Uniform distribution of stresses is an assumption that is frequently consideredÂ in the design process. Depending upon the way the force is applied to aÂ mechanical element for example, whether the force is an axial force or aÂ shear one the result is called pure tension (compression) or pure shear,Â respectively.
Let us consider a tension load F applied to the ends of a bar. If the bar isÂ cut at a section remote from the ends and we remove one piece, the effect ofÂ the removed part can be replaced by applying a uniformly distributed forceÂ of magnitude ?A to the cut end, where s is the normal stress and A theÂ cross-sectionalÂ area of the bar. The stress s is given by
This uniform stress distribution requires that the bar be straight and madeÂ of a homogeneous material, that the line of action of the force contain theÂ centroid of the section, and that the section be taken remote from the endsÂ and from any discontinuity or abrupt change in cross-section. Equation (1.1)Â and the foregoing assumptions also hold for pure compression.Â If aÂ body is in shear, one can assume the uniform stress Â distribution andÂ use