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Section 2-04 Uniform Stress

The assumption of a uniform distribution of stress is frequently made in design. The result is then often called pure tension, pure compression, or pure shear, depending upon how the external load is applied to the body under study. The word simple is sometimes used instead of "pure" to indicate that there are no other complicating effects. The tension rod is typical. Here a tension load F is applied through pins at the ends of the bar. The assumption of uniform stress means that if we cut the bar at a section remote from the ends, and remove the lower half, we can replace its effect by applying a uniformly distributed force of magnitude sigma * A to the cut end. So the stress sigma is said to be uniformly distributed. It is calculated from the equation

     sigma = F / A                              [2-11]

This assumption of uniform stress distribution requires that:

• The bar be straight and of a homogeneous material.
• The line of action of the force coincide with the centroid of the section.
• The section be taken remote from the ends and from any discontinuity or abrupt change in cross section.

The same equation and assumptions hold for simple compression. A slender bar in compression may, however, fail by buckling, and this possibility must be eliminated from consideration before equation [2-11] is used. (See section 3-10)

Use of the equation

     tau = F / A                              [2-12]