Shear stresses in prismatic beams with arbitrary cross-sections

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 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 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 elements are formulated. The developed procedure yields the relevant warping and torsion constants. Copyright © 1999 John Wiley & Sons, Ltd.