ANALYSIS OF YIELDED STEEL PLATE USING TOTAL STRAIN ENERGY THEORY

Abstract

This study aims to formulate an improved total strain energy yield theory equation for plane elements. This was done by formulating an applied stress equation for the analysis of plane elements such as rectangular plates. The mathematical Equation of total strain energy theory was modified to obtain a new general applied stress equation in terms of yield stress and stress factor. Polynomial shape parameters for the plate types considered were solved for n-values (plane vectors) which were substituted into the new general stress factor equation to obtain the specific stress factor equations for each plate type. Numerical application was made with mild steel as the plate material. With the values of the stress factor for each of the twelve plate types obtained, the applied stress for each plate type was
determined. Based on the values obtained, it was noticed that the values of the stress factors for the six plate types without a free edge were less than 1, while those values for the other six plate types with a free edge were greater than 1. As a result of these values of stress factors, the applied stresses for the plate types with a free edge were greater than the yield stress of 250MPa, which implies that failure is
imminent. This indicates the weak point of this yield theory in its original form. For the structure not to fail, a factor of safety is introduced thereby resulting in the design stress which is less than than the yield stress of the material, thereby providing a new equation for predicting the design stress of the plate types considered. Hence, this new design stress equation is adequate for predicting stress for the design of plane elements such as plates.