Column buckling direction: compression members tend to buckle about which principal axis or property direction, all else being equal?

Introduction / Context:
Elastic buckling of columns is a stability phenomenon. The critical buckling load depends on flexural stiffness EI about a given axis and the effective length. Designers must anticipate the likely buckling mode to size members and arrange bracing correctly.

Given Data / Assumptions:

• Slender compression members governed by Euler buckling.
• Uniform material and boundary conditions for the two principal axes.
• Small initial imperfections and eccentricities are present as in practice.

Concept / Approach:
Euler load Pcr = π^2 * E * I / (K * L)^2. For a given cross-section, I = A * r^2, where r is the radius of gyration about the axis. The axis with smaller r (weaker bending stiffness) gives a lower I and thus a smaller Pcr, so the member will preferentially buckle about that weak axis.

Step-by-Step Solution:
Relate I to r: I = A * r^2.Substitute into Pcr: smaller r → smaller I → smaller Pcr.Therefore, buckling initiates about the axis of least radius of gyration.

Verification / Alternative check:
Practical observation of angle, channel, and I-sections confirms weak-axis buckling unless braced. Design manuals specify different slenderness ratios (KL/r) for the two axes accordingly.

Why Other Options Are Wrong:
(b) and (c) ignore section properties; (d) is incorrect—buckling prefers the weakest stiffness path; (e) is opposite of reality.

Common Pitfalls:
Neglecting different end conditions (K), residual stresses, or initial crookedness; assuming symmetry when sections are monosymmetric.

Final Answer:
The axis with the least radius of gyration (weak axis)