Constrained torsion of prismatic bars

A theory is developed that allows the determination of three-dimensional displacements and stresses within finite length prismatic bars of arbitrary cross-section experiencing restrained torsion. This restraint arises from the twisting of a bar where one of its cross-sections is subject to displacement and slope constraints. The deformations within this bar are represented by an exponentially decaying residual solution superimposed on the classical Saint-Venant solution. Galerkin's method is used to solve the boundary value problem resulting from a simultaneous system of three quadratic eigenproblems subject to the stress free boundary condition due to the traction-free lateral surface of the bar. A three-dimensional finite element model is used for validation. (C) 2002 Elsevier Science B.V. All rights reserved.