1Example46TitleDynamicmodalresponsefor2-DrigidframeDescriptionPerformatimehistoryanalysisofastructureunderlateraldynamicloads.Calculatethenaturalfrequencies,themaximumdisplacementandthecorrespondingtime.VerificationExample2StructuralgeometryandanalysismodelExample463ModelAnalysisType2-DtimehistoryanalysisUnitSystemin,lbfDimensionLengthL=360inLevelheightH1(1st)=180inH2(2nd)=120inMassM1(1st)=136lbf⋅sec2/in(intheYdirection)M2(2nd)=66lbf⋅sec2/in(intheYdirection)Analysistimet=0.2secTimestep∆t=0.001secElementBeamElementMaterialModulusofelasticityE=30×106psiSectionPropertyColumns(1stfloor)MomentofinertiaIyy=248.6in4Columns(2ndfloor)MomentofinertiaIyy=106.3in4BeamsMomentofinertiaIyy=1.0×1015in4(Rigid)BoundaryConditionNodes1and2;ConstrainallDOFs.Nodes3~6;ConstrainDzandRx.(OnlyDyallowed)Nodes7and8;ConstrainDyofallnodesateachfloortothesenodes.(Masternodes)VerificationExample4AnalysisCaseImpulseloadsareappliedintheYdirection.1stfloor;P1(t)=10000(1-t/td)lbf(td=0.1)2ndfloor;P2(t)=20000(1-t/td)lbf(td=0.1)Numberofnaturalfrequenciestobecomputed=2ResultsEigenvalueAnalysisResultsDisplacementsExample465DisplacementsY-displacementsatthenode3Y-displacementsatthenode5VerificationExample6ComparisonofResultsNaturalFrequenciesUnit:HzResultRef.1SAP2000MIDAS/Gen1stmode11.811.811.8Naturalfrequency2ndmode32.932.932.9MaximumDisplacementsUnit:sec,inTimeatwhichthemaximumdisplacementoccurrs(t)Maximumdisplacement(δY,max)NodeSAP2000MIDAS/GenSAP2000MIDAS/Gen30.1710.1710.6730.67350.1230.1230.6740.674ReferencesPaz,Mario,“StructuralDynamics;TheoryandComputation”,3rdEdition,VanNostrandReinhold,NewYork,1991,Example11-1.“SAP90,ASeriesofComputerProgramsfortheFiniteElementAnalysisofStructures,StructuralAnalysisVerificationManual”,ComputerandStructures,Inc.,1992.Example467TimeHistoryLoadingData(a)Timehistoryloadsappliedatthe1stfloor(b)Timehistoryloadsappliedatthe2ndfloor
