土木建筑學(xué)院土木0401班焦本君外文翻譯第5頁(yè)共5頁(yè)濟(jì)南大學(xué)畢業(yè)設(shè)計(jì)用紙ReliabilityofFrameandShearWallStructuralSystems.I:StaticLoadingAhmedGhobarahAbstract:Anefficientandaccuratealgorithmisdevelopedtoevaluatethereliabilityofasteelframeandreinforcedconcreteshearwallstructuralsystemsubjectedtostaticloading.Inacompanionpaper,thealgorithmisextendedtoconsiderdynamicloading,includingseismicloading.Theconceptintegratesthefinite-elementmethodandthefirst-orderreliabilitymethod,leadingtoastochasticfiniteelement-basedapproach.Inthedeterministicfinite-elementrepresentation,thesteelframeisrepresentedbybeam-columnelementsandtheshearwallsarerepresentedbyplateelements.Thestiffnessmatrixforthecombinedsystemisthendeveloped.Thedeterministicfinite-elementalgorithmisverifiedusingacommerciallyavailablecomputerprogram.Thedeterministicalgorithmisthenextendedtoconsidertheuncertaintyintherandomvariables.Thereliabilityofasteelframewithandwithoutthepresenceofreinforcedconcreteshearwallsisevaluatedforthestrengthandserviceabilityperformancefunctions.TheresultsareverifiedusingMonteCarlosimulations.Thealgorithmquantitativelyconfirmsthebeneficialeffectofshearwalls,particularlywhenthesteelframeisweakinsatisfyingtheserviceabilityrequirementoflateraldeflection.Thealgorithmcanbeusedtoestimatethereliabilityofanycomplicatedstructuralsystemconsistingofdifferentstructuralelementsandmaterialswhensubjectedtostaticloading.Theprocedurewillbeusefulintheperformance-baseddesignguidelinesunderdevelopmentbytheprofession.keywords:Limitstates;Simulation;Shearwalls;Staticloads;Steelframes;Finiteelementmethod.IntroductionTherealisticreliabilityanalysisofcomplicatedstructuralsystemsconsistingofdifferenttypesofstructuralelementsandmaterialsisamajorchallengetoourprofession.Inmostcases,thelimitstateorperformancefunction(afunctionalrelationshipbetweentheload-andresistance-relatedvariablesandtheperformancecriterion)isimplicitinevaluatingthereliabilityofsuchsystems.Theanalyticaltechniquemostfrequentlyusedtocapturethemechanicalbehaviorofcomplicatedstructuralsystemsconsistingofdifferentmaterialsappearstobethefinite-elementmethod(FEM)-basedapproach.Finite-elementanalysisisapowerfultoolcommonlyusedinmanyengineeringdisciplinestoanalyzesimpleorcomplicatedstructuralsystems.Withthisapproach,itisstraightforwardtoconsidercomplicatedgeometricarrangements，varioussourcesofnonlinearity,differentmaterials,andtheloadpathtofailure.However,thedeterministicfinite-elementmethodfailstoconsidertheuncertaintyinthevariables,andthuscannotbeusedforreliabilityanalysis.Ontheotherhand,theavailablereliabilitymethodsfailtorepresentstructuresasrealisticallyaspossible.Ifthebasicvariablesareuncertain,everyquantitycomputedduringthedeterministicanalysisisalsouncertain.Thecurrentlyavailablereliabilitymethodscanstillbeusediftheuncertaintyintheresponsecanbetrackedintermsofthevariationofthebasicvariablesateverystepofthedeterministicanalysis.Tocapturethedesirablefeaturesofthesetwoapproaches,theyneededtobecombined,leadingtotheconceptofthestochasticfinite-elementmethod(SFEM)(HaldarandMahadevan2000b)。TheSFEMalgorithmforframestructureshasbeendevelopedbyseveralresearchers.However,themaindrawbackofframestructuresistheirinabilitytotransferhorizontalloads(e.g.,wind,earthquake,andoceanwaves)effectively.Theyarerelativelyflexible.Toincreasetheirlateralstiffness,bracingsystemsorshearwallsareneeded.HaldarandGao(1997)Attemptedtoconsiderbracingsystemsinasteelframestructure.Theyusedtrusselementsintheirmodel.However,therehasnotbeenanattempttoconsidershearwalls,representedbytwodimensionalplateelements,inaframeinthecontextofSFEM.NumericalExamplesToinvestigatetheeffectofshearwallsontheoverallreliability,bothaframewithoutshearwallsandaframewithshearwallsarestudiedinthisstudy.Allloadsareappliedstatically.Thereliabilityoftheframewithandwithoutshearwallsisevaluatedusingtheproposedalgorithm.TheaccuracyoftheproposedalgorithmisestablishedusingMonteCarlosimulations.ReliabilityAnalysisofFramewithoutShearWallsAtwo-storytwo-bayframeshowninFig.2(Fig.1withouttheshearwalls)isconsideredfirst.A36steelisused.Thestatisticalcharacteristicsofthecross-sectionalandmaterialpropertiesrequiredforthereliabilityanalysisaregiveninTable3.Theframeissubjectedtodead,live,andhorizontalloads.ThestatisticalpropertiesoftheseloadsaregiveninTable3.Forthestrengthlimitstate,thereliabilityofthemostcriticalbeamatnodeeandthemostcriticalcolumnatnodecareevaluatedusingtheproposedalgorithmwiththeperformancefunctionsrepresentedbyEqs.