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ChenetaL/JZhejiangUnivSciA20089(9):12511257

    ;JournalofZhejiangUniversitySCIENCEA

    ;ISSN1673-565X(Print);ISSN1862-1775(Online)

    ;www.zju.edu.cn~zus;wwwspdngedinkcom

    ;E-mail:jZUS@ZjU.edu.cn

    ;1251

    ;Cornerstrengthenhancementofhighstrengthcold-formedsteel ;atnormalroomandelevatedtemperatures

    ;JuCHEN,WeiliangJ1N{

    ;(DepartmentofCivilEngineering,Zh~iangUniversiHangzhou31002ZChina) ;E-mail:Jinwl@zju.edu.ca

    ;ReceivedNov.13,2007;revisionacceptedMar.24,2008

    ;Abstract:Inthisstudy,thesuitabilityofcurrentdesignmethodsforthe0.2%proofyieldstren

    gthofthecomerregionsforhigh

    ;strengthcoldformedsteelatnormalroomtemperaturewasinvestigated.Thecurrentstandardpredictionsaregenerallyaccurate

    ;foroutercomerspecimenbutconservativeforinnercomerspecimen.Basedontheexperimentalresults.ananalyticalmodelto

    ;predictthecomerstrengthofhighstrengthcoldformedsteelatnormalroomtemperature

    wasalsoproposed.Thecomparison

    ;indicatedthattheproposedmodelpredictedwellthecomerstrengthofhighstrengthcoldf

    ormedsteelnotonlyatnormalroom

    ;temperaturebutalsoatelevatedtemperatures.Itisshownthatthepredictionsobminedfromtheproposedmodelagreewellwim

    ;thetestresults.Generallythecomerstrengthenhancementofhighstrengthcold.formedsteeldecreaseswhenthetemperature

    ;increases.

    ;Keywords:Coldformedsteel,Comer,Elevatedtemperatures,Highstrengthsteel,Yieldstrength

    ;doi:10.1631/jzus.A0720056Documentcode:ACLCnumber:TU5 ;INTRODUCTION

    ;Light..gaugestructuralmembers(cold..formed

    ;steelandstainlessstee1)arecold.formedbyvariOUS

    ;methods,suchasrollformingandbrakepressing.

    ;Themechanicalpropertiesofcoldformedsections

    ;aresometimessubstantiallydifferentfromthoseof

    ;thesteelsheet,strip,plate,orbarbeforeforming,

    ;becausethecoldformingoperationincreasesthe

    ;yieldpointandtensilestrengthbutdecreasesthe

    ;ductility.Thepercentageincreaseintensilestrengthis ;muchsmallerthanthatinyieldstrength.withacon

    ;sequentmarkedreductioninthespreadbetweenyield ;pointandtensilestrength(Yu,2000).Thechangesin ;themechanicalpropertiesinducedbycoldworkare ;consideredasbeingcausedmainlybythreefacts: ;strainhardening,theBauschingereffect,andstrain ;aging(Chajeseta1.,l963).Sincethematerialinthe ;comersofasectioniscoldworkedtoaconsiderably

    ;higherdegreethanthatintheflatelements.theme

    ;chanicalpropertiesaredistinctindifferentpartsofthe ;crosssectionfYu,2000).

    ;Thecurrentdesignstandardsofcoldformed

    ;steelstructures.suchastheAustralian/NewZealand ;Standard(AS/NZS,2005)andNorthAmerican ;Specification(NAS,2001),explicitlypermitthe ;utilizationofthechangesinthematerialproperties ;thatresultfromacoldformingoperation.Howeve~

    ;themethodusedinAS/NZS(2005)andNAS(2001, ;wasbasedontheinvestigationofnormalstrength ;coldformedstee1.Recently.highstrengthcold

    ;formedsteelhavingyieldstrengthhigherthan450 ;MPaisusedwidelyandmanyresearchestowardsthe ;utilizationofhighstrengthcold..formedsteelarecar.. ;riedout(YangandHancock,2004a;2004b;Yanget ;a1.,2004).Therefore,thevalidationofthemethodfor ;predictingcomeryieldstrengthspecifiedincurrent ;standardsforhighstrengthcoldformedsteelneeds

    ;assessment.

