The Problem of Tension–Torsion of Pretwisted Elastic Beams Revisited

Abstract

A one-dimensional technical theory for pretwisted isotropic linearly elastic beams loaded in tension and torsion was developed. The analysis was based on a kinematically admissible field written in terms of three generalized displacements, which were determined from the theorem of minimum potential energy. A general analytical solution was developed. The problem of a pretwisted beam with a built-in end and loaded in tension and torsion at the other end was analyzed. The problem also was solved by carrying out detailed three-dimensional finite-element calculations. The predictions of the technical theory agreed very well with the results of the finite-element solution. The effects of Poisson’s ratio were examined, and the applicability of the model to beams of various lengths was discussed.