----------------------- | :----------------------: | :-------------------------------------------------------- | | Section classification | Table 5.2 (Sheet 1 of 3) | ε = √(235/fy), flange c/tf, web c/tw | | Bending resistance Mc,Rd | Clause 6.2.5 | Wpl for Class 1-2, Wel for Class 3, Weff for Class 4 | | Shear resistance Vc,Rd | Clause 6.2.6 | Av shear area, fy/√3 | | Shear buckling | Clause 6.2.6(6) | hw/tw > 72ε/η requires check | | Bending + shear interaction | Clause 6.2.8 | Reduced My,V,Rd when VEd > 0.5Vpl,Rd | | LTB — General method | Clause 6.3.2.2 | χLT from curve a-d per Table 6.4, αLT imperfection factor | | LTB — Simplified method | Clause 6.3.2.3 | For restrained tension flange | | Deflection | EN 1990 Annex A1.4.3 | L/250 for floor with finishes, L/200 for roof |

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.