GATE 2021 CE (CE1) – Question 30
The figure shows $\sigma_{xx}=40$ MPa, $\sigma_{yy}=35.6$ MPa and transformed $\sigma_{XX}=120$ MPa, with the inclined face at 30° to x and the X-normal at 60°. Find $|\sigma_{xy}|$ in MPa to one decimal place.
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Correct answer: 95 to 97
Explanation
For θ=60°, normal-stress transformation gives $120=40\cos^260^\circ+35.6\sin^260^\circ+2\tau_{xy}\sin60^\circ\cos60^\circ$. Hence $\tau_{xy}=(120-36.7)/0.8660254=96.1879$ MPa. Its absolute magnitude is **96.2 MPa**; the corresponding transformed shear is approximately −50 MPa, consistent with the diagram.