1Example9TitleBeamonelasticfoundationDescriptionAbeamrestsonanelasticfoundationandaconcentratedloadexertsatmid-span.Determinetheverticaldisplacementsandthebendingmomentsofthestructure.Onlyahalfmodelmaybeanalyzedduetosymmetry.(a)Beamonelasticfoundation(b)HalfmodelStructuralgeometryandanalysismodelVerificationExample2ModelAnalysisType2-Dstaticanalysis(X-Zplane)UnitSystemin,lbfDimensionLength50.0inElementBeamElementMaterialModulusofelasticityE=2.1×106psiSectionPropertyMomentofinertiaIyy=83.33333in4BoundaryConditionNode1;ConstrainDxandRy.Foundationstiffness;Ko=5.0×105lbf/in3TheZdirectionalstiffnessofeachnodecanbecalculatedbymultiplyingthetributarynodalareabythefoundationstiffness.(Widthofthebeamisassumedtobe1in.)LoadCaseAhalfconcentratedloadPisappliedinthe–Zdirectionduetosymmetry.P/2=1.0×104/2lbf=0.5×104lbfExample603ResultsZ-displacementsofthestructure(Node1)BendingmomentdiagramofthestructureVerificationExample4ComparisonofResultsUnits:in,lbfResult(Node1)TheoreticalADINAMIDAS/GenZ-displacement(δz)-1.6348×10-3-1.6348×10-3-1.6348×10-3Bendingmoment(My)1.53×1041.49×1041.49×104ReferencesTimoshenko,S..,“StrengthofMaterials,PartII”3rdEdition,D.VanNostrandCo.,1958.“ADINA,VerificationManual-LinearProblems”,Version6.1,ADINAR&D,Inc.,1992,ExampleA.41.
