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. Imagine a tension load P is applied through pins at the ends of a bar. The tension in the rod is typical. The assumption of uniform stress means that if the bar was cut at a section remote from the ends and one piece was removed, its effect can be replaced by applying a uniformly distributed force of magnitudeσA to the cut end. So the stress σ is said to be uniformly distributed. It is calculated from Eq1 from the lesson Normal Stress
(Eq1)
σ =
F
A
This assumption of uniform stress distribution requires that:
• The bar be straight and of a homogeneous material
• The line of action of the force contains the centroid of the section
• The section be taken remote from the ends and from any discontinuity or abrupt change in cross section
For simple compression, Eq1 is applicable with P normally being considered a negative quantity. Also, a slender bar in compression may fail by buckling, and this possibility must be eliminated from consideration before Eq1 is used.
There are some situations for shear in which it can be assumed that there is a uniform stress distrubution such as a bolt in shear as shown in the lesson Single and Double Shear. It is very difficult in practice to obtain a uniform distribution of shear stress, but occasions do arise in which this assumption may be utilized.