For compression members (columns) in steel structures, which cross-sectional form is generally the most economical due to a high radius of gyration per unit area?

Introduction / Context:
The economy of a steel column is strongly influenced by its radius of gyration and the distribution of material away from the centroid. Sections that place more area at larger radii reduce slenderness effects and increase buckling resistance for a given mass, making them economical for compression.

Given Data / Assumptions:

• Comparing typical rolled or fabricated sections for axial compression.
• Economy judged by strength and stiffness per unit weight.

Concept / Approach:
For a given cross-sectional area, moving material away from the centroid increases the second moment of area and radius of gyration r = sqrt(I/A). Hollow sections (tubular sections) are highly efficient because metal is concentrated in the shell, far from the neutral axis, giving higher buckling resistance per unit weight than solid forms like flats or solids.

Step-by-Step Solution:
Recognize that buckling load ∝ A * (r^2) for ideal columns. Compare geometry: tubular section maximizes r for a given A. Select tubular (hollow) section as the most economical form.

Verification / Alternative check:
Design tables show higher r for hollow circular and rectangular tubes when normalized by area. This translates to reduced slenderness λ = L/r and higher allowable compressive stress for the same mass.

Why Other Options Are Wrong:

• Solid rectangles/rounds/hexagonals and flat strips place more material near the centroid, yielding lower r for the same A.

Common Pitfalls:

• Ignoring local buckling limits of thin-walled tubes; proper thickness selection is still essential.

Final Answer:
Tubular (hollow) section.