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Behaviour

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BehaviourBehavi

    Behaviour

Chenetal/JZhejiangUnivSciA20089(11):1507-1513

    ;JournalofZhejiangUniversitySCIENCEA

    ;ISSN1673565X(Print);ISSN18621775(Online)

    ;wwwzjueducn~zus;www.spdngerlink.com

    ;Email:jzus@zju.edu.cn

    ;?’??’’’’’一一Benaviour0lcold-tormedstainlesssteelbeamsat

    ;elevatedtemperatures

    ;JuCHEN,Wei.1iangJINf{

    ;(DepartmentofCivilEngineering,ZhejiangUniversity,Hangzhou310058,China) ;E-mail:Jinwl@zju.edu.cn

    ;ReceivedApr.15,2008;revisionacceptedJune10,2008

    ;1507

    ;Abstract:Astudyofthebehaviourofconstructionalcoldformedstainlesssteelbeamsate

    levatedtemperatureswasconducted

    ;inthispaper.Anaccuratefiniteelementmodel(FEM)forstainlesssteelbeamswasdevelopedusingthefiniteelementprogram

    ;ABAQUS.Stainlessstee1beamshavingdifferentcrosssectionsweresimulatedinthisst

    udy.ThenonlinearFEMwasverified

    ;againsttheexperimentalresults.Generally,thedevelopedFEMcouldaccuratelysimulatethestainlesssteelbeams.Basedonthe

    ;hightemperaturestainlesssteelmaterialtestresults,aparametricstudywascarriedoutonstainlesssteelbeamsatelevatedtem.

    ;peraturesusingtheverifiedFEM.Bothhighstrengthstainlessstee1EN1.4462andnorma1strengthstainlessstee1EN1.4301were

    ;considered.Atotalof42stainlesssteelbeamsweresimulatedintheparametricstudy.Theeffectoftemperaturesonthebehaviour

    ;ofstainlesssteelbeamswasinvestigated.Inaddition.alimitingtemperatureforstainlesssteelbeamswasalsoproposed.

    ;Keywords:Elevatedtemperatures,Finiteelementmodel(FEM),Fire,Stainlesssteelbeams

    ;doi:10.1631/jzus.A0820285Documentcode:ACLCnumber:TU5

    ;INTRODUCT10N

    ;Coldformedstainlesssteelmembersarebeing

    ;increasinglyusedinarchitecturalandstmcturaIap

    ;plicationsbecauseofthedesirablefeaturesofthe

    ;materialcorrosionresistancedurabilitv,easy

    ;maintenance,pleasingappearance,recyclabilityand

    ;fireresistance.Acold.formedhollowsectionis

    ;formedbyrollinganannealedflatstripintoacircular

    ;hollowsection.whichisthenweldedattheedges. ;Theprocessiscompletedbyfurtherrollingintoa ;squareorrectangularhollowsection(SHSorRHS1. ;Thisprocessofformingbycoldworkingleadstoa

    ;considerableenhancementofthematerialproperties ;oftheannealedsteel,especiallyinthecomerportion ;ofthecross.section.Normallythecold.formingop

    ;erationincreasestheyieldpointandtensilestrength ;andatthesametimedecreasestheductility.More ;:Correspondingauthor

    ;ProjectsupportedbytheHiTechResearchandDevelopmentPro

    ;gram(863)ofChina(No.2006AA04Z422)andthePostdoctoralFund

    ;ofZhejiangProvince(No.113000X80703),China

    ;economicaldesignscanbeachievedbytakinginto ;accounttheenhancementofthematerialproperties ;duetocoldworking.

    ;Previousresearchconcentratedmostlyonthe ;behaviouranddesignofstainlesssteelmembersat ;normalroomtemperature(YoungandLiu.2003; ;GardnerandNethercot,2003;RasmussenetaL,2004: ;RealandMirambell,2005;Gardner,2005;Ashrafet ;a1..2005).However.researchintostainlesssteelat ;elevatedtemperaturesisratherlimited.Gardner(2007) ;andAla.OutinenandOksanenrl997)conducteda ;seriesofconcentriccompressiontestsonrectangular ;40mmx40mmx4mmhollowsectionscold.formed ;fromausteniticstainlessstee10ftvpePolarit(con

