Skip to content

    Under active development. New calculators and features ship every week. Everything currently runs free while the site matures — pricing pages are a preview, checkout is not open yet.

    Search ⌘K
    Calculates locally in your browser · EN 1993-1-1
    Steel / Eurocode 3

    Eurocode 3 steel check

    Cross-section resistance, shear, flexural buckling and bending to EN 1993-1-1, with the buckling curve, the relative slenderness and the reduction factor exposed. The catalog’s first non-US steel code.

    SteelS355Lcr4.00 mχ0.87
    Governing check
    Flexural buckling
    32% utilised
    Buckling resistance
    1551 kN
    χ 0.874
    Slenderness λ̄
    0.523
    curve b
    Verdict
    Pass
    γM0 = γM1 = 1.0
    EN 1993-1-1 checks
    Each resistance against its demand; the largest utilisation governs.
    EN 1993-1-1 checks
    CheckResistanceDemandUtilisation
    Cross-section, axial1775 kN500.028%
    Flexural buckling ◂1551 kN500.032%
    Bending195.3 kN·m50.026%
    Shear512.4 kN·m100.020%

    Nb,Rd = χ·A·fy/γM1 with χ = 0.874 on curve b.

    Inspect the model
    Choose a quick result view, a scaled comparison, or the complete diagnostic set.
    Buckling curves
    χ falls faster on curve d than on curve a — the imperfection matters.
    Buckling curves0.0000.2240.4480.6720.8961.120.20.20.40.40.60.60.80.81.01.01.21.21.51.52.02.0Curve aCurve bCurve cCurve d
    Canonical equations
    The exact relationships implemented by this engine.

    Nb,Rd = χ·A·fy/γM1 · §6.3.1.1.

    χ = 1/(Φ + √(Φ² − λ̄²)), Φ = 0.5[1 + α(λ̄ − 0.2) + λ̄²] · α from Table 6.1.

    λ̄ = √(A·fy/Ncr), Ncr = π²EI/Lcr² · The elastic critical force.

    engineering methodology

    A clear path from inputs to results.

    The catalog was US-only. This is the first non-US steel code: EN 1993-1-1 cross-section resistance, shear, flexural buckling and bending, with the buckling curve and the reduction factor shown so the check can be followed.

    Step-by-step methodWorked exampleAssumptions explained

    How to use

    1. Enter the section properties and the steel grade.
    2. Set the buckling length and pick the buckling curve for the axis.
    3. Read which check governs and by how much.

    The formula

    Nb,Rd=χAfyγM1,χ=1Φ+Φ2−λˉ2N_{b,Rd} = \frac{\chi A f_y}{\gamma_{M1}}, \qquad \chi = \frac{1}{\Phi + \sqrt{\Phi^2 - \bar\lambda^2}}

    Reference: EN 1993-1-1 §6.2 and §6.3.1, γM0 = γM1 = 1.0.

    Worked example

    5,000 mm² section, 4 m buckling length, S355

    Inputs
    • I 50 × 10⁶ mm⁴, curve b, 500 kN axial.
    Calculation path
    1. 1

      Ncr = π²EI/L² = 6,476 kN. λ̄ = √(Afy/Ncr) = 0.524. Φ = 0.692, χ = 0.874. Nb,Rd = 1,551 kN.

    Result

    χ 0.874; buckling at 32% utilisation.

    Interpreting the result

    The buckling curve encodes the imperfection and residual stress of the shape. Curve d is for thick welded sections and loses 40% more capacity than curve a at the same slenderness.

    Assumptions & limitations

    • γM0 = γM1 = 1.0, the recommended values.
    • Flexural buckling only; no lateral-torsional reduction.
    • Cross-section class not checked.
    • Axial and bending compared term by term.

    Frequently asked questions

    Which curve do I use?

    Table 6.2 of EN 1993-1-1 maps the section type and axis to a curve; hot-rolled I-sections are usually curve a or b about the strong axis.

    Why does χ flatten out?

    At high slenderness the member behaves like a cable in compression and the curve asymptotes.

    What is λ̄?

    The relative slenderness: the yield force over the elastic critical force, square-rooted.

    Can I use this for stainless?

    No — EN 1993-1-4 has different curves and a non-linear material model.

    Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.