土木工程专业钢筋混凝土结构抗震性能外文翻译文献

文献信息：文献标题：SeismicPerformanceofReinforcedConcreteBuildingswithMasonryInfill（砌体填充钢筋混凝土建筑的抗震性能研究）文献作者：GirmaZewdieTsige，AdilZekaria文献出处：《AmericanJournalofCivilEngineering》,2018,6(1):24-33字数统计：英文3088单词，16137字符；中文4799汉字外文文献：SeismicPerformanceofReinforcedConcreteBuildingswithMasonryInfillAbstractUnreinforcedmasonryInfillsmodifythebehaviorofframedstructuresunderlateralloads;however,inpractice,theinfillstiffnessiscommonlyignoredinframeanalysis,resultinginanunder-estimationofstiffnessandnaturalfrequency.ThestructuraleffectofhollowconcreteblockinfillisgenerallynotconsideredinthedesignofcolumnsaswellasotherstructuralcomponentsofRCframestructures.Thehollowconcreteblockwallshavesignificantin-planestiffnesscontributingtothestiffnessoftheframeagainstlateralload.Thescopeofpresentworkwastostudyseismicperformanceofreinforcedconcretebuildingswithmasonryinfillinmediumrisebuilding.Theofficemediumrisebuildingisanalyzedforearthquakeforcebyconsideringthreetypeofstructuralsystem.i.e.BareFramesystem,partially-infilledandfully-Infilledframesystem.Effectivenessofmasonrywallhasbeenstudiedwiththehelpoffivedifferentmodels.Infillsweremodeledusingtheequivalentstrutapproach.NonlinearstaticanalysesforlateralloadswereperformedbyusingstandardpackageETABS,2015software.Thecomparisonofthesemodelsfordifferentearthquakeresponseparameterslikebaseshearvsroofdisplacement,Storydisplacement,Storyshearandmemberforcesarecarriedout.Itisobservedthattheseismicdemandinthebareframeissignificantlylargewheninfillstiffnessisnotconsidered,withlargerdisplacements.Thiseffect,however,isnotfoundtobesignificantintheinfilledframesystems.Theresultsaredescribedindetailinthispaper.Keywords:BareFrame,InfilledFrame,EquivalentDiagonalStrut,Infill,PlasticHinge1.IntroductionInfillhavebeengenerallyconsideredasnon-structuralelements,althoughtherearecodessuchastheEurocode-8thatincluderatherdetailedproceduresfordesigninginfilledR/Cframes,presenceofinfillhasbeenignoredinmostofthecurrentseismiccodesexcepttheirweight.However,eventhoughtheyareconsiderednon-structuralelementsthepresenceofinfillinthereinforcedconcreteframescansubstantiallychangetheseismicresponseofbuildingsincertaincasesproducingundesirableeffects(tensionaleffects,dangerouscollapsemechanisms,softstory,variationsinthevibrationperiod,etc.)orfavorableeffectsofincreasingtheseismicresistancecapacityofthebuilding.Thepresentpracticeofstructuralanalysisisalsototreatthemasonryinfillasnon-structuralelementandtheanalysisaswellasdesigniscarriedoutbyonlyusingthemassbutneglectingthestrengthandstiffnesscontributionofinfill.Therefore,theentirelateralloadisassumedtoberesistedbytheframeonly.Contrarytocommonpractice,thepresenceofmasonryinfillinfluencetheover-allbehaviorofstructureswhensubjectedtolateralforces