    ;formingtomaterialnumbersEN1.4301andAISI ;304).GardnerandBaddoo(2006)conductedaseries ;oftestsonsixgrade1.4301stainlesssteelcolumnsand ;fourfiretestsongrade1.4301stainlesssteelbeams. ;ThetestedfourbeamsincludeoneRHSbeam(witha ;Classlcrosssection,formedbytwocoldrolled

    ;channels(weldedtiptotip),oneIsectionbeam(with

    ;aClass4cross..section)formedbytwocold..rolled ;1508Cheneta1./JZhejiangUnivSciA20089(11):15071513

    ;channelsfweldedbacktoback),andtwoI-section

    ;beamsofconstantfClass1)crosssection.Gardner

    ;andNg(2006)investigatedthetemperaturedevel’

    ;opmentinstructuralstainlesssteelsectionsexposedto ;fire.Thereforethereisstillalackofinformationon ;thebehaviourofcoldformedstainlesssteelbeamsat

    ;elevatedtemperatures.Withheightenedemphasisnow ;beingplacedontheperformanceofstructuresatele-

    ;vatedtemperatures(Bailey,2004),andanincreasing ;trendtowardstheuseofbaresteelwork(Wongela1., ;l998).itisimportanttoinvestigatethebehaviourof ;coldformedstainlesssteelmembersatelevatedtem

    ;peratures.

    ;Itcanbequitecostlyandtimeconsumingfor

    ;experimentalinvestigation.thereforenumerical ;methodshavebeenusedintheareaofsteelstructural ;fireresistantdesigninrecentyears.Thefiniteelement ;programABAQUS(2004)hasbeenwidelyusedto ;investigatethebehaviourofcoldformedstainless

    ;steelmembersatnormalroomtemperature.Inaddi- ;tion,ABAQUShasalsobeenusedtoinvestigate ;coldformedsteelmembersatelevatedtemperatures ;(Fengeta1.,2003:LeeandMahendran,2004). ;ThereforethefiniteelementprogramABAQUSis ;usedtosimulatecold.formedstainlesssteelbeamsat ;elevatedtemperaturesinthisstudy.

    ;FINITEELEMENTMODEL

    ;General

    ;Inthisstudythestainlesssteelbeamstestedby ;ZhouandYoung(2005)werefirstlysimulatedto ;verifythefiniteelementmodel(FEM).TheFEMwas ;developedaccordingtotheexperimentalsetup,as ;showninFig.1.Loaddisplacementnonlinearanaly

    ;siswasperformedintheanalysis.Inaddition.careful ;attentionwasgiventothechoiceoftheelementtype ;andmeshsizetocombineahighlevelofnumerical ;accuracyandstabilitywithoptimumcomputational ;efficiency.

    ;FiniteelementtVpeandmesh

    ;Afour-nodedoublycurvedshel1elementwith ;reducedintegrationandhourglasscontrol($4R51was ;usedinthesimulationofbeams.Theelementhasfive ;degreesoffreedompernode.Inthesimulationof ;beamsonlyhalfofthespecimenwasmodeledfor ;symmetry.Inordertochoosethefiniteelementmesh ;thatprovidesaccurateresultswithminimumcompu

    ;tationaltime.convergencestudieswereconducted.It ;wasfoundthatanapproximate10nllTlX10mm ;(1engthbywidth)ratioprovidesadequateaccuracyin ;modelingthebeamswithafinemeshinthecomer ;portion.asshowninFig.2.

    ;(a)

    ;Fig.1Comparisonof(a)experimentalspecimenand ;(b)FEMforbeamspecimenN40-40-2

    ;Comerportio

    ;Fig.2Finiteelementmeshofbeamspecimen ;N40..40-2

    ;Boundaryconditionsandloadapplication ;Followingthetestprocedurethebeamwas

    ;four-pointloaded.IntheFEM,thesupportplatewas ;modeledasarigidsurfacewhosemotionisgoverned ;bythereferencepoint.ThereferencepointOfthe ;supportplatewasrestrainedagainstx,Yandzdirec

    ;tionsdisplacementaswellasvandzaxesrotation

    ;butwasfreetorotateaboutthex.axis.Theloading ;Chenetal/dZhejiangUnivSciA20089(11):1507-1513 ;platewasalsomodeledasarigidsurface.Therefer. ;encepointoftheloadingplatewasrestrainedagainst ;xandzdirectionsdisplacementaswellasvand

