Computer-AidedCivilandInfrastructureEngineering23(2008)448464INDUSTRIALAPPLICATIONDynamicResponseofaRolloverProtectiveStructureDavidP.Thambiratnam&BrianJ.ClarkSchoolofUrbanDevelopment,FacultyofBuiltEnvironment&Engineering,QueenslandUniversityofTechnology,Brisbane,Australia&NimalJ.PereraSchoolofUrbanDevelopment,FacultyofBuiltEnvironment&Engineering,QueenslandUniversityofTechnology,Brisbane,AustraliaRobertBirdGroup,Brisbane,AustraliaAbstract:RollOverProtectiveStructures(ROPS)aresafetydevicesfittedtoheavyvehiclestoprovideprotectiontotheoperatorduringanaccidentalrollover.Atpresent,ROPSdesignstandardsrequirefull-scaledestructivetest-ingthatcanbeexpensive,timeconsuming,andunsuitableforsmallcompanies.Moreeconomicalanalyticalmeth-odsarenotpermittedduetoalackofunderstandingofpostyieldbehaviorandtheenergyabsorptioncapacityofROPS.Toaddressthis,acomprehensiveresearchprojectwasundertakentoinvestigateROPSbehaviorusingan-alyticaltechniquessupportedbyexperiments.Thisarti-clepresentsthedynamicimpactanalysisofabulldozerROPSusingcalibratedfiniteelementmodels.Resultsindi-catethat(1)ROPSpostshavesignificantinfluenceontheenergy-absorbingcapacity,(2)dynamicamplificationsinenergycouldbeupto25%,(3)stifferROPScausehighpeakdecelerationsthatmaybedetrimentaltotheoperator,and(4)analyticaltechniquesmaybeusedforevaluatingROPSperformance.1INTRODUCTIONHeavyvehiclesthatareusedintherural,mining,andconstructionindustriesaresusceptibletorolloversasTowhomcorrespondenceshouldbeaddressed.E-mail:.au.theyhaveahighcenterofgravityandcommonlyop-erateonslopinganduneventerrain.Asteelmoment-resistingframewitheithertwoorfourpostsisusuallyattachedtothesevehiclesabovetheoperatorscabinforprotectionduringrollovers.ThissafetydeviceiscalledaRolloverProtectiveStructure(ROPS)anditsroleistoabsorbsomeofthekineticenergy(KE)oftherollover,whilemaintainingasurvivalzonefortheoperator.ThedesignandanalysisofROPSiscomplexandrequiresdualcriteriaofadequateflexibilitytoabsorbenergyandadequatestiffnesstomaintainasurvivalzonearoundtheoperator.EvaluationtechniquesusedinthecurrentAustralianstandardforearthmovingmachineryprotectivestruc-turesAS22941997aresimplifiedandinvolvefull-scaledestructivetestingofROPSsubjectedtostaticloadsalongtheirlateral,vertical,andlongitudinalaxes.Thestandardisperformancebased,withcertainforceandenergyabsorptioncriteriathatarederivedfromempir-icalformulaerelatedtothetypeofmachineandoper-atingmass.Deflectionrestrictionsarealsoemployedtoenableasurvivalspaceknownasthedynamiclimitingvolume(DLV)tobemaintainedforthevehicleoperator.Thesesimplifiedprovisionsprovidedesignguidelinesthatwillsubstantiallyimprovetheoperatorschancesofsurvivalduringanaccidentalrollover.Thisformofcerti-ficationcanbetimeconsumingandextremelyexpensiveC2008Computer-AidedCivilandInfrastructureEngineering.PublishedbyBlackwellPublishing,350MainStreet,Malden,MA02148,USA,and9600GarsingtonRoad,OxfordOX42DQ,UK.Dynamicresponseofarolloverprotectivestructure449asestablishingtheforceandenergycriteriacaninvolvelargeloadsthatmaythereforerequiretheuseofaspe-cializedtestingfacility.CertificationofROPSbymoreeconomicalanalyti-calmodelingtechniquesiscurrentlynotpermittedbyROPSstandardsforearthmovingmachinerybothinAustraliaandinternationally.Reasonsfortheexclusionareattributedtoalackofknowledgeandresearchin-formationonthebehaviorofthesestructuresinthepostyieldregionandtheirenergy-absorptioncapacity.Pre-liminaryresearchhasshownpromisefortheuseofan-alyticaltechniquestomodelthenonlinearresponseofROPS.Theseanalyticalmethodswereverysimplifiedandinvolvedtheuseofelasto-plasticbeamelementstosimulatethebehaviorofROPSsubjectedtoastaticlateralload.Inrecentyears,substantialadvanceshavebeenmadeinbothcomputationalpowerandtheimple-mentationofadvancedelementtypesinFiniteElement(FE)techniquesthatcanaccuratelymodelandpredictthenonlinearresponseofstructures,particularlyinthepostyieldregion.ResearchcarriedoutonROPSbehav-iorusinganalyticalandexperimentaltechniquesincludethoseofClarketal.(2006a,b),KimandReid(2001),Tomasetal.(1997),Swan(1988),andHuckleretal.(1985).AcomprehensiveresearchprojectwasundertakenattheQueenslandUniversityofTechnologytoinves-tigateROPSbehaviorusingcomputersimulationssup-portedbyexperimentsto(1)enhanceourunderstandingofROPSbehavior,(2)improveenergyabsorptionandsafety,and(3)generateresearchinformationtofacili-tatethedevelopmentofanalyticaltechniquesfordesignandevaluationthatmaylessentheneedfordestructivefull-scaletesting(Clark,2006a).ThisarticletreatsthedynamicresponseoftheROPSmodelforaK275bulldozer,usingcalibratedFEmodels.TheexperimentaltestingandcalibrationofthecomputemodelofthisparticularROPSmodelarereportedelse-where(Clark,2006a,b).Thedynamicimpactloadsarecharacteristicofthosethatareexperiencedduringthesidewardsrolloverofavehicleonafirmslope.Asim-plifiedmethodbasedonaconservationofangularmo-mentumapproachreportedbyWatson(1967)isusedtoestimatethedynamicimpactparametersfortheROPSduringasidewardsoverturn.TheexplicitFEcodeLS-Dynav970wasusedtoconductthenecessarydynamicimpactmodelingforrolloverimpactsonfirmslopeswithinclinationsof15,30,and45.Theinfluenceofcon-trollingvariablessuchasROPSstiffness,impactveloc-ity,anddurationandrollslopeangleonthedynamicresponseoftheROPSwasstudied.Theresultsarecom-paredwiththosefrompreviousstaticanalysistoestab-lishtheeffectofpossibledynamicamplificationsandtheadequacyofcurrentstandardprovisions.1.1DynamicfiniteelementanalysisRolloversimulationusingFEanalysishasreceivedlit-tleattentionfromresearchers.Chouetal.(1998)high-lightedthatthemajordifficultyassociatedwithusingFEforrolloveranalysiswasthelargesimulationtimerequiredtocapturetheeventaccurately.Indirectparal-leltothis,Klose(1969)alsoemphasizedthattherolloverprocesswasextremelydifficulttomodelasitinvolvedthecomplexinteractionofnumerousparametersthatinfluencedthebehavioroftherollingvehicle.Intheopenliterature,theFEmodelingofrolloverprotectivestructuresunderdynamicloadinghasbeenlimitedtore-searchperformedbyTomasetal.(1997)andHarrisetal.(2000).TheworkperformedbyHarris(2000)examinedtherearwardrolloverofatractorwhereasTomassre-searchusedtheprogramMADYMOtostudytheeffectofROPSstiffnessandoccupantrestraintduringtheside-wardsrolloverofanearthmovingmachine.AlthoughthemodelingtechniquesemployedbyeachoftheseauthorshaveassistedwithassessingtheperformanceofROPSundersimulateddynamicimpactloads,littlecompari-sonhasbeenmadewithreferencetotheadequacyofthestaticloadingproceduresadoptedincurrentROPSstan-dardsandthepossibledynamicamplificationsthatmaytakeplaceduringsuchloadingconditions.WiththeseviewsinmindthesimplifiedprocedureproposedbyWat-son(1967)isusedasabasisforadynamicimpactstudytoinvestigatetheinfluenceofcriticalparametersthatcon-troltheresponsebehaviorofROPSsubjectedtosuchloadingconditions.2ROPSFORK275BULLDOZERTheK275bulldozerisacrawlertypedozerwithagrossvehicleweightofapproximately50tonscommonlyusedintheconstructionandminingindustriesforearthmov-ingpurposes.Rolloverprotectionfortheoccupantisaf-fordedthroughatwopostrollbartypeROPS,whichisshowninFigure1.ThisROPSisprimarilyafixedbaseportalframe,con-sistingoftwopostsandabeam,rigidlyconnectedtothechassisofthevehicle.InadditiontotheROPS,anaddi-tionalroofcanopysectionknownastheFallingObjectProtectiveStructure(FOPS),isincorporatedtoprovideprotectiontotheoperatorunderfallingobjects.Inthisstudy,theFOPS,whichisaseparatedetachablestruc-ture,wasomitted.Theoverallgeometryofthefull-scaleK275ROPSmodelwasestablishedfromsitemeasure-mentstakenatthemanufacturersstorageyard.Appro-priateRHS/SHSmembersizeswereselectedsothattheROPSwouldpossesssufficientstrengthandenergyab-sorptioncharacteristicsthatwouldenableittosuccess-fullypasstherequirementsoftheAustralianStandard.450Thambiratnam,Clark&PereraFig.1.K275bulldozerwithROPS.2.1Half-scaleROPSmodelPreviousresearchbySrivastavaetal.(1978)hasshownthatprinciplesofsimilitudemodelingcouldbesuccess-fullyappliedtoROPStestingtechniques,andcouldleadtolarge-scaleeconomicsavings.BasedontheresearchfindingsoftheseauthorstheprinciplesofsimilitudewereappliedtotheK275bulldozerROPStolessenfabrica-tioncostsandreducethemagnitudesofthetestloadstobeappliedtotheROPS.Reductioninthemagnitudesoftheloadswasessentialasafull-scaletestofROPSforavehiclesuchasthiswasextremelylargeandwouldre-quiretheuseofanextensivelaboratorytestingfacility.Ascalingfactor(forsize)wasthenselectedbetweenthemodelandprototypethatgaverisetothescalingfactorsof1/8forenergyabsorbedunderlateralload,1/4forloads,and1/2fordeflections.Ahalf-scalemodeloftheK275ROPSwithlength1,000mm,height900mm,andsectionproperties125755mmforthepostsand1251255mmforthebeam,wasdesignedandfabricatedandsubjectedtotheloadingandenergyre-quirementsofAS22941997.ThemembertypesusedfortheROPSconsistedof350gradeRHSwithfullpenetrationbutt-weldedmoment-resistingconnections.Thehalf-scaleK275ROPSmodelwasexperimentallytestedundertherequiredlateral,vertical,andlongitu-dinalloads(Clark,2006a).Theloadandenergymagni-tudesestablishedfromAS2294.21997weremodifiedtotakeintoaccountthesimilituderelationshipsestablishedforthismodel.Strainanddeflectionmeasurementswererecordedforeachloadingsequence.TheexperimentaltestingwasfollowedbyFEanalysisofthehalf-scaleROPSmodelunderthesameloads,us-ingtheprogramABAQUSstandardv6.3.ScalinglawsfromthesimilitudestudyalongwiththeprogramMSCPatranwereusedtodevelopthenecessarygeometryfortheFEmodel.Figures2and3showtheexperimentaltestingoftheROPSmodelunderlateralloadandtheFEmodelofFig.2.LateralloadtestingofK275ROPS.thesameROPS,respectively.Therectangularportion(inlightershade)atthetopright-handpostintheFEmodelshowstherigidbodyusedtoapplythedynamicimpactloadingdescribedlateroninthearticle.Thelat-eralloaddeflectionplotsobtainedexperimentallyandfromtheFEanalysisshowninFigure4demonstrateexcellentagreementbetweenthetwosetsofresults.ThevariationofthestresswithloadatthebaseoftheROPSpost(acriticalregion),alsoshowedexcellentagreementbetweentheexperimentalandanalyticalre-sults(Clark,2006a).ThiscalibratedFEROPSmodelwasusedforthedynamicanalysisunderlateralimpactloads.Fig.3.FiniteelementmodelofK275ROPS.Dynamicresponseofarolloverprotectivestructure451Fig.4.Lateralloaddeflectionresponsefromexperiment(LVDT1)a