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GATE 2018 ME (ME1) – Question 39

Mechanics of Materials · Transformation of stress and strain, Mohr circle · 2 marks · Multiple choice

The plane-stress state shown has σx = 100 kPa and τxy = 50 kPa. If the minimum principal stress is 10 kPa, σy is ______.

Diagram for GATE 2018 ME (ME1) question 39
  1. 9.45 kPa
  2. 18.88 kPa
  3. 37.78 kPa
  4. 75.50 kPa

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Show answer and explanation

Correct answer: (C) 37.78 kPa

Explanation

An in-plane principal stress λ obeys $(\sigma_x-\lambda)(\sigma_y-\lambda)-\tau_{xy}^2=0$. Insert λ = 10: $90(\sigma_y-10)=2500$, hence σy = 37.78 kPa (C). Here “minimum” means the smaller in-plane value; plane stress also has an out-of-plane zero principal stress.