Shear stresses in prismatic beams with arbitrary cross-sections

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