Slenderness ratio of a square column A vertical column has a square cross-section of side 10 cm and an overall (effective) length of 500 cm with pinned ends. Compute its slenderness ratio λ = L_e / r.

Introduction / Context:Slenderness ratio indicates the susceptibility of a column to buckling. For a given effective length L_e and radius of gyration r, λ = L_e / r classifies a column as short, intermediate, or long.

Given Data / Assumptions:

• Square cross-section: side a = 10 cm.
• Overall (effective) length L_e = 500 cm (pinned–pinned).
• Radius of gyration r = sqrt(I/A).

Concept / Approach:For a square of side a: I = a^4 / 12 and A = a^2, so r = sqrt(I/A) = a / √12. Then λ = L_e / r.

Step-by-Step Solution:

Verification / Alternative check:Using r^2 = I/A = (a^4/12) / a^2 = a^2/12 yields the same r value.

Why Other Options Are Wrong:

• 117.2 and 137.2 arise from incorrect r or L assumptions.
• 17.3 and 13.72 are off by an order of magnitude, likely mixing cm and mm.

Common Pitfalls:Confusing effective length with clear length, and mixing units; here all dimensions are in centimetres.

Final Answer:173.2