1Example45TitleSimplysupportedbeamsubjectedtoatravelingdynamicloadDescriptionAsimplysupportedbeamissubjectedtoadynamicforcetravelingalongthespanataconstantvelocity.Performatimehistoryanalysisanddeterminethedisplacements,velocitiesandaccelerationsatthemid-spanofthebeamwithatimehistory.VerificationExample2StructuralgeometryandanalysismodelExample453ModelAnalysisType2-Dtimehistoryanalysis(X-Zplane)UnitSystemin,lbfDimensionLengthL=480inAnalysistimet=0.8secTimestep∆t=0.001secElementBeamElementMaterialModulusofelasticityE=2.4×1011psiWeightdensityγ=0.1lbf/in3SectionPropertyAreaA=1.0in2MomentofinertiaIyy=0.083333in4BoundaryConditionNode1;ConstrainDxandDz.(Hingesupport)Node21;ConstrainDz.(Rollersupport)VerificationExample4AnalysisCaseAconcentratedloadwhichvarieswithtimetravelsata600in/secvelocityandactsinthe–Zdirection.Thatis,ittakes0.04secforaloadtomovebetweentwoadjacentnodes.Time(sec)Unitload(lbf)0.0000.041.00.080Forceappliedtoanode=Multiplierforthetimehistorydata×UnitloadNow,themultiplierforthetimehistorydataisdefinedastheloadunderwhichthemaximumdeflectionbecomesaunitdisplacementwhenaconcentratedloadisappliedtothemid-spanofthebeam.Thus,themaximumdeflection,δmax=PL3/(48EI)=1occurswiththeload8680.6lbf.Example455ResultsTimeHistoryAnalysisResultsZ-displacementsatthenode11VerificationExample6Z-velocitiesatthenode11Z-accelerationsatthenode11Example457ComparisonofResultsUnit:inZ-displacementatthenode11(δZ)TimeTheoreticalADINAMIDAS/Gent1=0.04sec-0.0152-0.0160-0.0147t2=0.08sec-0.1080-0.1071-0.1091t3=0.12sec-0.3103-0.3053-0.3152ReferencesBiggs,J.M.,“IntroductiontoStructuralDynamics”,McGraw-Hill,NewYork,1964,pp.315∼318.“ADINA,VerificationManual-LinearProblems”,Version6.1,ADINAR&D,Inc.,1992,ExampleA.58.VerificationExample8TimeHistoryLoadingData
