Given are four bamboo columns with identical material and geometric properties but different end conditions. Arrange them in the increasing order of their first buckling loads (figure: A free–fixed; B fixed–fixed; C hinged–hinged; D hinged–fixed)
- AA, B, C, D
- BA, C, D, BCorrect
- CA, C, B, D
- DA, D, C, B
Solution
Concept
Effective length and buckling load
Formula
Pcr ∝ 1/Le²
Step-by-step solution
1. Free–fixed: Le = 2L (lowest). 2. Hinged–hinged: Le = L. 3. Hinged–fixed: Le = 0.7L. 4. Fixed–fixed: Le = 0.5L (highest). 5. Increasing Pcr: A, C, D, B.
Explanation
Smaller effective length gives a larger buckling load.
Why the other options are wrong
Other orders do not follow Le.
Shortcut
Pcr ∝ 1/Le².
Correct answer: B) A, C, D, B