GATE Civil Engineering (CE) 2018 Shift 1 Solved Paper

A plate in equilibrium is subjected to uniform stresses along its edges with magnitude ${\mathit{\sigma }}_{\mathit{x}\mathit{x}}=30\mathit{M}\mathit{P}\mathit{a}$ and ${\mathit{\sigma }}_{\mathit{y}\mathit{y}}=50\mathit{M}\mathit{P}\mathit{a}$ as shown in the figureThe Young's modulus of the material is $2\times {10}^{11}\mathit{N}∕{\mathit{m}}^2$ and the Poisson's ratio is $0.3.$ If ${\mathit{\sigma }}_{\mathit{z}\mathit{z}}$ is negligibly small and assumed to be zero, then the strain ${\mathit{\epsilon }}_{\mathit{z}\mathit{z}}$ is