EN 1993-1-3 Cold-Formed Steel — Cold-Formed Design per Eurocode 3
Complete guide to cold-formed steel member design per EN 1993-1-3:2006. Effective width method, distortional buckling, local buckling interaction, lipped channel sections, Z-sections, and sheeting. Worked example with lipped channel purlin in S350GD.
Quick access: HSS Section Properties → | Compact Section Limits → | All European References →
Design Framework — EN 1993-1-3
EN 1993-1-3 supplements EN 1993-1-1 for cold-formed members and sheeting. Key differences from hot-rolled design:
| Aspect | Hot-Rolled (EN 1993-1-1) | Cold-Formed (EN 1993-1-3) |
|---|---|---|
| Section class | Usually 1 or 2 | Often Class 4 (slender) |
| Local buckling | Cross-section classification | Effective width method |
| Distortional buckling | Not considered | Must be checked (Clause 5.5) |
| Shear lag | Not critical for standard rolled | Consider for wide flanges |
| Material | EN 10025 | EN 10149, EN 10346 |
| Thickness range | Usually > 3 mm | 0.45-8 mm typical |
Steel Grades for Cold-Formed Sections
| Grade | f_yb (MPa) | f_u (MPa) | Typical Application |
|---|---|---|---|
| S220GD | 220 | 300 | Light purlins, cladding |
| S250GD | 250 | 330 | Standard purlins |
| S280GD | 280 | 360 | Intermediate strength |
| S320GD | 320 | 390 | Main members |
| S350GD | 350 | 420 | Heavy purlins, structural |
| S550GD | 550 | 560 | High-strength applications |
Effective Width Method — Clause 4.4
For Class 4 cold-formed sections, the effective cross-section is calculated per EN 1993-1-5.
Flat Compression Elements (Internal)
b_eff = ρ × b
Where ρ is the reduction factor:
ρ = 1.0 for λ̄_p ≤ 0.748
ρ = (λ̄_p - 0.188) / λ̄_p² for λ̄_p > 0.748
Where λ̄p = (b/t) / (28.4 × ε × √(kσ))
Flat Compression Elements (Outstand)
ρ = 1.0 for λ̄_p ≤ 0.748
ρ = (λ̄_p - 0.188) / λ̄_p² for λ̄_p > 0.748
Where k_σ depends on edge restraint conditions.
Distortional Buckling — Clause 5.5
Distortional buckling is unique to cold-formed sections — the flange and lip assembly rotates relative to the web. The critical elastic distortional buckling stress σ_cr,d must be determined using:
- Numerical analysis (finite strip, e.g., CUFSM)
- Simplified methods per ANNEX E of EN 1993-1-3
- Manufacturer design tables
The relative slenderness for distortional buckling:
λ̄_d = √(f_yb / σ_cr,d)
Reduction factor: χ_d = 1.0 for λ̄_d ≤ 0.65
χ_d = 1.47 - 0.723 × λ̄_d for 0.65 < λ̄_d ≤ 1.38
χ_d = 0.66 / λ̄_d for λ̄_d > 1.38
Worked Example — Lipped Channel Purlin
| Parameter | Value |
|---|---|
| Section | Lipped channel 200×65×20×2.0 (C200-20) |
| Steel grade | S350GD (f_yb = 350 MPa) |
| Span | 6.0 m (simply supported) |
| Purlin spacing | 1.5 m |
| Load | 0.6 kN/m² dead + 0.75 kN/m² imposed |
Section Properties
| Property | Value |
|---|---|
| A_gross | 654 mm² |
| I_y | 374 × 10⁴ mm⁴ |
| I_z | 46 × 10⁴ mm⁴ |
| W_el,y | 37.4 × 10³ mm³ |
Effective Section (Web in Bending)
| Parameter | Value |
|---|---|
| Web depth h_w | 200 - 2×2 = 196 mm |
| t | 2.0 mm |
| h_w / t | 98 |
| ε = √(235/350) | 0.82 |
| k_σ (web in bending) | 23.9 (internal element) |
| λ̄_p | (98) / (28.4 × 0.82 × √23.9) = 0.87 |
| ρ | (0.87 - 0.188) / 0.87² = 0.90 |
| b_eff | 0.90 × 196 = 176 mm |
Bending Resistance
M_c,Rd = W_eff × f_yb / γ_M0
With the reduced web depth, W_eff ≈ 32.5 × 10³ mm³
M_c,Rd = 32.5×10³ × 350 / 1.00 = 11.4 kN·m
This is approximately 15% lower than the gross section capacity of 13.1 kN·m, reflecting the effective width reduction.
Fastening and Connections — Clause 8
| Fastener Type | EN Standard | Typical Spacing |
|---|---|---|
| Self-drilling screw | EN ISO 15480 | 300-600 mm |
| Self-tapping screw | EN ISO 15481 | 200-400 mm |
| Blind rivet | EN ISO 15977 | 300-500 mm |
| Powder-actuated fastener | — | 200-400 mm |
Minimum edge distance for screw connections: 3 × d (or 1.5 × d for the sheeting manufacturer's recommendation). End distance: 3 × d minimum.
Frequently Asked Questions
What is the difference between local buckling and distortional buckling in cold-formed steel?
Local buckling involves the buckling of individual plate elements (flange, web) with the intersection lines remaining straight. Distortional buckling involves rotation of the entire flange-lip assembly about the flange-web junction, causing cross-sectional distortion. Distortional buckling typically governs for lipped channels with intermediate spans (3-8 m) and is checked per EN 1993-1-3 Clause 5.5 using the critical buckling stress σ_cr,d.
What effective width method does EN 1993-1-3 use for cold-formed sections?
EN 1993-1-3 references EN 1993-1-5 for the effective width method. The plate slenderness λ̄p = (b/t) / (28.4ε√kσ) determines the reduction factor ρ. For λ̄_p ≤ 0.748, ρ = 1.0 (no reduction). For slender elements, ρ = (λ̄_p - 0.188) / λ̄_p². The effective widths are summed to form the effective cross-section for resistance calculations.
Related Pages
- HSS Section Properties — CHS, RHS, SHS tables
- Compact Section Limits — Class 1-4 per Table 5.2
- European Steel Properties — fy/fu mechanical properties
- All European References
Educational reference only. Design per EN 1993-1-3:2006 and EN 1993-1-5:2006. Effective width method per Clause 4.4. Distortional buckling per Clause 5.5. Verify section geometry against manufacturer datasheets. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent verification.
Design Resources
Calculator tools
Reference pages