.Whenmasonryinfillareconsideredtointeractwiththeirsurroundingframes,thelateralstiffnessandthelateralloadcapacityofthestructurelargelyincrease.Therecentadventofstructuraldesignforaparticularlevelofearthquakeperformance,suchasimmediatepost-earthquakeoccupancy,(termedperformancebasedearthquakeengineering),hasresultedinguidelinessuchasATC-40(1996)FEMA-273(1996)andFEMA-356(2000)andstandardssuchasASCE-41(2006),amongothers.Thedifferenttypesofanalysesdescribedinthesedocuments,pushoveranalysiscomesforwardbecauseofitsoptimalaccuracy,efficiencyandeaseofuse.Theinfillmaybeintegralornon-integraldependingontheconnectivityoftheinfilltotheframe.Inthecaseofbuildingsunderconsideration,integralconnectionisassumed.Thecompositebehaviorofaninfilledframeimpartslateralstiffnessandstrengthtothebuilding.ThetypicalbehaviorofaninfilledframesubjectedtolateralloadisillustratedinFigures1(a)and(b).Figure1.Behaviorofinfilledframes(Govindan,1986).InthispresentpaperfivemodelsofofficebuildingwithdifferentconfigurationofmasonryinfillaregeneratedwiththehelpofETABS2015andeffectivenesshasbeenchecked.Pushoveranalysisisadoptedfortheevaluationoftheseismicresponseoftheframes.EachframeissubjectedtopushoverloadingcasealongnegativeX-direction.2.BuildingDescriptionMulti-storeyrigidjointedframemixedusebuildingG+9(Figure2),wasselectedintheseismiczone(ZoneIV)ofEthiopiaanddesignedbasedontheEthiopianBuildingCodeStandardESEN:2015andEuropeanCode-2005.ETABS2015wasusedfortheanalysisanddesignofthebuildingbymodelingasa3-Dspaceframesystem.Figure2.Typicalbuildingplan.SeismicperformanceispredictedbyusingperformancebasedanalysisofsimulationmodelsofbareandinfillednonductileRCframebuildingswithdifferentarrangementofmasonrywall.Thestructurewillbeassumedtobenew,withnoexistinginfilldamage.BuildingData:1.Typeofstructure=Multi-storeyrigidjointedframe2.Layout=asshowninfigure23.Zone=Iv4.ImportanceFactor=15.SoilCondition=hard6.Numberofstories=Ten(G+9)7.HeightofBuilding=30m8.Floortofloorheight=3m9.Externalwallthickness=20cm10.Internalwallthickness=15cm11.Depthofthefloorslab=15cm12.depthofroofslab=12cm13.Sizeofallcolumns=70×70cm14.Sizeofallbeams=70×40cm15.Dooropeningsize=100×200cm16.Windowopeningsize=200×120cm3.StructuralModelingandAnalysisTounderstandtheeffectofmasonrywallinreinforcedconcreteframe,withatotaloffivemodelsaredevelopedandpushoveranalysishasbeenmadeinstandardcomputerprogramETABS2015.InthisparticularstudypushoverloadingcasealongnegativeX-axisisconsideredtostudyseismicperformanceofallmodels.Sincetheoutofplaneeffectisnotstudiedinthispaper,onlytheequivalentstrutalongX-axisareconsideredtostudytheinplaneeffectandmasonrywallsalongY-axisarenotconsideredinallmodels.Fromthisdifferentcondition,allmodelsareidentifiedbytheirnameswhicharegivenbelow.3.1.DifferentArrangementoftheBuildingModelsTounderstandtheeffectofmasonrywallinreinforcedconcreteframe,withatotaloffivemodelsaredevelopedandpushoveranalysishasbeenmadeinstandardcomputerprogramETABS2015.InthisparticularstudypushoverloadingcasealongnegativeX-axisisconsideredtostudyseismicperformanceofallmodels.Model1:-Barereinforcedconcreteframe:masonryinfillwallsareremovedfromthebuildingalongallstoriesModel2:-Reinforcedconcreteframewith75%ofmasonrywallremovedfromfullyinfilledframeFigure3.PlanViewModel2.Model3:-ReinforcedconcreteframewithhalfofofmasonrywallremovedfromfullyinfilledframeFigure4.PlanViewofModel3.Model4:-Reinforcedconcreteframewith25%ofmasonrywallremovedfromfullyinfilledframeFigure5.PlanviewofModel4.Model5:-Fullyinfilledreinforcedconcreteframe(Baseframe)Figure6.PlanviewofModel5.3.2.ModelingofMasonryInfillInthecaseofaninfillwalllocatedinalateralloadresistingframethestiffnessandstrengthcontributionoftheinfillareconsideredbymodellingtheinfillasanequivalentcompressionstrut(Smith).Becauseofitssimplicity,severalinvestigatorshaverecommendedtheequivalentstrutconcept.Inthepresentanalysis,atrussedframemodelisconsidered.Thistypeofmodeldoesnotneglectthebendingmomentinbeamsandcolumns.Rigidjointsconnectthebeamsandcolumns,butpinjointsatthebeam-to-columnJunctionsconnecttheequivalentstruts.Infillparameters(effectivewidth,elasticmodulusandstrength)arecalculatedusingthemethodrecommendedbySmith.ThelengthofthestrutisgivenbythediagonaldistanceDofthepanel(Figure7)anditsthicknessisgivenbythethicknessoftheinfillwall.Theestimationofwidthwofthestrutisgivenbelow.TheinitialelasticmodulusofthestrutEiisequatedtoEmtheelasticmodulusofmasonry.AsperUBC(1997),Emisgivenas750fm,wherefmisthecompressivestressofmasonryinMPa.Theeffectivewidthwasfoundtodependontherelativestiffnessoftheinfilltotheframe,themagnitudeofthediagonalloadandtheaspectratiooftheinfilledpanel.Figure7.Strutgeometry(GhassanAl-Chaar).Theequivalentstrutwidth,a,dependsontherelativeflexuralstiffnessoftheinfilltothatofthecolumnsoftheconfiningframe.Therelativeinfilltoframestiffnessshallbeevaluatedusingequation1(Stafford-SmithandCarter1969):Usingthisexpression,Mainstone(1971)considerstherelativeinfilltoframeflexibilityintheevaluationoftheequivalentstrutwidthofthepanelasshowninequation2.Where:λ1=Relatireinfilltoframestiffnessgarameterα=Equivalentwidthofinfillstrut,cmEm=modulusofelasticityofmasonryinfill,MPaEc=modulusofelasticityofconfiningframe,MPaIcolumn=momentofinertiaofmasonryinfill,cm4t=Grossthicknessoftheinfill,cmh=heightoftheinfillpanel,cmθ=Angleoftheconcentricequivalentstrut,radiansD=Diagonallengthofinfill,cmH=Heightoftheconfiningframe,cm3.3.EccentricityofEquivalentStrutTheequivalentmasonrystrutistobeconnectedtotheframemembersasdepictedinFigure8.Theinfillforcesareassumedtobemainlyresistedbythecolumns,andthestrutsareplacedaccordingly.Thestrutshouldbepin-connectedtothecolumnatadistancelcolumnfromthefaceofthebeam.ThisdistanceisdefinedinEquations3and4andiscalculatedusingthestrutwidth,a.Figure8.Placementofstrut(GhassanAl-Chaar).3.4.PlasticHingePlacementPlastichingesincolumnsshouldcapturetheinteractionbetweenaxialloadandmomentcapacity.Thesehingesshouldbelocatedataminimumdistancelcolumnfromthefaceofthebeamasshowninfigure9.Hingesinbeamsneedonlycharacterizetheflexuralbehaviorofthemember.Figure9.Plastichingeplacement(GhassanAl-Chaar).3.5.AnalysisoftheBuildingModelsThenon-structuralelementsandcomponentsthatdonotsignificantlyinfluencethebuildingbehaviorwerenotmodeled.Thefloorslabsareassumedtoactasdiaphragms,whichensureintegralactionofalltheverticallateralload-resistingelements.Beamsandcolumnsweremodeledasframeelementswiththecenterlinesjoinedatnodes.Rigidoffsetswereprovidedfromthenodestothefacesofthecolumnsorbeams.Thestiffnessforcolumnsandbeamsweretakenas0.7EcIg,0.35EcIgrespectivelyaccountingforthecrackinginthemembersandthecontributionofflangesinthebeams.TheweightoftheslabwasdistributedtothesurroundingbeamsasperESEN1992:2015.ThemassoftheslabwaslumpedattheCentreofmasslocationateachfloorlevel.Thiswaslocatedatthedesigneccentricityfromthecalculatedcentreofstiffness.DesignlateralforcesateachstoreylevelwereappliedattheCentreofmasslocationsindependentlyintwohorizontaldirections(X-andY-directions).Staircasesandwatertankswerenotmodeledfortheirstiffnessbuttheirmasseswereconsideredinthestaticanddynamicanalyses.ThedesignspectrumforhardsoilasspecifiedinESEN1998:2015wasusedfortheanalysis.Theeffectofsoil-structureinteractionwasignoredintheanalyses.Thecolumnswereassumedtobefixedatthelevelofthebottomofthebaseslabsofrespectiveisolatedfootings.Figure10.Force-DeformationRelationforPlasticHingeinPushoverAnalysis(Habibullah.etal.,1998).4.AnalysisResultsandDiscussionsTheresultsofpushoveranalysisofreinforcedconcreteframewithdifferentconfigurationofmasonrywallarepresented.AnalysisofthemodelsunderthestaticanddynamicloadshasbeenperformedusingEtabs2015software.AllrequireddataareprovidedinsoftwareandanalyzedfortotalfivemodelstogettheresultintermsofBaseshearvsmonitoredroofdisplacement,Storeyshear,storydisplacementandElementforce.Subsequentlytheseresultsarecomparedforreinforcedconcreteframewithdifferentconfigurationofmasonrywall.4.1.BaseShearvsMonitoredRoofDisplacementCurveBasedupontheDisplacementcoefficientmethodofASCE41-13allthefivebuildingmodelsareanalyzedinETABS2015standardstructuralsoftwareandthestaticpushovercurveisgeneratedasshowninfigure11.Figure11.Pushoveranalysisresultfor10-storyRCbuilding.Thepresenceoftheinfillwallbothstrengthensandstiffensthesystem,asillustratedinfigure11.Forthecasestudybuilding,thefully-