GATE 2017 CE (CE1) – Question 52
Two linear-elastic columns have $E=2\times10^5$ MPa, square cross-section of side 10 mm and length 1 m. Column 1 is fixed-free; column 2 is fixed-pinned. Using Euler theory, find the ratio of buckling load of column 2 to that of column 1, to one decimal place.
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Correct answer: 7.9 to 8.3
Explanation
Euler load is $P_{cr}=\pi^2EI/(KL)^2$. For column 1, $K_1=2$. The exact fixed-pinned solution has $K_2\simeq0.699$ (often approximated by 0.7). Since E, I and L are identical, $P_{cr,2}/P_{cr,1}=(2/0.699)^2\simeq8.18$, rounding to 8.2. Using $K=0.7$ gives 8.16 and the same rounded result.