18.18: Saint-Venant’s Principle

The principle of Saint-Venant postulates that the stress distribution within a structural member does not rely on the precise method of load application except in the vicinity of the load application points. Consider a scenario where loads are centrally applied on two plates. In this case, the plates move toward each other without any rotation. This movement causes the member to contract in length and expand in width and thickness. Uniform deformation across all elements and maintaining straight members and plane sections facilitate a consistent distribution of strains and stresses.

However, when loads are concentrated, the elements close to the application points endure large stresses, while those positioned further away stay largely unaffected. Yet, deformations tend to equalize in the case of elements distant from the ends, leading to a more even distribution of strain and stress. Interestingly, beyond a distance equivalent to the member's width, the stress distribution becomes detached from the mode of load application, a key aspect of Saint-Venant's principle. While applying this principle, it is important to remember that the actual loading and the loading used to calculate the stresses must be statically equivalent. Furthermore, this principle does not apply to computing stresses near the load application points.

Consider a member with plates on both ends. When loads are applied centrally on the plates, they move towards each other without rotating, causing the member to shorten with an increase in width and thickness.

A uniform distribution of strains and stresses is achieved by maintaining straight member and plane sections, along with uniform deformation across all elements.

If the loads are concentrated and directly applied to the member, elements near the load application point experience higher stresses, while distant areas remain unaffected.

In elements far away from the ends, the deformations tend to balance out, leading to a more uniform distribution of strains and stresses.

Beyond a distance equal to the member's width, the stress distribution becomes independent of the load application mode. This statement is the Saint-Venant's principle.

While applying Saint-Venant's principle, it is important to note that the actual loading and the loading used to determine the stresses must be statically equivalent, and it cannot be used to calculate stresses near the load application points.