2CEE421L.MatrixStructuralAnalysis{DukeUniversity{Fall2014{H.P.GavinThe - PDF document

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2CEE421L.MatrixStructuralAnalysis{DukeUniversity{Fall2014{H.P.GavinThe - PPT Presentation

LMxM1 x L1M2x LThetotalpotentialenergyofabeamwiththeseforcesandmomentsisU1 2ZL0M2 EIdx1 2ZL0V2 GAdxByCastiglianosTheorem1U M1ZL0MxMx M1 EIdxZL0VxVx M1 GAdx0BZL0 ID: 436968

LM(x)=M1 x L1!+M2x LThetotalpotentialenergyofabeamwiththeseforcesandmomentsis:U=1 2ZL0M2 EIdx+1 2ZL0V2 G(A=)dxByCastigliano'sTheorem 1=@U @M1=ZL0M(x)@M(x) @M1 EIdx+ZL0V(x)@V(x) @M1 G(A=)dx=0B@ZL0

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