Buckling of compression members – Direction of buckling tendency\nCompression members (columns/struts) tend to buckle preferentially in which direction?

Introduction / Context:
Column stability depends on flexural stiffness EI about potential buckling axes. The effective slenderness ratio determines the critical Euler load; weaker bending axes buckle first.

Given Data / Assumptions:

• Prismatic, initially straight column under axial compression.
• Elastic buckling (Euler regime) with appropriate end conditions.

Concept / Approach:
The radius of gyration r = sqrt(I/A). For a given axial load and member, the slenderness ratio λ = L_e / r governs buckling. Smaller r means larger λ and lower critical load, so buckling occurs about the axis with least r (and least I).

Step-by-Step Explanation:
Compute r_x and r_y for principal axes.Compare slenderness ratios λ_x and λ_y; the larger one indicates the weaker direction.Expect buckling about the axis with least r (i.e., least flexural stiffness).

Verification / Alternative check:
Euler load P_cr = π^2 * E * I / (L_e^2). For the axis with smaller I, P_cr is smaller; initial imperfections trigger buckling there first.

Why Other Options Are Wrong:
Buckling is not along the load axis (axial shortening). “Any direction” ignores anisotropy of section stiffness. Minimum area alone is not decisive unless it correlates with least I and least r. Greatest I would be the strongest direction, not the weakest.

Common Pitfalls:
Ignoring end-restraint effects on L_e; overlooking weak-axis bracing requirements in design.

Final Answer:
In the direction of least radius of gyration