For a compression member, the Slenderness Ratio is defined as the ratio of
- AIts total length to the radius of gyration.
- BIts effective length to the least radius of gyration.Correct
- CThe width of the section to its thickness.
- DThe applied axial load to the cross-sectional area.
Solution
Concept
Slenderness Ratio of Compression Members
Formula
λ = Leff / rmin (Effective Length / Least Radius of Gyration)
Step-by-step solution
1. Review the definition of slenderness ratio for a compression member. 2. Recall the standard formula for slenderness ratio: λ = Leff / rmin, which is the ratio of effective length to the least radius of gyration. 3. Compare the definition with the given choices and select Option (b) as the correct answer.
Explanation
The slenderness ratio of a compression member (like a column) measures how prone it is to buckling. It is calculated by dividing the effective length of the member by its least radius of gyration, which represents how thin or flexible the member is in its weakest direction.
Shortcut
To remember the Slenderness Ratio formula (λ = Effective Length / Least Radius of Gyration), use the memory rule "Effective over Least": - Numerator: Effective Length (accounts for support conditions, not just total length) - Denominator: Least Radius of Gyration (buckling always occurs about the weakest/least axis)
Common mistake
A common mistake is selecting Option A by using the total actual length instead of the effective length, which accounts for end support conditions. Another frequent error is forgetting that the slenderness ratio depends specifically on the least radius of gyration, as buckling always occurs about the weakest axis of the cross-section.
Correct answer: B) Its effective length to the least radius of gyration.