GATE ME 2022 Set 1 — Question 26
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Machine Design → Beams & Columns → Elastic Constants & Poisson's Ratio
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Question
Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following statement(s) is/are TRUE?
Correct answer
(A) A body subjected to hydrostatic pressure has no shear stress.; (B) If a long solid steel rod is subjected to tensile load, then its volume increases.
Solution
Let's evaluate each statement:
- Statement (A): Under hydrostatic pressure, the state of stress is . The maximum shear stress is . Thus, there is no shear stress. TRUE.
- Statement (B): For a rod under tensile load , the volumetric strain is . For steel, Poisson's ratio , which is less than . Therefore, , meaning the volume increases. TRUE.
- Statement (C): Maximum shear stress theory (Tresca) is primarily used for ductile materials. Brittle materials are typically analyzed using Maximum Principal Stress theory (Rankine). FALSE.
- Statement (D): Zero shear force () implies a constant bending moment (). According to the Euler-Bernoulli beam theory, . If is a non-zero constant, the curvature is constant, and the elastic curve is a circular arc, not a straight line. A straight line requires . FALSE.
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