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GATE 2024 AE – Question 32

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

A material has Poisson's ratio $\nu = 0.5$ and Young's modulus E = 2500 MPa. The percentage change in its volume when subjected to a hydrostatic stress of magnitude 10 MPa is ______ (answer in integer).

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Correct answer: 0

Explanation

The volumetric strain under hydrostatic stress $\sigma$ is $\frac{\Delta V}{V} = \frac{3(1 - 2\nu)\sigma}{E}$. With $\nu = 0.5$ the factor $(1 - 2\nu)$ is zero, so the material is incompressible and the volume does not change: 0%.