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Saint Venant Principle: Definition, and Application
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Saint-Venant released the original statement in French in 1855. Although this informal assertion is commonly known among structural and mechanical engineers, more recent mathematical research provides a rigorous interpretation in the context of partial differential equations. Richard von Mises provided an early example of this interpretation in 1945.
As long as the boundary is geometrically short, the Saint-Venant Principle permits electricians to replace intricate stress distributions or weak boundary conditions with simpler ones. Similarly to electrostatics, where the product of the distance and electric field owing to the ith moment of the load (with 0th being the net charge, 1st being the dipole, 2nd being the quadrupole) decays as over space, Saint-Venant Principle indicates that high order moment of mechanical load (the moment with order higher than torque) decays so fast that it never needs to be considered for regions far from the short boundary. As a result, the Saint-Venant Principle can be viewed as a statement about the asymptotic behavior of the Green’s function under a point load.
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Table of content
Saint Venant Principle
When considering loads applied to corroded structures, St Venant’s Principle, which is used to describe how loads and stresses behave in an axially loaded element, maybe a consideration. The original concept developed by the French elasticity theorist Adhemar Jean Claude Barre de Saint-Venant, is as follows:
Suppose the forces operating on a tiny section of an elastic body’s surface are replaced by another statically equivalent system of forces acting on the same surface. Saint Venant Principle is essential for the GATE exam as well. In that case, this redistribution of loading creates significant changes in stresses locally. Still, it does not affect stresses at huge distances about the linear dimensions of the surface on which the forces are altered.
This increase in stress, also known as a stress riser, occurs during abrupt changes in the material’s cross-section.
Simple Explanation of Saint Venant Principle
Saint-Venant’s Principle asserts that stress measured at any point on an axially loaded cross-section is uniform if it is far enough away from the point of load application or if there is any discontinuity in the member’s cross-section. In other words, when we compute stress using conventional methods, i.e.,
σ = P / A
we assume that we are sufficiently far from the point of application or any discontinuity for the normal stress to be uniform.
When a point load is applied to a surface, the stress is concentrated at the point of application and eventually equalizes as the distance from the point increases. This stress increase, also known as a stress riser, occurs when the material’s cross-section changes abruptly.
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Application of St Venant’s Principle to Thin Structures
It is commonly known that Saint-Venant’s Principle can not be applied to thinner constructions such as shells, beams, and trusses; similarly, it can be to a more solid object. St Venant’s Principle is also extensively used in forming MCQ-based questions in the GATE question paper.
Because the load routes in a thin structure are significantly more limited, disturbances go further than expected. This is the same behavior as the hole in the last illustration but more pronounced.
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