About Column Buckling

Column buckling is a mode of failure that occurs in slender structural elements under compressive stress. When the applied load reaches a critical value, a perfectly straight column under compression becomes unstable and exhibits a sudden sideways deflection (buckling).

Euler’s Buckling Formula

Where:
Pcr = Critical buckling load
E = Modulus of elasticity
I = Moment of inertia of the cross-section
K = Effective length factor (depends on end conditions)
L = Length of the column

Johnson Formula

Where:
A = Cross-sectional area
σy = Yield strength of the material
r = Radius of gyration (r = √(I/A))

Slenderness Ratio

The slenderness ratio determines whether Euler’s formula or Johnson’s formula should be used. For high slenderness ratios (typically λ > 100), Euler’s formula is more appropriate. For lower slenderness ratios, Johnson’s formula provides better results.