A short reinforced concrete column has a rectangular cross-section 15 cm × 20 cm. What is the maximum recommended unsupported length to prevent excessive slenderness effects?

Introduction / Context:Column slenderness influences stability and second-order effects. To classify and design a member as a short column, codes restrict the maximum unsupported length with respect to the least lateral dimension, reducing the risk of buckling and magnified deflections under axial load and bending.

Given Data / Assumptions:

• Rectangular section: 15 cm × 20 cm.
• Least lateral dimension = 15 cm.
• Rule: limit unsupported length to a multiple of the least dimension for short-column behavior.

Concept / Approach:

A common limit for reinforced concrete is: maximum unsupported length ≤ 60 × least lateral dimension. This cap, along with end restraints and slenderness checks, ensures the member remains within short-column design assumptions.

Step-by-Step Solution:

Verification / Alternative check:

Even with L ≤ 9.0 m, column design must still verify slenderness ratios about both axes; the limit primarily prevents obviously slender behavior.

Why Other Options Are Wrong:

• 10.0 m, 11.0 m, 12.0 m: Exceed the 60× limit for a 15 cm least dimension.
• 7.5 m: More conservative than necessary per the cited rule; not the asked upper bound.

Common Pitfalls:

• Using the greater lateral dimension (20 cm) instead of the least (15 cm) when applying the limit.
• Ignoring end-restraint conditions which alter effective length for slenderness calculations.

Final Answer:

9.0 m