Compression Members MCQ with answer and solution

Concept

Column load capacity depends on material strength for short columns and on flexural rigidity (EI) and slenderness ratio for long columns.

Formula

P_cr = π²EI / Lₑ²; λ = Lₑ / r

Step-by-step solution

1. The material, area and length are given. 2. A short column fails by crushing, so strength of material governs. 3. A long column fails by buckling, so the Euler load P_cr = π²EI / Lₑ²governs. 4. P_cr depends on flexural rigidity EI and effective length. 5. Slenderness ratio λ = Lₑ/ r combines length, area and moment of inertia. 6. So the capacity is governed by both flexural rigidity and slenderness ratio.

Explanation

For a given material, area and length, the load capacity depends on how easily the column buckles. Buckling depends on flexural rigidity (EI) and on slenderness ratio (Lₑ/r). So both together govern the capacity.

Shortcut

Column capacity: short means strength, long means buckling (EI and slenderness).

Common mistake

Thinking only material strength decides the column load.