Column Buckling (Euler – Johnson)
Stability of a strut under axial compression: Euler's formula for slender members, the Johnson parabola (including yield) for intermediate slenderness.
Critical buckling load P_cr64.9kN
- Allowable load P_cr / n
- 21.6 kN
- Critical stress σ_cr
- 92 MPa
- Slenderness λ = L_e / i
- 150
- Transition slenderness λ_c
- 133
- Formula used
- Euler (elastic)
- Effective length L_e = K·L
- 3 m
- λ = 150 — compression members usually keep λ ≤ 200
METHOD
How it is calculated
λ = K·L / i λ_c = π·√(2E / σ_y) λ ≥ λ_c: σ_cr = π²E / λ² (Euler) λ < λ_c: σ_cr = σ_y − (σ_y·λ / 2π)² / E (Johnson) P_cr = σ_cr · A
ASSUMPTIONS & NOTES
- Enter the weak-axis second moment as I_min.
- Defaults are for a Ø60.3 × 4 steel pipe.
- Steel structures are designed with the EN 1993-1-1 buckling curves (χ factor); this tool is for preliminary sizing.
Results are for preliminary design and checking; base the final design on the governing standard and safety factors.
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