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外文翻译

毕业设计（论文）

外文翻译

设计（论文）题目：

鄞西小学4号教学楼

结构设计与预算

学院名称：

建筑工程学院

专业：

土木工程

班级：

房建-071

姓名：

娄佳君学号07404010214

指导教师：

袁坚敏职称讲师

2011年2月28日

外文原文：

Lateralstiffnessestimationinframesanditsimplementationtocontinuummodels

forlinearandnonlinearstaticanalysis

TubaEro˘glu·SinanAkkar

Received:

23April2010/Accepted:

17November2010

©SpringerScience+BusinessMediaB.V.2010

Abstract

Continuummodelisausefultoolforapproximateanalysisoftallstructuresincludingmoment-resistingframesandshearwall-framesystems.Incontinuummodel,discretebuildingsaresimplifiedsuchthattheiroverallbehaviorisdescribedthroughthecontributionsofflexuralandshearstiffnessesatthestorylevels.Therefore,accuratedeterminationoftheselateralstiffnesscomponentsconstitutesoneofthemajorissuesinestablishingreliablecontinuummodelseveniftheproposedsolutionisanapproximationtoactualstructuralbehavior.Thisstudyfirstexaminesthepreviousliteratureonthecalculationoflateralstiffnesscomponents（i.e.flexuralandshearstiffnesses）throughcomparisonswithexactresultsobtainedfromdiscretemodels.Anewmethodologyforadaptingtheheightwisevariationoflateralstiffnesstocontinuummodelispresentedbasedonthesecomparisons.Theproposedmethodologyisthenextendedforestimatingthenonlinearglobalcapacityofmomentresistingframes.Theverificationsthatcomparethenonlinearbehaviorofrealsystemswiththoseestimatedfromtheproposedproceduresuggestitseffectiveusefortheperformanceassessmentoflargebuildingstocksthatexhibitsimilarstructuralfeatures.Thisconclusionisfurtherjustifiedbycomparingnonlinearresponsehistoryanalysesofsingle-degree-of-freedom（sdof）systemsthatareobtainedfromtheglobalcapacitycurvesofactualsystemsandtheirapproximationscomputedbytheproposedprocedure.

Keywords

Approximatenonlinearmethods·Continuummodel·Globalcapacity·

Nonlinearresponse·Framesanddualsystems

T.Ero˘glu

DepartmentofCivilEngineering,AkdenizUniversity,07058Antalya,Turkey

e-mail:

etuba@metu.edu.tr

S.Akkar（B）

DepartmentofCivilEngineering,MiddleEastTechnicalUniversity,06531Ankara,Turkey

e-mail:

sakkar@metu.edu.tr

1Introduction

Reliableestimationofstructuralresponseisessentialintheseismicperformanceassessmentanddesignbecauseitprovidesthemajorinputwhiledescribingtheglobalcapacityofstructuresunderstronggroundmotions.Withtheadventofcomputertechnologyandsophisticatedstructuralanalysisprograms,theanalystsarenowabletorefinetheirstructuralmodelstocomputemoreaccuratestructuralresponse.However,attheexpenseofcapturingdetailedstructuralbehavior,theincreasedunknownsinmodelingparameters,whencombinedwiththeuncertaintyingroundmotions,maketheinterpretationsofanalysisresultscumbersomeandtimeconsuming.Complexstructuralmodelingandresponsehistoryanalysiscanalsobeoverwhelmingforperformanceassessmentoflargebuildingstocksorthepreliminarydesignof

newbuildings.Thecontinuummodel,inthissense,isanaccomplishedapproximatetoolforestimatingtheoveralldynamicbehaviorofmomentresistingframes（MRFs）andshearwall-frame（dual）systems.

Continuummodel,asanapproximationtocomplexdiscretemodels,hasbeenusedextensivelyintheliterature.Westergaard（1933）usedequivalentundampedshearbeamconceptformodelingtallbuildingsunderearthquakeinducedshocksthroughtheimplementationofshearwavespropagatinginthecontinuummedia.Later,thecontinuousshearbeammodelhasbeenimplementedbymanyresearchers（e.g.Iwan1997;GülkanandAkkar2002;Akkaretal.2005;ChopraandChintanapakdee2001）toapproximatetheearthquakeinduceddeformationdemandsonframesystems.TheideaofusingequivalentshearbeamswasextendedtothecombinationofcontinuousshearandflexuralbeamsbyKhanandSbarounis（1964）.

HeidebrechtandStaffordSmith（1973）definedacontinuummodel（hereinafterHS73）forapproximatingtallshearwall-frametypestructuresthatisbasedonthesolutionofafourthorderpartialdifferentialequation（PDE）.Miranda（1999）presentedthesolutionofthisPDEunderasetoflateralstaticloadingcasestoapproximatethemaximumroofandinterstorydriftdemandsonfirst-modedominantstructures.Later,HeidebrechtandRutenberg（2000）showedadifferentversionofHS73methodtodrawtheupperandlowerboundsofinterstorydriftdemandsonframesystems.MirandaandTaghavi（2005）usedtheHS73modeltoacquiretheapproximatestructuralbehaviorupto3modes.Asafollowupstudy,MirandaandAkkar（2006）extendedtheuseofHS73tocomputegeneralizeddriftspectrumwithhighermodeeffects.Continuummodelisalsousedforestimatingthefundamentalperiodsofhigh-risebuildings（e.g.DymandWilliams2007）.Morerecently,Gengshuetal.（2008）studiedthesecondorderandbucklingeffectsonbuildingsthroughtheclosedformsolutionsofcontinuoussystems.

