If a compression member of a steel structure is effectively held in position and restrained against rotation at both the ends, then which of the following options represents the effective length of the member?
- A0.65 times of the actual lengthCorrect
- B2.0 times of the actual length
- C1.2 times of the actual length
- D0.80 times of the actual length
Solution
Concept
Effective length depends on end restraint. Both ends fixed (position and rotation held) gives KL = 0.65L as per IS 800.
Formula
Le = K × L, K = 0.65 for both ends fixed
Step-by-step solution
1. Both ends are held in position, so no sway. 2. Both ends are restrained against rotation, so both ends are fixed. 3. For fixed-fixed members, IS 800 gives recommended K = 0.65. 4. So Le = 0.65 L.
Explanation
When both ends are fixed in position and direction, the column bends in a short curve. Theory gives 0.5L, but end fixity is never perfect in practice. So IS 800 recommends 0.65L.
Why the other options are wrong
B: 2.0L is for one end fixed and the other end free (cantilever). C: 1.2L is for one end fixed and the other end restrained in rotation but free in position. D: 0.80L is for one end fixed and the other end hinged.
Shortcut
Fixed-fixed = 0.65L, fixed-hinged = 0.8L, hinged-hinged = 1.0L, fixed-free = 2.0L.
Common mistake
Writing the theoretical value 0.5L instead of the code value 0.65L.
Correct answer: A) 0.65 times of the actual length