X. On the resistance to torsion of certain forms of shafting, with special reference to the effect of keyways

Abstract

The object of the present paper is to obtain solutions of the problem of torsion for cylinders whose cross-sections are bounded by confocal conics. It is mainly an extension of de Saint-Venant’s investigations, and is based upon his general equations of torsion. The method employed depends upon the use of conjugate functions ξ and η, such that ξ = const, represents confocal ellipses and η = const, confocal hyperbolas.