1Example51TitleP-Deltaeffectanalysesforthreeplanarcolumns.DescriptionPerformP-Deltaeffectanalysesfor3differentcolumnscases(PureSway,NoSwayandNoShear).Computethemaximumdisplacements,shearforcesandinternalmomentsforeachcase.Structuralgeometryandanalysismodel2ModelAnalysisType2-D,P-DeltaeffectanalysisUnitSystemin,lbfDimensionLengthL=100.0inRelativedisplacementtolerance0.001ElementBeamelementMaterialModulusofelasticityE=29.0×106psiSectionPropertyAreaA=1.0in2MomentofinertiaIyy=1/12in4BoundaryConditionNodes1,4and7;ConstrainallDOFs.Node3;ConstrainRy.Node6;ConstrainDx.Example513AnalysisCasePureSway;Anaxialforce,P1=1191.5lbfisappliedtothenode3inthe–Zdirection,andalateralforce,P2=100.0lbfisappliedtothenode3intheXdirection.NoSway;Anaxialload,P3=2431.5lbfisappliedtothenode6inthe-ZdirectionandabendingmomentaboutYaxis,100.0lbf-inisappliedatthenode6.NoShear;Anaxialforce,P4=298.0lbfisappliedatthenode9inthe-ZdirectionandabendingmomentaboutYaxis,100.0lbf-inisappliedtothenode9.MaximumnumberofiterationfortheP-Deltaeffectanalyses=54ResultsDisplacementsMemberForcesExample515ComparisonofResultsUnit:in,lbf-in,radCaseResultTheoreticalSAP2000MIDAS/GenLateraldisplacementatthetop6.8496.8236.820PureSwayEndmoment9084.09064.99062.8Rotationaldisplacementatthetop0.001700.001680.00168Endmoment-102.0-101.2-101.2NoSwayEndshear-2.02-2.01-2.01Lateraldisplacementatthetop0.4200.4200.420Rotationaldisplacementatthetop0.007520.007510.00751NoShearEndmoment225.2225.0225.1ReferencesLivesley,R.K.,andChandler,D.B.,“StabilityFunctionsforStructuralFrameworks”,ManchesterUniversityPress,UK,1956.“SAP90,ASeriesofComputerProgramsfortheFiniteElementAnalysisofStructures,StructuralAnalysisVerificationManual”,ComputerandStructures,Inc.,1992,Example26.
