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GATE 2018 ME (ME1) – Question 16

Mechanics of Materials · Transformation of stress and strain, Mohr circle · 1 mark · Multiple choice

For algebraically largest and smallest principal stresses $\sigma_1,\sigma_3$, maximum shear stress is ______.

  1. $(\sigma_1+\sigma_3)/2$
  2. $(\sigma_1-\sigma_3)/2$
  3. $\sqrt{(\sigma_1+\sigma_3)/2}$
  4. $\sqrt{(\sigma_1-\sigma_3)/2}$

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Show answer and explanation

Correct answer: (B) $(\sigma_1-\sigma_3)/2$

Explanation

The largest Mohr circle has diameter $\sigma_1-\sigma_3$. Its radius is the maximum shear stress, $(\sigma_1-\sigma_3)/2$ (B).