A column with maximum equivalent length has:
Try it first: pick an option, then read the explanation.
Correct answer: D. one end fixed and the other end free
Asked in SSC JE 03/03/2017 (Morning); SSC JE 01/03/2017 (Morning)
Detailed Explanation
Compare the four equivalent lengths: l, l/2, l/√2 and 2l.
Why “one end fixed and the other end free” Is Correct
The maximum is 2l, for one end fixed and the other free.
| End conditions | Effective length le (Euler) | Crippling load P = π²EI/le² | Relative to hinged–hinged |
|---|---|---|---|
| Both ends hinged (pinned) | L | π²EI/L² | 1 |
| One end fixed, other free | 2L | π²EI/4L² | 1/4 |
| One end fixed, other hinged | L/√2 ≈ 0.707L | 2π²EI/L² | 2 |
| Both ends fixed | L/2 | 4π²EI/L² | 4 |
Longest effective length → smallest buckling load (fixed–free); shortest effective length → largest load (fixed–fixed).
Why the Other Options Are Wrong
- A. both ends hinged: Both hinged: l.
- B. both ends fixed: Both fixed: l/2 — the minimum.
- C. one end fixed and the other end hinged: Fixed–hinged: l/√2.
Key Point
Max equivalent length: fixed–free (2l). Min: fixed–fixed (l/2).
Key Concepts for Students
- Maximum le ↔ minimum buckling load.
- A free end can sway and rotate.
- Equivalent length = effective length.
Practice more: this is question 24 in Columns and Struts MCQs – Part 2. Try the whole set and check every answer instantly.