What is the relation between equivalent length (Le) and actual length (l) for a column with one end fixed and the other free?
Try it first: pick an option, then read the explanation.
Correct answer: D. Le = 2l
Asked in SSC JE 23/09/2019 (Morning); SSC JE 24/01/2018 (Evening)
Detailed Explanation
Mirror the fixed–free column about its fixed base: the combined shape is a half sine wave of length 2l with zero moment at both tips — a pin-ended column of length 2l.
Why “Le = 2l” Is Correct
Hence Le = 2l, and P = π²EI/(4l²).
Why the Other Options Are Wrong
- A. Le = 3l: 3l is not a theoretical effective length for any standard case.
- B. Le = 2.5l: 2.5l is not a standard value.
- C. Le = l/4: l/4 is far too short; even fixed–fixed gives only l/2.
Key Point
Fixed–free: Le = 2l (largest effective length, smallest Euler load).
Key Concepts for Students
- Le is the distance between inflection points on the buckled shape.
- IS 800 also takes 2.0L for this case.
- Doubling Le cuts the buckling load to one quarter.
Practice more: this is question 8 in Columns and Struts MCQs – Part 1. Try the whole set and check every answer instantly.