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TSINGHUASCIENCEANDTECHNOLOGYISSN1007021420/21PP124130VOLUME11,NUMBER1,FEBRUARY2006PUSHOVERANALYSISOFTHESEISMICBEHAVIOROFACONCRETEFILLEDRECTANGULARTUBULARFRAMESTRUCTURENIEJIANGUOWYS,QINKAIU,XIAOYANO†DEPARTMENTOFCIVILENGINEERING,TSINGHUAUNIVERSITY,BEIJING100084,CHINA;†DEPARTMENTOFCIVILENGINEERING,UNIVERSITYOFSOUTHERNCALIFORNIA,LOSANGELES,CA90089,USAABSTRACTTOINVESTIGATETHESEISMICBEHAVIOROFCONCRETEFILLEDRECTANGULARSTEELTUBECFRTSTRUCTURES,APUSHOVERANALYSISOFA10STORYMOMENTRESISTINGFRAMEMRFCOMPOSEDOFCFRTCOLUMNSANDSTEELBEAMSWASCONDUCTEDTHERESULTSSHOWTHATPUSHOVERANALYSISISSENSITIVETOTHELATERALLOADPATTERNS,SOTHEUSEOFATLEASTTWOLOADPATTERNSTHATAREEXPECTEDTOBOUNDTHEINERTIAFORCEDISTRIBUTIONSISRECOMMENDEDTHEMΦCURVESANDNMINTERACTIONSURFACESOFTHECFRTCOLUMNSCALCULATEDEITHERBYHAN’SFORMULAEORBYTHEUSCRCPROGRAMREINFORCEDCONCRETEPROGRAMPUTFORWARDBYUNIVERSITYOFSOUTHERNCALIFONIAARESUITABLEFORFUTUREPUSHOVERANALYSESOFCFRTSTRUCTURESTHEP∆EFFECTAFFECTSTHEMRFSEISMICBEHAVIORSERIOUSLY,ANDSOSHOULDBETAKENINTOACCOUNTINMRFSEISMICANALYSISINADDITION,THREEKINDSOFRCSTRUCTURESWEREANALYZEDTOALLOWACOMPARISONOFTHEEARTHQUAKERESISTANCEBEHAVIOROFCFRTSTRUCTURESANDRCSTRUCTURESTHERESULTSSHOWTHATTHEDUCTILITYANDSEISMICPERFORMANCEOFCFRTSTRUCTURESARESUPERIORTOTHOSEOFRCSTRUCTURESCONSEQUENTLY,CFRTSTRUCTURESARERECOMMENDEDINSEISMICREGIONSKEYWORDSCONCRETEFILLEDRECTANGULARSTEELTUBE;PUSHOVERANALYSIS;CAPACITYCURVE;REINFORCEDCONCRETEINTRODUCTIONOVERTHEPASTTWENTYYEARSTHESTATICPUSHOVERPROCEDUREHASBEENPRESENTEDANDDEVELOPEDBYSEVERALAUTHORS,INCLUDINGSAIIDIANDSOZEN1,FAJFARANDGASPERSIC2,BRACCIETAL3,AMONGSTOTHERSTHISMETHODISALSODESCRIBEDANDRECOMMENDEDASATOOLFORDESIGNANDASSESSMENTPURPOSESFORTHESEISMICREHABILITATIONOFEXISTINGBUILDINGS4THEPURPOSEOFPUSHOVERANALYSISISTOEVALUATETHEEXPECTEDPERFORMANCEOFASTRUCTURALSYSTEMBYESTIMATINGITSSTRENGTHANDDEFORMATIONDEMANDSINDESIGNEARTHQUAKESBYMEANSOFASTATICINELASTICANALYSIS,ANDBYCOMPARINGTHESEDEMANDSTOAVAILABLECAPACITIESATTHEPERFORMANCELEVELSPUSHOVERANALYSISISBASICALLYANONLINEARSTATICANALYSISTHATISPERFORMEDBYIMPOSINGANASSUMEDDISTRIBUTIONOFLATERALLOADSOVERTHEHEIGHTOFASTRUCTUREANDINCREASINGTHELATERALLOADSMONOTONICALLYFROMZEROTOTHEULTIMATELEVELCORRESPONDINGTOTHEINCIPIENTCOLLAPSEOFTHESTRUCTURETHEGRAVITYLOADREMAINSCONSTANTDURINGTHEANALYSISPUSHOVERANALYSISISVERYUSEFULINESTIMATINGTHEFOLLOWINGCHARACTERISTICSOFASTRUCTURE1THECAPACITYOFTHESTRUCTUREASREPRESENTEDBYTHEBASESHEARVERSUSTOPDISPLACEMENTGRAPH;2THEMAXIMUMROTATIONANDDUCTILITYOFCRITICALMEMBERS;3THEDISTRIBUTIONOFPLASTICHINGESATTHEULTIMATELOAD;AND4THEDISTRIBUTIONOFDAMAGEINTHESTRUCTURE,ASEXPRESSEDINTHEFORMOFLOCALDAMAGEINDICESATTHEULTIMATELOADALTHOUGHPUSHOVERANALYSESOFREINFORCED﹡RECEIVED20040630;REVISED20041107SUPPORTEDBYTHEOVERSEASYOUTHCOOPERATIVEFOUNDATIONOFTHENATIONALNATURALSCIENCEFOUNDATIONOFCHINANO50128807﹡﹡TOWHOMCORRESPONDENCESHOULDBEADDRESSEDEMAILNIEJGMAILTSINGHUAEDUCN;TEL861062772457NIEJIANGUOWYSETALPUSHOVERANALYSISOFTHESEISMICBEHAVIOROF125CONCRETERCSTRUCTURESANDSTEELSTRUCTURESHAVEBEENCARRIEDOUTBYMANYRESEARCHERSANDDESIGNERS,ATPRESENTPUSHOVERANALYSESFORTHECONCRETEFILLEDSTEELTUBECFTSTRUCTURESARERARELYREPORTEDINTHELITERATURECFTCOLUMNSHAVEBECOMEINCREASINGLYPOPULARINSTRUCTURALAPPLICATIONSTHISISPARTLYDUETOTHEIREXCELLENTEARTHQUAKERESISTANTPROPERTIESSUCHASHIGHSTRENGTH,HIGHDUCTILITY,ANDLARGEENERGYABSORPTIONCAPACITY5ATPRESENT,THEORETICALANALYSISOFTHESESTRUCTURESFOCUSESMOSTLYONTHESTATICBEHAVIOROFTHECFTMEMBERS,SUCHTHATTHESEISMICRESPONSESOFTHECFTSTRUCTURESHAVEBEENRARELYSTUDIEDSOMERESEARCHONTHESEISMICBEHAVIOROFCFTSTRUCTURESIS,HOWEVER,DOCUMENTEDINTHELITERATURETHEELASTOPLASTICTIMEHISTORYANALYSISOFCFTSTRUCTURESHASBEENDISCUSSEDBYLIETAL6THEIRRESULTSSHOWTHATNOIRREPARABLEDAMAGEOCCURSINSTRUCTURESUNDERINTENSEEARTHQUAKELOADING,WHICHDEMONSTRATESTHATCFTSTRUCTURESEXCELINSEISMICPERFORMANCETHESEISMICBEHAVIORSOFFOURKINDSOF5STORYFRAMESTRUCTURESTHATARECOMPOSEDOFCFTANDOFRCCOLUMNSHAVEBEENSTUDIEDBYHUANGETAL7THESAP2000PROGRAMWASUSEDINTHETIMEHISTORYANALYSESFORCALCULATINGTHESEISMICRESPONSESOFTHESTRUCTURESTHEDYNAMICBEHAVIORANDEARTHQUAKERESPONSEOFTHECFTANDRCSTRUCTURESWEREANALYZEDTHEAUTHORSCONCLUDETHATTHEEARTHQUAKERESISTANCEBEHAVIOROFCFTSTRUCTURESISEXCELLENTCOMPAREDTOTHATOFRCSTRUCTURESEXPERIMENTALINVESTIGATIONOFA2SPAN,3STORYMODELOFACFTFRAMEHASBEENCARRIEDOUTUNDERVERTICALSTABLELOADSANDLATERALCYCLICLOADSBYLIETAL8BASEDONTHECFTFRAMEMODELEXPERIMENT,ANONLINEARFINITEELEMENTANALYSISWASCOMPLETED9THECALCULATEDRESULTSCOINCIDEDWITHTHETESTRESULTS,PROVIDINGAPRACTICALMETHODFORTHESEISMICDESIGNOFCFTFRAMESALTHOUGHTHESEISMICBEHAVIOROFCFTFRAMESTRUCTURESHASBEENINVESTIGATEDBYMANYRESEARCHERSINRECENTYEARS,THEDIFFERENTELASTOPLASTICANALYSISMETHODSARECONFINEDBYTHEIRRATIONALITY,APPLICABILITY,ANDEFFICIENCYTHESEMETHODSNEEDTOBEMODIFIEDREGARDINGASPECTSOFTHEIRMECHANICALMODELS,HYSTERETICCHARACTERISTICS,ANDCALCULATIONEFFICIENCY,ANDMOREEXPERIMENTALRESEARCHSTILLNEEDSTOBECARRIEDOUTTOCHECKTHEACCURACYOFTHESEANALYSISMETHODSALTHOUGHCONCRETEFILLEDSTEELRECTANGULARTUBULARCOLUMNSAREINFERIORTOCONCRETEFILLEDSTEELCIRCULARTUBULARCOLUMNSINTERMSOFBEARINGCAPACITY,THEYARESUPERIORINMANYOTHERASPECTS,SUCHASBEAMCOLUMNCONNECTIONCONSTRUCTABILITY,STABILITY,ANDFIRERESISTANCETHEREFORE,THEYAREINCREASINGLYUSEDFORHIGHRISEBUILDINGSINMANYCOUNTRIESALLAROUNDTHEWORLDHOWEVER,APPLICATIONOFCONCRETEFILLEDRECTANGULARSTEELTUBECFRTSTRUCTURESISSTILLRESTRICTEDBECAUSEOFTHELACKOFENGINEERINGINFORMATIONONTHEOVERALLSEISMICBEHAVIOROFCFRTSTRUCTURESFORTHEPURPOSEOFINVESTIGATINGTHESEISMICRESPONSESUNDERSEVEREEARTHQUAKECONDITIONS,APUSHOVERANALYSISOFA10STORYCFRTSTRUCTUREHASBEENCARRIEDOUTANDISREPORTEDINTHISPAPER1PUSHOVERANALYSISA10STORYMOMENTRESISTINGFRAMESTRUCTURETHATISCOMPOSEDOFCONCRETEFILLEDRECTANGULARSTEELTUBECOLUMNSANDSTEELBEAMSWASSTUDIEDTHEPLAN,ELEVATION,ANDTYPICALCROSSSECTIONSOFSTRUCTURALMEMBERSOFTHECFRTFIG1PLAN,ELEVATION,ANDTYPICALCROSSSECTIONSOFSTRUCTURALMEMBERSOFTHECFRTSTRUCTUREMMTSINGHUASCIENCEANDTECHNOLOGY,FEBRUARY2006,111124130126STRUCTUREARESHOWNINFIG1THESAP2000PROGRAMISUSEDFORTHEPUSHOVERANALYSISOFTHECFRTSTRUCTURETHEFLOORSOFTHEBUILDINGARE100MMDEEP,ANDAREMODELEDASSHELLELEMENTSINSAP2000THEDIMENSIONSANDMATERIALPROPERTIESOFTHESTRUCTURALMEMBERSARESHOWNINTABLE1INSAP2000THECFRTCOLUMNSANDSTEELBEAMSAREMODELEDASFRAMEELEMENTSTABLE1DIMENSIONSANDMATERIALPROPERTIESOFTHESTRUTURALMEMBERSOFTHECFRTSTRUCTURESTORYNOSTEELBEAMSMMCFRTCOLUMNSMM1,2700300132470020370030013247001846692300132070018710692300132070016MATERIALPROPERTYQ345Q345C4011HINGEPROPERTIESINFRAMESTRUCTURESPLASTICHINGESUSUALLYFORMATTHEENDSOFBEAMSANDCOLUMNSUNDEREARTHQUAKEACTIONFORBEAMELEMENTS,PLASTICHINGESAREMOSTLYCAUSEDBYUNIAXIALBENDINGMOMENTS,WHEREASFORCOLUMNELEMENTS,PLASTICHINGESAREMOSTLYCAUSEDBYAXIALLOADSANDBIAXIALBENDINGMOMENTSTHEREFORE,INPUSHOVERANALYSISDIFFERENTTYPESOFPLASTICHINGESSHOULDBEAPPLIEDFORTHEBEAMELEMENTSANDTHECOLUMNELEMENTSSEPARATELYINSAP2000,THEM3HINGEISUSEDTOSIMULATETHEPLASTICHINGECAUSEDBYUNIAXIALMOMENT,SOUSERDEFINEDM3HINGESAREAPPLIEDTOTHESTEELBEAMSINTHISMODELTOCALCULATEMOMENTROTATIONCURVESOFTHESTEELBEAMS,THEFOLLOWINGASSUMPTIONSAREADOPTED1ACLASSICALBILINEARISOTROPICHARDENINGMODELISAPPLIEDTOREPRESENTTHESTRESSSTRAINBEHAVIOROFTHESTEELBEAM;AND2PLANESECTIONSREMAINPLANETHETYPICALMΦCURVEFORTHESTEELBEAMSISSHOWNINFIG2FIG2MΦCURVEOFSTEELBEAMSINTHE1ST3RDSTORIESSIMILARLY,THEPMMHINGEISUSEDBYSAP2000TOSIMULATETHEPLASTICHINGECAUSEDBYAXIALLOADANDBIAXIALBENDINGMOMENTSUSERDEFINEDPMMHINGESARETHEREFOREAPPLIEDTOTHECFRTCOLUMNSINTHISMODELTHEMΦCURVESANDNMINTERACTIONSURFACESOFTHECFRTCOLUMNSARECALCULATEDUSINGBOTHHAN’SFORMULAE10ANDTHEUSCRCPROGRAMRCPROGRAMPUTFORWARDBYUNIVERSITYOFSOUTHERNCALIFORNIA,FORTHEPURPOSEOFCOMPARISONTHETYPICALN−MINTERACTIONSURFACEANDMΦCURVEOFTHECFRTCOLUMNSARESHOWNINFIG3FIG3NMINTERACTIONSURFACEANDMΦCURVEOFCFRTCOLUMNSINTHE1STAND2NDSTORIES12LATERALLOADPATTERNSTHELATERALLOADPATTERNSAREINTENDEDTOREPRESENTTHEDISTRIBUTIONOFINERTIAFORCESINADESIGNEARTHQUAKE11ITISCLEARTHATTHEDISTRIBUTIONOFINERTIAFORCESWILLVARYWITHTHESEVERITYOFTHEEARTHQUAKEIE,THEEXTENTOFINELASTICDEFORMATIONSANDWITHTIMEDURINGANEARTHQUAKESINCENOSINGLELOADPATTERNCANCAPTURETHEVARIATIONSINTHELOCALDEMANDSEXPECTEDINADESIGNEARTHQUAKE,TWOLATERALLOADPATTERNSTHATAREEXPECTEDTOBOUNDTHEINERTIAFORCEDISTRIBUTIONSAREUSEDINTHISPUSHOVERANALYSISONEISANINVERTEDTRIANGULARLATERALLOADPATTERNCALCULATEDBYTHEBASESHEARMETHOD;THEOTHERISTHEDESIGNLATERALLOADPATTERNCALCULATEDUSINGSAP2000INCLUDINGHIGHERMODEEFFECTSTHENIEJIANGUOWYSETALPUSHOVERANALYSISOFTHESEISMICBEHAVIOROF127HORIZONTALLOADSAREAPPLIEDINTHEXDIRECTIONANDYDIRECTIONINTURNFORTHEPURPOSEOFINVESTIGATINGTHESEISMICBEHAVIOROFTHEWHOLESTRUCTUREASDONGETALMENTIONEDINREF12,THEP∆EFFECTSERIOUSLYAFFECTSTHESTABILITYOFANUNBRACEDFRAMETHEREFORE,PUSHOVERANALYSESWITHANDWITHOUTACCOUNTINGFORTHEP∆EFFECTARECARRIEDOUTINORDERTOINVESTIGATETHEP∆EFFECTONTHESEISMICBEHAVIOROFTHECFRTSTRUCTURE13RESULTSTHERESULTSOFTHEPUSHOVERANALYSISCANBEUSEDTOESTIMATETHEPOTENTIALDUCTILITYOFTHESTRUCTURE,TOEVALUATEITSLATERALLOADRESISTANTCAPACITY,ANDTOIDENTIFYTHEFAILUREMECHANISMITISTHUSIMPORTANTTOANALYZETHEPUSHOVERRESULTSTOOBTAINTHESEISMICBEHAVIOROFTHECFRTSTRUCTURE131LOADDEFORMATIONRELATIONSHIPTHECAPACITYOFTHESTRUCTUREASREPRESENTEDBYTHEBASESHEARVERSUSTOPDISPLACEMENTGRAPHISVERYUSEFULINESTIMATINGTHESEISMICBEHAVIOROFASTRUCTUREINAPUSHOVERANALYSISTHECAPACITYCURVESOBTAINEDINTHEPUSHOVERANALYSESARESHOWNINFIG4,FROMWHICHWEFINDTHATFORTHECASESACCELXYHANP−,ACCELXYUSCRCP−,EQXYHANP−,EQXYUSCRCP−,ANDEQXYHANPTHETERMINATIONISCAUSEDBYEXCEEDINGTHETARGETTOPDISPLACEMENT16M,WHILEFORTHECASESACCELXYHANP,ACCELXYUSCRCP,ANDEQXYUSC,RCPTHETERMINATIONISCAUSEDBYTHEFORMATIONOFAPLASTICMECHANISMFORTHEWHOLESTRUCTURETHEINITIALSTIFFNESSVALUESANDYIELDBASESHEARSOFTHECASESUSINGACCELXYLATERALLOADPATTERNSAREHIGHERTHANTHECASESUSINGEQXYLATERALLOADPATTERNSTHEREFORE,THECONCLUSIONCANBEDRAWNTHATTHEPUSHOVERANALYSISRESULTSARESENSITIVETOLATERALLOADPATTERNSMOREOVER,THETRENDSOFTHECAPACITYCURVESINTHEXDIRECTIONANDINTHEYDIRECTIONARESIMILAR,ASSHOWNINFIG4CONSEQUENTLY,THESEISMICBEHAVIOROFTHEWHOLESTRUCTURECANBEEVALUATEDBYONEOFTHEDIRECTIONSFORTHISCASEASSHOWNINFIG4,THECAPACITYCURVESAREALMOSTTHESAMEINTHEELASTICREGIONDESPITETHEDIFFERENTMΦCURVESANDNMINTERACTIONSURFACESOFTHECFRTCOLUMNSTHEPOSTY
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