SAINT - VENANT PRINCIPLE BASICS AND CIVIL ENGINEERING TUTORIALS

SAINT - VENANT PRINCIPLE BASIC INFORMATION
What Is The Saint - Venant Principle?


Saint-Venant’s principle states that in a body under the action of a system of forces which are applied in a limited region of its boundary, the stresses and strains induced by those forces in another region of the body, located at a large distance from the region where the forces are applied, do not depend on the particular way the forces are applied, but only on their resultant.

This “large distance” may be considered, in most cases, as the largest dimension of the region where the forces are applied.

This principle does not have a formal, general and exact demonstration as yet, but it has been verified in so many cases, both experimentally and numerically, that it is accepted as valid by the generality of authors on this subject.

It is a very useful principle, since complex force systems may be reduced to their resultants, which substantially simplifies and reduces the computation effort in practical problems. Besides, it is a very helpful tool in the theoretical development of solutions for problems in Theory of Elasticity and Strength of Materials.


As an example, let us consider the prismatic bar represented in Fig. 56 under the action of three systems of forces with equal resultants: the stresses at a grater distance than the transversal dimension 2b from the upper end of the bar may be accepted as equal in the three cases.

This principle is also valid in the cases of non-isotropic materials, nonlinear material behaviour, plastic and viscous deformations and material heterogeneity. Furthermore, the validity of this principle is not limited to small deformations.

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