The GATE Grind

GATE 2025 AE – Question 26

Structures · Strength of materials: Strain energy, Castigliano's principles, three-dimensional Hooke's law, plane stress and strain, Euler buckling · 1 mark · Multiple choice

For a homogeneous, isotropic material, the relation between the shear modulus ($G$), Young's modulus ($E$), and Poisson's ratio ($\nu$) is ____.

  1. $G = 2E(1 + \nu)$
  2. $2G = E(1 + \nu)$
  3. $E = 2G(1 + \nu)$
  4. $2E = G(1 + \nu)$

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Correct answer: (C) $E = 2G(1 + \nu)$

Explanation

For an isotropic material only two of the elastic constants are independent, and $G = \frac{E}{2(1 + \nu)}$, which is $E = 2G(1 + \nu)$.