Whilethetheoreticalapplicationsofcontinuummodelareabundantasbrieflyaddressedabove,itspracticalimplementationisratherlimitedasthedeterminationofequivalentflexural（EI）andshear（GA）stiffnessestorepresenttheactuallateralstiffnessvariationindiscretesystemshavenotbeenfullyaddressedintheliterature.ThisflawhasalsorestrictedtheefficientuseofcontinuummodelbeyondelasticlimitsbecausethenonlinearbehaviorofcontinuummodelsisdictatedbythechangesinEIandGAinthepost-yieldingstage

Thispaperfocusesontherealisticdeterminationoflateralstiffnessforcontinuummodels.EIandGAdefinedindiscretesystemsareadaptedtocontinuummodelsthroughananalyticalexpressionthatconsiderstheheightwisevariationofboundaryconditionsindiscretesystems.TheHS73modelisusedasthebasecontinuummodelsinceitiscapableofrepresentingthestructuralresponsebetweenpureflexureandshearbehavior.Theproposedanalyticalexpressionisevaluatedbycomparingthedeformationpatternsofcontinuummodelandactualdiscretesystemsunderthefirst-modecompatibleloadingpattern.TheimprovementsonthedeterminationofEIandGAarecombinedwithasecondprocedurethatisbasedonlimitstateanalysistodescribetheglobalcapacityofstructuresrespondingbeyondtheirelasticlimits.Illustrativecasestudiesindicatethatthecontinuummodel,whenusedtogetherwiththeproposedmethodologies,canbeausefultoolforlinearandnonlinearstaticanalysis.

2Continuummodelcharacteristics

TheHS73modeliscomposedofaflexuralandshearbeamtodefinetheflexural（EI）andshear（GA）stiffnesscontributionstotheoveralllateralstiffness.ThemajormodelparametersEIandGAarerelatedtoeachotherthroughthecoefficientα（Eq.1）.

Asαgoestoinfinitythemodelwouldexhibitpuresheardeformationwhereasα=0indicatespureflexuraldeformation.NotethatitisessentialtoidentifythestructuralmembersofdiscretebuildingsfortheirflexuralandshearbeamcontributionsbecausetheoverallbehaviorofcontinuummodelisgovernedbythechangesinEIandGA.Equation2showsthecomputationofGAforasinglecolumnmemberinHS73.ThevariablesIcandhdenotethecolumnmomentofinertiaandstoryheight,respectively.TheinertiatermsIb1andIb2thataredividedbythetotallengthsl1andl2,respectively,definetherelativerigiditiesofbeamsadjoiningtothecolumnfromtop（seeFig.3inthereferredpaper）.

Equation2indicatesthatGA（shearcomponentoftotallateralstiffness）iscomputedasafractionofflexuralstiffnessofframesorientedinthelateralloadingdirection.Accordingly,theflexuralpart（EI）oftotalstiffnessiscomputedeitherbyconsideringtheshear-wallmembersintheloadingdirectionand/orothercolumnsthatdonotspanintoaframeinthedirectionofloading.Thisassumptionworksfairlywellfordualsystems.However,itmayfailinMRFsbecauseitwilldiscardtheflexuralcontributionsofcolumnsalongtheloadingdirectionandwilllumptotallateralstiffnessintoGA.Essentially,thisapproximationwillreducetheentireMRFtoashearbeamthatwouldbeaninaccuratewayofdescribingMRFbehaviorunlessallbeamsareassumedtoberigid.Tothebestofauthors’knowledge,studiesthatuseHS73modeldonotdescribethecomputationofαindepthwhilerepresentingdiscretebuildingsystemsascontinuummodels.Inmostcasesthesestudiesassigngenericαvaluesfordescribingdifferentstructuralbehaviorspanningfrompureflexuretopureshear1.Thisapproachisdeemedtoberationaltorepresenttheoreticalbehaviorofdifferentstructures.However,theabovehighlightedfactsaboutthecomputationoflateralstiffnessrequirefurtherinvestigationtoimprovetheperformanceofHS73modelwhilesimplifyinganactualMRFasacontinuummodel.Inthatsense,itisworthwhiletodiscusssomeimportantstudiesonthelateralstiffnessestimationofframes.ThesecouldbeusefulfortheenhancedcalculationsofEIandGAtodescribethetotallateralstiffnessincontinuumsystems.

3LateralstiffnessapproximationsforMRFs

TherearenumerousstudiesonthedeterminationoflateralstiffnessinMRFs.ThemethodsproposedinMuto（1974）andHosseiniandImagh-e-Naiini（1999）（hereinafterM74andHI99,respectively）arepresentedinthispaperandtheyarecomparedwiththeHS73approachforitsenhancementindescribingthelateraldeformationbehaviorofstructuralsystems.Equation3showsthetotallateralstiffness,k,definitionofM74foracolumnatanintermediatestory.

TheparametersIc,h,Ib1,Ib2,l1andl2havethesamemeaningsasinEq.

（2）.

NotethatEq.

（2）p