infilledframehasapproximately3timeslargerintialstiffnessand1.5timesgreaterpeakstrengththanthebareframe.Infigure11,thefirstdropinstrengthforthefullyandpartially-infilledframeisduetothebrittlefailureofmasonrymaterialsinitiatinginthefirst-storyinfillwalls.Thisbehaviorafterfirst-storywallfailureisduetowall-frameinteractionanddependsontherelativestrengthoftheinfillandframing.So,basedontheseresults,infillwallscanbebeneficialaslongastheyareproperlytakenintoconsiderationinthedesignprocessandthefailuremechanismiscontrolled.4.2.StoryDisplacementforDifferentModelsFigure12.showsthecomparativestudyofseismicdemandintermsoflateralstorydisplacementamongstallthefivetypesofreinforcedconcreteframewithdifferentconfigurationofinfill.Thelateraldisplacementobtainedfromthebareframemodelisthemaximumwhichisabout60%greaterthanthatoffullyinfilledframe,nearly50%greaterthanthatofframewith25%ofthemasonrywallreduced,about40%greaterthanthatofframewith50%ofthemasonrywallreducedand30%greaterthanthatofframewith75%ofthemasonrywallreduced.Figure12.ComparisonofStorydisplacementsfordifferentmodels.Thus,theinfillpanelreducestheseismicdemandofreinforcedconcretebuildings.Thelateralstorydisplacementisdramaticallyreducedduetointroductionofinfill.Thisprobablyisthecauseofbuildingdesignedinconventionalwaybehavingnearelasticallyevenduringstrongearthquake.4.3.MemberForcesInthisprojecttounderstandtheeffectofdifferentconfigurationofinfillinreinforcedconcreteframe;studyofthebehaviorofthecolumninallmodelsforaxialloadswasconducted.TotaloffivenonlinearmodelsareanalyzedinETABS2015andallmodelshavesameplanofbuilding,thereforethepositionandlabelofcolumnsaresameinallplansofmodelswhichisshowninfigure2.Afteranalysisconsiderthecolumnno.1(C1)showninfigure2.fromallmodelsforpushoverloadcaseandgettheaxialforcesofcolumnatperformancepointateverystoryfromsoftware,whichisgivenintable1andthevaluesforeachmodeliscomparedwiththebareframemodel.Table1.Comparisonofaxialforcefordifferentmodels.(KN)Fromthisobservation,itisevidentthatwhenaninfilledframeisloadedlaterally,thecolumnstakethemajorityoftheforceandshearforceexertedontheframebytheinfillwhichismodeledastheeccentricequivalentstruts.Generally,therelativeincreaseofaxialforceisobservedwhenthepercentageofinfillinreinforcedconcreteframeincreases.Itisobservedthatfullyinfilledreinforcedconcreteframeshowedaround10%increaseinaxialforcerelativetobareframemodel.Theotherinfillmodelsshowedalesserincrease.Theeffectofinfilloncolumnsistoincreasetheshearforceandtoreducebendingmoments.Ingeneralcomparedtobareframemodel,theinfilledmodelspredictedhigheraxialandshearforcesincolumnsbutlowerbendingmomentsinbothbeamsandcolumns.Thus,theeffectofinfillpanelistochangethepredominantlyaframeactionofamomentresistingframesystemtowardstrussaction.4.4.StoryShearStoryshearisthetotalhorizontalseismicshearforceatthebaseofstructure.Resultsfromstaticpushoveranalysisatperformancepointforthecasestudybuildingsareshowninfigure13.Figure13.Comparisonofstoryshearfordifferentmodel.Asobservedfromthefigure13thestoryshearcalculatedonthebasisofbareframemodelgavealesservaluethantheotherinfilledframes;Itwasobservedthatthestoryshearinfullyinfilledframeisnearly15%greatercomparedtobareframemodelandframewith25%ofthemasonrywallreducedwasnearly10%greatercomparedtothebareframe,framewith50%ofthemasonrywallreducedisnearly8%greatercomparedtothebareframeandframewith75%ofthemasonrywallreducedisabout5%greatercomparedtothebareframe.Sincethebareframemodelsdonottakeintoaccountthestiffnessrenderedbytheinfillpanel,itgivessignificantlylongertimeperiod.Andhencesmallerlateralforces.Andwhentheinfillismodeled,thestructurebecomesmuchstifferthanthebareframemodel.Therefore,ithasbeenfoundthatcalculationofearthquakeforcesbytreatingRCframesasordinaryframeswithoutregardstoinfillleadstounderestimationofbaseshear.Thisisbecauseofbareframeishavinglargervalueoffundamentalnaturaltimeperiodascomparedtoothermodelsduetoabsenceofmasonryinfillwalls.Fundamentalnaturalperiodgetincreasedandthereforebasesheargetreduced.5.ConclusionsFromaboveresultsitisclearthatpushovercurveshowanincreaseininitialstiffness,strength,andenergydissipationoftheinfilledframe,comparedtothebareframe,despitethewall’sbrittlefailuremodes.Duetotheintroductionofinfillthedisplacementcapacitydecreasesasdepictedfromthedisplacementprofile(Figure12).Thelateraldisplacementobtainedfromthebareframemodelisthemaximumwhichisabout60%greaterthanthatofinfilledframe.Thepresenceofmasonrywallsistochangeaframeactionofamomentresistingframestructuretowardsatrussaction.Wheninfillsarepresent,shearandaxialforcedemandsareconsiderablyhigherleavingthebeamorcolumnvulnerabletoshearfailure.Theaxialforceandshearforceofthebareframeislessthanthatoftheinfilledframe.Columnstakethemajorityoftheforcesexertedontheframebytheinfillbecausetheeccentricallymodeledequivalentstrutstransferstheaxialloadandshearforcetransferredfromtheactionoflateralloadsdirectlytothecolumns.Thestoryshearcalculatedonthebasisofbareframemodelgavealesservaluethantheotherinfilledframes.Itwasobservedthatfullyinfilledframeisnearly15%greatercomparedtobareframemodel;framewith25%ofthemasonrywallreducedwasnearly10%greatercomparedtothebareframe;framewith50%ofthemasonrywallreducedisnearly8%greatercomparedtothebareframeandframewith75%ofthemasonrywallreducedisabout5%greatercomparedtothebareframe.Thisisbecausethebareframemodelsdonottakesintoaccountthestiffnessrenderedbytheinfillpanel,itgivessignificantlylongertimeperiod.中文译文：砌体填充钢筋混凝土建筑的抗震性能研究摘要无配筋砌体填充对框架结构在侧向荷载作用下的受力性能有很大的影响，但在实际应用中，往往忽略了框架结构的填充刚度，导致对框架结构的刚度和固有频率的估计不足。在钢筋混凝土框架结构的柱体设计及其他结构构件的设计中，一般不考虑空心砌块填充的结构效应。空心混凝土砌块墙具有显著的平面内刚度，对框架抗侧向荷载的刚度起着重要的作用。本研究的工作范围是研究中高层建筑砌体填充钢筋混凝土结构的抗震性能。通过考虑三种结构体系，即裸框架体系、部分填充框架体系和全填充框架体系，对办公中高层建筑进行了地震力分析。采用五种不同的模型对砌体墙的有效性进行了研究。填充物采用等效撑杆法建模。采用ETABS2015标准软件包对侧向荷载进行了非线性静力分析。对不同的地震反应参数，如基底剪力与顶层位移、层间位移、层剪力和构件内力等进行了比较。结果表明，在不考虑填充刚度、位移较大的情况下，裸框架结构的抗震需求明显增大。然而，这种效应在填充框架系统中并不显著。文中对结果进行了详细的描述。关键词：裸框架，填充框架，等效斜撑，填充，塑性铰

