Compression Members MCQ with answer and solution

Concept

A good column section has equal moment of inertia about both principal axes, so there is no weak axis for buckling.

Formula

P_cr = π² E I_min / L_e² ; r = √(I/A)

Step-by-step solution

1. A column buckles about the axis with the least moment of inertia (I_min). 2. Buckling load P_cr = π² E I_min / L_e². 3. If I_xx = I_yy, there is no weak axis, and the material is used fully in both directions. 4. So the best section has the same I about both perpendicular axes through its CG. 5. So the answer is (D).

Explanation

A compression member fails by buckling about its weakest axis. If the moment of inertia is the same about both axes, there is no weak axis and the section is used most efficiently. That is why tubes, pipes and box sections are ideal for columns.

Why the other options are wrong

(A) Greater length increases slenderness and lowers the buckling load. (B) Unevenly distributed material creates a weak axis. (C) Different I values mean the column buckles about the smaller I, so material is wasted.

Shortcut

Best column = I_xx = I_yy, with material spread far from the CG (for example a tube or box).

Common mistake

Thinking that a large I about one axis is enough; buckling is controlled by the minimum I.