    ;Ontheotherhand,thecurrentdesignstandards ;ofstainlesssteelstructures.suchastheAustra

    ;

    ;1252Cheneta1./dZhejiangUnivSciA20089f9J:12511257

    ;lian/NewZealandStandardfAS/NZS,200l1and ;ASCEStandardfASCE.2002).alsoallowthein

    ;creaseinstrengthobtainedfromcoldformingprocess

    ;tobetakenintoconsiderationinthedesign.Itisstated ;intheAS/NZSf200l1andASCEf2002)that”The

    ;increaseinyieldstressduetocoldformingortem

    ;perrolling,orboth,maybepartlyorcompletelylost ;byprocesssuchaswelding,annealingorotherheat ;treatmentcarriedoutafterforming.’’Thisimplicitly

    ;meansthatthetemperaturewouldaffectthestrength ;enhancementofthecornerduetocold.forming.

    ;However.thereisnosuchinformationforthe ;coldformedcarbonsteelintheAustralian/NewZea

    ;landStandardfAS/NZS.2005)andNorthAmerican ;Specification(NAS,20011.Therefore,itisalsoi1TI

    ;portanttostudytheeffectoftemperatureonthe ;strengthenhancementofthecornerregionofcold

    ;formedstee1.Inthisstudy.theefrectOftemperature ;onthecoldformedsteelcornerstrengthwasinves

    ;tigated.

    ;TESTPR0GRAM

    ;Aseriesofhighstrengthcoldformedsteelflat

    ;couponspecimensaretestedatnormalroomand ;elevatedtemperaturesbyChenandYoung(2006; ;2007).Thetestedcoldformedsteelcouponspeci

    ;mensincludeflatcouponspecimensofcoldformed

    ;steelgradeG450andG550havingnominalyield ;strengthof450MPaand550MPa,respectively.In ;addition,twokindsofcornercouponspecimens: ;innerandoutercornercouponspecimensof ;coldformedsteelgradG450.asshowninFig.1.were ;alsotestedatnormalroomandelevatedtemperatures. ;Thetestspecimenswerepreparedinaccordancewith ;theASTMStandardE2192fASTM.1997)andAus

    ;tralianStandardAS2291fAS.1979).Thetensile ;testingmachineusedinthisstudywasanMTS810 ;UniversaltestingmachineOf100kNcapacity.The ;heatingdevicewasanMTSModel653hightem

    ;peraturefurnacewiththemaximumtemperatureof ;1400.C.asshowninFig.2a.Thefumacewascon

    ;trolledbyanMTSmodel409.83temperaturecon

    ;troller.AnMTSModel632.53F11ofaxialexten

    ;someterwasusedtomeasurethestrainofthemiddle ;partofthecouponspecimens.asshowninFig.2b. ;Detailsofthehightemperaturetestswerepresented ;byChenandYoung(2006;2007).Measuredstress

    ;straincurvesofthecold.formedsteelG450for1.9 ;mmflatcornerspecimen,innercornercoupon ;specimenandoutercornercouponspecimenatnor

    ;malroomtemperatureareshowninFig.3. ;Fig.1Couponspecimen

    ;Fig.2Testdevice.(a)Heatingdevice;(b)Extensom- ;eter

    ;

    ;

;

    ;?

    ;Strainf%,

    ;Fig.3Measuredstressstraincurves

    ;

    ;CURRENTDESIGNMETH0D

    ;Cheneta1./JZhejiangUnivSciA20089f9J:12511257

    ;ThecurrentNAS(2004)andAS/NZS(2005)

    ;canbeusedtocalculat~thecomeryieldstrength,as ;showninEqs.(1)(3).AsmentionedintheINTRO.

    ;DUCT10N,themethodwasiustdevelopedbasedon ;normalstrengthcold.formedstee1.Hence,theaD. ;propriatenessofthemethodonthehighstrength ;coldformedsteelshouldbefurtherinvestigatedfu

    ;ther.Inthisstudy,theyieldstrengthisdefinedasthe ;0.2%proofyieldstrength.

    ;=

    ;,

    ;=

    ;3.69(F./)0.819(F~v/)1.79,

    ;m=0.192(F./)0.068,

    ;(2)

    ;(3)

    ;whereFcisthetensileyieldpointofthecomer,Fwis ;thetensileyieldpointofthevirginsteel,isthe ;tensilestrengthofvirginsteel,Ristheinsidebend ;radiusandfisthebasemetalthickness.Thepredic

    ;tionsfortheyieldstrengthenhancementfromthe ;currentstandardsarecomparedwithtestresultsin ;T{lble1.Itisshownthatthepredictionsaregenerally ;accurateforoutercomerspecimenbutveryconser

    ;vativeforinnercomerspecimen.

