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GATE 2021 MT – Question 58

Mechanical Behaviour of Materials · Elasticity stress and strain · 2 marks · Numerical answer

A plate is in plane strain with $\epsilon_{zz}=0$, $\sigma_{xx}=\sigma_{yy}\ne0$, and $\tau_{xy}=\tau_{xz}=\tau_{yz}=0$. For Poisson ratio 0.3, $\sigma_{zz}/\sigma_{xx}$ is ______ (one decimal place).

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Correct answer: 0.6 to 0.6

Explanation

For isotropic elasticity, εzz=[σzz−ν(σxx+σyy)]/E=0. With σxx=σyy=σ, σzz=2νσ.

Therefore the requested ratio σzz/σ=2×0.3=**0.6**.