(13)and(14).Fortheserviceabilitylimitstate,thehorizontaldriftofthetopflooratnodeaandtheverticaldeflectionofthebeamatthemidspanatnodedarechecked.InEq.(20),theprescribedhorizontaldriftatthetopfloorisconsideredtonotexceedh/400,wherehistheheight006Fftheframe.Thus,isequalto1.83cminthisexample.Similarly,theprescribedverticaldeflectioninthemidspanofthebeamisconsideredtobel/360undertheunfactoredliveload,wherelisthespanlengthofthebeam.Inthiscase,isconsideredtobe2.54cm.ConsideringalltherandomvariablesgiveninTable3,thecorrespondingreliabilityindexesandtheprobabilitiesoffailureatdifferentnodepointsareevaluated.TheresultsaresummarizedinTable4.Fortheframewithoutshearwalls,theprobabilityoffailureofthebeamisfoundtobe0.0039,and10,000simulationswereusedtocapturethisbehavior.Forthehorizontaldrift,theprobabilityoffailureisclosetozero.Consideringthepracticalaspectsofsupercomputerutilization,100,000simulationswereusedtocapturethisbehavior:TheMonteCarlosimulationresultsaresummarizedinTable4.ReliabilityAnalysisofFramewithShearWallsTheframeshowninFig.2isreinforcedwithshearwallsasshowninFig.1.Thestatisticalpropertiesoftwoadditionalvariablesrelatedtotheshearwalls,Ecandν,aregiveninTable3.Thebuildingisassumedtocontainfivesimilarframesconnectedbyrigiddiaphragmsatthefloorlevels.Onlythecenterframeofthebuildingisassumedtohaveshearwalls.Althoughthephysicalthicknessoftheshearwallis12.7cm,consideringthepresenceoffivesimilarframesandtherigidbehaviorofdiaphragms,theeffectivethicknessperframeisassumedtobe2.54cminthisstudy.ThecombinedsystemissubjectedtothethreestaticloadsgiveninTable3.Afterthetensilestressofeachshearwallexceedstheprescribedtensilestressofconcrete,thedegradationoftheshearwallstiffnessisassumedtobereducedto40%oftheoriginalstiffness.Theprobabilityoffailureofthecombinedsystemiscalculatedusingtheproposedalgorithm.Forthestrengthlimitstate,theprobabilityoffailureofacolumn,representedbyNodeeginFigs.1and2,isestimated.Fortheserviceabilitylimitstate,thehorizontaldeflectionatthetopofthecombinedsystem(pointainFigs.1and2)isevaluated.TheresultsaresummarizedinTable4.Asbefore,10,000simulationsareusedforthestrengthlimitstateand100,000simulationsareusedfortheserviceabilitylimitstate.Forboththestrengthandserviceabilitylimitstates,thereliabilityindexesestimatedbytheproposedalgorithmandtheMonteCarlosimulationtechniquearesimilar.Theresultsclearlyindicatethattheproposedalgorithmcanbeusedtoestimatetheprobabilityoffailureofacombinedsystemconsistingofframeandshearwallsunderstaticloading.Thereliabilityofthecolumndidnotchangesignificantlyduetothepresenceofshearwalls.However,thehorizontaldriftatthetopoftheframereducedsignificantlyandtheprobabilityoffailureofthecombinedsysteminserviceabilitybecamealmostzero.Thisisexpected.Forthecombinedsystem,thecontrollinglimitstatehaschangedfromserviceabilitytostrength.Thissimpleexampleclearlydemonstratesthebeneficialeffectofshearwallsincarryinghorizontalloads.Italsodemonstratesthattheproposedalgorithmcanbeusedtoestimatethereliabilityofacomplicatedstructuralsystemunderstaticloadingconditions,broadeningtheapplicationpotentialofreliabilitymethods.ConclusionsAnefficientandaccuratealgorithmisdevelopedtoevaluatethereliabilityofasteelframeandRCshearwallstructuralsystem.Thesteelframeisrepresentedbybeam-columnelementsandtheshearwallsarerepresentedbyplateelements.Astochasticfiniteelement-basedapproachconsistingofthereliabilityapproach,thefirst-orderreliabilityanalysisprocedure,andthefinite-elementmethodisproposed.Thereliabilityofaframewithandwithoutshearwallsisevaluatedforthestrengthandserviceabilityperformancefunctions.TheresultsareverifiedusingtheMonteCarlosimulationtechnique.Theproposedstochasticfinite-element-basedalgorithmisreasonableforevaluatingthereliabilityofacombinedsystemconsistingofframeandshearwallsforstaticloading.ItgivessimilarresultsforboththestrengthandserviceabilityperformancefunctionscomparedtotheresultsfromMonteCarloSimulation.Asexpected,thisstudyshowedthatthereliabilityofaframeforhorizontaldeflectioncouldbesignificantlyimprovedwiththehelpofshearwalls.TheproposedalgorithmtoevaluatethereliabilityofacombinedsystemconsistingofsteelframesandRCshearwallsforstaticloadingisveryunique.Itproducesaccurateandefficientresults,andcanbeusedinthefuturetoevaluatethereliabilityofcomplicated