The buckling load will be maximum for a column if
- AOne end of the column is clamped and the other end is free
- BBoth ends of the column are clampedCorrect
- CBoth ends of the column are hinged
- DOne end of the column is hinged and the other end is free
Solution
Concept
Effect of end conditions on the buckling load
Formula
Pcr = π²EI / Le²; Le = 0.5 L (fixed–fixed), 0.7 L (fixed–pinned), L (pinned–pinned), 2 L (fixed–free)
Step-by-step solution
1. Buckling load is inversely proportional to the square of the effective length. 2. The smallest effective length (0.5 L) belongs to a column fixed at both ends. 3. So both ends clamped give the maximum load.
Explanation
A column with both ends clamped has the least effective length, 0.5L, and therefore the greatest buckling load (4 times that of a hinged column).
Shortcut
Fixed–fixed = 4×, fixed–hinged ≈ 2×, hinged–hinged = 1×, fixed–free = 0.25×.
Common mistake
Choosing hinged ends because they are the "standard" condition.
Correct answer: B) Both ends of the column are clamped