European Beam Capacity Calculator — EN 1993-1-1

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Design per EN 1993-1-1 Clause 6.2

Calculate the bending and shear resistance of European hot-rolled steel sections per Eurocode 3. The calculator supports IPE, HEA, HEB, and HEM sections with S235, S275, S355, and S460 steel grades.

Supported Sections and Grades

• IPE sections — IPE 80 to IPE 750, the standard European I-section for beams
• HEA sections — HEA 100 to HEA 1000, wide flange with light flange thickness
• HEB sections — HEB 100 to HEB 1000, wide flange with medium flange thickness
• HEM sections — HEM 100 to HEM 1000, wide flange with heavy flange thickness
• Steel grades — S235 (EN 10025-2), S275, S355 (most common), S460

Design Checks Performed

• Section classification — Class 1, 2, 3, or 4 per EN 1993-1-1 Table 5.2
• Bending moment resistance — Mc,Rd = Wpl × fy / γM0 for Class 1-2 sections
• Lateral-torsional buckling — Mb,Rd = χLT × Wy × fy / γM1 per Clause 6.3.2
• Shear resistance — Vc,Rd = Av × (fy/√3) / γM0 per Clause 6.2.6
• Shear buckling — Checked when hw/tw > 72ε/η per Clause 6.2.6(6)
• Deflection — Serviceability limits per EN 1990 Annex A1.4.3

Worked Example

Problem: Check an IPE 400 beam in S355 steel for a 6.0 m simply supported span with a factored UDL of 30 kN/m.

Solution:

• Section: IPE 400, S355 (fy = 355 MPa)
• Section class: Class 1 (compact)
• Plastic modulus Wpl,y = 1307 cm³
• Design moment: MEd = 30 × 6.0² / 8 = 135 kNm
• Moment resistance: Mc,Rd = 1307 × 10³ × 355 / 1.0 = 464 kNm
• Utilisation: 135/464 = 0.29 (29%) — OK
• Design shear: VEd = 30 × 6.0 / 2 = 90 kN
• Shear resistance: Vc,Rd = 4268 × (355/√3) / 1.0 = 874 kN
• Utilisation: 90/874 = 0.10 (10%) — OK

Result: IPE 400 in S355 is adequate. Moment governs at 29% utilisation.

Second Worked Example — Laterally Unrestrained HEA Beam

Problem: Check an HEA 280 beam in S275 steel for an 8.0 m simply supported span with a factored UDL of 15 kN/m. Assume no intermediate lateral restraint. Load applied to top flange.

Solution:

1. Section properties: HEA 280, S275 (fy = 275 MPa, tf = 13 mm) Wpl,y = 1110 cm³, Iy = 13700 cm⁴, Iz = 4760 cm⁴ It = 62 cm⁴ (torsion constant), Iw = 785000 cm⁶ (warping constant)
2. Class check: Class 1 for both flange and web
3. Design moment: MEd = 15 × 8.0²/8 = 120 kNm
4. Cross-section resistance: Mc,Rd = 1110 × 10³ × 275 / 1.0 = 305 kNm
5. Elastic critical moment Mcr (LTB, Clause 6.3.2.2): For simply-supported beam with UDL on top flange, C1 = 1.13, kz = kw = 1.0 Mcr = C1 × (π² × E × Iz / L²) × ÃƒÂ¢Ã‚ÂˆÃ‚Âš[Iw/Iz + (L² × G × It)/(π² × E × Iz)] Mcr = 1.13 × (π² × 210000 × 4760 × 10⁴ / 8000²) × ÃƒÂ¢Ã‚ÂˆÃ‚Âš[785000/4760 + (8000² × 81000 × 62 × 10⁴)/(π² × 210000 × 4760 × 10⁴)] × 10⁻⁶ Mcr = 218 kNm
6. Non-dimensional slenderness: λ̄LT = √(Wy × fy / Mcr) = √(1110 × 10³ × 275 / 218 × 10⁶) = √(1.40) = 1.18
7. Reduction factor χLT (Clause 6.3.2.3, curve 'b' for HEA with h/b ≤ 2): αLT = 0.34, λ̄LT,0 = 0.4 ΦLT = 0.5 × [1 + 0.34 × (1.18 - 0.4) + 1.18²] = 0.5 × [1 + 0.265 + 1.392] = 1.329 χLT = 1 / (1.329 + √(1.329² - 1.18²)) = 1 / (1.329 + √(1.766 - 1.392)) = 1 / (1.329 + 0.612) = 0.515
8. LTB resistance: Mb,Rd = 0.515 × 1110 × 10³ × 275 / 1.0 = 157.3 kNm
9. Check: 120 ≤ 157.3 → OK (usage: 76%)