    ;zaxesrotationbutwasfreetomoveinvdirectionand ;rotateaboutthexaxis.Theconstraintbetweenthe

    ;loading/supportplateandspecimenwassimulated ;usingacontactsurface.asshowninFig.3.Theweb ;stifrenerplateswhichstiffenthesectionattheload ;andSupportpointsweresimulatedbyincreasingthe ;approximate70%thicknessoftheelementsatthe ;correspondingparts.Thuslocalfailureattheloading ;andsupportpointswasprevented.Theloadwasap- ;pliedatthereferencepointoftheloadingplate.The ;nonlineargeometryparameter(NLGEOM)wasin. ;cludedtodealwiththelargedisplacementanalysis. ;Fig.3Boundaryconditionsandloadapplicationoffinite ;elementmodelforspecimenN40-40-2

    ;Materialmodeling

    ;IntheFEMthemeasuredstressstraincurves

    ;wereused.Thestaticstressstraincurveswerefirst

    ;obtainedbyknowingthestaticloadsneartothe0.2% ;proofstressandultimatestress.Sincetheanalysis ;involveslargeinelasticstrains.thenominal(engi

    ;neering)staticstressstraincurvewasconvertedtoa

    ;truestressandplastictruestraincurve.Thetruestress ;andplastictruestrainwerespecifiedinABA0US ;(2004).Anotherimportantissueisthermalexpansion. ;Stainlesssteelexpandsmorethancarbonsteelat ;elevatedtemperatures.However,thespecimensin. ;vestigatedinthisstudyarefreefromthermalexpan

;sionandthereforeitisnotincluded.

    ;VERIFICAT10NOFFINITEELEMENTMODEL

    ;Young(2005)weremodeledinthisstudy.Themeas. ;uredcrosssectiondimensionsandmaterialproperties ;reportedinZhouandYoung(2oo5)wereincorporated ;intheFEM.Theultimatemomentsofthestainless ;steelbeamsobtainedfromfiniteelementanalysis ;(FEA)(J)I.FEA)arecomparedwiththetestresults ;(Mu.TEST)presentedbyZhouandYoung(2005)in ;Tlable1.Thetestspecimensarelabeledsuchthatthe ;steeltypesandcrosssectiondimensionscouldbe

    ;identifiedfromthelabe1.Forexample.thelabeled ;‘NlO0—50.2’definesthespecimenhavingnormal

    ;strengthmaterialandnominaloveralldepthofthe ;webOf100mm.overallflangewidthOf50mm.and ;thicknessof2.0mm.Themeanvaluesoftheultimate ;momentratio(.TEsT/Mu.FEA)are0.97withthecor

    ;respondingcoefficientsofvariation(COV)0.025.A ;maximumdifierenceinultimatemomentsof7%was ;observedbetweentestandnumericalresultsfora ;beamspecimenofN12060.2.Thecomparisonindi

    ;caresthattheultimatemomentsofbeamspredictedby ;theFEAareaccurate.Inadditiontheloadvsmid

    ;spandeflectioncurveobtainedfromtheFEAwas ;comparedwithtestresultsofspecimenH40402,as

    ;showninFig.4.ItisalsoshownthattheFEAresultsof ;theloadvsmidspandeflectioncurveagreewellwith ;thetestresults.

    ;Table1ComparisonofFEAresultswithstainlesssteel ;beamtestresults

    ;ThestainlesssteelbeamstestedbyZhouandCOV:Coefficientsofvariation

    ;1510

    ;4.O

    ;3.O

    ;2.O

    ;1.O

    ;Chenetal/JZhejiangUnivSciA20089(11):1507-1513 ;Deflectionf1nm)

    ;Fig.4Comparisonofmomentvsmid-spandeflection ;curvesobtainedfromtestresultsofspecimenH40--40?-2 ;withFEAresults

