If a steel column is designed for its stability, then the slenderness ratio is defined as the:
- Aratio of the least lateral dimension to the length
- Bratio of the length to the least lateral dimensionCorrect
- Cratio of the length to the depth
- Dratio of the length to the maximum lateral dimension
Solution
Concept
Slenderness ratio shows how slender a column is. It compares the column length with its smallest cross-section property, because buckling happens about the weakest axis.
Formula
λ = KL / rmin
Step-by-step solution
1. A column buckles about its weakest axis. 2. So slenderness is measured using length and the least lateral dimension (or least radius of gyration). 3. Slenderness ratio = length / least lateral dimension. 4. This matches option B.
Explanation
Slenderness ratio is length divided by the least lateral dimension. For steel, the exact form is effective length divided by the least radius of gyration (KL/rmin). A higher value means the column buckles more easily.
Why the other options are wrong
A: This is the inverse ratio. C: Depth may not be the least dimension. D: Buckling depends on the least dimension, not the maximum.
Shortcut
Slenderness = length / weakest (least) dimension.
Common mistake
Using the maximum dimension or writing the ratio upside down.
Correct answer: B) ratio of the length to the least lateral dimension