A Modified Design Stress Equation Based On Maximum Shear Stress Theory

Abstract

The aim of this study was to formulate a new design stress equation for the analysis of two-dimensional plane elements using the maximum shear stress yield criterion known as the Tresca yield criterion. The existing Tresca yield equation was modified for a two-dimensional plane element to obtain a new general applied stress equation in terms of yield stress and stress factor. To get the specific applied stress equation for the twelve plate types considered, the polynomial shape parameters were solved to obtain the specific stress factor equation. To get the numerical value of the stress factor, a 1m by 1m mild steel of yield stress 250MPa, with deflection values taken at the point of maximum deflection, was analyzed. The numerical values of the stress factor for each plate type obtained were observed to be all less than unity, giving rise to a very high applied stress for plate types with no free edge and a moderately high stress for plate types with one free edge. This revealed the weakness of the existing yield criterion that may lead to failure. To improve this, a correction factor to take care of this limitation was introduced to the stress factor to have a factor of safety that will result in a design stress which is less than the yield stress of the material, by so doing ensuring safety. Therefore, the new design stress equation was found appropriate for predicting stress for the design of plane rectangular plates with one free edge, while this yield criterion is not advisable for use with plates without a free edge.