GATE 2026 CE (CE2) – Question 16

Solid Mechanics · Simple stress and strain relationships · 1 mark · Multiple choice

A plane strain problem (in X-Y plane) must satisfy the condition:

$\sigma_{zz} = 0$
$\epsilon_{zz} = \epsilon_{xz} = \epsilon_{yz} = 0$
$\sigma_{xx} \neq \sigma_{xy} \neq \sigma_{xz} \neq 0$
$\epsilon_{xx} \neq \varepsilon_{yy} \neq \epsilon_{xy} \neq 0$

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Correct answer: (B) $\epsilon_{zz} = \epsilon_{xz} = \epsilon_{yz} = 0$

Explanation

Plane strain means there is no deformation in the out-of-plane (Z) direction, so $\epsilon_{zz} = \epsilon_{xz} = \epsilon_{yz} = 0$. The normal stress $\sigma_{zz}$ is not zero in general, because it is needed to keep $\epsilon_{zz}$ at zero. $\sigma_{zz} = 0$ is the condition for plane stress.