18.18 : 圣维南原理

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.