On the General Solution of the Torsion Problem of a Cylinder (4th Report)

Abstract

The torsion problem for a circular cylinder with a number of longitudinal notches has been solved mathematically. In the particular case of one notch, the relations between the maximum stress and the radius of curvature at the bottom of the notch or the depth of notch are clarified. As an example, the problem for a circular shaft with one keyway, in the form of the practical use, is solved. The results are compared with those obtained experimentally or numerically by the previous writers. We find there is a considerable discrepancy between the former and the latter in the results obtained theoretically and experimentally.