UK Cold-Formed Steel Design -- BS EN 1993-1-3 Purlin and Sheeting Rail Design

Cold-formed steel sections -- predominantly Z and C purlins, sheeting rails, and light steel framing members -- form the secondary structural system in virtually every UK industrial and commercial building. BS EN 1993-1-3:2006 provides the design rules for cold-formed members and sheeting, with the UK National Annex confirming the recommended values and adding supplementary guidance for UK practice. This reference covers the effective width method for local buckling, distortional buckling of edge stiffeners, the design of Z and C purlins under gravity and wind uplift, and worked examples for UK roof and wall cladding systems in S350GD and S390GD steel to BS EN 10346.

Regulatory Framework and Material Grades

Cold-formed structural steel is produced from hot-rolled coil that is cold-worked through roll-forming or press-braking into the final section shape. The base material is specified to BS EN 10346:2015, Continuously hot-dip coated steel flat products for cold forming.

The standard UK material grades for structural cold-formed sections are:

The GD suffix denotes hot-dip galvanised coating, with the zinc coating mass (e.g., Z275 = 275 g/m^2 total both sides) specified for corrosion protection. For UK internal environments (C1-C2 per BS EN ISO 12944), Z275 provides adequate durability. For coastal or industrial environments (C3-C4), Z350 or Z450 is specified.

Note that the yield and ultimate strengths quoted are for the base steel. The cold-forming process increases the yield strength in the corners and bends by up to 20%, an effect that EN 1993-1-3 permits to be taken into account through an enhanced average yield strength fya.

The Effective Width Method -- Local Buckling

Cold-formed sections have high width-to-thickness ratios compared to hot-rolled sections. Individual plate elements (flanges, webs, lips) are susceptible to local buckling before the gross section reaches yield. Clause 5.5 of EN 1993-1-3 provides the effective width method to account for this.

The effective width beff of a plane compression element is:

beff = rho x b_p

Where b_p is the notional flat width of the element and rho is the reduction factor:

For internal compression elements: rho = 1.0 for lambda_p,bar <= 0.673; rho = (lambda_p,bar - 0.055(3 + psi)) / lambda_p,bar^2 for lambda_p,bar > 0.673

For outstand compression elements: rho = 1.0 for lambda_p,bar <= 0.748; rho = (lambda_p,bar - 0.188) / lambda_p,bar^2 for lambda_p,bar > 0.748

The plate slenderness lambda_p,bar = sqrt(fy / sigma_cr), where sigma_cr is the elastic critical buckling stress of the plate element.

Effective Section Properties for a Z Purlin

Consider a Z 200 x 2.0 purlin in S350GD (fy = 350 MPa, fu = 420 MPa, t = 2.0 mm). The cross-section comprises:

• Top flange outstand: b = 65 mm (flat width), t = 2.0 mm, b/t = 32.5
• Web: h = 200 mm, t = 2.0 mm, h/t = 100
• Bottom flange outstand: symmetrical
• Lip stiffeners: c = 20 mm, t = 2.0 mm

The flange b/t = 32.5: for S350 (epsilon = sqrt(235/350) = 0.819), the limiting b/t for Class 4 is 14 x epsilon = 11.5 for outstand flanges. The actual b/t >> 11.5, confirming that local buckling governs and the effective width method must be applied.

lambda_p,bar (flange) = (b/t) / (28.4 x epsilon x sqrt(k_sigma)) where k_sigma = 0.43 for an outstand flange with a free edge (unstiffened).

lambda_p,bar = 32.5 / (28.4 x 0.819 x sqrt(0.43)) = 32.5 / (23.26 x 0.656) = 32.5 / 15.26 = 2.13 > 0.748

rho = (2.13 - 0.188) / 2.13^2 = 1.942 / 4.537 = 0.428

The effective flange width beff = 0.428 x 65 = 27.8 mm. Only about 43% of the nominal flange width is effective in compression due to local buckling. The ineffective portion is concentrated at the free edge.

Distortional Buckling of Edge Stiffeners

The lip stiffener on a Z or C section is itself a compression element that can buckle in a distortional mode, rotating about the flange-web junction. Clause 5.5.3.2 of EN 1993-1-3 provides the check:

The spring stiffness K of the flange supporting the lip is calculated from the flange bending stiffness and geometric parameters. If K is insufficient, the lip stiffener buckles and the flange then behaves as an unstiffened element -- a catastrophic loss of effective section.

For the Z 200 x 2.0 purlin with lip c = 20 mm:

• The adequacy of the lip is checked by comparing the lip slenderness to the limit.
• If the lip is too slender (c/b < 0.2 is a typical rule), intermediate stiffeners or a different section profile is required.

In UK practice, standard purlin profiles from manufacturers such as Albion, Kingspan, and Tata Steel have optimised lip dimensions that satisfy the distortional buckling check for the published design tables. The designer verifies the tabulated capacities rather than performing the distortional buckling calculation from first principles.

Purlin Design for Gravity Loading (Downward)

UK purlins typically span 5-8 m between main frames, supporting the roof cladding and insulation. Under gravity loading (dead + snow), the purlin bends about its major axis and may be subject to lateral-torsional buckling. However, the roof sheeting, if adequately fastened, provides continuous lateral restraint to the top flange in the downward load case, suppressing LTB.

