The Uniform Torsion of an Incomplete Tore

Abstract

A stress system is determined which gives as the resultant over any terminal cross-section a single force acting along the axis of the tore. This will yield a close approximation to the stresses in a helical spring of small pitch. The method used is that of finding a stress function analogous to the ordinary torsion function subject to a certain boundary condition and the problem is solved in toroidal harmonics. The stresses and resultant force are evaluated in term of the dimensions of the tore and compared with the results of known approximate theories.