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GATE 2021 ME (ME2) – Question 27

Machine Design · Design for static and dynamic loading, failure theories · 1 mark · Multiple choice

The von Mises stress at a point in a body subjected to forces is proportional to the square root of the

  1. Total strain energy
  2. Plastic strain energy
  3. Dilatational strain energy
  4. Distortional strain energy

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Show answer and explanation

Correct answer: (D) Distortional strain energy

Explanation

Von Mises yielding is based on distortion energy, the part associated with shape change. In isotropic elasticity, $u_d=\sigma_{VM}^2/(6G)$.

Thus equivalent stress is proportional to √u_d. **Answer: D**. Hydrostatic dilatation does not contribute to von Mises stress.