Eurocode 3 Steel Beam Design Calculator (Bending & Shear)

Check bending, shear and lateral torsional buckling resistance of steel I- and H-beams according to EN 1993‑1‑1 (Eurocode 3).

For educational and preliminary design only. Always verify results against the full Eurocode and your National Annex.

1. Input Data

Steel & Safety Factors

Section Properties (about major axis)

Enter properties for an I- or H-section. Units: mm, mm², mm³, mm⁴.

Geometry & LTB

Design Actions (ULS)

Enter design values (already factored) for the critical section.

2. Results (Design Resistances & Utilisation)

Bending resistance –

MRd = – kNm
Utilisation ηM = –

Shear resistance –

VRd = – kN
Utilisation ηV = –

Interaction & LTB –

ηint = –
χLT = –

Eurocode 3 steel beam design – what this calculator does

This tool implements the core ultimate limit state (ULS) checks for a steel beam according to EN 1993‑1‑1 (Eurocode 3). It focuses on major-axis bending of I- and H-sections under uniform or point loading, including:

  • Section classification (user input: Class 1–4).
  • Plastic or elastic bending resistance MRd (6.2.5).
  • Shear resistance VRd (6.2.6).
  • Shear–bending interaction (6.2.8) via a simplified expression.
  • Lateral torsional buckling (LTB) reduction factor χLT based on an approximate Mcr.

Key formulas used (simplified)

Design yield strength
fy,d = fy / γM0
Bending resistance (major axis)
For Class 1–2 (plastic):
Mpl,Rd = Wpl,y · fy / γM0

For Class 3 (elastic):
Mel,Rd = Wel,y · fy / γM0

Lateral torsional buckling reduction:
Mb,Rd = χLT · MRk / γM1
Shear resistance
Vpl,Rd = (Av · fy) / (√3 · γM0)
For rolled I/H sections we approximate Av ≈ A.
Shear–bending interaction (simplified)
If VEd < 0.5 · Vpl,Rd → no reduction.
If VEd ≥ 0.5 · Vpl,Rd:
MRd,red = MRd · (1 − ρ), with ρ ≈ 2 · (VEd/Vpl,Rd − 0.5).
Lateral torsional buckling (LTB)
Non-dimensional slenderness:
λLT = √(Wpl,y · fy / Mcr)

Reduction factor (buckling curve with imperfection factor α):
φ = 0.5 · [1 + α (λLT − 0.2) + λLT2]
χLT = min(1, 1 / [φ + √(φ² − λLT2)])

The elastic critical moment Mcr is estimated using a simplified expression that depends on the unbraced length, end restraint factor C1, and the torsional and warping constants (IT, Iw). For preliminary design this is usually sufficient, but for critical members you should verify Mcr with specialist software or hand calculations.

How to use the Eurocode 3 beam design calculator

  1. Choose the steel grade and partial factors γM0, γM1 according to your National Annex.
  2. Enter the section properties from your steel tables (A, Wpl,y, Wel,y, Iy, IT, Iw).
  3. Specify span, unbraced length and end restraint to capture lateral torsional buckling.
  4. Input the design bending moment MEd and shear force VEd at the critical section.
  5. Click “Run Eurocode 3 Checks” and review the utilisation ratios and pass/fail badges.

Limitations and assumptions

  • Only major-axis bending of doubly symmetric I/H sections is considered.
  • Class 4 sections are not fully supported (effective section properties are not calculated).
  • LTB is handled with a single-span approximation; continuous beams and complex loading are not explicitly covered.
  • Serviceability limit states (deflection, vibration) are not checked.
  • National Annex-specific parameters (e.g. k-factors, ψ-factors) are not explicitly implemented.

Always consult EN 1993‑1‑1, EN 1993‑1‑5 and your National Annex, and have designs checked by a qualified structural engineer before construction.

FAQ

Can I use tabulated section properties from manufacturers?

Yes. Most steel producers publish A, Iy, Wpl,y, Wel,y, IT and Iw for their standard sections. Simply copy those values into the calculator using the same units (mm, mm², mm³, mm⁴, mm⁶).

What utilisation ratio should I aim for?

For preliminary design, many engineers aim for a maximum utilisation between 0.7 and 0.9 to allow for detailing changes, secondary effects and rounding. A utilisation above 1.0 indicates that the member does not meet the Eurocode 3 requirement for that limit state.