The effective length ratio 'K' for a column in frame with no sideway is limited between:
- A0 and 1.0
- B0 and 0.5
- C0.5 and 1.0Correct
- D0.25 and 0.5
Solution
Concept
In a braced frame (no sway), K lies between 0.5 (both ends fixed) and 1.0 (both ends pinned).
Formula
Le = K × L, with 0.5 ≤ K ≤ 1.0 for no-sway frames
Step-by-step solution
1. No sway means the column ends cannot move sideways relative to each other. 2. The best end condition is both ends fixed, so K = 0.5. 3. The worst end condition is both ends pinned, so K = 1.0. 4. So for a no-sway frame, 0.5 ≤ K ≤ 1.0.
Explanation
In a braced frame, the top of the column cannot move sideways. The column can at most behave like a pinned-pinned column (K = 1.0) and at best like a fixed-fixed column (K = 0.5). So K always lies between 0.5 and 1.0.
Why the other options are wrong
A: K cannot be below 0.5 even with full fixity. B: Range 0 to 0.5 is not possible for a real column. D: Range 0.25 to 0.5 is below the fixed-fixed limit of 0.5.
Shortcut
No sway: 0.5 to 1.0. Sway: 1.0 to infinity.
Common mistake
Mixing up sway and no-sway frames. In a sway frame, K is 1.0 or more.
Correct answer: C) 0.5 and 1.0