Nonuniform elastic torsion

Abstract

Linear and nonlinear uniform torsion of prismatic members has been much studied, but even in the linear case nonuniform torques have been comparatively neglected. Thin-walled cross-sections have received useful approximate treatments by Goodier and others, but a general theory seems still to be lacking. The linear theory given here corresponds to standard theories for varying elastic flexure. The torque may vary continuously or discontinuously along the member but, as with flexure, we deliberately avoid specifying in detail how it is applied. The present analysis is for cross-sections with two axes of symmetry. The examples given include an important one illustrating the possible sensitivity of beams to eccentricity of loading.