Slenderness of an RCC column — a 32 cm diameter circular column has effective length 4.40 m. Compute its slenderness ratio using l_eff / r.

Introduction / Context:
Slenderness ratio indicates a column’s susceptibility to buckling and influences design checks in reinforced concrete. For circular sections, the radius of gyration r simplifies neatly, so this is a quick substitution problem that reinforces the definition of slenderness for columns.

Given Data / Assumptions:

• Circular RCC column diameter d = 32 cm.
• Effective length l_eff = 4.40 m = 440 cm.
• Slenderness ratio (Euler form) = l_eff / r, where r is radius of gyration about the critical axis.

Concept / Approach:

For a circular section: I = (π d^4) / 64 and A = (π d^2) / 4. Hence r = sqrt(I/A) = sqrt(d^2 / 16) = d / 4. Substitute to obtain the column’s slenderness ratio without lengthy calculations.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

An alternative is to compute I and A first, then r = sqrt(I/A); both approaches give r = 8 cm and slenderness = 55.

Why Other Options Are Wrong:

Values 40, 45, 50, and 60 arise from arithmetic mistakes, unit confusion, or using least dimension instead of radius of gyration in the definition.

Common Pitfalls (misconceptions, mistakes):

Mixing up definitions: some design checks use l_eff / least lateral dimension; the slenderness ratio here is clearly defined with r, so use l_eff / r.

Final Answer:

55