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首页 legeron的滞回本构

legeron的滞回本构.pdf

legeron的滞回本构

李法雄
2012-12-09 0人阅读 举报 0 0 暂无简介

简介:本文档为《legeron的滞回本构pdf》,可适用于高等教育领域

ofeSltre,hepregasendcosentsAmeones:ovconstashoweCofinedintermsofallowabledamage,whicharerelatedtoecomentintheengineeringcommunityonhowtheseprogramsnomicconsiderationsForcertainseismicevents,theownercanselectthelevelofdamageheiswillingtoacceptForprivateowners,thedecisionmaybedrivenentirelybyweighingthecostofrepairreconstruction,theadditionalcostofseismicresistance,andprobabilityofoccurrenceofearthquakeTherefore,thelevelofperformanceistobebasedonlifecycleconsiderationsratherthanonconstructioncostaloneForgovernmentandpublicagencies,additionalconsiderationsaretakenintoaccount,suchaspublicsafetyanddefinitionofprioritytransportationnetworkandfacilitiesshouldbeusedorwhatmaterialconstitutivelaws,typeofelements,ordiscretizationtechniquesshouldbeusedTheobjectiveofthispaperistopresentamethodtopredictglobalaswellaslocalbehaviorofstructurescomposedofbeamsandcolumnswhosebehavioriscontrolledbyflexureThemethodisbasedondamagemechanicsofreinforcedconcretestructuresThematerialconstitutivelawsusedintheprogramarepresentedItisshownthattheresultsdependonelementsizeguidanceonchoosingtheelementlengthsispresentedThreeexamplesofapplicationarepresentedinordertoillustratemethoduseanddemonstratethisapproach’svalueinsolvingengineeringproblemsConstitutiveLawsConcreteAccuratemodelingofconcreteunderseismicloadingrequiresaccountingforthefollowingphenomena:~!crackingintension~!confinementeffectincompressionand~!cyclicbehaviorDamagemechanicsmaterialconstitutivelawsareusedtorepresentthesephenomenaDamagemechanicsusesdamagevariablestoquantifythedamagestateofmaterialsForthetypeofstructuresofinteresthere,aunilateraldamagelawissufficient,whereonlytwodamagevariablesareneededtodescribetheconcreteaxialbehavior:DfordamageintensionandDfordamageinAssociateProfessor,DeptofCivilEngineering,UnivofSherbrooke,Sherbrooke,QC,CanadaJKRIformerly,SeniorBridgeEngineer,JacobsCivil,WoodAve,Iselin,NJProfessor,DeptofCivilEngineering,UnivofSherbrooke,Sherbrooke,QC,CanadaJKREmail:patrickpaultreusherbrookecaProfessor,LaboratoireSols,Solides,Structures,InstitutNationalPolytechniquedeGrenoble,FranceNoteAssociateEditor:KhalidMMosalamDiscussionopenuntilNovember,SeparatediscussionsmustbesubmittedforindividualpapersToextendtheclosingdatebyonemonth,awrittenrequestmustbefiledwiththeASCEManagingEditorThemanuscriptforthispaperwassubmittedforreviewandpossiblepublicationonApril,approvedonNovember,ThispaperispartoftheJournalofStructuralEngineering,Vol,No,June,©ASCE,ISSN–$JOURNALOFSTRUCTURALENGINEERING©ASCEJUNEDamageMechanicsModelingofConcretFrédéricLégeron,MASCEPatrickPauAbstract:PerformancebaseddesignofstructuresisbecomingtprogramscapableofpredictingtheperformanceofstructuresdurinobtainedfromtheseprogramsdependonthetypesofelementsaresultscanbesensitivetothesizeoftheelementsThispaperpreelementsanddamagemechanicsmodelingofconcretebehaviorbehaviorofthedifferentmaterialsispresentedandsomeguidancprogramisusedtopredictthebehaviorofthreedifferentstructur~HSC!beamstestedmonotonically,HSCcolumnstestedunderearthquaketypeloadingbythepseudodynamictestmethodItisresultsDOI:~ASCE!