GATE 2021 CE (CE2) – Question 47
A 1.5 m inner-diameter cylindrical water tank is supported by a solid 75 mm steel column, fixed at its base and free at its top, of height 4 m. E=200 GPa, water density=1000 kg/m³, g=10 m/s². Ignore tank weight. Find maximum water depth in m to one decimal before column buckling.
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Correct answer: 2.5 to 2.9
Explanation
A fixed-free column has effective length 2L=8 m. With $I=\pi d^4/64$, Euler load is $P_{cr}=\pi^2EI/(2L)^2$. Equate this to water weight $\rho g(\pi D^2/4)h$. Substituting gives h=2.71077 m, so **2.7 m**. Using L rather than 2L would overestimate allowable depth fourfold.