An Approach to Torsion Problem of a Circular Shaft with Multiple-Notches

Abstract

In this paper, an approximate solution is derived for a twisted shaft with circumferential notches periodically situated along its length. The solution for the extreme case where the dimensions of notches are infinitely small, has been obtained previously by Neuber. The present solution, however, is of sufficient accuracy for practical use even in the range of moderate dimensions of notches. The maximum torsional stress has been evaluated for various values of the radius of a notch. The ratio of maximum stress for multiple-notches to the corresponding one for a single-notch has been obtained, using two different formulas for a single-notch, previously obtained by Sonntag and Okubo respectively, and the validity of the two formulas is discussed.