Analysis of Restrained Torsion

Abstract

A procedure is presented for determining the stress and deformation in prismatic members with general cross sections due to end restraints in torsion. The end restraint conditions are represented by superposition of a system of eigenvectors, each depicting a self‐equilibrated end effect. These eigendata, which may be called the Saint‐Venant end solutions, are extracted from an algebraic ei‐gensystem of a two‐dimensional finite element model of the cross section. The dominant (lowest nonzero) eigenvalue and corresponding eigenvector are associated with the behavior that persists the greatest distance into the interior from the end. Examples on elliptical and rectangular cross‐sectional members and on wide flange and angle beams are presented to illustrate the procedure. Comparison of the present results with those determined by approximate analysis and ad hoc methods leads to some understanding of the factors that influence the attenuation of the stresses and deformations in restrained torsion.