GATE 2020 ME (ME1) – Question 40

Mechanics of Materials · Euler theory of columns · 2 marks · Multiple choice

The truss has four members of length l and flexural rigidity EI, and one member of length $l\sqrt2$ and rigidity 4EI. It carries the pair of outward forces P shown. Find the smallest P at which any member buckles.

Diagram for GATE 2020 ME (ME1) question 40

$\sqrt2\pi^2EI/l^2$
$\pi^2EI/l^2$
$2\pi^2EI/l^2$
$\pi^2EI/(2l^2)$

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Correct answer: (C) $2\pi^2EI/l^2$

Explanation

Joint equilibrium makes each side a tensile member of force P/√2, while the diagonal is in compression P. Only the diagonal can buckle. Its pin-ended Euler capacity is $\pi^2(4EI)/(\sqrt2L)^2=\mathbf{2\pi^2EI/L^2}$. Hence **C**. Applying Euler buckling to the tensile sides would be incorrect.