An integral equation solution of the torsion problem

Abstract

The classical torsion problem of St Venant is formulated mathematically as a Neumann boundary-value problem for the warping function. This can be found numerically on the boundary by means of an integral equation method applicable to cross-sections of any shape or form. A single digital computer program assembles and solves the relevant equations, yields the torsional rigidity and boundary shear stress, and evaluates the warping function and stress components at any selected array of points throughout the cross-section. An accuracy of 1% in the torsional rigidity and maximum shear stress can be attained without undue effort.