On the Stress Concentration Problem of a Shaft with an Annular Groove of a Circular-arc Form under Tension

Abstract

This paper is concerned with the stress concentration problems of an elastic circular solid cylinder (shaft) with an annular groove of a circular-arc form notch under tension (compression). The form factors (stress concentration factors) and the stress distributions at several cross sections of the shaft are shown. The form factors shown in this paper are compared with Peterson's results obtained from the so-called Neuber's formula. The method of solution used in the paper is to distribute axisymmetric body forces in the interior of a shaft with no grooves and to determine the intensities of the body forces thus distributed so as to satisfy the boundary conditions of the surface of an annular groove. For this purpose, we use Green's functions for axisymmetric body force problems of a circular solid cylinder, which were shown in a previous paper.