1Example44TitleSimplysupportedbeamsubjectedtodynamicloadsDescriptionAsteelbeamissubjectedtodynamicloads.Assumethattheweightofthebeamisnegligible.Determinethetimeatwhichthemaximumdeflectionoccursandthecorrespondingbendingstresses.2StructuralgeometryandanalysismodelExample443ModelAnalysisType2-DtimehistoryanalysisUnitSystemin,lbfDimensionLengthL=240inMassM=25.9067lbf⋅sec2/in(intheZdirection)Analysistimet=0.1secTimestepΔt=0.001secElementBeamelementMaterialModulusofelasticityE=30×106psiSectionPropertyDepthH=18.00inMomentofinertiaIyy=800.6in4BoundaryConditionNode1;ConstrainDz.(Rollersupport)Node3;ConstrainDyandDz.(Hingesupport)AnalysisCaseTimestepforceactsintheZdirection.Thetimestepforcedataareasfollows:Time(sec)Force(lbf)0.00000.075200000.100200004ResultsDisplacementsStressesExample445Z-displacementsatthenode2ComparisonofResultsUnit:sec,in,psiResultTheoreticalSAP2000MIDAS/GenTimeatwhichthemaximumdisplacementoccurs(t)0.0920.0930.093Maximumdisplacement(δz,max)0.3310.3360.336Maximumbendingstress(σmax)18.6×10318.87×10318.87×103ReferencesBiggs,J.M.,“IntroductiontoStructuralDynamics”,McGraw-HillBookCo.,NewYork,1964,p.50,ExampleE.6TimeHistoryLoadingData
