Multiaxial Stress Concentration in Filleted Shafts

Abstract

In a previous paper, popular stress concentration factor charts for shoulder filleted shafts in bending and tension were shown to be in error, and more accurate solutions were published. In this paper, improved stress concentration factor information is presented for torsional loading, based on detailed finite element analyses. The new solutions agree with previous design charts, but cover a wider range of geometries. A concise engineering equation is presented for the stress concentration factor and maximum equivalent stress under each of three loading modes, along with another equation that reveals the location of each maximum stress component in the fillet. It is shown that the maximum stress locations for bending and tension loading are approximately the same, but can differ significantly from the maximum torsional stress location. In those cases, sharp surface gradients can cause the maximum equivalent notch stress under combined bending/axial and torsional loading to be overestimated when computed based on the maximum stress concentration factors for each load component. An example is used to demonstrate how the surface strain gradient causes the placement and size of a strain gage to have a strong influence on strain measurements.