Uniformly Distributed Stresses

Uniform distribution of stresses is an assumption that is frequently considered in the design process. Depending upon the way the force is applied to a mechanical element for example, whether the force is an axial force or a shear one the result is called pure tension (compression) or pure shear, respectively.
Let us consider a tension load F applied to the ends of a bar. If the bar is cut at a section remote from the ends and we remove one piece, the effect of the removed part can be replaced by applying a uniformly distributed force of magnitude ?A to the cut end, where s is the normal stress and A the cross-sectional area of the bar. The stress s is given by

This uniform stress distribution requires that the bar be straight and made of a homogeneous material, that the line of action of the force contain the centroid of the section, and that the section be taken remote from the ends and from any discontinuity or abrupt change in cross-section. Equation (1.1) and the foregoing assumptions also hold for pure compression. If a body is in shear, one can assume the uniform stress  distribution and use

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