EN 1993-1-3 Cold-Formed Steel Design — Effective Width, Distortional Buckling & Purlin Design

Complete reference for EN 1993-1-3:2006 cold-formed steel design. Covers the effective width method for local buckling (Clause 5.5), distortional buckling of edge stiffeners (Clause 5.5.3), the reduced thickness method for lip stiffeners, design of C and Z purlins under gravity and wind uplift, and screwed connection design (Clause 8). Includes fully worked examples for a Z 200 purlin in S350GD under gravity and a C 202 purlin under wind uplift.

Quick access: Beam Capacity Calculator | EN 1993 Beam Design | EN 1993 Column Buckling | EN 1993 Steel Grades

Why Cold-Formed Design Is Different

EN 1993-1-3 exists because the rules in EN 1993-1-1 (hot-rolled design) fail for thin-gauge members. Three fundamental differences:

1. All sections are Class 4. Width-to-thickness ratios far exceed Class 3 limits. Local buckling is not binary failure — it is progressive loss of effective section.
2. Distortional buckling exists. The edge stiffener (lip) rotates about the flange-web junction — an instability mode EN 1993-1-1 has no equivalent for.
3. Connections are screws, not bolts. Self-tapping screws work by thread engagement in the base material — a fundamentally different mechanism from bolt shear and bearing.

Material Grades — EN 10346:2015

Zinc coating Z275 (275 g/m² total) provides C2 durability. For C3 (coastal/industrial), specify Z350 or Z450. S350GD (f_u/f_yb = 1.20) is the sweet spot — higher grades provide more strength but with reduced ductility and more brittle screw failure modes.

The Effective Width Method — Local Buckling (Clause 5.5)

Plate elements in compression buckle at a stress below yield. But unlike a column, the plate does not collapse — it redistributes stress to the supported edges. The effective width method quantifies this:

Reduction Factor ρ

For internal compression elements: ρ = 1.0 when λ_p,bar ≤ 0.673; ρ = (λ_p,bar - 0.055(3 + ψ)) / λ_p,bar² when λ_p,bar > 0.673.

For outstand compression elements: ρ = 1.0 when λ_p,bar ≤ 0.748; ρ = (λ_p,bar - 0.188) / λ_p,bar² when λ_p,bar > 0.748.

λp,bar = √(f_yb / σ_cr), where σ_cr = kσ × (π²E) / (12(1-ν²)) × (t/bp)². kσ = 4.0 for internal element in uniform compression, 0.43 for outstand with free edge, 1.70 for outstand with lip stiffener.

Worked Example — Z 200×2.0 Purlin, S350GD

Top flange: b = 65 mm, t = 2.0 mm. b/t = 32.5. ε = √(235/350) = 0.819. Class 3 limit for outstand = 14ε = 11.5. b/t = 32.5 >> 11.5 → Class 4.

λ_p,bar = 32.5 / (28.4 × 0.819 × √0.43) = 32.5/15.26 = 2.13. ρ = (2.13 - 0.188)/2.13² = 0.428. Effective flange width: b_eff = 0.428 × 65 = 27.8 mm. Only 43% of nominal flange width is effective.

Gross Z_x = 41.5 × 10³ mm³. Effective Z_x ≈ 30.0 × 10³ mm³ (28% reduction). M_c,Rd = 30.0 × 350 / 1.00 = 10.5 kNm.

For 6.0 m span at 1.8 m spacing under 1.0 kN/m²: M_Ed = 1.0 × 1.8 × 6.0²/8 = 8.1 kNm. UC = 8.1/10.5 = 0.77 — adequate but with limited reserve.

Distortional Buckling — The Lip Stiffener Check (Clause 5.5.3)

The lip on a C or Z section is itself a compression element. The reduced thickness method:

Spring Stiffness K and Reduction Factor χ_d

K = (E × t³) / (4(1 - ν²)) × 1/(b_1²h_w + b_1³ + 0.5b_1²b_2k_f). σ_cr,s = 2√(K × E × I_s) / A_s. λ_d = √(f_yb/σ_cr,s).

χ_d: λ_d ≤ 0.65 → 1.0; 0.65 < λ_d < 1.38 → 1.47 - 0.723λ_d; λ_d ≥ 1.38 → 0.66/λ_d.