1.简介填充物通常被认为是非结构构件，虽然有诸如欧洲规范Eurocode8这样的规范，其中包含了设计填充钢筋混凝土框架的相当详细的程序，但在目前的大多数抗震规范中，填充物的存在被忽略了，除了它们的重量。然而，即使它们被认为是非结构构件，但在某些情况下，钢筋混凝土框架中填充物的存在会在很大程度上改变建筑物产生不良影响的地震反应(张拉效应、危险的倒塌机制、柔性底层、振动周期的变化等)，或增加建筑物抗震能力的有利影响。目前的结构分析方法也是将砌体填充物视为非结构构件，分析和设计时只考虑填充物的质量，而忽略了填充物的强度和刚度贡献。因此，假定整个侧向荷载仅由框架抵抗。与通常的做法相反，砌体填充物的存在会影响结构在承受侧向力时的整体性能。当考虑砌体填充物与周围框架相互作用时，结构的侧向刚度和侧向承载能力大大增加。最近出现的针对特定级别地震性能的结构设计，如地震后立即入住（称为基于性能的地震工程），产生了诸如ATC-40（1996）、FEMA-273（1996）和FEMA-356（2000）等指导方针，以及诸如ASCE-41（2006）等标准。在这些文件中描述的不同类型的分析，采用了静力弹塑性分析，因为它具有最佳的准确性、效率和易用性。填充物可以是整体的，也可以是非整体的，这取决于填充物与框架的连接性。在考虑建筑物的情况下，假设是整体连接。填充框架的综合性能赋予建筑物侧向刚度和强度。图1（a）和（b）说明了填充框架在侧向荷载下的典型行为。图1.填充框架的行为（GovdIn，1986）本文利用ETABS2015软件生成了五种不同砌体填充结构的办公建筑模型，并对其有效性进行了检验。静力弹塑性分析被用于评估框架的地震反应。每个框架沿负X方向承受推覆载荷情况。2.建筑描述在埃塞俄比亚地震区（IV区）中选择了多层刚性连接框架混合建筑G+9（图2），并根据埃塞俄比亚建筑法规标准ESEN：2015和欧洲规范CODE-2005进行了设计。将ETABS2015作为一个三维空间框架系统建模，对该建筑进行了分析和设计。图2.典型的建筑平面图采用基于性能的分析方法，对不同砌体墙布局的裸钢筋混凝土框架和填充非延性钢筋混凝土框架结构的抗震性能进行了预测。该结构将被假定为新的，没有现有的填充损坏。建筑数据：1.结构类型=多层刚性连接框架2.布局=如图2所示3.地带=Iv4.重要性系数=15.土壤条件=坚硬6.楼层数=10（G+9）7.建筑高度=30m8.楼层高度=3m9.外壁厚度=20cm10.内壁厚度=15cm11.楼板深度=15cm12.屋面板深度=12cm13.所有柱的尺寸=70×70cm14.所有梁的尺寸=70×40cm15.门孔尺寸=100×200cm16.开窗尺寸=200×120cm3.结构建模与分析为了解砌体墙在钢筋混凝土框架中的作用，开发了五种模型，并在标准计算机程序ETABS2015中进行了静力弹塑性分析。在本文的研究中，考虑了负X轴的推覆荷载情况，对所有模型的抗震性能进行了研究。由于本文不研究平面外效应，所以只考虑沿X轴的等效撑杆来研究平面内效应，并且在所有模型中都不考虑沿Y轴的砌体墙。从这个不同的条件来看，所有的模型都由它们的名字来标识的，如下所示。3.1.建筑模型的不同布局为了解砌体墙在钢筋混凝土框架中的作用，开发了五种模型，并在标准计算机程序ETABS2015中进行了静力弹塑性分析。在本文的研究中，考虑了负X轴的推覆荷载情况，对所有模型的抗震性能进行了研究。模型1——裸钢筋混凝土框架，砌体填充墙沿着所有楼层从建筑物中移走模型2——钢筋混凝土框架，75%的砖墙从完全填充的框架中移除图3.平面图模型2模型3——钢筋混凝土框架，一半的砖墙从完全填充的框架中移除图4.平面图模型3模型4——钢筋混凝土框架，25%的砖墙从完全填充的框架中移除图5.平面图模型4模型5——全填充钢筋混凝土框架（基础框架）图6.平面图模型53.2.砌体填充建模对于位于抗侧力框架内的填充墙，通过将填充物建模为等效撑杆来考虑填充物的刚度和强度贡献(Smith)。由于它的简单性，一些研究者推荐了等效撑杆概念。在本文的分析中，考虑了桁架模型。这种模型没有忽略梁和柱的弯矩。刚性节点连接梁和柱，但梁柱连接处的销接头连接等效撑杆。填充参数（有效宽度、弹性模量和强度）采用Smith推荐的方法计算。支柱的长度由面板的对角线距离D给出（图7），其厚度由填充墙的厚度给出。下面给出了支柱的宽度w的估计。支柱Ei的初始弹性模量等于Em砌体的弹性模量。根据UBC（1997），Em给出为750fm，其中fm是砌体在MPa中的压缩应力。计算结果表明，填充物的有效宽度取决于填充物与框架的相对刚度、斜向载荷的大小和填充板的纵横比。图7.支柱几何结构(GhassanAl-Chaar)等效撑杆宽度α取决于填充物相对于约束框架柱的抗弯刚度。对框架刚度的相对填充应使用方程式1进行评估（Stafford-Smith和Carter，1969）：利用这个表达式，Mainstone(1971)在计算面板的等效撑杆宽度时考虑了对框架的灵活性的相对填充，如方程2所示。其中，λ1=相对填充与框架刚度参数α=填充撑杆的等效宽度，cmEm=砌体填充的弹性模量，MPaEc=约束框架的弹性模量，MPalcolumn=砌体填充惯性矩，cm4t=填充物的总厚度，cmh=填充板的高度，cmθ=同心等效撑杆的角度，radiansD=填充物的对角线长度，cmH=约束框架的高度，cm3.3.等效撑杆的偏心率如图8所示，等效的砌体撑杆与框架构件连接。假定填充力主要由支柱抵抗，并相应地放置撑杆。撑杆应与支柱在距梁面一段距离的lcolumn处用销连接。这个距离在方程3和4中定义，并使