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.
Download Formulas for GATE Mechanical Engineering - Machine Design
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.
Download Formulas for GATE Mechanical Engineering - Fluid Mechanics and Machinery
|Important GATE Notes|
|Work Done By A Force||Motion Under Gravity|
|Dynamic Resistance||Static Resistance|
|Ideal Diode||Bettis Theorem|
|Work Done By A Constant Force||Application Layer Protocols|
|Castiglianos Theorem||Portal Frames|
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