GATE 2022 MT – Question 63
The stress tensor is $\begin{bmatrix}130&30&0\\30&50&0\\0&0&0\end{bmatrix}$ MPa. Its maximum shear stress is ______ MPa (nearest integer).
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Correct answer: 70 to 70
Explanation
The in-plane principal stresses are $90\pm\sqrt{40^2+30^2}=140,40$ MPa. The third is zero. Absolute maximum shear is $(140-0)/2=\boxed{70}$ MPa, exceeding the in-plane maximum of 50 MPa.