Saint-Venant's Principle

Definition - What does Saint-Venant's Principle mean?

Saint-Venant's Principle is used to describe the behavior of loads and stresses in an axially loaded member, and may be a factor when considering loads placed upon corroded structures. Developed by the French elasticity theorist, Adhémar Jean Claude Barré de Saint-Venant, the original wording of the principle is as follows:

If the forces acting on a small portion of the surface of an elastic body are replaced by another statically equivalent system of forces acting on the same portion of the surface, this redistribution of loading produces substantial changes in the stresses locally but has a negligible effect on the stresses at distances which are large in comparison with the linear dimensions of the surface on which the forces are changed.

Corrosionpedia explains Saint-Venant's Principle

Saint-Venant's Principle simply states that the stress measured at any point on an axially loaded cross section is uniform given that the measured location is far enough away from the point of load application or any discontinuity in the member’s cross section. In other words, when we calculate stress by conventional methods, i.e.,

σ = P / A

we have assumed that we are reasonably far away from the point of application or any discontinuity such that the normal stress is uniform.

In reality, when a point load is applied to a surface, the stress is concentrated at the point of application and eventually evens out as the distance from the point is increased. This increase in stress, also known as a stress riser, also occurs during abrupt changes in the material’s cross section.

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