GATE 2025 ME – Question 56

Mechanics of Materials · Stress, strain and elastic constants · 2 marks · Numerical answer

The state of stress at a point is shown in the figure given below. Under plane stress assumption, the normal strain along the thickness direction ($\varepsilon_{zz}$) is ____________ (rounded off to 2 decimal places).

Use the Young's Modulus E = 200 GPa and Poisson's ratio $\nu$ = 0.27.

A stress element with 350 GPa normal stresses on the left and right faces, 150 GPa normal stresses on the top and bottom faces, and 50 GPa shear stresses on the faces.

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Correct answer: -0.69 to -0.67

Explanation

Under plane stress, $\sigma_z = 0$ and the strain through the thickness is $\varepsilon_{zz} = -\frac{\nu}{E}(\sigma_x + \sigma_y)$. The shear stress does not affect it. With $\sigma_x = 350$ and $\sigma_y = 150$ (using the units as printed) and $E = 200$, we get $\varepsilon_{zz} = -\frac{0.27}{200}(350 + 150) = -0.675$, which rounds to $-0.68$.