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GATE 2023 MN – Question 13

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

A shear stress acts tangentially on the top of a block of width $w$ and height $h$, producing a small top displacement $\Delta w$ as shown. Find the engineering shear strain.

Diagram for GATE 2023 MN question 13
  1. $\Delta w/w$
  2. $\Delta w/h$
  3. $2\Delta w/w$
  4. $2\Delta w/h$

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Show answer and explanation

Correct answer: (B) $\Delta w/h$

Explanation

Shear strain measures the change in angle between initially perpendicular material lines. For a small deformation, γ = tanγ ≈ top displacement/block height = Δw/h. Thus B. The block width is not the separation between the top and fixed bottom surfaces.

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