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2. (3 points) When loading is applied at a point on a body, the stress distributions at different cross sections are different. However, the stress distribution becomes uniform at locations far from the applied load. This is due to which principle? Name the principle.

2. (3 points) When loading is applied at a point on a body, the stress distributions at different cross sections are different. However, the stress distribution becomes uniform at locations far from the applied load. This is due to which principle? Name the principle.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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**2. Concept of Stress Distribution in Loaded Bodies** When loading is applied at a point on a body, the stress distributions across different cross sections vary. However, the stress distribution becomes uniform at locations far from the applied load. This is explained by a fundamental principle in mechanics. Identify and name this principle. **Diagrams and Analysis:** 1. **Left Diagram (Body with Load P):** - A vertical body with an applied load (P) at the top. - The body shows a grid pattern with noticeable distortion near the load and support areas. - **Area Near Load:** Lines distort due to stress concentration. - **Middle Area:** Lines remain straight, indicating uniform stress, away from disturbances. - **Area Near Support:** Lines distort again due to stress concentration. 2. **Sections a-a, b-b, and c-c:** - **Section a-a:** Close to the load, showing significant line distortion. - **Section b-b:** Further down, still some line distortion. - **Section c-c:** Far from the load, lines are straight with uniform stress distribution, represented mathematically as \(\sigma_{\text{avg}} = \frac{P}{A}\), where \(P\) is the applied load and \(A\) is the area. **Your Answer:** This phenomenon is described by Saint-Venant's Principle, which states that the difference in the effects of two different but statically equivalent loads becomes negligible at sufficiently large distances from the load.
Transcribed Image Text:**2. Concept of Stress Distribution in Loaded Bodies** When loading is applied at a point on a body, the stress distributions across different cross sections vary. However, the stress distribution becomes uniform at locations far from the applied load. This is explained by a fundamental principle in mechanics. Identify and name this principle. **Diagrams and Analysis:** 1. **Left Diagram (Body with Load P):** - A vertical body with an applied load (P) at the top. - The body shows a grid pattern with noticeable distortion near the load and support areas. - **Area Near Load:** Lines distort due to stress concentration. - **Middle Area:** Lines remain straight, indicating uniform stress, away from disturbances. - **Area Near Support:** Lines distort again due to stress concentration. 2. **Sections a-a, b-b, and c-c:** - **Section a-a:** Close to the load, showing significant line distortion. - **Section b-b:** Further down, still some line distortion. - **Section c-c:** Far from the load, lines are straight with uniform stress distribution, represented mathematically as \(\sigma_{\text{avg}} = \frac{P}{A}\), where \(P\) is the applied load and \(A\) is the area. **Your Answer:** This phenomenon is described by Saint-Venant's Principle, which states that the difference in the effects of two different but statically equivalent loads becomes negligible at sufficiently large distances from the load.
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