1Example41Title3-D,2-storyframestructureDescriptionGivenisa3-D,2-storyframestructurewithrigiddiaphragmfloors.Calculatethenaturalperiodsofthestructure.Determinethedisplacementsateachfloor.Thestructureissymmetricalinbothdirectionsinplan.Thecenterofgravityateachflooriseccentricfromthegeometriccenter.Structuralgeometryandanalysismodel2ModelAnalysisType3-DresponsespectrumanalysisUnitSystemft,kipDimensionLength70ftWidth50ftHeight26ftFloormassMx=My=6.21118kips⋅sec2/ftDampingratioξ=0.04(4%)Gravitationalaccelerationg=32.2ft/sec2Responsespectrumdata(Accelerationswithrespecttoperiods)Unit:ft/sec2Period(sec)0.0100.0Xacceleration0.40.4ElementBeamelementMaterialModulusofelasticityEcolumn=3.5×105ksfEbeam=5.0×105ksfSectionPropertyColumnsAreaA=4.00ft2MomentofinertiaIyy=1.25ft4(=Izz)BeamsMomentofinertiaIyy=2.61ft4(Strongaxis)Example413BoundaryConditionNodes1~9;ConstrainallDOFs.Nodes28,29;ConstrainDx,DyandRzofallnodesateachfloortothesenodes.(Masternodes)AnalysisCaseFloormassesareassignedtothemasternodesateachfloorinthedirectionsofXandY-axes.TheresponsespectrumdataareappliedintheXdirection.Numberofnaturalfrequenciestobecomputed=4MethodofModeCombinationSRSS(SquareRootoftheSumoftheSquares)ResultsEigenvalueanalysisresultsDisplacementresults4(a)1stvibrationmode(b)2ndvibrationmodeVibrationmodesofthestructureDisplacementsforthestructureExample415ComparisonofResultsNaturalPeriodsUnit:secModeofvibrationRef.1SAP2000MIDAS/Gen1st0.22710.22710.22712nd0.21560.21560.21563rd0.07330.07330.07334th0.07200.07200.0720GlobalX-displacementattheMasterNode29Unit:ftNodeRef.1SAP2000MIDAS/Gen290.02010.02010.0201ReferencesPeterson,F.E.,“EASE2,ElasticAnalysisforStructuralEngineering,ExampleProblemManual”,EngineeringAnalysisCorporation,Berkeley,California,1981.“SAP90,ASeriesofComputerProgramsfortheFiniteElementAnalysisofStructures,StructuralAnalysisVerificationManual”,ComputerandStructures,Inc.,1992,Example3.
