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Strain energy density and total strain energy
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analytical check applied load arbitrary constants xA axis bending calculation Castigliano's second theorem centre Chapter column matrix computation Consider contragredience coordinate cross-section deflexion deformations diagonal matrix direct force distribution due due to unit effects elastic elements equal example expression flexibility matrix flexural fu fu fu given hinge influence coefficients inner product Input integral ith member leading diagonal linear machine matrix F matrix inversion method multiplication null matrix obtained pin-jointed frame plane frame portal portal frame premultiplying prestress principal axes relation release system released structure ring rotation scale factor set xx shear force shown in Figure Simpson's rule space frame statical indeter statical indeterminacy statically determinate statically indeterminate structure strain energy stress resultant distribution structural analysis structural problem structure Figure symmetrical matrix temperature theorem tion transformation matrix transpose triangular matrix unit diagrams unsymmetrical whilst write written zero