Columns under compressive loading: What do we call a column that primarily fails by direct compressive stress (crushing) rather than by elastic buckling?

Introduction / Context:
Columns may fail either by direct compressive crushing or by elastic instability (buckling). Correctly identifying the governing failure mode is essential for sizing members and choosing the right formula (crushing stress versus Euler or Rankine theory).

Given Data / Assumptions:

• Prismatic column under axial compression.
• Low slenderness ratio (small effective length to radius of gyration).
• Material behaves elastically up to crushing strength.

Concept / Approach:
Failure mode depends primarily on slenderness ratio. Short, stocky members (small slenderness) develop high compressive stresses before they can deflect laterally; thus they fail by direct compression (crushing). Long, slender members fail by buckling at stresses well below crushing strength. Intermediate columns require combined formulas (e.g., Rankine–Gordon).

Step-by-Step Solution:

Verification / Alternative check:
Compare Euler load P_cr ∝ 1 / (Le^2) with material crushing load P_c = A * sigma_c. For small Le, P_cr ≫ P_c, so crushing occurs first, confirming the classification as a short column.

Why Other Options Are Wrong:

• Long column: dominated by buckling, not direct crushing.
• Medium column: mixed behavior; not necessarily direct-stress failure.
• Weak column: vague term; weakness is not the defining criterion.

Common Pitfalls:
Using Euler's formula for stocky members; ignoring end conditions that change effective length; forgetting to check material crushing stress first for low slenderness ratios.

Final Answer:
short column