Result: HEA 280 in S275 is adequate for the 8.0 m span. LTB governs at 76% utilisation — significantly higher than the fully restrained case. For longer spans or heavier loads, consider a deeper section (HEA 300+) or provide intermediate lateral restraint.

EN 1993-1-1 Clause Reference

Serviceability and Deflection — Eurocode Approach

EN 1990 Annex A1.4.3 defines characteristic load combinations for serviceability:

• Characteristic combination (irreversible limit states): Gk + Qk,1 + Σ ψ0,i Qk,i
• Frequent combination (reversible): Gk + ψ1,1 Qk,1 + Σ ψ2,i Qk,i
• Quasi-permanent combination (long-term): Gk + Σ ψ2,i Qk,i

Typical deflection limits per EN 1993-1-1:

• Floors with brittle finishes: δmax ≤ L/250 for characteristic combination
• Roofs: δmax ≤ L/200 for characteristic combination
• Camber: Pre-camber ≤ L/300 to offset dead load deflection

For the IPE 400 example under service loads (unfactored UDL = 21.4 kN/m): Δ = 5 × 21.4 × 6000⁴ / (384 × 210000 × 231 × 10⁶) = 10.5 mm < 6000/250 = 24 mm → OK.

Related Resources

• European Beam Design Guide
• European Steel Grades
• European Column Buckling Guide
• Section Properties Calculator

FAQ

What steel grades does the calculator support? S235, S275, S355, and S460 per EN 10025-2. S355 is the default and most commonly used grade for structural steel in Europe.

Does it check lateral-torsional buckling? Yes. The calculator determines the reduction factor χLT based on the non-dimensional slenderness λLT and the appropriate buckling curve per EN 1993-1-1 Clause 6.3.2.

What is the difference between EN 1993-1-1 and EN 1993-1-5 for beams? Clause 6.2 of EN 1993-1-1 covers the basic cross-section resistance. EN 1993-1-5 covers plate buckling for slender webs (Class 4 sections) — the calculator flags when this is required.

Can I use UK National Annex values? The calculator uses the recommended values from EN 1993-1-1 (γM0 = 1.0, γM1 = 1.0). For UK NA modifications, refer to the UK-specific guidance page.

How are the buckling curves selected for LTB? Per EN 1993-1-1 Table 6.4, the LTB buckling curve depends on the cross-section type and h/b ratio. For rolled I-sections with h/b ≤ 2: curve 'b' (αLT = 0.34). For h/b > 2: curve 'c' (αLT = 0.49). For welded sections, curve 'd' (αLT = 0.76) may apply. More severe curves produce lower χLT values.

How does the bending and shear interaction work? Per EN 1993-1-1 Clause 6.2.8, when VEd exceeds 50% of Vpl,Rd, the moment resistance is reduced to My,V,Rd using a reduced yield strength for the shear area: (1 - ρ) × fy where ρ = (2VEd/Vpl,Rd - 1)². For hot-rolled I-sections with equal flanges bending about the major axis, the simplified formula My,V,Rd = (Wpl,y - ρ × Aw²/4tw) × fy / γM0 may be used.

What about plate girders and Class 4 sections? For slender webs (hw/tw > 72ε/η), the calculator flags that EN 1993-1-5 (plated structural elements) considerations apply. Class 4 sections use effective widths beff from EN 1993-1-5 Clause 4.4, with the reduction factor ρ based on plate slenderness λ̄p. Effective section properties (Weff, Aeff) replace gross properties for all resistance checks.

Which partial factors apply to beam design? Per EN 1993-1-1 Clause 6.1: γM0 = 1.00 for cross-section resistance (all classes), γM1 = 1.00 for member buckling resistance, and γM2 = 1.25 for fracture resistance at bolt holes (tension). The same factors apply across Eurocode-participating countries unless modified by the National Annex.

Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.