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GATE 2022 ME (ME1) – Question 26

Mechanics of Materials · Stress, strain and elastic constants · 1 mark · Multiple select

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?

  1. A body subjected to hydrostatic pressure has no shear stress.
  2. If a long solid steel rod is subjected to tensile load, then its volume increases.
  3. Maximum shear stress theory is suitable for failure analysis of brittle materials.
  4. If a portion of a beam has zero shear force, then the corresponding portion of the elastic curve of the beam is always straight.

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Show answer and explanation

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.

Explanation

Under hydrostatic pressure all the normal stresses are equal and the shear stresses vanish (A true). Under tension the volume strain is $\frac{\sigma}{E}(1 - 2\nu) > 0$ since $\nu < 0.5$ (B true). The maximum shear stress theory is meant for ductile materials (C false). Zero shear force means that the bending moment is constant, which can be non-zero, and then the beam is bent in a circular arc and not straight (D false).