Question

Which of the following statement(s) about the elastic flexural buckling load of columns is/are correct?

• A. The buckling load increases with increase in flexural rigidity of the column.
• B. The buckling load increases with increase in the length 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.

Hint:

Remember Euler's buckling load formula $P_{cr} = \dfrac{\pi^2 EI}{(KL)^2}$. Buckling depends on stiffness ($EI$), length, and end conditions, but not directly on density.

Answer 1

The Correct Option is A, C, D

Step 1: Euler's buckling formula.
The elastic buckling load for a column is: \[ P_{cr} = \frac{\pi^2 EI}{(K L)^2} \] where - $E$ = Young's modulus, - $I$ = area moment of inertia, - $L$ = column length, - $K$ = effective length factor (depends on end conditions).

Step 2: Effect of flexural rigidity.
Flexural rigidity $EI$ appears in numerator. Higher $EI$ $\Rightarrow$ larger $P_{cr}$. Thus, (A) is true.

Step 3: Effect of length.
Column length appears squared in denominator: $(KL)^2$. Larger $L$ $\Rightarrow$ smaller $P_{cr}$. So (B) is false (load decreases, not increases).

Step 4: Effect of boundary conditions.
Boundary conditions determine $K$. For example: - Both ends pinned: $K=1$. - One end fixed, other free: $K=2$. - Both ends fixed: $K=0.5$. So end conditions strongly affect $P_{cr}$. Thus, (C) is true.

Step 5: Effect of density.
Formula contains $E$, $I$, $L$, $K$ — no direct dependence on material density. Density matters only in self-weight buckling but not in Euler's formula. Thus, (D) is true.

Step 6: Final check.
Correct statements are (A), (C), (D). \[ \boxed{\text{Correct statements: (A), (C), and (D)}} \]