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GATE 2026 AE – Question 40

Structures · Strength of materials: stress and strain, stress-strain curves, trusses, bars, beams and shafts, determinate and indeterminate · 2 marks · Multiple choice

Consider a unit square body as shown in the figure below. The body is subjected to the deformation field $u = -ay$ and $v = ax$, where 'a' is a constant. Due to the application of this deformation field, the body undergoes _______ in the x-y plane.

A unit square with one corner at the origin O of the x-y axes.
  1. biaxial deformation
  2. pure shear
  3. pure bending
  4. rigid body rotation

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Correct answer: (D) rigid body rotation

Explanation

The strains are $\varepsilon_x = \frac{\partial u}{\partial x} = 0$, $\varepsilon_y = \frac{\partial v}{\partial y} = 0$ and $\gamma_{xy} = \frac{\partial u}{\partial y} + \frac{\partial v}{\partial x} = -a + a = 0$. There is no strain at all. The displacement is $(u, v) = a(-y, x)$, a rotation about the origin by the small angle $a$, so the body only rotates as a rigid body.