Short column criterion: When is a column classified as “short”? Choose the standard slenderness-based definition.

Introduction / Context:
Columns are classified as short or long based on their tendency to fail by crushing or by buckling. Slenderness ratio governs the dominant failure mode and the analysis method (material strength vs. stability).

Given Data / Assumptions:

• Slenderness ratio = L / k_min, where L is effective length and k_min is least radius of gyration.
• Typical steel design heuristics: short if L/k_min ≲ 80 (some codes use different thresholds).
• Elastic behaviour up to failure criterion.

Concept / Approach:
Low slenderness implies stocky columns with minimal buckling tendency; failure is governed by material crushing (compressive stress limit). High slenderness increases susceptibility to elastic instability (Euler buckling), requiring stability checks.

Step-by-Step Solution:

Verification / Alternative check:
Compare with Euler critical load formula P_cr = π^2 E I / L_e^2; small L/k increases P_cr sharply, making buckling less critical, consistent with “short column.”

Why Other Options Are Wrong:
Absolute length or area alone (a, b) do not decide buckling behaviour.“More than 80” (d) corresponds to a long/slender column.Load magnitude (e) is not a classification criterion.

Common Pitfalls:
Ignoring effective length (end restraints); using area instead of radius of gyration; applying the same slenderness limit to all materials without checking the relevant code.

Final Answer:

When the slenderness ratio (L / k_min) is less than about 80