On Torsion of Prismatic Bodies

Abstract

The method of decaying residual solution is applied to obtain an approximate interior solution for the torsion of slender prismatic elastic bodies under different end conditions. The approximate solution is generally accurate up to terms that are exponentially small in the length‐to‐cross‐sectional‐width ratio. For stress end conditions, the result is identical to the classical Saint‐Venant torsion solution. Similar types of simple solutions, not known previously, are obtained for different types of mixed end conditions. For displacement conditions at both ends, the corresponding Saint‐Venant type result requires an accurate solution of a canonical problem for a semi‐infinite prismatic body that is to be obtained once and for all. The solution of the canonical problem is elementary for a circular cross section. The approximate interior solution in that case is identical to the known exact interior solution.