GATE 2023 AE – Question 47

Correct answer: (A) The buckling load increases with increase in flexural rigidity of the column.; (C) The boundary conditions of the column affect the buckling load.; (D) The buckling load is NOT directly dependent on the density of the material used for the column.

Explanation

**Euler's elastic buckling load** for a column of length $L$, modulus $E$ and second moment of area $I$:
$$P_{cr}=\frac{\pi^2EI}{(KL)^2},$$
where $K$ is the effective-length factor set by the end conditions.

• **A. Increases with flexural rigidity $EI$.** True. ✓
• **B. Increases with the length $L$.** False. $P_{cr}\propto1/L^2$, so a longer column buckles at a lower load.
• **C. Depends on the boundary conditions.** True, through $K$ (pinned-pinned $K=1$, fixed-free $K=2$, fixed-fixed $K=0.5$). ✓
• **D. Not directly dependent on the density.** True. The formula contains only $E$, $I$, $K$ and $L$. ✓

Answer **A, C and D**.