1Example37TitleEigenvalueandstaticanalysisofa5-levelpyramidbuildingunderlateralloads.DescriptionPerformtheeigenvalueanalysisofapyramidbuilding.Calculatethenaturalfrequenciesandthedisplacementsofeachfloorduetostaticlateralloads.2StucturalanalysismodelExample373Plandimensionsofeachfloor4ModelAnalysisType3-DstaticandeigenvalueanalysisUnitSystemin,kipDimensionLength70×12inWidth70×12inHeight5×12.125×12inFloormassM=100psf=1.7972×10-6kips∙sec2/inNodes42~45arethemasternodesforthe4th~1stlevelsinadecendingorderrespectively.Gravitationalaccelerationg=386.4in/sec2Massandrotationalmassmomentofinertiaateachfloor.FloorMasternodeMass,MX=MYRotationalmassmomentofinertia,Im4420.0507246238.60873430.20289863817.73912440.456521719327.30441450.811594261083.8261ElementBeamelementMaterialModulusofelasticityE=29500ksiPoisson’sratioν=0.3Example375SectionPropertyHorizontalbeamsAreaA=13.5in2EffectiveShearAreaAsy=6.5016in2Asz=6.1105in2TorsionalstiffnessIxx=1.22in4MomentofinertiaIyy=712.0in4(Strongaxis)Izz=22.5in4(Weakaxis)DiagonalsAreaA=11.7in2EffectiveShearAreaAsy=2.97in2Asz=7.532in2TorsionalstiffnessIxx=1.12in4MomentofinertiaIyy=146.0in4(Strongaxis)Izz=49.1in4(Weakaxis)BoundaryConditionNodes6~41(atanincrementof5);ConstrainallDOFs.Nodes42~45;ConstrainDx,DyandRzofallnodesateachleveltothesenodes.(Masternodes)AnalysisCaseFloormassesareassignedtothemasternodesinthedirectionsofXandY-axes.RotationalmassmomentofinertiaaboutZ-axis,Im=M×(b2+h2)/12isassignedtoeachmasternode..LoadCase1;Alateralload,20kipsisappliedtothemasternodesateachfloorintheXdirection.LoadCase2;Alateralload,20kipsisappliedtothemasternodesateachfloorinthedirection45degreescounterclockwisefromtheX-axis.Numberofnaturalfrequenciestobecomputed=96ResultsEigenvalueAnalysisResultsDisplacementsExample377VibrationmodesofthestructureX-displacementsofthestructure(Node1)8ComparisonofResultsNaturalPeriodsUnit:secNaturalperiodModeETABSMIDAS/Gen1st0.120980.120982nd0.120980.120983rd0.063090.063094th0.063090.063095th0.060990.060996th0.039760.039767th0.039760.039768th0.029630.029639th0.023880.02388DisplacementsateachlevelUnit:inDisplacementETABSMIDAS/GenLoadCaseLevelδXδYδXδY1st0.015030.015032nd0.027950.027953rd0.040480.040484th0.054810.0548115th0.071170.071171st0.010630.010630.010630.010632nd0.019760.019760.019760.019763rd0.028620.028620.028620.028624th0.038760.038760.038760.0387625th0.050330.050330.050330.05033Example379Reference“ETABS,ExamplesManual”,Version6.0ComputersandStructures,Inc.,Berkeley,California,1994,Example18.