    ;PARAMETRICSTUDY

    ;TheverificationshowedthattheFEMof

    ;stainlesssteelbeamsatelevatedtemperatureswas

    ;reasonablyaccurate.Henceparametricstudywas ;carriedouttoinvestigatethebehaviourofstainless ;steelbeamsatelevatedtemperatures.Cold.formed ;highstrengthstainlessstee1structuralmembershave ;beenincreasinglyusedinstructuralapplications ;(YoungandLiu.2005).However,thereisnodata ;availableonthematerialbehaviorofcold.formed ;highstrengthstainlesssteelmembersatelevated ;temperatures.Thereforethebehaviourofhigh ;strengthstainlesssteelbeamswasalsoinvestigatedin ;thispaper.Threekindsofbeamsections,namely ;50.1002.40.402.10O.502,areinvestigatedinthe

    ;parametricstudy.Thecross.sectiondimensionsare ;showninTable2usingthesymbolsdefinedinFig.5. ;Thosesectionsarechosensothatboththin.walled ;andcompactsectionsofrectangularandsquaresec

    ;tionsareincluded.

    ;Anexperimentalinvestigationofthemechanical ;propertiesofhighstrengthandnormalstrength ;stainlesssteelatelevatedtemperatureshasbeen ;conductedbyChenandYoungf2006).Thetestpro. ;gramincludedtwostainlesssteelgradesOfEN1.4462 ;andEN1.4301withnominalyieldstrengthsof793 ;MPaand398MPa.respectively.Theyieldstrength ;fy,T)andelasticmodulus(ET)ofstainlesssteelgrades ;ofEN1.4462andEN1.430latelevatedtemperatures ;——

    ;(a)

    ;I+——

    ;(b)

    ;Fig.5Definitionofsymbols.(a)Squarehollowsection; ;(b)Rectangularhollowsection

    ;Table2Dimensionsforspecimensofparametricstudy ;‘Thethicknessfis2.0rnm;theradiusriis2.0ram;thelengthLis

    ;1440iTlln

    ;multilinearstress.straincurvetobeused.Thefirst ;partofthemultilinearcurverepresentstheelastic ;partuptotheproportionallimitstresswithmeasured ;elasticmodulusandPoisson’sratio.Inthisstudy,the

    ;Poisson’sratioistakenas0.3underfireconditions.

    ;Generally.thePoisson’sratioisassumedtobeinde—

    ;pendentoftemperature(Kaitila,2002;Zha,2003). ;Thelabelingsystemforthestainlesssteelbeamsat ;elevatedtemperaturesissimilartothatusedfornor.

    ;ma1roomtemperature.Intheparametricstudy.the ;temperatureisalsoconsideredinthelabelingsystem. ;Therefore.theleRer”T”isaddedinthelabels.For

    ;example.thelabel”H40—40—2T22”definesthespeci—

    ;menofH4040—2atatemperatureof22.C.where’’T’’

    ;indicatesthetemperatureofthespecimenfollowedby ;thevalueofthetemperatureindegreeCelsius.The ;temperaturevalueschosenintheparametricstudyare ;22,320,450,550,660,760and960.C.

    ;werepresentedinTable3.Inthesimulationofbeams ;atelevatedtemperatures,thestressstraincurvesofDISCUSSION ;bothhighandnormalstrengthstainlesssteelobtained ;byChenandYoung(2006)wereused.ThematerialTheultimatemomentofhighstrengthan

    dnormal

    ;behaviourprovidedbyABAQUS(2004)allowsastrengthstainlesssteelbeams(,T)obtain

    edfromthe

    ;?,

    ;???,?_

    ;_(?lZ0

    ;Cheneta1./JZhejiangUnivSciA20089(11):1507-1513 ;FEAareshowninTables4and5.respectively.In ;addition,themomentvsmidspandeflectioncurvesof

    ;specimenseriesH40402andN40402werealso

    ;plotted,asshowninFigs.6aand6b,respectively.Itis ;shownthatthemomentvsmidspandeflectioncurves

    ;atelevatedtemperaturesaregenerallysimilartothose ;atnormalroomtemperature.Whentemperaturein. ;creases,themidspandeflectioncorrespondingtothe ;maximummomentalsoincreasesfortemperatures ;lowerthan660.C.whichmeansthatthedeformation ;capacityofstainlesssteelbeamsincreases.However. ;thedeformationcapacityofstainlesssteelbeamsde

    ;creaseswhenthetemperatureishigherthan660.C. ;Theloadratiooftheultimatemomentof

    ;stainlesssteelbeamswasplottedagainstdifferent ;temperaturesinFigs.7aand7bforhighstrength ;1511

