The GATE Grind

GATE 2025 AE – Question 30

Structures · Strength of materials: stress and strain, stress-strain curves, trusses, bars, beams and shafts, determinate and indeterminate · 1 mark · Multiple choice

In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being $90^o$. The lengths of the undeformed diagonals are 20 cm. ABCD deforms as shown by the dotted lines. Upon deformation, diagonal AC reduces to 19.96 cm and BD increases to 20.04 cm. In the given $x$-$y$ coordinate system, the engineering shear strain $\gamma_{xy}$ is equal to ____.

A square plate ABCD with its diagonals along the axes: A and C on the x axis and B and D on the y axis. In the deformed (dotted) shape A and C each move inwards by 0.02 cm and B and D each move outwards by 0.02 cm.
  1. 0
  2. 0.002
  3. 0.004
  4. -0.004

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) 0

Explanation

The diagonals lie along the $x$ and $y$ axes and stay along them, since the deformation is symmetric about both. The corners only move along the axes, so $\varepsilon_x = -\frac{0.04}{20} = -0.002$ and $\varepsilon_y = +0.002$, and the right angle between the axes is not changed: $\gamma_{xy} = 0$. (The shear strain of the sides in the rotated 45 degree frame is not zero, but the question asks for the given $x$-$y$ system.)