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GATE 2019 CE (CE2) – Question 39

Solid Mechanics · Transformation of stress, Mohr circle · 2 marks · Multiple choice

The plane-stress element shown has horizontal tensile stress 80 MPa, vertical compressive stress 20 MPa and clockwise shear 25 MPa. Through what indicated positive angle θ (degrees) should it rotate to obtain planes of maximum shear stress?

Diagram for GATE 2019 CE (CE2) question 39
  1. 13.3
  2. 26.6
  3. 31.7
  4. 48.3

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Show answer and explanation

Correct answer: (C) 31.7

Explanation

Take $\sigma_x=80$, $\sigma_y=-20$, $\tau_{xy}=-25$ MPa. Principal rotation satisfies $\tan2\theta_p=2\tau_{xy}/(\sigma_x-\sigma_y)=-0.5$, so $\theta_p=-13.2825^\circ$. Maximum-shear planes are 45° from principal planes. The indicated positive rotation is $45-13.2825=$ **31.7°, C**.