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.

Aspects of stress in optimal shaft shoulder fillet

“…The stress concentration factor is typically found in charts in textbooks 1,2 and also in more recent articles. 3,4 The charts are given for circular fillets and for the three different loading situations separately. Many charts are based on experimental results from photoelasticity.…”

Performance Evaluation of Stress Concentration Factor for Shoulder Fillet on Round Bar under Bending Loading

“…The number of equations presented by Pilkey [6], Young et al [7] and S M. Tipton et al [8] are altered in the form of fillet radius by Bhavesh Patel et al [5] for bending loading conditions through mathematical formulation for the same range of h/r (0.1 ≤ ℎ/ ≤ 2.0 to 2.0 ≤ ℎ/ ≤ 20) as mentioned in the Petersons SCF handbook [6]. Also in the paper [5], a range of SCFs were given for various modified equations of fillet radius.…”

Optimal shape design of shoulder fillets for flat and round bars under various loadings

“…If a bar is subject to axial loading or bending moment, the stress concentration factor is usually defined as the ratio of the largest first principal stress σ 1 at the fillet to the nominal stress S nom [40,41] …”

“…If the bar is subject to torsion, K t is defined as the ratio of the maximum shear stress in the fillet, τ max , to the nominal shear stress τ nom [41] …”