Column classification by slenderness ratio\n\nColumns with slenderness ratio (effective length/radius of gyration) less than about 80 are commonly classified as:

Introduction / Context:
Column behavior shifts from crushing/yielding to elastic buckling as slenderness increases. Designers classify columns to choose appropriate strength models (yield-based vs. buckling-based).

Given Data / Assumptions:

• Slenderness ratio λ = L_e / r, where L_e is effective length and r is radius of gyration.
• Reference threshold around λ ≈ 80 (varies with code and material).
• Axial compression predominant.

Concept / Approach:
Short columns (low slenderness) fail by material yielding or crushing rather than elastic buckling. As λ increases, columns transition to inelastic and then elastic buckling regimes, termed medium or long columns in various texts.

Step-by-Step Solution:
If λ <≈ 80 → short: strength governed by compressive yield stress with small buckling influence.Intermediate λ → combined effects; empirical curves used.High λ → long columns governed by Euler buckling.

Verification / Alternative check:
Compare Euler critical stress σ_cr = π^2 E / (λ^2) with yield stress; the crossover near λ ≈ 80 (for steels) indicates when buckling becomes dominant.

Why Other Options Are Wrong:
“Long” corresponds to high slenderness; “weak” is not a standard classification term; “medium” refers to the inelastic region; “inelastic columns” describes behavior, not the stated threshold.

Common Pitfalls:
Using a single universal threshold without checking the material and code; ignoring end conditions in L_e; misusing λ based on total length instead of effective length.

Final Answer:
short columns