~!:~!CEDatabasesubjectheadings:DamageSeismicresponselementsLocalizationIntroductionPerformancebasedearthquakeengineering~PBEE!hasbeenoneofthemostimportantrecentadvancesinseismicengineering~FEMA!Performancebasedearthquakeengineeringinvolvesdesignofconstructionswhoseperformanceundervarioustypesofseismicloadingsrespondstothediverseneedsoftheowner,users,andsocietyInPBEE,performancelevelsaredeDownloadedSeptoRedistribuNonlinearSeismicBehaviortructuresMASCEandJackyMazars,MASCEferredseismicdesignmethodItsuserequiresspecialnumericalismiceventwellintothenonlinearrangeSeismicanalysisresultsnstitutivemateriallawsusedForonetypeofelementused,theasimplifiedfiniteelementanalysisprogrambasedonmultilayerethodtoidentifythevariousparametersrequiredtodefinethestructuralmodelingusingthistypeofprogramisprovidedThiserreinforcednormalstrengthconcreteandhighstrengthconcretentaxialloadandcyclicflexure,andbridgepierssubjectedtonthatpredictionsareinexcellentagreementwithexperimentalncretestructuresHighstrengthconcretesConfinementFiniteAnaccuratepredictionofdamageresultingfromaspecificseismiceventisthereforeofprimeimportanceforPBEEIndeed,inabilitytodosoremovesallinterestinPBEEVarioustechniquesareusedtopredicttheperformanceofastructureunderaseismiceventNonlinearpushoverandtimehistoryanalysiswithfiniteelementprogramsarebyfarthemostcommontoolsformediumtolargestructuresHowever,thereisnogeneralagreetionsubjecttoASCElicenseorcopyrightVisithttp:wwwascelibraryorgs,−sf→Fssd=sf,Fssd=sdcompressionThesetwodamagevariablesreflectthedifferentmechanismsofdeteriorationintensionandincompression,andcanbeviewedasthematerial’smemory,recordingtheirreversibledamagethatthematerialhasaccumulatedDamagecannotberecovered,andvariesfromforanundamagedmaterialtoforatotallyruinedoneInasimpleway,adamagevariablerepresentshowmuchundamagedmaterialofaninitialunitvolumeofmaterialremainsafteracertainloadinghistoryBasedontheworkofMazars~!,thedamagelawusedherewasfirstproposedbyLaBorderie~!Initsgeneralformthislawisthreedimensional~D!butispresentedhereinitsuniaxialformulationwherethetotalstrainisgivenby«=«e«isdwhere«eand«i=elasticandinelasticstrain,respectively,andaregivenby«e=sEs−Dds−Es−Ddsd«i=bDEs−DdFssdbDEs−DdsdinwhichE=initialtangentYoung’smodulusbi=materialconstantss=positivepartofthestressands−=negativepartofthestressandareexpressedbys→s=s,s−=sds,→s=,s−=swhereFssd=crackclosurefunction,whichprovidesastiffnessrecoveryprocedurefromtensiontocompressionandmodelsthecrackclosuremechanism~seeFig!Specifictestshavebeenrealizedtocharacterizetheeffectofdamageintensionwhenthespecimenisloadedincompression~Ramtanietal!Thesetestshaveshownthatitisnecessarytoreachacertainlevelofcompressionsfforthecrackstobecompletelyclosed~unilateraleffect!Testshavealsoshownthatthechoiceofalinearcrackclosurefunctionisavalidassumption~Mazarsetal!andcanbewrittenass→Fssd=s,Fssd=sd−sf,s,→Fssd=sS−ssfD,Fssd=−ssfsdFigBehaviorofconcretemodeledwiththeLaBorderiemodelJOUDownloadedSeptoRedistribuwheresf=crackclosurestress,whichisthestressatwhichthecrackissupposedtobetotallyclosedandconcretestiffnessisnolongeraffectedbythepreviouscycleintensionHence,oncethecrackisclosed,itisassumedthatconcretebehaviorincompressionisunaffectedbyaccumulateddamageintensionThisassumptioniscommonlyacceptedandbackedbyexperimentalevidenceinuniaxialloading~Ramtanietal!AscanbeseenfromEqs~!