Worked Example — Z 200×2.0 Lip Adequacy

Lip: c = 20 mm, t = 2.0 mm. I_s = 2.0 × 8000/12 = 1333 mm⁴. A_s = (20 + 13.9) × 2.0 = 67.8 mm². K ≈ 0.397 N/mm². σ_cr,s = 2√(0.397 × 210000 × 1333)/67.8 = 311 MPa. λ_d = √(350/311) = 1.061. χ_d = 1.47 - 0.723 × 1.061 = 0.703. t_red = 0.703 × 2.0 = 1.41 mm.

With the reduced lip, recompute flange effective width — the lip is now less effective, so flange effective width further reduces. For this section, χ_d = 0.70 is marginal. A lip of 25 mm would bring χ_d above 0.85. Many UK manufacturers use lips of 22-25 mm on Z 200 purlins.

Purlin Design — Gravity and Wind Uplift

Gravity Loading (Downward)

Roof sheeting restrains the top (compression) flange. Lateral-torsional buckling is prevented. Design: M_c,Rd = W_eff × f_yb / γ_M0.

Wind Uplift (Critical Case)

Bottom flange enters compression and is UNRESTRAINED. Lateral-torsional buckling governs. EN 1993-1-3 Clause 10.1.4 and Annex A: M_b,Rd = χ_LT × W_eff × f_yb / γ_M1.

Worked Example — Z 200×2.0 Under Uplift

Span: 6.0 m. Wind uplift: w_uplift = -1.2 kN/m². Load per purlin: w_Ed = 1.2 × 1.8 = 2.16 kN/m. M_Ed = 2.16 × 6.0²/8 = 9.72 kNm.

M_cr ≈ 8.5 kNm (elastic lateral-torsional buckling with top flange restrained). λ_LT,bar = √(25,000 × 350 / 8.5×10⁶) = 1.014. For cold-formed sections, α_LT = 0.34: χ_LT = 0.588. M_b,Rd = 0.588 × 25,000 × 350/1.00 = 5.14 kNm.

UC = 9.72/5.14 = 1.89 — FAILS.

Solution: Add anti-sag rods at mid-span (L_restrained = 3.0 m). M_cr ≈ 4 × 8.5 = 34.0 kNm. λ_LT,bar = √(8.75/34.0) = 0.507. χ_LT ≈ 0.92. M_b,Rd = 8.05 kNm. UC = 9.72/8.05 = 1.21 — still high. Use Z 250×2.0 or reduce purlin spacing.

Wind uplift governs purlin design in UK practice — the unrestrained bottom flange reduces moment capacity by 40-60%.

Screwed Connections (Clause 8)

Shear Resistance

F_v,Rd = 0.65 × f_u,screw × A_s / γ_M2. For SFS SD6-H 6.3 mm (A_s = 20.1 mm², f_u = 800 MPa): F_v,Rd = 8.36 kN. UKCA declared values typically exceed this — for SD6-H, declared shear is 12.0 kN per ETA.

Tension (Pull-Out)

F_t,Rd = 0.65 × d × t × f_u,sheet / γ_M2. For 6.3 mm screw in 2.0 mm S350GD: F_t,Rd = 2.75 kN per screw. For a purlin cleat with 4 screws: 11.0 kN total.

Minimum Distances

Practical Design Summary

1. Determine loads: Dead + imposed + wind uplift per EN 1991.
2. Select purlin from manufacturer tables (Metsec, Ayrshire, Kingspan).
3. Check gravity bending — effective section properties, M_Ed ≤ M_c,Rd.
4. Check wind uplift — M_b,Rd with unrestrained bottom flange. Add anti-sag rods if needed.
5. Check deflection — L/200 imposed, L/150 total (UK NA minimum).
6. Design cleat connections — screw shear and tension at reactions.
7. Specify sheeting fasteners — screw type, spacing, EPDM sealing washers.

For 90% of UK industrial buildings, steps 2-4 are satisfied by manufacturer load-span tables. First-principles cold-formed design is for non-standard sections or cost optimisation.

Educational reference only. Verify all values against the current EN 1993-1-3 and UK National Annex. Cold-formed design is highly section-specific — manufacturer-published tables incorporate testing that may exceed code formula capacities. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent verification by a qualified structural engineer.