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HEATSTRAIGHTENINGDAMAGEDSTEELPLATEELEMENTSBYRRICHARDAVENT,1DAVIDJMUKAI,2PAULFROBINSON,3ANDRANDYJBOUDREAUX4ABSTRACTTHEFUNDAMENTALELEMENTOFANYSTRUCTURALSTEELSHAPEISTHEFLATPLATEDAMAGETOBRIDGESTRUCTURESCONSISTSOFTHESEPLATEELEMENTS,INCOMBINATION,BENTABOUTTHEIRSTRONGAND/ORWEAKAXESTHEPURPOSEOFTHISPAPERISTODESCRIBEEXPERIMENTALANDANALYTICALRESEARCHONHEATSTRAIGHTENINGASAPPLIEDTOPLATESANDTOPRESENTRELATEDENGINEERINGCRITERIAFORITSUSEANEXPERIMENTALPROGRAMWASCONDUCTEDTOEVALUATETHERESPONSEOFPLATESTOHEATSTRAIGHTENINGANDTOIDENTIFYIMPORTANTPARAMETERSINFLUENCINGBEHAVIOROVER300HEATSWEREAPPLIEDTOAVARIETYOFPLATESTHEPRIMARYFACTORSINFLUENCINGSTRAIGHTENINGWERETHEANGLEOFTHEVEEHEAT,STEELTEMPERATUREDURINGHEATING,ANDEXTERNALRESTRAININGFORCESTHEPLASTICROTATIONAFTERHEATINGWASDIRECTLYPROPORTIONALTOTHESEPARAMETERSTOAIDENGINEERSINPREDICTINGPLATEMOVEMENTSDURINGHEATSTRAIGHTENING,ASIMPLEMATHEMATICALFORMULAWASDEVELOPEDTHISEQUATIONRELATESTHEAVERAGEPLASTICROTATIONPERVEEHEATTOVEEANGLE,STEELTEMPERATURE,MAGNITUDEOFRESTRAININGFORCE,COEFFICIENTOFTHERMALEXPANSION,ANDYIELDSTRESSTHEFORMULACOMPARESWELLTOTHEEXPERIMENTALDATAANDISTHEFIRSTSIMPLEFORMULAAVAILABLETHATINCLUDESTHEPARAMETERSOFHEATINGTEMPERATUREANDMAGNITUDEOFRESTRAININGFORCETHEFORMOFTHISANALYTICALAPPROACHALSOWILLLENDITSELFTOWARDEXTENSIONS,INCLUDINGTHEBEHAVIOROFROLLEDSHAPES,AXIALLYLOADEDMEMBERS,ANDCOMPOSITEANDNONCOMPOSITEGIRDERSINTRODUCTIONTHEFUNDAMENTALELEMENTOFANYSTRUCTURALSTEELSHAPEISTHEFLATPLATEDAMAGETOBRIDGESTRUCTURESCONSISTSOFTHESEPLATEELEMENTS,INCOMBINATION,BENTABOUTTHEIRSTRONGAND/ORWEAKAXESTHEPURPOSEOFTHISPAPERISTODESCRIBEEXPERIMENTALANDANALYTICALRESEARCHONHEATSTRAIGHTENINGASAPPLIEDTOPLATESANDTOPRESENTRELATEDENGINEERINGDESIGNCRITERIAFORITSUSETHISWORKFORMSTHEBASISFOREXTENSIONSTOHEATSTRAIGHTENINGOFROLLEDSHAPESSEVERALDETAILEDSTUDIESHAVEBEENCONDUCTEDFORVEEHEATSAPPLIEDTOPLATESTHEVEEHEATISTHEUSUALHEATINGPATTERNFORSTRAIGHTENINGPLATESBENTABOUTTHEIRSTRONGAXISANDISEXPLAINEDINDETAILINALATERSECTIONTHESESTUDIESHAVEATTEMPTEDTOIDENTIFYPARAMETERSTHATINFLUENCEVEEHEATSANDTODEVELOPPREDICTIVEMODELSBASEDONTHISDATANICHOLLSANDWEERTH1972DESCRIBEDTHEBENDSPRODUCEDBY211VEEHEATSWHOSEAPEXANGLEVARIEDFROM247TO607IN67INCREMENTSAPPLIEDTO10MM3/8INTHICKA36STEELPLATETHEVEEDEPTHWASALSOVARIEDOVERFULLDEPTH,THREEFOURTHDEPTH,ANDONEHALFDEPTHNOATTEMPTWASMADETOEVALUATETHEEFFECTOFTHESEPARAMETERSOTHERTHANTHEGENERALRESULTTHATTHEGREATERTHEVEEANGLEANDDEPTH,THEGREATERTHEBENDPRODUCEDROEDER1986ALSOCONDUCTEDASTUDYONUNDAMAGEDVEEHEATEDPLATESHEEMPLOYEDSOPHISTICATEDMONITORINGEQUIPMENTSUCHASTHERMOCOUPLES,CONTACTPYROMETERS,ANDSTRAINGAUGES,ASWELLASMORECONVENTIONALTOOLSSUCHASVERNIERCALIPERANDASTEELRULERHISWORKISPARTICULARLYSIGNIFICANTASTHEFIRSTATTEMPTTOBOTHEXPERIMENTALLYANDANALYTICALLYQUANTIFYHEATSTRAIGHTENINGBEHAVIORFORPLATESOVERAWIDERANGEOFPARAMETERSTHEPARAMETERSINCLUDEDVEEGEOMETRY,SPECIMENGEOMETRY,HEATINGTEMPERATUREANDRATE,STEELGRADE,RESTRAININGFORCE,INITIALRESIDUALSTRESSES,ANDQUENCHINGROEDER’SCONCLUSIONSWEREBASEDONAPPROXIMATELY60HEATSOVERAWIDERANGEOFPARAMETERSASARESULTTHEREWERERELATIVELYFEWREPETITIVEHEATSUSINGIDENTICALPARAMETERSALTHOUGHTRENDSCOULDBEDRAWNFROMTHISDATA,ITSSPARSENESSLIMITEDTHEQUANTITATIVEVALUEOFTHERESULTSHOWEVER,HISRESEARCHPROVIDEDTHEINITIALBASISFORMUCHOFTHEEXPERIMENTALWORKREPORTEDHEREROEDER’SMOSTSIGNIFICANTCONCLUSIONSWEREAPRACTICALANDSAFEUPPERHEATINGTREATMENTLIMITIS6507C1,2007FCHANGESINMATERIALPROPERTIESARESMALLWHENTHEHEATINGTEMPERATUREREMAINSBELOWTHEPHASETRANSITIONTEMPERATUREOFAPPROXIMATELY7207C1,3307FTHEROTATIONPRODUCEDBYAVEEHEATISDIRECTLYPROPORTIONALTOVEEANGLEANDHEATINGTEMPERATURETHEROTATIONPRODUCEDBYAVEEHEATISDIRECTLYPROPORTIONALTORESTRAININGFORCESTHATPRODUCECOMPRESSIONINTHEOPENENDOFTHEVEEDURINGHEATINGQUENCHINGISEFFECTIVEANDMAYINCREASEVEEHEATROTATIONS,BUTHEATINGTEMPERATURESSHOULDBEKEPTBELOWTHEPHASETRANSITIONTEMPERATUREALTHOUGHSOMEPRACTITIONERSRECOMMENDQUENCHINGONLYIFTHESTEELTEMPERATUREISBELOW7007FOR3707CPLASTICSTRAINOCCURSPRIMARILYWITHINTHEVEEHEATREGIONPLASTICSTRAINISSOMEWHATSENSITIVETOGEOMETRYOFTHEPLATEHOWEVER,MUCHOFTHISSENSITIVITYCANBEATTRIBUTEDTODIFFERENCESINRATEOFHEATINGANDHEATFLOWTHERESEARCHDESCRIBEDINTHISPAPEREXTENDSROEDER’SWORKANDINCLUDESENOUGHREPETITIVEDATAPOINTSTOQUANTIFYTHESEANDOTHERCONCLUSIONSLITERATUREONHEATSTRAIGHTENINGHASBEENAVAILABLEFORMANYYEARSASREVIEWEDINASTATEOFTHEARTPAPERBYAVENT1989HOWEVER,ENGINEERINGQUANTIFICATIONOFTHEPROCESSHASBEENLACKINGTHEHANDFULOFPRACTITIONERSCURRENTLYUSINGTHEMETHODRELYEXTENSIVELYONTHEIRMANYYEARSOFEXPERIENCETOGUIDETHEMTHROUGHAREPAIRANENGINEERLACKINGTHISWEALTHOFEXPERIENCENEEDSASETOFANALYTICALPROCEDURESTODETERMINEHOWBESTTOAPPLYTHEHEATSTRAIGHTENINGPROCESSTOAPARTICULARREPAIRTHESEANALYTICALTOOLS,FORREASONSOFECONOMY,SHOULDBERELATIVELYFAST,EASYTOAPPLY,ANDALLOWFORSUCHCONSIDERATIONSASDIFFERENTVEEGEOMETRIES,TEMPERATURERANGES,EXTERNALLOADINGS,ANDSUPPORTRESTRAINTSATPRESENT,TWOEXTREMESEXIST1OVERLYSIMPLISTICMODELSHOLT1965,1971；MOBERG1979THATCANNOTTAKEINTOACCOUNTTHEEFFECTOFEITHERTEMPERATUREVARIATIONSORINTERNALANDEXTERNALRESTRAINT；AND2COMPREHENSIVECOMPUTERMODELSFORCHIN1962；BURBANK1968；WEERTH1971；HORTON1973；ROEDER1985,1986,1987BASEDONELASTICPLASTICFINITEELEMENTORFINITESTRIPSTRESSANALYSISCOMBINEDWITHASIMILARTHERMALANALYSISWHEREASTHEFORMERISTOOSIMPLISTICTOACCURATELYPREDICTBEHAVIOR,THELATTERREQUIRESSUCHLENGTHYCOMPUTATIONALEFFORTASTONOTBEPRACTICALFORDESIGNOFFICEUSEASARESULT,THEREISANEEDFORANANALYTICALMODELTHATOFFERSBOTHPRACTICALITYANDCOMPREHENSIVEINCLUSIONOFALLIMPORTANTVARIABLESTOACCURATELYPREDICTBEHAVIORANIMPORTANTCONSIDERATIONNOTINCLUDEDINTHEMORESIMPLEFORMULATIONSISTHEINFLUENCEOFEXTERNALANDINTERNALRESTRAININGFORCESEXTERNALFORCESTYPICALLYAREAPPLIEDTOPRODUCEBENDINGMOMENTSTENDINGTOSTRAIGHTENTHEMEMBERTHEEXTERNALFORCES,PRODUCINGCOMPRESSIONONTHEOPENENDOFTHEVEEDURINGHEATING,WILLINCREASETHEAVAILABLECONFINEMENTAND,THEREFORE,INCREASETHEROTATIONPRODUCEDPERHEATTHEFIELDAPPLICATIONSCITEDBYBOTHHOLTANDMOBERGINVOLVEDTHEUSEOFRESTRAININGFORCESBECAUSEINMOSTCASESTHEMATERIALRESTRAINTALONEWILLBELESSTHANPERFECTCONFINEMENT,ITSEEMSLIKELYTHATANYCORRELATIONBETWEENTHEPREDICTEDANDACTUALMOVEMENTINTHESTRUCTURESBEINGREPAIRED,ASNOTEDBYBOTHHOLTANDMOBERG,ISPRIMARILYDUETOTHEINFLUENCEOFTHEEXTERNALFORCESANIMPROVEDANALYTICALMODELSHOULDINCLUDETHEEFFECTSOFBOTHINTERNALANDEXTERNALRESTRAINTSTHEPURPOSEOFTHISPAPERISTOQUANTIFYTHEPARAMETERSINFLUENCINGTHEHEATSTRAIGHTENINGOFPLATEELEMENTSANDTODEVELOPSIMPLEYETEFFICIENTPROCEDURESFORPREDICTINGTHERESPONSEOFDEFORMEDSTEELPLATESDURINGTHEHEATSTRAIGHTENINGPROCESSTHEAPPROACHCHOSENWASTOFIRSTIDENTIFYALLPARAMETERSTHATHAVEANIMPORTANTINFLUENCEONTHEHEATSTRAIGHTENINGPROCESSTHISPHASEWASACCOMPLISHEDBYSTUDYINGTHEEXPERIMENTALDATAAVAILABLEFROMPREVIOUSRESEARCHASWELLASBYCONDUCTINGANEXTENSIVEEXPERIMENTALPROGRAMTOPROVIDEADDITIONALDATAAFTERSYNTHESIZINGTHISEXPERIMENTALDATA,ANANALYTICALPROCEDUREFORPREDICTINGMEMBERRESPONSEWASDEVELOPEDEVALUATIONOFRESULTSOFEXPERIMENTALPROGRAMVEEANGLERESEARCHERSAGREETHATONEOFTHEMOSTFUNDAMENTALPARAMETERSINFLUENCINGTHEPLASTICROTATIONOFAPLATEISTHEVEEANGLEHOLT1971；ROEDER1986；AVENT1989THEDATASHOWSAFAIRLYLINEARRELATIONSHIPBETWEENPLASTICROTATIONANDVEEANGLEFORTHISREASON,MOSTDATAWILLBEPLOTTEDWITHTHEVEEANGLEASTHEORDINATEANDPLASTICROTATIONWPASTHEABSCISSAAFIRSTORDERLEASTSQUARESCURVEFITWILLSOMETIMESBESHOWNPLOTSINSUCCEEDINGSECTIONSSHOWACONSISTENTPROPORTIONALRELATIONSHIPBETWEENTHESEVARIABLESDEPTHOFVEEPASTRESEARCHERSHOLT1971；ROEDER1985HAVECONCLUDEDTHATTHEPLASTICROTATIONISPROPORTIONALTOTHEDEPTHRATIORD,WHICHISTHERATIOOFVEEDEPTHDVTOPLATEWIDTHWAREVIEWOFROEDER’STESTDATAINTHERANGEOF6507C68071,2007F61507ISINCONCLUSIVEASTOVEEDEPTHEFFECTRECOGNIZINGTHATTHEDATAWASSPARSE,NEITHERTHEDEPTHRATIOOF075NOR067PRODUCEDPLASTICROTATIONSTHATWERECONSISTENTLYHIEARCHIALTOFURTHEREVALUATETHISBEHAVIOR,ASERIESOFTESTSWASCONDUCTEDFORDEPTHRATIOSOF05,075,AND10ANDVEEANGLESRANGINGFROM207TO607ATLEASTTHREEHEATSWERECONDUCTEDONINITIALLYSTRAIGHTPLATESFOREACHCASEANDTHERESULTSAVERAGEDTHERESULTSARESHOWNINFIG2FORACOMBINATIONOFTHREEDEPTHRATIOS,THREEVEEANGLES,ANDTWOJACKINGRATIOSTHEJACKINGRATIOSREFLECTTHATAJACKINGFORCEWASUSEDTOCREATEAMOMENTATTHEVEEHEATZONEEQUALTOEITHER25OR50OFTHEULTIMATEBENDINGCAPACITYOFTHEPLATEASCANBESEENFROMFIG2,THEDEPTHRATIOSOF75AND100TRACKEACHOTHERWELLINFACTTHE75DEPTHRATIORESULTEDINSLIGHTLYLARGERPLASTICROTATIONSINALLBUTONEOFTHESIXCASESTHE50DEPTHRATIORESULTEDINANERRATICBEHAVIORWHENCOMPAREDTOTHEOTHERTWOINTHREEOFTHESIXCASESTHE50DEPTHRATIOPRODUCEDMUCHSMALLERPLASTICROTATIONSINTHEOTHERTHREECASES,THEPLASTICROTATIONSWERESIMILARTOFURTHERVERIFYTHISBEHAVIOR,ASERIESOFPLATESWASDAMAGEDANDSTRAIGHTENEDTHEDEGREEOFDAMAGEWASLARGEENOUGHTHATATLEAST20HEATSWEREREQUIREDFORMOSTOFTHESEPLATESTHEREFORE,MORESTATISTICALLYSIGNIFICANTAVERAGEPLASTICROTATIONSWEREOBTAINEDFROMTHESETESTSRESULTSARECOMPAREDINFIG3FORAJACKINGRATIOOF05ANDTWOVEEDEPTHRATIOS,075AND10AGAINTHEPATTERNOFPLASTICROTATIONSDOESNOTHAVEADIRECTCORRELATIONTOTHEVEEDEPTHRATIOSTHEREFORE,ALTHOUGHITWOULDSEEMINTUITIVETHATINCREASINGTHEVEEDEPTHWOULDINCREASETHEPLASTICROTATION,THEREISNOEXPERIMENTALJUSTIFICATIONFORSUCHAGENERALSTATEMENTITCANBECONCLUDEDTHATTHEVARIATIONOFVEEDEPTHRATIOSBETWEEN075AND10HASLITTLEINFLUENCEONPLASTICROTATIONHOWEVER,AVEEDEPTHRATIOOF50MAYREDUCETHEPLASTICROTATIONSPLATETHICKNESSANDWIDTHRESEARCHERSHAVEGENERALLYCONSIDEREDPLATETHICKNESSTOHAVEANEGLIGIBLEEFFECTONPLASTICROTATIONTHEONLYRESERVATIONHASBEENEXPRESSEDTHATTHEPLATESHOULDBETHINENOUGHTOALLOWARELATIVELYUNIFORMPENETRATIONOFTHEHEATTHROUGHTHETHICKNESS
