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GATE 2021 AE – Question 21

Structures · Strength of materials: Transformation of stress and strain, Mohr's circle, combined loading and failure criteria · 1 mark · Multiple choice

For the plane stress state $\sigma_x=-80$ MPa, $\sigma_y=-20$ MPa and $\tau_{xy}=-30$ MPa, the indicated maximum-shear plane angle to the x-axis is

source diagram and its labels are reproduced in the attached image.
  1. 45°
  2. -45°
  3. 22.5°
  4. -22.5°

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Correct answer: (D) -22.5°

Explanation

$\tan2\theta_s=-(\sigma_x-\sigma_y)/(2\tau_{xy})=-1$. The illustrated maximum-shear plane has $\theta_s=-22.5^\circ$.