–~!,loadingandunloadingincompressiontakeplaceonthesamelinearpath,withnohysteresis,whendamageisunchangedAlthoughthishystereticbehaviorisobservedexperimentally,itseffectisverysmallcomparedtothehysteresisresultingfromstressreversalfollowingincreaseindamage,whichisaccountedforbythemodelThedamageprogressisconsistentwiththermodynamicsofirreversibleprocessInthisframework,letusintroducetheenergyreleaserateYi~i=fortensionorforcompression!Y=sEs−DdbFssdEs−DdsdY=s−Es−DdbsEs−DdsdThedamagethresholdishandledinaclassicalmannerusingtheloadingfunctionfi=Yi−Zi,whereZi=thresholddependentonthehardeningvariablesBeforeloading,thedamagethresholdisequaltotheinitialthresholdsZi=YidandDi=Whenloadingincreases,YiincreasesuptoYisfi=dZiandDiremainunchangedIfloadingkeepsonincreasing,YiYi,thenZi=YianddamageincreasesasDi=−fAisYi−YidgBii=,sdwhereAiandBi=materialconstantsWhenloadingisreversedYidecreasesDiandZiremainunchangedDamagewillonlyincreasewhenYireachesthenewthresholdofdamageZiduringthenextloadingcycleThemodeliscontrolledbymaterialconstants:E,A,B,Y,b,A,B,Y,b,sfThemodulusofelasticityEisknownfromtestresultsorthevaluerecommendedbytherelevantcodeisusedOtherconstantsareseparatedintotwotypes:~!thoseaffectingthemonotonicbehaviorand~!thosecontrollingthecyclicbehaviorNotethattensionandcompressionconstantsareselectedseparatelyTheconstantbcontrolstheevolutionofplasticstrainduringcyclictestsincompressionThisvalueshouldbebasedontestdataHowever,suchtestsarescarceandtoevaluatebforgeneraluse,anumericalmodelbasedonexperimentalevidenceisusedDoddandCooke~!haveproposedsuchamodelanddemonstrateditsadequacytopredictcyclicbehaviorofnormalstrengthconcreteLietal~!haveshownitsgoodperformanceforhighstrengthconcrete~HSC!Themodelrelatesthepermanentstrain~strainatzerostress!tothemaximumreachedstrainandcorrespondingstressaswellasthestrainatpeakstressAssumingapurecompressiontestsD=d,whens=,thestraindeterminedbyEq~!isRNALOFSTRUCTURALENGINEERING©ASCEJUNEtionsubjecttoASCElicenseorcopyrightVisithttp:wwwascelibraryorgtheresponseofa“numerical”cylinderusingthedamagemodelonthestress–straincurvepredictedbytheconfinementmodel«i=bDEs−DdsdwhereD=damagevalue,whichisconstantalongtheunloadingpathsincenodamageisaddedduringunloadingThestrain,«u,justbeforeunloadingis«u=suEs−Dd«isdTheDoddandCooke~!modelprovidesarelationbetween«iand«uas«i=«u−s«u−«adsusu−E«asdwhere«a=a˛«u«ccsd«ccisthestrainatpeakoftheconfinedstress–straincurve~seeFig!anda=maxS«cc«u«cc«u«ccDsdsuisdeterminedforacertain«ufromtheconfinedstress–strainrelationshipofconcreteincompressionproposedbyLégeronandPaultre~!describedbelow«iisdeterminedbyEq~!ThesethreevaluesarereplacedinEq~!todetermineDbisobtainedfromEq~!Theprocedurecaneasilybeusedtofindbforawiderangeofunloadingstrain«uBasedontheDoddandCookmodel,bvariesveryslightly,whichreinforcestheconceptofamaterialconstantInthisresearchprogram,anaveragevalueoveranappropriatestrainrangeisusedBasedonawiderangeofidentifications,astartingvalueoffccisrecommended,wherefcc=strengthofconfinedconcreteasdescribedinLégeronandPaultre~!ThemodelissetupforthegeneralDcase,butisusedinauniaxialformulationincorporatingconfinementduetolateralpressurethatmaycome,inapassiveway,fromtransversereinforcementWhenconfinementisconsidered,theconstantsA,B,andYmustbeappropriatelyselectedParameterYcontrolsthedamagethresholdincompressionIncreasingYresultsingreaterstressrangeoverwhichthebehaviorofconcreteislinearItalsoincreasesthemaximumstrengthwithoutmodifyingpeakstrainParametersAandBcontrolthemaximumstressandductility,respectivelyIncreasingAdecreasesthestrengthandthestrainatpeakIncreasingBdecreasesductilitywhileincreasingslightlythestrengthTheseconstantsareidentifiedbyfittingFigCussonandPaultrestress–strainmodelforconfinedconcreteJOURNALOFSTRUCTURALENGINEERING©ASCEJUNEDownloadedSeptoRedistribuproposedLégeronandPaultre~!AnexampleofafittedcurvewillbeshowninthesectiononexampleofapplicationsThismodelwasselectedsinceithasbeentestedforawiderangeofconcretestrengths,confinementsteelyieldstrengths,andconfigurations,anddifferentloadingtypes~LégeronandPaultre!Thestress–straincurveusedforconfinedconcreteispresentedinFigItisbeyondthescopeofthispapertopresenttheconfinementmodel,butmoreinformationcanbefoundinLégeronandPaultre~!TheparameterbcontrolsthecyclicbehaviorintensionFromtestresults,itcanbetakenas~Légeron!b=ftsdwhereft=concretetensilestrengthInmonotonictension,itisassumedthatthereisnodamageuptothetensilestrengthThethresholdofdamageYisdetermineddirectlyfromEq~!Y=ftEbftEsdItisdifficulttoexperimentallyobtainthecompletetensilestress–straincurveofconcretewithastablepostpeakbehaviorItisacceptedthatpostpeakbehaviorofconcreteintensionisrelatedtotheamountanddistributionofreinforcementTheparametersdefiningthepostpeaksofteningarefittedtothetensionstiffeningbehaviorofreinforcedconcretepresentedbyVecchioandCollins~!Asforthecaseofcompression,theconstantsAandBaredeterminedbyfittingtheresponseofa“numericalcylinder”usingthedamagemodeltothestress–straincurvepredictedwithVecchioandCollins’stensionstiffeningmodelWhenthepostpeakbehaviorintensionisnotcritical,whichisgenerallythecasewithseismicanalysis,A=B=canbeusedThesevaluesgiveasharppostpeaksofteningItmustbenotedthat,undercyclicloading,thecrackinterfacedeterioratesfasterthanundermonotonicloadingandthereforeA=B=isgenerallyagoodfitforcyclicandseismicloadingThemechanismofcrackclosureiscontrolledbythesocalled“crackclosurestress”sfThecrackclosurestressisverymuchaffectedbyconcretestrengthandplacementmethod~crackroughness!Formonolithicstructures,sfisintherangeofthetensilestrengthandcanbetakenassf=−fcsdForconcretewithdryjoints,sfcanbesignificantlylowerTheidentificationproceduremayseemtedious,although,withsomeexperience,itcanbedonequitefast,sinceonlyA,B,andYrequireatrialanderrorprocedureAlltheotherparametersarecalculateddirectlyTosimplifythetaskforusers,setsofvaluescorrespondingtotypicalconcretesandtypicallevelsofconfinementareavailableinadesignprocessTheidentificationstepisreducedtoselectingasetofparametersthatcorrespondtotheconcreteusedForcasesforwhichdataarenotprovided,usingasetofvaluesclosetothecaseathandasastartingpointacceleratestheparameteridentificationprocessReinforcingSteelAdamagemechanicsbehaviorallawcanbeusetomodelthecyclicbehaviorofreinforcingsteel~Ragueneau!However,tionsubjecttoASCElicenseorcopyrightVisithttp:wwwascelibraryorgasimplificationofthemodelproposedbyDoddandCooke~!isusedherewithabilinearenvelopecurve~Fig!Thestresssisexpressedass=se−spsdwherese=«EssdIfthestrainisthemaximumexperiencedstraininthatdirection,thestressisfoundfromthebilinearcurveOtherwisesp=S«−«a«b−«aDpfEss«b−«ad−sbgsdwherep=EsS−cEsDs«b−«adEss«b−«ad−sbsdAllthevariablesinEqs~!–~!aredescribedinFigThealgorithmrequiresstoringthelastpointofcrossingwiththexaxis~strainorzerostressaxis!«aandthelastmaximumstrainreachedineachdirection«btogetherwithcurrentmaximumstrainThelastmaximumstrainisthepointafterwhichtheresponsecomesbacktothebilinearenvelopecurveAnexampleofthepredictionoftestresultsonsteelcouponsobtainedbyDoddandCooke~!ispresentedinFigThemodelgenerallydescribesthebehaviorofreinforcingsteelverywellEFiCoS:TwoDimensionalLayeredFiniteElementProgramTheprogramusedinthisresearchisEFiCoS,aDlayeredbeamelementsdamagemechanicsbasedfiniteelementprogramThemultilayerbeamelementusedisaBernouillitypebeamelementwithdegreesoffreedompernode~Fig!Thedamagevariablesareevaluatedatthecenterofeachlayer,halfwaybetweenthetwonodesPlanesectionsareassumedtoremainplaneandthestrainatthepointofevaluationofdamageineachlayerisfoundwithclassicalinterpolationpolynomialsNodalforcesanddisplacementsarefoundbysolvingthefollowingequation:FigDoddandCookemodelforcyclicbehaviorofreinforcingsteelJOUDownloadedSeptoRedistribuF=KsDdUFisDdsdwhereKsDd=globalsecantstiffnessmatrix,whichdependsonthedamagestateofthestructureUandF=nodaldisplacementsandforces,respectivelyandFisDd=inelasticforcevectorTheassemblyoftheglobalstiffnessmatrixisperformedbyadditionoftheelementstiffnessmatricesusingthedirectstiffnessmethodprocedureTheelementstiffnessmatrixinthelocalcoordinateisKe=kk−k−kkk−kkk−k−kkSYMkkk−kksdwherek=Loj=NEjsDjdbjhjk=Loj=NEjsDjdbjhjyjk=−Loj=NEjsDjdbjhjyjsdk=Loj=NEjsDjdbjhjyjk=Loj=NEjsDjdbjhjyjwhereN=numberoflayersmakingupthesectionhjandbj=heightandwidthoflayerj,respectivelyyj=distanceofthecenteroflayerjtothesectioncentroidandEjsDjd=equivalentmodulusofelasticityoflayerj,functionofdamagevariableDjForconcretelayerj,theequivalentmodulusofelasticityisgivenbyEjsDjd=s−DjdEcjsdwherethecorrespondingdamagevariableDjisuseddependingiftheconcreteisintensionorcompressionForlayersmadeupofFigPredictionofcyclictestonsteelcouponsRNALOFSTRUCTURALENGINEERING©ASCEJUNEtionsubjecttoASCElicenseorcopyrightVisithttp:wwwascelibraryorgconcreteandreinforcingsteel,theequivalentmodulusofelasticityisdeterminedasfollows:EjsDjd=s−rjds−DjdEcjrjEsjsdwhererj=volumetricratioofthelongitudinalreinforcementsteelinthelayerTheelementalinelasticforcevectorisFeiT=fff−f−fgsdwheref=Loi=Nfs−DjdEcj«jisjprjgbjhjsdandf=−Loj=Nfs−DjdEcj«jisjprjgbjhjyjsdwhere«ji=inelasticstraininlayerjandsjp=stressgivenbyEq~!forthereinforcementsteelinlayerjEFiCoSanalysisiscontrolledbyforceordisplacementDisplacementcontrolisparticularlysuitedforsofteningstructuresThenonlinearalgorithmisrobustandconvergenceisreachedevenforverysteeppostpeaksoftening,aswillbedemonstratedinthefollowingexamplesEarthquakeeffectsareaccountedforbyapplyingdisplacementandv

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