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HEATSTRAIGHTENINGDAMAGEDSTEELPLATEELEMENTSByR.RichardAvent,1DavidJ.Mukai,2PaulF.Robinson,3andRandyJ.Boudreaux4ABSTRACTThefundamentalelementofanystructuralsteelshapeistheflatplate.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.NichollsandWeerth1972describedthebendsproducedby211veeheatswhoseapexanglevariedfrom247to607in67incrementsappliedto10mm3/8in.thickA36steelplate.Theveedepthwasalsovariedoverfulldepth,threefourthdepth,andonehalfdepth.Noattemptwasmadetoevaluatetheeffectoftheseparametersotherthanthegeneralresultthatthegreatertheveeangleanddepth,thegreaterthebendproduced.Roeder1986alsoconductedastudyonundamagedveeheatedplates.Heemployedsophisticatedmonitoringequipmentsuchasthermocouples,contactpyrometers,andstraingauges,aswellasmoreconventionaltoolssuchasverniercaliperandasteelruler.Hisworkisparticularlysignificantasthefirstattempttobothexperimentallyandanalyticallyquantifyheatstraighteningbehaviorforplatesoverawiderangeofparameters.Theparametersincludedveegeometry,specimengeometry,heatingtemperatureandrate,steelgrade,restrainingforce,initialresidualstresses,andquenching.Roedersconclusionswerebasedonapproximately60heatsoverawiderangeofparameters.Asaresulttherewererelativelyfewrepetitiveheatsusingidenticalparameters.Althoughtrendscouldbedrawnfromthisdata,itssparsenesslimitedthequantitativevalueoftheresults.However,hisresearchprovidedtheinitialbasisformuchoftheexperimentalworkreportedhere.RoedersmostsignificantconclusionswereApracticalandsafeupperheatingtreatmentlimitis6507C1,2007F.Changesinmaterialpropertiesaresmallwhentheheatingtemperatureremainsbelowthephasetransitiontemperatureofapproximately7207C1,3307F.Therotationproducedbyaveeheatisdirectlyproportionaltoveeangleandheatingtemperature.Therotationproducedbyaveeheatisdirectlyproportionaltorestrainingforcesthatproducecompressionintheopenendoftheveeduringheating.Quenchingiseffectiveandmayincreaseveeheatrotations,butheatingtemperaturesshouldbekeptbelowthephasetransitiontemperaturealthoughsomepractitionersrecommendquenchingonlyifthesteeltemperatureisbelow7007For3707C.Plasticstrainoccursprimarilywithintheveeheatregion.Plasticstrainissomewhatsensitivetogeometryoftheplate.However,muchofthissensitivitycanbeattributedtodifferencesinrateofheatingandheatflow.TheresearchdescribedinthispaperextendsRoedersworkandincludesenoughrepetitivedatapointstoquantifytheseandotherconclusions.LiteratureonheatstraighteninghasbeenavailableformanyyearsasreviewedinastateoftheartpaperbyAvent1989.However,engineeringquantificationoftheprocesshasbeenlacking.Thehandfulofpractitionerscurrentlyusingthemethodrelyextensivelyontheirmanyyearsofexperiencetoguidethemthrougharepair.Anengineerlackingthiswealthofexperienceneedsasetofanalyticalprocedurestodeterminehowbesttoapplytheheatstraighteningprocesstoaparticularrepair.Theseanalyticaltools,forreasonsofeconomy,shouldberelativelyfast,easytoapply,andallowforsuchconsiderationsasdifferentveegeometries,temperatureranges,externalloadings,andsupportrestraints.Atpresent,twoextremesexist1OverlysimplisticmodelsHolt1965,1971Moberg1979thatcannottakeintoaccounttheeffectofeithertemperaturevariationsorinternalandexternalrestraintand2comprehensivecomputermodelsForChin1962Burbank1968Weerth1971Horton1973Roeder1985,1986,1987basedonelasticplasticfiniteelementorfinitestripstressanalysiscombinedwithasimilarthermalanalysis.Whereastheformeristoosimplistictoaccuratelypredictbehavior,thelatterrequiressuchlengthycomputationaleffortastonotbepracticalfordesignofficeuse.Asaresult,thereisaneedforananalyticalmodelthatoffersbothpracticalityandcomprehensiveinclusionofallimportantvariablestoaccuratelypredictbehavior.Animportantconsiderationnotincludedinthemoresimpleformulationsistheinfluenceofexternalandinternalrestrainingforces.Externalforcestypicallyareappliedtoproducebendingmomentstendingtostraightenthemember.Theexternalforces,producingcompressionontheopenendoftheveeduringheating,willincreasetheavailableconfinementand,therefore,increasetherotationproducedperheat.ThefieldapplicationscitedbybothHoltandMoberginvolvedtheuseofrestrainingforces.Becauseinmostcasesthematerialrestraintalonewillbelessthanperfectconfinement,itseemslikelythatanycorrelationbetweenthepredictedandactualmovementinthestructuresbeingrepaired,asnotedbybothHoltandMoberg,isprimarilyduetotheinfluenceoftheexternalforces.Animprovedanalyticalmodelshouldincludetheeffectsofbothinternalandexternalrestraints.Thepurposeofthispaperistoquantifytheparametersinfluencingtheheatstraighteningofplateelementsandtodevelopsimpleyetefficientproceduresforpredictingtheresponseofdeformedsteelplatesduringtheheatstraighteningprocess.Theapproachchosenwastofirstidentifyallparametersthathaveanimportantinfluenceontheheatstraighteningprocess.Thisphasewasaccomplishedbystudyingtheexperimentaldataavailablefrompreviousresearchaswellasbyconductinganextensiveexperimentalprogramtoprovideadditionaldata.Aftersynthesizingthisexperimentaldata,ananalyticalprocedureforpredictingmemberresponsewasdeveloped.EVALUATIONOFRESULTSOFEXPERIMENTALPROGRAMVeeAngleResearchersagreethatoneofthemostfundamentalparametersinfluencingtheplasticrotationofaplateistheveeangleHolt1971Roeder1986Avent1989.Thedatashowsafairlylinearrelationshipbetweenplasticrotationandveeangle.Forthisreason,mostdatawillbeplottedwiththeveeangleastheordinateandplasticrotationwpastheabscissa.Afirstorderleastsquarescurvefitwillsometimesbeshown.Plotsinsucceedingsectionsshowaconsistentproportionalrelationshipbetweenthesevariables.DepthofVeePastresearchersHolt1971Roeder1985haveconcludedthattheplasticrotationisproportionaltothedepthratioRd,whichistheratioofveedepthdvtoplatewidthW.AreviewofRoederstestdataintherangeof6507C68071,2007F61507isinconclusiveastoveedeptheffect.Recognizingthatthedatawassparse,neitherthedepthratioof0.75nor0.67producedplasticrotationsthatwereconsistentlyhiearchial.Tofurtherevaluatethisbehavior,aseriesoftestswasconductedfordepthratiosof0.5,0.75,and1.0andveeanglesrangingfrom207to607.Atleastthreeheatswereconductedoninitiallystraightplatesforeachcaseandtheresultsaveraged.TheresultsareshowninFig.2foracombinationofthreedepthratios,threeveeangles,andtwojackingratios.Thejackingratiosreflectthatajackingforcewasusedtocreateamomentattheveeheatzoneequaltoeither25or50oftheultimatebendingcapacityoftheplate.AscanbeseenfromFig.2,thedepthratiosof75and100trackeachotherwell.Infactthe75depthratioresultedinslightlylargerplasticrotationsinallbutoneofthesixcases.The50depthratioresultedinanerraticbehaviorwhencomparedtotheothertwo.Inthreeofthesixcasesthe50depthratioproducedmuchsmallerplasticrotations.Intheotherthreecases,theplasticrotationsweresimilar.Tofurtherverifythisbehavior,aseriesofplateswasdamagedandstraightened.Thedegreeofdamagewaslargeenoughthatatleast20heatswererequiredformostoftheseplates.Therefore,morestatisticallysignificantaverageplasticrotationswereobtainedfromthesetests.ResultsarecomparedinFig.3forajackingratioof0.5andtwoveedepthratios,0.75and1.0.Againthepatternofplasticrotationsdoesnothaveadirectcorrelationtotheveedepthratios.Therefore,althoughitwouldseemintuitivethatincreasingtheveedepthwouldincreasetheplasticrotation,thereisnoexperimentaljustificationforsuchageneralstatement.Itcanbeconcludedthatthevariationofveedepthratiosbetween0.75and1.0haslittleinfluenceonplasticrotation.However,aveedepthratioof50mayreducetheplasticrotations.PlateThicknessandWidthResearchershavegenerallyconsideredplatethicknesstohaveanegligibleeffectonplasticrotation.Theonlyreservationhasbeenexpressedthattheplateshouldbethinenoughtoallowarelativelyuniformpenetrationoftheheatthroughthethickness.
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