Free Tool · EN 1993-1-1 §6.3.1

Column Buckling Calculator

Calculate the flexural buckling resistance Nb,Rd per EN 1993-1-1 §6.3.1. Computes λ̄ for both y-y and z-z axes, auto-selects governing axis, picks buckling curve from Table 6.2, and returns χ and Nb,Rd. HEA, HEB, HEM, IPE, UC, UB. S235–S460.

N Ed L cr buckling mode
Column Parameters
Use Lcr = K·L. K=1.0 pin-pin, 0.5 fixed-fixed, 0.7 fixed-pin
EN: γM1 = 1.0 (recommended value, used by NL, DE, BE)
Enter to compute utilisation η = NEd / Nb,Rd
Buckling Results
1812.4
Nb,Rd (kN) — z-z governs
Governing axis z-z
λ̄0.895
φ1.019
χ0.664
Buckling curve B (α = 0.34)
Ncr3406.4 kN
Npl,Rd2727.8 kN
Nb,Rd1812.4 kN
y-y: χ = 0.923 2518.3 kN
z-z: χ = 0.664 1812.4 kN
1. Section: HEA 240 | S355 (fy = 355 N/mm²)
A = 7,684 mm² | iy = 104 mm | iz = 58.5 mm
Curves: y-y = A, z-z = B (EN 1993-1-1 Table 6.2)

2. λ1 = 93.9 · ε, where ε = √(235/fy)
ε = √(235/355) = 0.814 | λ1 = 76.4

3. Non-dimensional slenderness λ̄ (§6.3.1.2 Eq 6.50)
Governing axis: z-z | i = 58.5 mm | Lcr = 4 m
λ̄ = (Lcr/i) / λ1 = (4000/58.5) / 76.4 = 0.895

4. Reduction factor χ (§6.3.1.2 Eq 6.49)
Curve B → α = 0.34
φ = 0.5 × [1 + α(λ̄ − 0.2) + λ̄²] = 0.5 × [1 + 0.34 × (0.895 − 0.2) + 0.895²] = 1.019
χ = 1 / (φ + √(φ² − λ̄²)) = 0.664

5. Nb,Rd (§6.3.1.1 Eq 6.47)
Nb,Rd = χ · A · fy / γM1 = 0.664 × 7,684 × 355 / 1 = 1812.4 kN
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Related tools
Lateral-torsional buckling (§6.3.2) Column base plate (§6.2.8) Section classification (Table 5.2) Beam moment capacity (§6.2.5)

FAQ

What is the non-dimensional slenderness λ̄ in EN 1993-1-1?
λ̄ = √(A·fy / Ncr) where Ncr = π²EI / Lcr² is the elastic critical force. For Class 1–3 sections it simplifies to λ̄ = (Lcr/i) / λ₁ where λ₁ = 93.9·ε and ε = √(235/fy). A column with λ̄ ≤ 0.2 is not susceptible to flexural buckling.
How are the buckling curves a₀, a, b, c, d selected?
EN 1993-1-1 Table 6.2 assigns buckling curves based on section type, flange thickness, and buckling axis. For HEA/HEB with tf ≤ 40mm: curve a (y-y) and b (z-z). IPE sections use a (y-y) and b (z-z). Heavier sections with tf > 40mm move to curves b/c or c/d. The z-z axis always uses a less favourable curve due to the lower radius of gyration.
What imperfection factors α apply to each curve?
Per Table 6.1: a₀ = 0.13, a = 0.21, b = 0.34, c = 0.49, d = 0.76. The higher α is, the more the capacity is reduced at intermediate slenderness (λ̄ ≈ 0.5–1.5). Curve d (α = 0.76) is typically for laced built-up or heavily welded members.
What buckling length Lcr should I use for a column in a frame?
For a pin-pin column Lcr = L. For a fixed-pin column (flag pole) Lcr = 2L. For a fixed-fixed column Lcr = 0.5L. In practice most column bases are nominally pinned so Lcr ≈ L for non-sway frames and Lcr = 2L for sway frames. Use NA/EN 1993-1-1 §5.2 for full frame stability analysis.
Is γM1 = 1.0 for all national annexes?
Yes — the Dutch (NEN), German (DIN), and Belgian national annexes all set γM1 = 1.0, the same as the base EN 1993-1-1 recommended value. The UK NA (BS EN) was also 1.0. Some older pre-NA designs used 1.1 for structures not following EN 1993.