For a column with a non-symmetrical cross-section subjected to axial compression, the slenderness ratio governing buckling is based on
- AThe larger radius of gyration and the actual length of the column
- BThe smaller radius of gyration and the effective length corresponding to end conditionsCorrect
- CThe average radius of gyration and the unsupported length
- DThe least lateral dimension and the actual length of the column
Solution
Concept
Governing radius of gyration in column buckling
Formula
λmax = K·L / rmin
Step-by-step solution
1. Elastic critical buckling load of a column follows Euler's formula Pcr = π2 × E × I / (KL)2. 2. Since I = A × r2, buckling load is minimized along the axis having the smallest moment of inertia and smallest radius of gyration rmin. 3. Therefore, maximum slenderness ratio λmax = KL / rmin governs buckling. 4. Hence, buckling is governed by the smaller radius of gyration and the effective length corresponding to end conditions. Answer: B
Explanation
Column buckling is a stability failure that inherently occurs about the axis of weakest flexural rigidity. Consequently, the governing slenderness ratio is always computed using the minimum (smaller) radius of gyration and the corresponding effective length.
Why the other options are wrong
A) The larger radius of gyration gives the stiffest axis, which will not buckle first. C) Average radius of gyration has no physical stability significance. D) Least lateral dimension does not account for mass distribution in asymmetric rolled steel shapes.
Shortcut
Buckling always governs about the weakest axis: use rmin and effective length.
Common mistake
Selecting the larger radius of gyration, which yields the minimum slenderness ratio and dangerously overestimates column capacity.
Correct answer: B) The smaller radius of gyration and the effective length corresponding to end conditions