1Example52TitleP-Deltaeffectanalysisofaportalframe.DescriptionShownbelowisa2-D,onestory,onebay,portalframesupportedatthebasesubjectedtoasymmetricloadandaneccentricloadseparately.Comparethedisplacements,shearforcesandbendingmomentsbetweentheresultsbasedonaP-Deltaeffectanalysisandaconventionalframeanalysis.Structuralgeometryandanalysismodel2ModelAnalysisType2-DP-DeltaanalysisUnitSystemin,lbfDimensionHeightH=100.0inWidthB=100.0inRelativedisplacementtolerance0.001ElementBeamelementMaterialModulusofelasticityE=29×106psiSectionPropertyAreaA=1.0in2MomentofinertiaIyy=1/12in4BoundaryConditionNodes1,3,5and7;ConstrainallDOFs.AnalysisCaseCase1;Asymmetricload,1000lbfisappliedtothemid-pointoftheelementinthe-Zdirection.Case2;Aneccentricload,1000lbfisappliedtothefirstquarterpointoftheelementinthe-Zdirection.MaximumnumberofiterationfortheP-Deltaeffectanalysis=5Example523ResultsDisplacements(P-Deltaeffectanalysis–EX52-1)MemberForces(P-Deltaeffectanalysis-EX52-1)4Displacements(Conventionalanalysis–EX52-2)MemberForces(Conventionalanalysis-EX52-2)Example525Bendingmomentdiagramofthestructure(P-Deltaeffectanalysis)Bendingmomentdiagramofthestructure(Conventionalanalysis)6ComparisonofResultsSymmetricLoadCaseUnit:rad,lbf-in,lbfP-DeltaeffectanalysisConventionalanalysisResultTheoreticalSAP2000MIDAS/GenTheoreticalSAP2000MIDAS/GenRotationaldisplacement(θ2)0.091920.091780.091790.086200.086200.08621Moment(M12)4606.64589.14588.94166.74166.74166.5Moment(M21)8254.08260.48260.38333.38333.38333.2Shearforce(F)128.6128.5128.5125.0125.0125.0EccentricLoadCaseUnit:rad,lbf-in,lbfP-DeltaeffectanalysisConventionalanalysisResultTheoreticalSAP2000MIDAS/GenTheoreticalSAP2000MIDAS/GenLateraldisplacement(δ)1.8931.8941.8931.3851.3851.385Rotationaldisplacement(θ6)0.10130.10140.10140.09240.09240.0924Rotationaldisplacement(θ8)0.03670.03670.03670.03690.03690.0370Moment(M21)2544.92550.92551.22455.42455.42455.6Moment(M21)6088.66183.66183.46919.66919.66919.2Moment(M21)4456.94503.54502.83794.63794.63794.1Moment(M21)6153.06124.96125.05580.45580.45580.7Shearforce(F)101.4101.6101.693.7593.7593.75Example527ReferencesLivesley,R.K.,andChandler,D.B.,“StabilityFunctionsforStructuralFrameworks”,ManchesterUniversityPress,UK,1956.“SAP90,ASeriesofComputerProgramsfortheFiniteElementAnalysisofStructures,StructuralAnalysisVerificationManual”,ComputerandStructures,Inc.,1992,Example27.
