As per Euler's theory, for which of the following end conditions is the longest effective length of a column obtained?
Try it first: pick an option, then read the explanation.
Correct answer: C. When one end of the column is fixed and the other end is free
Asked in SSC JE 05/06/2024 (9 am–11 am)
Detailed Explanation
The effective length is the length of an equivalent pin-ended column with the same buckling load — the distance between inflection points of the buckled shape.
Why “When one end of the column is fixed and the other end is free” Is Correct
A column fixed at the base and free at the top bends into a quarter sine wave; it behaves like half of a pin-ended column of length 2L, so le = 2L — the longest of all.
Why the Other Options Are Wrong
- A. When both the ends of the column are hinged: Both hinged: le = L.
- B. When one end of the column is fixed and the other end is hinged: Fixed–hinged: le = L/√2 ≈ 0.707L.
- D. When both the ends of the column are fixed: Both fixed: le = L/2 — the shortest.
Key Point
le: fixed–free 2L > hinged–hinged L > fixed–hinged L/√2 > fixed–fixed L/2.
Key Concepts for Students
- Longer le means a smaller Euler load (P ∝ 1/le²).
- Fixed–free columns include flagpoles and cantilever posts.
- IS 800 also recommends 2.0L for this case.
Practice more: this is question 3 in Columns and Struts MCQs – Part 1. Try the whole set and check every answer instantly.