The GATE Grind

GATE 2020 AE – Question 38

Structures · Strength of materials: Strain energy, Castigliano's principles, three-dimensional Hooke's law, plane stress and strain, Euler buckling · 2 marks · Multiple choice

At what Poisson ratio does shear modulus equal bulk modulus for an isotropic solid?

  1. 1/2
  2. 1/4
  3. 1/6
  4. 1/8

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Correct answer: (D) 1/8

Explanation

Use $G=E/[2(1+\nu)]$ and $K=E/[3(1-2\nu)]$. Equating them gives $2(1+\nu)=3(1-2\nu)$, hence 8ν = 1 and ν = 1/8, D.

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