    ;Table1Comparisonofstandardpredictedyield ;strengthwithtestresults

    ;?t:comerstrengthenhancementobtainedfromtestresults; ;?.dd:comers~engthenhancementpredictedbythecurrent ;standards

    ;PROPOSEDMETHOD

    ;AnanalyticalmodelwasdevelopedbyKarren ;(1967)topredicttheyieldstrengthatthecomerof ;coldformedsteelsectionsatnormalroomtempera. ;ture.Thestrainhardeningfunctionwasrepresentedin ;theplasticpartofthestressstraincurvebyapower

    ;function:

;where=1

    ;=

    ;(,

    ;1253

    ;(4)

    cr2)+(cr2cr3)+() ;(

    ;isthegeneralizedstress,equivalentstressoreffective ;stress,:is

    ;thegeneralizedstrain,equivalentstrainoreffective ;strain.

    ;Inthecaseofthepurelyflexuralmodelwhichis ;inaconditionofplanestrain,thestrainfunctioninthe ;comercouldbewrittenas

    ;=.nm

    ;?,

    ;whereisthecomerradius,androisthecomerradius ;ofthemiddlelayer.

    ;Thentheaveragecomeryieldstrengthcouldbe ;obtainedbyintegratingtheeffectivestressfromEq.(4) ;overthefu11areaofacomer:

    ;=

    ;,

    ;wherefistheplatethickness.

    ;SubstitutingEq.(5)intoEq.(6)yields ;kr6

    ;721rm

    ;=

    ;[r(.n]k+,

    ;(6)

    ;lnx

    ;H

    ;whereaistheinsidecomerradius,andbistheout

    ;sidecomerradius.

    ;Itisfoundthatforvaluesofa/tlessthan10. ;Eq.(7)couldbeapproximatedbyEq.(8): ;=

    ;(8)

    ;Fortheuniaxialtension,Eq.(4)couldbereduced ;to=s).Therefore,thestrengthcoefficientkand ;

    ;1254Cheneta1./JZhejiangUnivSciA20089f9J:1251?1257 ;thestrainhardeningexponentF/couldbedetermined ;fromthetensilecoupontests.Inthisstudy,thetwo ;parametersforhighstrengthsteelareobtainedfrom

    ;thehighstrengthsteelexperimentalresults.Intotal30 ;highstrengthcoldformedsteelcouponspecimensare ;testedusingthedevicedescribedabove.Thenominal ;andmeasuredmaterialpropertiesofthetestcoupon ;specimensarepresentedin6les2-4Basedonthe

    straincurvesobtained ;plasticrangeofthetruestress

    ;fromthetensilecoupontestresults,thestrengthCO

    ;ecientkandthestrainhardeningexponentofthe

    ;testedhighstrengthcoldformedsteelcouldbeOb

    ;tained.asshowninFig.4.Equationsforthetwopa

    ;rametersarealsoproposed,asshowninEqs.(9)(10)

    ;andEqs.(11)(12)forcoldformedsteelG500and

    ;G450,respectively.Thus,newpredictionsofthe ;comerstrengthofhighstrengthcoldformedsteelare

    ;proposed,asshowninEqs.(13)-(16).Thepredictions ;ofthecomerenhancementofthecomerstrength ;obtainedfromtheproposedequationarecompared ;withtestresults,asshowninTable5.

    ;ForG550

    ;k=2.8Fu1.5Fy,

    ;=

    ;0.2Fu/Fy0.126;

    ;ForG450

    ;k=2.8Fu1.6Fy.

    ;=

    ;0.2Fu/Fy0.134

    ;Table2TestresultsofcouponspecimenG5501.0mmatnormalroomtemperature

    ;(9)

    ;(10)

    ;(11)

    ;(12)

    ;CoV=coefficientofvariance

    ;Table3TestresultsofcouponspecimenG4501.5mmatnormalroomtemperature

    ;CoV:coefficientofvariance

    ;

    ;Chenetaf./JZhejiangUnivSciA20089f9J:12511257

    ;Table4TestresultsofcouponspecimenG4501.9mmatnormalroomtemperature(Chenan

    dYoung,2007)

    ;COV:coefficientofvariance

    ;Fig.4Determinationofcoefficientintheproposed ;model

    ;Table5Comparisonofproposedmodelpredictedyield ;strengthwithtestresultsatnormalroomtemperature ;?.test;COIT1crstrengthenhancementobtainedfromtestresults;

    ;A.p:cornerstrengthenhancementobtainedbyprediction ;ForG550

    ;=

    ;3.65(Fu/)0.728(Fu/F.)1.75,

    ;=0.171(F~V)O.073;

    ;ForG450

    ;=

    ;3.70(F~/)0.728(F~v/F.)1.88,

    ;=

    ;o.171(F)0.08.

