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GATE 2018 CE (CE1) – Question 39

Solid Mechanics · Simple stress and strain relationships · 2 marks · Multiple choice

A plate in equilibrium carries uniform tensile edge stresses $\sigma_{xx}=30$ MPa and $\sigma_{yy}=50$ MPa as shown. Given $E=2\times10^{11}$ N/m², ν = 0.3 and $\sigma_{zz}=0$, strain $\epsilon_{zz}$ is ______.

Diagram for GATE 2018 CE (CE1) question 39
  1. $-120\times10^{-6}$
  2. $-60\times10^{-6}$
  3. 0.0
  4. $120\times10^{-6}$

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Show answer and explanation

Correct answer: (A) $-120\times10^{-6}$

Explanation

Isotropic elasticity gives $\epsilon_{zz}=[\sigma_{zz}-\nu(\sigma_{xx}+\sigma_{yy})]/E$. Substituting gives $-0.3(30+50)/200000=-120\times10^{-6}$ (A). Zero out-of-plane stress does not imply zero strain.