On the history of torsional stress concentrations in shafts: From electrical analogies to numerical methods

Abstract

This article proposes a retrospective on experimental and numerical methods developed throughout the past century to solve the torsion problem in shafts, with particular emphasis on the determination of shear stress concentration factors in discontinuities of typical use in shaft design. This article, in particular, presents the theory and related solutions distinguishing between two classes of geometries: shafts with constant cross section and axisymmetric shafts with variable diameter. Emphasis is given to approaches based on physical analog methods and, in particular, those based on electrical analogies proposed since about 1925. Experimental methods based on structural physical models and numerical formulations are also reviewed, and a number of results from different approaches are collected and compared for two typical design case studies: a constant section shaft with a keyway and an axisymmetric shaft with a shouldered fillet.