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GATE 2026 CE (CE2) – Question 17

Solid Mechanics · Transformation of stress, Mohr circle · 1 mark · Multiple choice

Which one of the following stress conditions represents the state of pure shear stress?

Four stress elements (A) to (D), each a square with arrows of magnitude 40 on its faces. In (A) the left and right faces are pulled outward and the top and bottom faces are pushed inward, with a shear arrow of 40 on each face. In (B) all four faces are pulled outward, with the same shear arrows. In (C) all four faces are pushed inward, with the same shear arrows. In (D) all four faces are pulled outward with no shear arrows.
  1. Option A in the figure
  2. Option B in the figure
  3. Option C in the figure
  4. Option D in the figure

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Show answer and explanation

Correct answer: (A) Option A in the figure

Explanation

A state of pure shear has zero mean normal stress, $\sigma_x + \sigma_y = 0$, so the principal stresses are equal and opposite. In option A the left and right faces carry a tension of 40 and the top and bottom faces carry a compression of 40, so $\sigma_x + \sigma_y = 0$. In B both normal stresses are tensile and in C both are compressive, so each has a non-zero mean stress. D has only normal stresses. A is the only state that reduces to pure shear on planes turned through 45°.