The GATE Grind

GATE 2022 AE – Question 41

Structures · Strength of materials: Strain energy, Castigliano's principles, three-dimensional Hooke's law, plane stress and strain, Euler buckling · 2 marks · Multiple choice

A horizontal load F is applied at R on the shown two-member truss. Both members are prismatic, have cross-sectional area $A_0$ and Young’s modulus E. The horizontal displacement of R is:

source diagram and its labels are reproduced in the attached image.
  1. 0
  2. $Fl/(EA_0)$
  3. $\sqrt2Fl/(EA_0)$
  4. $2Fl/(EA_0)$

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Correct answer: (C) $\sqrt2Fl/(EA_0)$

Explanation

Each member has length $\sqrt2l$ and force magnitude $F/\sqrt2$. Strain energy is $F^2\sqrt2l/(2EA_0)$; its derivative gives $\delta_R=\sqrt2Fl/(EA_0)$.