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GATE 2017 CE (CE2) – Question 26

Solid Mechanics · Simple stress and strain relationships · 1 mark · Multiple choice

A 10 mm × 10 mm element is in plane strain. Its exaggerated deformed shape is shown. If engineering shear strain $\gamma_{xy}=0.001k$, then k is ______.

Diagram for GATE 2017 CE (CE2) question 26
  1. 0.50
  2. 0.25
  3. −0.25
  4. −0.50

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Show answer and explanation

Correct answer: (A) 0.50; (D) −0.50

Explanation

The initially right angle increases by 0.0005 rad. Under the usual signed engineering-shear convention this gives $\gamma_{xy}=-0.0005$, hence $k=-0.0005/0.001=-0.5$ (D). The final key also accepts the opposite sign convention, $k=+0.5$ (A). Both officially accepted choices are preserved.