    ;stainlesssteelandnormalstrengthstainlesssteel, ;respectively.Theloadratioisdefinedasthemaxi

    ;mummomentofabeamatelevatedtemperatures ;(mu,T)comparedtothatatnormalroomtemperature ;(Mu.n01),asshowninEq.(1):

    ;Loadratio=,T/Mu’no1.(1)

    ;Itisshownthatthespecimenlostapproximately

    ;30%Ofitsstrengthwhenthetemperaturereached450 ;.C.Forhighandnormalstrengthstainlesssteelbeams. ;theloadratiodecreasesrapidlywhenthetemperature ;reaches660.Cand550.C.respectively.Forcon

    ;servatism.550.Cwasconsideredasthelimiting ;temperatureforbothhighandnormalstrength ;stainlesssteelbeams.

    ;Table3MaterialpropertiesofstainlesssteelEN1.4462andEN1.4301atelevatedtemperatu

    resusedinthepa-

    ;rametricstudy

    ;Table4UltimatemomentsforhighstrengthstainlesssteelbeamsobtainedfromtheFEA

    ;SpecimenMu.T(kN’m)SpecimenMu.T(kN’m)SpecimenMu.T(kN’m)

    ;H5OlOO.2T226.6H4040.2T223.4H10050.22214.6

    ;H501002T3205.0H40.40.2T3202.7H100502T320l1.5

    ;H5O1002T4504.9H40402T4502.5H100502T450l1.1

    ;H50100.2T5504.8H40402T5502.4H10050.2T55010.4

    ;H501002T6603.8H40402T6601.9H100502T6607.8

    2T7602.6H40402T7601.1H10O502T7604.8 ;H50l00

    ;H50.1002T9600.3H40402T9600.1H1OO502T9600.6

    ;Table5UltimatemomentsfornormalstrengthstainlesssteelbeamsobtainedfromtheFEA

    ;Specimen.T(kN.m)SpecimenMu.T(kNm)SpecimenMu.T(kN’m)

    ;N501002T224.1N4040.2T222.0N100.502T228.9

    ;N501002T3203.5N40.402T3201.4Nl00502T3206.4

    ;N5O.1O0.2T45O3.4N40-402T450l_3Nl00.50-2T4506.2 ;N50l00.2T5503.0N40.402T5501.2N10050.2T5505.5

    ;N501002T6602.9N40.402T6601.1Nl0O502T6605.2

    ;N50100.2T7601.8N40.402T7600.7N10O50.2T7603.4

    ;N501002T9601.0N40.402T9600.2N1O0.50.2T9601.4 ;1512

    ;0

    ;

    ;0

    ;Cheneta1./dZhejiangUnivSciA20089(11):1507-1513 ;Deflection(mm)

    ;(a)

    ;Deflectionf1nm1

    ;(b)

    ;Fig.6MomentVSmidspandeflectioncurvesofspecimenseries(a)H40-402and(b)N40-40-2at

    ;elevatedtemperatures

    ;0

    ;=

    ;

    ;0

;Temperature(.C)Temperature(.C)

    ;(a)(b)

    ;Fig.7Loadratioof(a)highstrengthand(b)normalstrengthstainlesssteelbeamsatelevatedt

    emperatures

    ;Thereductionratioofyieldstrength)and

    ;elasticmodulusfwerealsoplottedinFig.7for ;comparison.ItiSshownthatforhighstrength ;stainlessstee1.theloadratiocurvesaresimilartothe ;reductionratiocurvesofmaterialproperties.For ;normalstrengthstainlessstee1.theloadratiocurves ;aregenerallybetweenthereductionratiocurvesof ;yieldstrengthandelasticmodulus.Thereduction ;ratiocurvesofelasticmoduluscouldbeconsideredas ;upperboundarywhilethereductionratioCurvesof ;yieldstrengthcouldbeconsideredaslowerboundary. ;CONCLUSION

    ;Thispaperfocusesonthebehaviourofstainless ;steelbeamsatelevatedtemperatures.Anaccurate ;FEMwasdevelopedandverifiedagainstexperi- ;mentalresults.ItiSshownthattheFEMcansimulate ;thestainlesssteelbeamsaccurately.Thereforeap?

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