GATE 2017 ME (ME2) – Question 17
At a point, $\sigma_x=\sigma_y=\sigma_z=\tau_{xz}=\tau_{zx}=\tau_{yz}=\tau_{zy}=0$ and $\tau_{xy}=\tau_{yx}=50$ MPa. The maximum normal stress is ______ MPa.
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Correct answer: 49.9 to 50.1
Explanation
The stress tensor has xy block [[0,50],[50,0]] and zero z stress. Its eigenvalues are+50,−50 and0MPa, since the xy characteristic equation is λ²−2500=0. Hence the maximum normal stress over all planes is **50MPa**.