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:

Steel Grades for Cold-Formed Sections

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

Section Properties

Effective Section (Web in Bending)

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

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.

Effective Width Method -- EN 1993-1-3 Clause 5.2

The heart of cold-formed design per EN 1993-1-3 is the effective width method, which accounts for local buckling of thin plate elements at stresses below yield. Key steps:

1. Determine stress distribution in each plate element (compression, bending, or combined)
2. Calculate buckling factor k_sigma based on stress ratio psi and support conditions (Table 5.3 for internal compression elements, Table 5.4 for outstands)
3. Compute plate slenderness lambda*p = sqrt(Fy / sigma_cr) where sigma_cr = k_sigma * pi^2 _ E _ t^2 / (12 _ (1 - nu^2) * b^2)
4. Determine reduction factor rho from EN 1993-1-5 Section 4.4:
   • Internal compression: rho = (lambda_p - 0.055*(3+psi)) / lambda_p^2 <= 1.0
   • Outstand compression: rho = (lambda_p - 0.188) / lambda_p^2 <= 1.0
5. Effective width beff = rho * b (for each element)
6. Effective section properties computed from the reduced (effective) cross-section
7. Shift of neutral axis eN accounted for in bending resistance

Worked Example: Lipped Channel Web in Bending

Given: C 200 x 75 x 20 x 2.0 (S350GD, Fy = 350 N/mm^2)

• Web: h = 200 mm, t = 2.0 mm (internal element in bending, psi = -1)
• k_sigma = 23.9 (pure bending, simply supported edges)

sigma_cr = 23.9 * pi^2 * 210000 * 2.0^2 / (12 * 0.91 * 200^2)
         = 23.9 * 9.870 * 210000 * 4.0 / (12 * 0.91 * 40000)
         = 23.9 * 8,290,800 / 436,800
         = 198,110,120 / 436,800
         = 453.6 N/mm^2

lambda_p = sqrt(350 / 453.6) = sqrt(0.771) = 0.878

rho = (0.878 - 0.055 * (3 - 1)) / 0.878^2 = (0.878 - 0.110) / 0.771 = 0.768 / 0.771 = 0.996

beff = 0.996 * 200 = 199.2 mm (near-full effective)

At this slenderness, the web is effectively fully effective for bending. For a thinner 1.0 mm web: lambda_p = sqrt(350 / 113.4) = 1.758, rho = (1.758 - 0.110)/3.091 = 0.533, beff = 107 mm -- over 46% reduction.

Connection Design for Cold-Formed Steel (EN 1993-1-3 Clause 8)

Cold-formed steel connections use self-drilling screws, blind rivets, or bolts (in thicker members). Key design checks differ from hot-rolled connections:

For thin sheet (t <= 2.0 mm), bearing and tilting/bearing typically govern. Screw spacing minimums: 3d edge distance, 5d end distance in direction of load.

Design Resources

Calculator tools

• Cold-Formed Steel Calculator
• CFS Wall Stud Calculator

Reference pages

• EU Cold Formed