The actual length of a prismatic compression member is 3 m. Calculate its effective length if one of its ends is restrained against both translation and rotation, and the other end is restrained against rotation but free to translate.
Try it first: pick an option, then read the explanation.
Asked in SSC JE 04/12/2023 (9 am–11 am)
Detailed Explanation
One end is fully fixed. The other end cannot rotate but can sway sideways — like the top of a column in a sway frame with a stiff beam. Theoretically le = L for this case, but IS 800 (Table 11) and IS 456 (Table 28) recommend a larger design value because full fixity is never achieved.
\[ l_{e} = 1.2\,L = 1.2 \times 3 = 3.6\ \text{m} \]
Why “3.6 m” Is Correct
Using the code's recommended factor of 1.2, the effective length is 3.6 m.
| Restraint at the two ends (IS 800 Table 11 / IS 456 Table 28) | Theoretical le | Recommended le |
|---|---|---|
| Held in position and restrained in direction at both ends (fixed–fixed) | 0.5L | 0.65L |
| Fixed at one end, held in position but free to rotate at the other (fixed–hinged) | 0.7L | 0.80L |
| Held in position at both ends, free to rotate (hinged–hinged) | 1.0L | 1.0L |
| Fixed at one end; other end restrained in rotation but free to translate (sway) | 1.0L | 1.2L |
| Fixed at one end; other end free (not held in position nor restrained in direction) | 2.0L | 2.0L |
| Hinged at one end; other end restrained in rotation but free to translate | 2.0L | 2.0L |
Code values are larger than the theoretical ones for restrained ends because perfect fixity is never achieved in practice.
Why the Other Options Are Wrong
- A. 2.8 m: 2.8 m (≈ 0.93L) does not correspond to any code case.
- C. 6 m: 6 m = 2L applies to a fixed–free column (or hinged + sway-restrained in rotation).
- D. 3.2 m: 3.2 m is not a code value for these restraints.
Key Point
Fixed at one end, other end rotation-fixed but free to sway: le = 1.2L (IS 800 / IS 456).
Key Concepts for Students
- Theoretical le for this case is L; the code adds 20% for imperfect fixity.
- For fixed–fixed, IS 800 uses 0.65L instead of the theoretical 0.5L.
- Sway (translation) at an end always increases the effective length.
Practice more: this is question 4 in Columns and Struts MCQs – Part 1. Try the whole set and check every answer instantly.