete-filledsteelcirculartubularcolumnsintermsofbearingcapacity,theyaresuperiorinmanyotheraspects,suchasbeam-columnconnectionconstructability,stability,andfireresis-tance.Therefore,theyareincreasinglyusedforhigh-risebuildingsinmanycountriesallaroundtheworld.However,applicationofconcrete-filledrectangularsteeltube(CFRT)structuresisstillrestrictedbecauseofthelackofengineeringinformationontheoverallseismicbehaviorofCFRTstructures.Forthepurposeofinvestigatingtheseismicresponsesundersevereearthquakeconditions,apush-overanalysisofa10-storyCFRTstructurehasbeencarriedoutandisre-portedinthispaper.1Push-OverAnalysisA10-storymomentresistingframestructurethatiscom-posedofconcrete-filledrectangularsteeltubecolumnsandsteelbeamswasstudied.Theplan,elevation,andtypicalcross-sectionsofstructuralmembersoftheCFRTFig.1Plan,elevation,andtypicalcross-sectionsofstructuralmembersoftheCFRTstructure(mm)TsinghuaScienceandTechnology,February2006,11(1):124-130126structureareshowninFig.1.TheSAP2000programisusedforthepush-overanalysisoftheCFRTstruc-ture.Thefloorsofthebuildingare100mmdeep,andaremodeledasshellelementsinSAP2000.Thedi-mensionsandmaterialpropertiesofthestructuralmembersareshowninTable1.InSAP2000theCFRTcolumnsandsteelbeamsaremodeledasframeelements.Table1DimensionsandmaterialpropertiesofthestruturalmembersoftheCFRTstructureStoryNo.Steelbeams(mm)CFRTcolumns(mm)1,270030013247002037003001324700184-66923001320700187-10692300132070016MaterialpropertyQ345Q345C401.1HingepropertiesInframestructuresplastichingesusuallyformattheendsofbeamsandcolumnsunderearthquakeaction.Forbeamelements,plastichingesaremostlycausedbyuniaxialbendingmoments,whereasforcolumnelements,plastichingesaremostlycausedbyaxialloadsandbiaxialbendingmoments.Therefore,inpush-overanalysisdifferenttypesofplastichingesshouldbeappliedforthebeamelementsandthecol-umnelementsseparately.InSAP2000,theM3hingeisusedtosimulatetheplastichingecausedbyuniaxialmoment,souser-definedM3hingesareappliedtothesteelbeamsinthismodel.Tocalculatemoment-rotationcurvesofthesteelbeams,thefollowingassumptionsareadopted:1)aclassicalbilinearisotropichardeningmodelisappliedtorepresentthestress-strainbehav-iorofthesteelbeam；and2)planesectionsremainplane.ThetypicalM-curveforthesteelbeamsisshowninFig.2.Fig.2M-curveofsteelbeamsinthe1st-3rdstoriesSimilarly,thePMMhingeisusedbySAP2000tosimulatetheplastichingecausedbyaxialloadandbiaxialbendingmoments.User-definedPMMhingesarethereforeappliedtotheCFRTcolumnsinthismodel.TheM-curvesandN-MinteractionsurfacesoftheCFRTcolumnsarecalculatedusingbothHansformulae10andtheUSC-RCprogram(RCprogramputforwardbyUniversityofSouthernCalifornia),forthepurposeofcomparison.ThetypicalNMinterac-tionsurfaceandM-curveoftheCFRTcolumnsareshowninFig.3.Fig.3-NMinteractionsurfaceand-McurveofCFRTcolumnsinthe1stand2ndstories1.2LateralloadpatternsThelateralloadpatternsareintendedtorepresentthedistributionofinertiaforcesinadesignearthquake11.Itisclearthatthedistributionofinertiaforceswillvarywiththeseverityoftheearthquake(i.e.,theextentofinelasticdeformations)andwithtimeduringanearthquake.Sincenosingleloadpatterncancapturethevariationsinthelocaldemandsexpectedinade-signearthquake,twolateralloadpatternsthatareex-pectedtoboundtheinertiaforcedistributionsareusedinthispush-overanalysis.Oneisaninvertedtriangularlateralloadpatterncalculatedbythebaseshearmethod；theotheristhedesignlateralloadpatterncalculatedusingSAP2000includinghighermodeeffects.TheNIEJianguo(WyS)etalPush-OverAnalysisoftheSeismicBehaviorof127horizontalloadsareappliedintheX-directionandY-directioninturnforthepurposeofinvestigatingtheseismicbehaviorofthewholestructure.AsDongetal.mentionedinRef.12,the-Peffectseriouslyaffectsthestabilityofanunbracedframe.There-fore,push-overanalyseswithandwithoutaccountingforthe-Peffectarecarriedoutinordertoinvestigatethe-PeffectontheseismicbehavioroftheCFRTstructure.1.3ResultsTheresultsofthepush-overanalysiscanbeusedtoes-timatethepotentialductilityofthestructure,toevalu-ateitslateralloadresistantcapacity,andtoidentifythefailuremechanism.Itisthusimportanttoanalyzethepush-overresultstoobtaintheseismicbehavioroftheCFRTstructure.1.3.1Load-deformationrelationshipThecapacityofthestructureasrepresentedbythebaseshearversustopdisplacementgraphisveryuse-fulinestimatingtheseismicbehaviorofastructureinapush-overanalysis.Thecapacitycurvesobtainedinthepush-overanalysesareshowninFig.4,fromwhichwefindthatforthecasesAccelX(Y)-Han-P,AccelX(Y)-USC-RC-P,EQX(Y)-Han-P,EQX(Y)-USC-RC-P,andEQX(Y)-Han-P+theterminationiscausedbyexceedingthetargettopdisplacement(1.6m),whileforthecasesAccelX(Y)-Han-P+,Ac-celX(Y)-USC-RC-P+,andEQX(Y)-USC,RC-P+theterminationiscausedbytheformationofaplasticmechanismforthewholestructure.Theinitialstiff-nessvaluesandyieldbaseshearsofthecasesusingAccelX(Y)lateralloadpatternsarehigherthanthecasesusingEQX(Y)lateralloadpatterns.Therefore,theconclusioncanbedrawnthatthepush-overanaly-sisresultsaresensitivetolateralloadpatterns.More-over,thetrendsofthecapacitycurvesintheX-directionandintheY-directionaresimilar,asshowninFig.4.Consequently,theseismicbehaviorofthewholestructurecanbeevaluatedbyoneofthedirec-tionsforthiscase.AsshowninFig.4,thecapacitycurvesarealmostthesameintheelasticregiondespitethedifferent-Mcurvesand-NMinteractionsurfacesoftheCFRTcolumns.Thepost-yieldstiffnessvaluesforcasesusing-Mand-NMcurvescalculatedbyHansformulaearehigherthanthosecalculatedbyUSC-RCpro