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GATE 2024 MN – Question 22

Geomechanics and Ground Control · Geomechanics · 1 mark · Multiple choice

For major/minor principal stresses σ₁ and σ₃=−σ₁/2, find maximum shear stress.

  1. 4σ₁/3
  2. 3σ₁/4
  3. σ₁/2
  4. σ₁/4

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Correct answer: (B) 3σ₁/4

Explanation

Maximum shear stress is half the principal-stress difference. Substituting gives(σ₁−(−σ₁/2))/2=3σ₁/4, B. The sign of the minor principal stress must be retained when taking the difference.

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