    ;(13)

    ;(14)

    ;(15)

    ;(16)

    ;1255

    ;whereFuisthetensilestrengthofthecomer,Fyisthe ;tensileyieldpointofthecomer.

    ;EFFECTOFTEMPERATIJIE

    ;Thematerialpropertiesofcold.formedsteelat ;elevatedtemperaturesaredifferentfromthoseat

     ;normalroomtemperature.asshowninT{lble6.Ac

    ;cordingly,thecomerstrengthenhancementcouldbe ;differentfromthoseatnormalroomtemperature.The ;equationsforthecomerstrengthenhancementof ;coldformedsteelatnormalroomtemperaturewere ;alsousedtopredictthecomerstrengthenhancement ;ofcoldformedsteelG4501.9innlatelevatedtem

    ;peraturesbyusingtheyieldstrengthandtheultimate ;strengthOfflatcouponspecimens.Thepredicted ;strengthenhancementofinnerandoutercomer ;speclmensatelevatedtemperaturesarecompared ;withtestresultsinTable7.Itisshownthatthepre

    ;dictedvaluesaregenerallyhigherthanthetestresults, ;whichmeansthattheproposedequationsforthe ;comerstrengthenhancementatnormalroomtem

    ;peraturearenotsuitableforthatatelevatedtem

    ;peratures.Thereasonmavbeexplainedasfollows: ;thesteelmembersectionswerecoldformedatnor-

    ;malroomtemperature.Withthetemperaturein. ;creasing,theeffectofcoldformingwasgradually

    ;changed,resultinginthatthepredicteddataarenot ;identicalwiththetestresults.especiallyat320.C. ;moreover,itcouldbeconcludedthatthecomer ;

    ;1256Cheneta1./JZhejiangUnivSciA20089f9J:1251-1257 ;Table6Measuredmaterialpropertiesatelevatedtemperatures ;F-T”ultimatestrengthofvirginalsheetatelevatedtemperature;F-T:yieldstrengthofvirginalsheetatelevatedtemperature

    ;Table7Comparisonofproposedmodelpredictedyieldstrengthwithtestresultsatelevatedt

    emperatures

    ;?c*tcst~comerstrengthenhancementobtainedfromtestresults;AFy.-preled:comerstren

    gthenhancementobtainedbyprediction

    ;strengthenhancementgenerallydecreasesasthe ;temperatureincreases.

    ;CONCLUSION

    ;Thecomerstrengthenhancementofhigh.

    ;strengthcold.formedsteelwasinvestigatedinthis ;study.Twokindsofcold.formedstee1.steelgrade ;G550andG450,wereinvestigatedbothatthenormal ;roomandelevatedtemperatures.Thesuitabilityof ;currentAustralian/NewZealandandNorthAmerican ;standardsforhighstrengthcold.formedsteelcomer ;strengthenhancementwasinvestigated.Itisshown ;thatthesetwostandardpredictionsaregenerallyac. ;curateforoutercomerspecimenbutveryconserva

    ;tiveforinnercomerspecimen.Therefore.anana. ;1yticalmodelwasproposedforcold.formedsteel ;gradeG450andG550.Thestrengthcoefficientkand ;thestrain.hardeningexponentwereobtainedfrom ;themeasuredstress.straincurves.Theproposed ;modelaccuratelypredictedthecomerstrengthen. ;hancement.Inaddition,theproposedmodelwasalso ;usedtopredictthecomerstrengthenhancementof ;highstrengthcold..formedsteelatelevatedtempera.. ;turesbysubstitutingthereducedmaterialproperties. ;Andthepredictionsareprovedtobegenerallyun. ;conservative.Therefore,theeffectoftemperatureon ;thecomerstrengthenhancementcouldnotbene. ;glected.Thecomerstrengthenhancementdecreases ;whenthetemperatureincreases.

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