Saint-Venant's Principle

The principle of Saint- Venant ( by Barré de Saint- Venant ) is a simplification for calculating the strength of components dar. It states that local irregular stress distributions can be computationally neglected at points at which a force is applied, as these subside very quickly. The photoelasticity gives a vivid picture thereof. In the practical strength of only those portions of a component are calculated, on which no external forces are effective.

In a tensile test at a tensile bar elongation is measured only in the center region, since there is a constant tension in the cross-sectional area for this reason.

In the complete formulation:

If the force acting on a small part of the surface of an elastic body force is replaced by an equivalent system of forces, this charge redistribution causes significant changes only for the local stresses produced: but not areas that are large compared to the contaminated surface.

The principle was proposed by the French mathematician Jean Claude Barré de Saint- Venant.

Next quantifiable is the statement by considerations of Timoshenko. For example, the bending beam can be a decay length define which roughly corresponds to the beam diameter.

• Strength of Materials