Euler
Buckling calculation
Euler buckling of a slender column: F_cr, critical stress and slenderness λ.
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Questions
What is F_cr?+
The critical Euler load: F_cr = π² E I / L_eff². Above this load the strut buckles elastically, regardless of material strength.
What is L_eff?+
The buckling length L_eff = k · L. k follows from the end condition: pinned-pinned k=1, fixed-free k=2, fixed-fixed k=0.5, fixed-pinned k≈0.699.
Why a warning at low λ?+
Euler applies to slender struts. At low slenderness (rule of thumb λ < 100) the formula overestimates real strength; use Tetmajer or the Johnson parabola instead.
Does this replace EN 1993-1-1?+
No. This is ideal Euler theory: no initial curvature, no partial safety factors. For critical structures, use the standard or an FEM check.