Shear stresses in prismatic beams with arbitrary cross-sections. International journal for numerical methods in engineering 45

Abstract In this paper the approximate computation of shear stresses in prismatic beams due to Saint–Venant torsion and bending using the finite element method is inves-tigated. The shape of the considered cross–sections may be arbitrary. Furthermore the basic coordinate system lies arbitrarily to the centroid, and not necessarily in principal directions. For numerical reasons Dirichlet boundary conditions of the flexure problem are transformed into Neumann boundary conditions introducing a conjugate stress function. Based on the weak formulation of the boundary value problem isoparametric finite ele-ments are formulated. The developed procedure yields the relevant warping and torsion constants