GATE 2019 ME (ME1) – Question 52
At a component point, $\sigma_{xx}=100$ MPa, $\sigma_{yy}=220$ MPa and $\sigma_{xy}=\sigma_{yx}=80$ MPa; all other stress components are zero. Yield strength is 468 MPa. Find safety factor by maximum-shear-stress theory, to one decimal place.
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Correct answer: 1.7 to 1.9
Explanation
The in-plane principal stresses are $160\pm\sqrt{60^2+80^2}=260,60$ MPa. The third principal stress is zero. Tresca equivalent stress is $260-0=260$ MPa, so safety factor is $468/260=\mathbf{1.8}$.