1Example40Title3-D,2-storyunsymmetricalstructureDescriptionAssumethateachflooractsasarigiddiaphragm.Calculatethenaturalfrequencies.Performaresponsespectrumanalysis.VerificationExample2StructuralgeometryandstructuralanalysismodelExample403ModelAnalysisType3-DresponsespectrumanalysisUnitSystemft,kipDimensionLength50ftWidth25ftHeight25ftFloormassMx=My=3.88kips⋅sec2/ftRotationalmassmomentofinertiaMzz=1011kips⋅sec2/ftDampingratioξ=0.05(5%)Gravitationalaccelerationg=32.2ft/sec2Responsespectrumdata(Accelerationswithrespecttoperiods)Unit:ft/sec2Period(sec)0.00.10.1250.1670.1820.2000.2500.333Acceleration0.4000.5810.6280.7870.94391.00560.79800.8806Period(sec)0.4310.5000.6671.0001.2732.00010.00100.0Acceleration0.92121.04660.64180.48220.25860.16020.01020.0ElementBeamelementMaterialModulusofelasticityE=432000ksfSectionPropertyColumnsAreaA=2.25ft2MomentofinertiaIyy=0.4219ft4(=Izz)BeamsMomentofinertiaIyy=0.6667ft4VerificationExample4BoundaryConditionNodes1~6;ConstrainallDOFs.Nodes19and20;ConstrainDx,DyandRzofallnodesateachfloortothesenodes.(Masternodes)AnalysisCaseFloormassesareassignedtothemasternodesateachfloorinthedirectionsofXandY-axes.MassmomentofinertiaaboutZ-axisisassignedtoeachmasternodes.Theresponsespectrumdataactinthedirection30degreescounterclockwisefromtheX-axis.Numberofnaturalfrequenciestobecomputed=6ResultsEigenvalueAnalysisResultsDisplacementsExample405(a)1stvibrationmode(b)2ndvibrationmode(c)3rdvibrationmode(d)4thvibrationmode(e)5thvibrationmode(f)6thvibrationmodeVibrationmodesofthestructureVerificationExample6ComparisonofResultsUnit:secNaturalperiodVibrationmodeSAP2000MIDAS/Gen1st0.41460.41462nd0.37530.37533rd0.24360.24364th0.11480.11485th0.11030.11036th0.07290.0729Unit:ftDisplacementatthemasternodeNodeDisplacementcomponentSAP2000MIDAS/GenXdisplacement0.04890.0489Ydisplacement0.03410.034019Zrotationaldisplacement0.00030.0003Xdisplacement0.10600.1059Ydisplacement0.07820.078220Z-rotationaldisplacement0.00080.0008Reference“SAP90,ASeriesofComputerProgramsfortheFiniteElementAnalysisofStructures,StructuralAnalysisVerificationManual”,ComputerandStructures,Inc.,1992,Example8.Example407ResponseSpectrumData
