🏛️ Euler Buckling

The critical buckling load of a slender column for the four classic support conditions, with slenderness and critical stress.

Column

Length L [m] E [GPa] I (weaker axis) [cm⁴] A [cm²] optional, for slenderness

The default values are an HEA 200 steel column about its weak axis (I = 1336 cm⁴, A = 53.8 cm²). Use I about the weaker axis from your profile table, or get it from Section Properties.

Results

Formula

N_cr = π² · E · I / (K · L)², where K·L is the effective (buckling) length. The column buckles about its weaker axis, so use the smaller I. Slenderness λ = K·L / i with i = √(I/A), and the critical stress σ_cr = N_cr / A.

Euler's formula is valid only for slender, perfectly straight, elastic columns. Real columns have imperfections and yield before that; codes such as Eurocode 3 use buckling curves (the reduction factor χ) that give a much lower design resistance, especially for medium slenderness. Use this tool to understand the influence of length and supports, not for design.

For learning and quick checks only. Real structures must be designed by a licensed engineer according to the valid standards.