Saint-Venant Principle

Saint-Venant Principle 

in the theory of elasticity, a principle stating that a system of forces in equilibrium applied to some segment of a solid body produces stresses in that body that rapidly diminish with increasing distance from the segment. Thus, at distances greater than the maximum linear dimensions of the region of load application, the stresses and deformations are negligibly small. Therefore, the Saint-Venant principle establishes the local nature of the effect of self-equilibrated external loads. The principle was formulated by A. Saint-Venant in 1855.

In engineering practice, another statement of the Saint-Venant principle is used: if the forces acting on a small segment of an elastic body are replaced by another system of forces that acts on the same segment of the body and is statistically equivalent (that is, has the same resultant and moment as the given force), then in the new system of forces a change in the stressed state occurs only in the regions close to the applied load. At points of the elastic body distant from the site of application of forces by distances sufficiently large in comparison with the linear dimensions of the surface to which the forces are applied, the effect of the redistribution of forces will be infinitesimal.

The Saint-Venant principle permits the substitution of a set of boundary conditions (effective forces) by another (for example, a set more convenient for static calculation) under the condition that the resultant and moment of the new system retain the values of the former system.