Non-Linear Elastic Non-Uniform Torsion (No. R828)

Abstract

This paper is concerned with large twist rotations of elastic thin-walled open section beams which induce additional longitudinal stresses which exert non-linear “Wagner” stiffening torques. The non-linear behaviour of a narrow rectangular beam is first analysed and then this is extended to elastic beams of general cross-section. Expressions are derived for the non-linear “Wagner” section constants for narrow rectangular sections, doubly symmetric I-sections, and mono-symmetric equal angle sections. A general finite element method of analyzing non-linear torsion is described, and used to develop a computer program FENLT. This program can analyse a beam of general cross-section under any combination of concentrated and distributed torques and concentrated bimoments, and which may be prevented from twisting or warping at points along its length. The program is validated by comparison with closed form or numerical solutions for a number of simple examples.