HEATSTRAIGHTENINGDAMAGEDSTEELPLATEELEMENTSByR.RichardAvent,1DavidJ.Mukai,2PaulF.Robinson,3andRandyJ.Boudreaux4ABSTRACT:Thefundamentalelementofanystructuralsteelshapeistheflatplate.Damagetobridgestructuresconsistsoftheseplateelements,incombination,bentabouttheirstrongand/orweakaxes.Thepurposeofthispaperistodescribeexperimentalandanalyticalresearchonheatstraighteningasappliedtoplatesandtopresentrelatedengineeringcriteriaforitsuse.Anexperimentalprogramwasconductedtoevaluatetheresponseofplatestoheatstraighteningandtoidentifyimportantparametersinfluencingbehavior.Over300heatswereappliedtoavarietyofplates.Theprimaryfactorsinfluencingstraighteningweretheangleoftheveeheat,steeltemperatureduringheating,andexternalrestrainingforces.Theplasticrotationafterheatingwasdirectlyproportionaltotheseparameters.Toaidengineersinpredictingplatemovementsduringheatstraightening,asimplemathematicalformulawasdeveloped.Thisequationrelatestheaverageplasticrotationperveeheattoveeangle,steeltemperature,magnitudeofrestrainingforce,coefficientofthermalexpansion,andyieldstress.Theformulacompareswelltotheexperimentaldataandisthefirstsimpleformulaavailablethatincludestheparametersofheatingtemperatureandmagnitudeofrestrainingforce.Theformofthisanalyticalapproachalsowilllenditselftowardextensions,includingthebehaviorofrolledshapes,axiallyloadedmembers,andcompositeandnoncompositegirders.INTRODUCTIONThefundamentalelementofanystructuralsteelshapeistheflatplate.Damagetobridgestructuresconsistsoftheseplateelements,incombination,bentabouttheirstrongand/orweakaxes.Thepurposeofthispaperistodescribeexperimentalandanalyticalresearchonheatstraighteningasappliedtoplatesandtopresentrelatedengineeringdesigncriteriaforitsuse.Thisworkformsthebasisforextensionstoheatstraighteningofrolledshapes.Severaldetailedstudieshavebeenconductedforveeheatsappliedtoplates.Theveeheatistheusualheatingpatternforstraighteningplatesbentabouttheirstrongaxisandisexplainedindetailinalatersection.Thesestudieshaveattemptedtoidentifyparametersthatinfluenceveeheatsandtodeveloppredictivemodelsbasedonthisdata.NichollsandWeerth(1972)describedthebendsproducedby211veeheatswhoseapexanglevariedfrom247to607in67incrementsappliedto10-mm(3/8-in.)thickA36steelplate.Theveedepthwasalsovariedoverfulldepth,three-fourthdepth,andonehalfdepth.Noattemptwasmadetoevaluatetheeffectoftheseparametersotherthanthegeneralresultthatthegreatertheveeangleanddepth,thegreaterthebendproduced.Roeder(1986)alsoconductedastudyonundamagedveeheatedplates.Heemployedsophisticatedmonitoringequipmentsuchasthermocouples,contactpyrometers,andstraingauges,aswellasmoreconventionaltoolssuchasverniercaliperandasteelruler.Hisworkisparticularlysignificantasthefirstattempttobothexperimentallyandanalyticallyquantifyheatstraighteningbehaviorforplatesoverawiderangeofparameters.Theparametersincludedveegeometry,specimengeometry,heatingtemperatureandrate,steelgrade,restrainingforce,initialresidualstresses,andquenching.Roedersconclusionswerebasedonapproximately60heatsoverawiderangeofparameters.Asaresulttherewererelativelyfewre-petitiveheatsusingidenticalparameters.Althoughtrendscouldbedrawnfromthisdata,itssparsenesslimitedthequantitativevalueoftheresults.However,hisresearchprovidedtheinitialbasisformuchoftheexperimentalworkreportedhere.RoedersmostsignificantconclusionswereApracticalandsafeupperheatingtreatmentlimitis6507C(1,2007F).Changesinmaterialpropertiesaresmallwhentheheatingtemperatureremainsbelowthephasetransitiontemperatureofapproximately7207C(1,3307F).Therotationproducedbyaveeheatisdirectlyproportionaltoveeangleandheatingtemperature.Therotationproducedbyaveeheatisdirectlyproportionaltorestrainingforcesthatproducecompressionintheopenendoftheveeduringheating.Quenchingiseffectiveandmayincreaseveeheatrotations,butheatingtemperaturesshouldbekeptbelowthephasetransitiontemperaturealthoughsomepractitionersrecommendquenchingonlyifthesteeltemperatureisbelow7007For(3707C).Plasticstrainoccursprimarilywithintheveeheatregion.Plasticstrainissomewhatsensitivetogeometryoftheplate.However,muchofthissensitivitycanbeattributedtodifferencesinrateofheatingandheatflow.TheresearchdescribedinthispaperextendsRoedersworkandincludesenoughrepetitivedatapointstoquantifytheseandotherconclusions.Literatureonheatstraighteninghasbeenavailableformanyyearsasreviewedinastate-of-the-artpaperbyAvent(1989).However,engineeringquantificationoftheprocesshasbeenlacking.Thehandfulofpractitionerscurrentlyusingthemethodrelyextensivelyontheirmanyyearsofexperiencetoguidethemthrougharepair.Anengineerlackingthiswealthofexperienceneedsasetofanalyticalprocedurestodeterminehowbesttoapplytheheat-straighteningprocesstoaparticularrepair.Theseanalyticaltools,forreasonsofeconomy,shouldberelativelyfast,easytoapply,andallowforsuchconsiderationsasdifferentveegeometries,temperatureranges,externalloadings,andsupportrestraints.Atpresent,twoextremesexist:(1)Overlysimplisticmodels(Holt1965,1971；Moberg1979)thatcannottakeintoaccounttheeffectofeithertemperaturevariationsorinternalandexternalrestraint；and(2)comprehensivecomputermodels(ForChin1962；Burbank1968；Weerth1971；Horton1973；Roeder1985,1986,1987)basedonelastic-plasticfinite-elementorfinite-stripstressanalysiscombinedwithasimilarthermalanalysis.Whereastheformeristoosimplistictoaccuratelypredictbehavior,thelatterrequiressuchlengthycomputationaleffortastonotbepracticalfordesignofficeuse.Asaresult,thereisaneedforananalyticalmodelthatoffersbothpracticalityandcomprehensiveinclusionofallimportantvariablestoaccuratelypredictbehavior.Animportantconsiderationnotincludedinthemoresimpleformulationsistheinfluenceofexternalandinternalrestrainingforces.Externalforcestypicallyareappliedtoproducebendingmomentstendingtostraightenthemember.Theexternalforces,producingcompressionontheopenendoftheveeduringheating,willincreasetheavailableconfinementand,therefore,increasetherotationproducedperheat.ThefieldapplicationscitedbybothHoltandMoberginvolvedtheuseofrestrainingforces.Becauseinmostcasesthematerialrestraintalonewillbelessthanperfectconfinement,itseemslikelythatanycorrelationbetweenthepredictedandactualmovementinthestructuresbeingrepaired,asnotedbybothHoltandMoberg,isprimarilyduetotheinfluenceoftheexternalforces.Animprovedanalyticalmodelshouldincludetheeffectsofbothinternalandexternalrestraints.Thepurposeofthispaperistoquantifytheparametersinfluencingtheheatstraighteningofplateelementsandtodevelopsimpleyetefficientproceduresforpredictingtheresponseofdeformedsteelplatesduringtheheat-straighteningprocess.Theapproachchosenwastofirstidentifyallparametersthathaveanimportantinfluenceontheheat-straighteningprocess.Thisphasewasaccomplishedbystudyingtheexperimentaldataavailablefrompreviousresearchaswellasbyconductinganextensiveexperimentalprogramtoprovideadditionaldata.Aftersynthesizingthisexperimentaldata,ananalyticalprocedureforpredictingmemberresponsewasdeveloped.EVALUATIONOFRESULTSOFEXPERIMENTALPROGRAMVeeAngleResearchersagreethatoneofthemostfundamentalparametersinfluencingtheplasticrotationofaplateistheveeangle(Holt1971；Roeder1986；Avent1989).Thedatashowsafairlylinearrelationshipbetweenplasticrotationandveeangle.Forthisreason,mostdatawillbeplottedwiththeveeangleastheordinateandplasticrotationwpastheabscissa.Afirst-orderleast-squarescurvefitwillsometimesbeshown.Plotsinsucceedingsectionsshowaconsistentproportionalrelationshipbetweenthesevariables.DepthofVeePastresearchers(Holt1971；Roeder1985)haveconcludedthattheplasticrotationisproportionaltothedepthratioRd,whichistheratioofveedepthdvtoplatewidthW.AreviewofRoederstestdataintherangeof6507C(6807)1,2007F(61507)isinconclusiveastoveedeptheffect.Recognizingthatthedatawassparse,neitherthedepthratioof0.75nor0.67producedplasticrotationsthatwereconsistentlyhiearchial.Tofurtherevaluatethisbehavior,aseriesoftestswasconductedfordepthratiosof0.5,0.75,and1.0andveeanglesrangingfrom207to607.Atleastthreeheatswereconductedoninitiallystraightplatesforeachcaseandtheresultsaveraged.TheresultsareshowninFig.2foracombinationofthreedepthratios,threeveeangles,andtwojackingratios.Thejackingratiosreflectthatajackingforcewasusedtocreateamomentattheveeheatzoneequaltoeither25or50%oftheultimatebendingcapacityoftheplate.AscanbeseenfromFig.2,thedepthratiosof75and100%trackeachotherwell.Infactthe75%depthratioresultedinslightlylargerplasticrotationsinallbutoneofthesixcases.The50%depthratioresultedinanerraticbehaviorwhencomparedtotheothertwo.Inthreeofthesixcasesthe50%depthratioproducedmuchsmallerplasticrotations.Intheotherthreecases,theplasticrotationsweresimilar.Tofurther