GATE 2019 ME (ME1) – Question 50
The prismatic beam shown is pinned at both ends, length π m, square side 6 mm, E = 200 GPa and $\alpha=3\times10^{-6}\ \mathrm{K^{-1}}$. Find minimum uniform temperature rise causing Euler buckling (K).
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Correct answer: 1 to 1
Explanation
Equate restrained thermal compression and Euler load: $EA\alpha\Delta T=\pi^2EI/L^2$. Thus $\Delta T=\pi^2(I/A)/(\alpha L^2)$. For the square, $I/A=b^2/12=3\times10^{-6}$ m². Substitution with $L=\pi$ m gives **1 K**.