Slenderness ratio of a long column is:
Try it first: pick an option, then read the explanation.
Correct answer: D. length of column divided by least radius of gyration
Asked in SSC JE 22/01/2018 (Evening)
Detailed Explanation
Slenderness ratio is a dimensionless ratio of two lengths: the column's effective length and its least radius of gyration.
\[ \lambda = \frac{l_e}{r_{min}},\qquad r_{min}=\sqrt{I_{min}/A} \]
Why “length of column divided by least radius of gyration” Is Correct
It is the length of the column divided by the least radius of gyration.
Why the Other Options Are Wrong
- A. area of cross-section divided by radius of gyration: Area / r has units of length — not a slenderness ratio, and it ignores the column length.
- B. area of cross-section divided by least radius of gyration: Same error — length, not area, goes in the numerator.
- C. radius of gyration divided by area of cross-section: r/A is not a meaningful slenderness measure.
Key Point
λ = le / rmin — always use the least r because buckling occurs about the weakest axis.
Key Concepts for Students
- λ is dimensionless.
- The larger λ, the lower the safe stress.
- For a circle rmin = d/4; for a rectangle rmin = b/√12 (b = smaller side).
Practice more: this is question 16 in Columns and Struts MCQs – Part 2. Try the whole set and check every answer instantly.