GATE 2025 MT – Question 32
The hydrostatic stress for the stress tensor $$\boldsymbol\sigma=\begin{bmatrix}150&0&0\\0&-100&100\\0&100&250\end{bmatrix}\ \mathrm{MPa}$$ is ______ MPa (in integer).
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Correct answer: 100 to 100
Explanation
The hydrostatic stress is the mean normal stress, $\sigma_h=\operatorname{tr}(\boldsymbol\sigma)/3$. Shear components do not enter the trace.
Thus $\sigma_h=(150-100+250)/3=\boxed{100\ \mathrm{MPa}}$. This uses the tensile-positive mean-stress convention.