1Example53TitleBucklinganalysesofacolumnDescriptionDeterminethebucklingmodesandthecorrespondingcriticalloadsofacolumnsubjectedtoaverticalloadwithvariousboundaryconditions.StructuralgeometryandboundaryconditionsVerificationExample2ModelAnalysisTypeBucklinganalysisUnitSystemm,tonfDimensionLength15mElementBeamelementandplateelement(Thicktype)MaterialModulusofelasticityE=10000tonf/m2SectionPropertyBeamelementSolidrectangular0.25×0.25mPlateelementThickness0.25mBoundaryConditionCase1:Thetopendisarollerandthebottomisapinsupport.Case2:Thetopendisfreeandthebottomisafixedsupport.Case3:Lateraldisplacementandrotationaldisplacementofthetopendareconstrainedandthebottomisafixedsupport.Case4:Thetopendisarollerandthebottomisafixedsupport.Example533ResultsBucklingAnalysisResultsCase1:Thetopendisarollerandthebottomisapinsupport.beamelementmodelplateelementmodelCase2:Thetopendisfreeandthebottomisafixedsupport.BeamelementmodelPlateelementmodelVerificationExample4Case3:LateralandrotationaldisplacementofthetopendareconstrainedandthebottomisafixedsupportBeamelementmodelPlateelementmodelCase4:Thetopendisarollerandthebottomisafixedsupport.BeamelementPlateelementExample535ComparisonofResultsUnit:tonfCriticalloadfor1stbucklingMIDAS/GenCaseTheoreticalBeamelementPlateelement10.57120.57080.571220.14280.14280.142832.28462.27962.284641.16841.16701.1684※Criticalload:LoadappliedintheLoadCase×EigenvalueCase1:Pcr=22LEIπCase2:Pcr=224LEIπCase3:Pcr=224LEIπCase4:Pcr=22046.2LEIπReferenceGere&Timoshenko“MechanicsofMaterials”Chapter11