The design check is then a simple bending check:

M_Ed / M_c,Rd <= 1.0

Where M_c,Rd = Weff x fya / gamma_M0.

Gamma_M0 = 1.00 per UK NA to BS EN 1993-1-3.

For the Z 200 x 2.0 purlin with the effective section properties computed above, the effective section modulus Weff,y is significantly less than the gross Wel,y. The capacity is correspondingly reduced.

Purlin Design for Wind Uplift (Upward)

Under wind uplift, the loading direction reverses, and the bottom flange is in compression. The roof sheeting is now on the tension side and does not provide restraint. The purlin is susceptible to lateral-torsional buckling under wind uplift.

EN 1993-1-3 Clause 10.1.4 provides the design method, which is typically implemented through manufacturer design tables rather than manual calculation. The key factors are:

• Rotational restraint k_phi provided by the sheeting to the top flange through the fasteners
• Lateral restraint provided by anti-sag bars or sag rods at intermediate points
• Torsional stiffness of the purlin itself, which is modest for thin-walled open sections

For a typical UK purlin span of 6 m with anti-sag rods at midspan (3 m from supports), the effective length for LTB under wind uplift is approximately 3 m. The manufacturer's design software or tables should be consulted for the specific uplift capacity.

Worked Example -- Gravity Load Purlin Design

Given:

• Roof purlin, simply supported span L = 6.0 m
• Purlin spacing: 1.8 m
• Dead load (cladding + insulation + services): 0.25 kN/m^2
• Snow load (UK, altitude < 100 m, basic snow load 0.50 kN/m^2 to BS EN 1991-1-3)
• Steel grade: S350GD + Z275

Load per purlin: Dead: g_k = 0.25 x 1.8 = 0.45 kN/m Snow: s = 0.50 x 1.8 = 0.90 kN/m (assuming uniform snow, no drift)

ULS combination (EN 1990 Equation 6.10, UK NA): w_Ed = 1.35 x 0.45 + 1.5 x 0.90 = 0.61 + 1.35 = 1.96 kN/m

Bending moment: M_Ed = w_Ed x L^2 / 8 = 1.96 x 6.0^2 / 8 = 8.82 kN.m

Section selection: From manufacturer tables for a Z purlin at 6.0 m span, S350GD, gravity loading, with top flange laterally restrained by sheeting: Z 200 x 2.0: M_c,Rd = 9.5 kN.m (typical) > 8.82 kN.m. OK.

Deflection check (SLS): w_SLS = 0.45 + 0.90 = 1.35 kN/m delta = 5 x 1.35 x 6.0^4 / (384 x E x I_eff) For Z 200 x 2.0, I_eff is based on effective section properties. Typical SLS deflection limit: L/200 = 30 mm for purlins supporting brittle finishes, or L/150 = 40 mm for metal roofing. Check against manufacturer's tabulated I_eff and deflection.

UK National Annex Provisions

The UK NA to BS EN 1993-1-3 confirms the following:

1. gamma_M0 = 1.00 for cross-section resistance.
2. gamma_M1 = 1.00 for buckling resistance.
3. gamma_M2 = 1.25 for net section rupture at fastener holes.
4. The effective width method of Clause 5.5 is adopted without modification.
5. The UK NA references BS 5950-5 for certain aspects of purlin design not covered in EN 1993-1-3, particularly for sleeved purlin systems and anti-sag bar detailing.
6. For fire design of cold-formed members, the UK NA to BS EN 1993-1-2 provides specific guidance, including the critical temperature method for cold-formed purlins, which differs from hot-rolled members due to the different rate of strength degradation with temperature.

Design Resources

• UK Steel Grades Reference -- EN 10025-2 grade selection
• UK Steel Properties -- fy, fu, Charpy
• UK Beam Design Guide -- Hot-rolled beam design
• UK Steel Chemical Composition -- Element limits
• All UK Steel Design References -- complete library

Frequently Asked Questions

What steel grade is standard for UK cold-formed purlins?

S350GD + Z275 is the standard steel grade for UK cold-formed purlins, specified to BS EN 10346. The 350 MPa minimum yield strength provides an optimal balance of strength and formability for roll-forming. The Z275 zinc coating (275 g/m^2) provides adequate corrosion protection for internal building environments (corrosivity categories C1-C2). For external or aggressive environments, S350GD + Z350 or S390GD + Z350 is specified.

Why must the effective width method be used for cold-formed sections?

Cold-formed sections have width-to-thickness ratios that substantially exceed the Class 3 limits for hot-rolled sections (e.g., b/t = 32.5 for a typical Z purlin flange vs 14 x epsilon = 11.5 for Class 3). Local buckling of the thin plate elements occurs at stresses below yield. The effective width method per EN 1993-1-3 Clause 5.5 accounts for this by reducing the effective cross-section to only that portion of each plate element that remains stable at the yield stress. The reduction can be substantial -- a flange may be only 40-50% effective.

Does the UK NA modify the EN 1993-1-3 design rules?

The UK NA to BS EN 1993-1-3 adopts the recommended values without significant modification: gamma_M0 = gamma_M1 = 1.00, gamma_M2 = 1.25. The UK NA references BS 5950-5 for complementary guidance on sleeved purlin systems and anti-sag bar detailing, which are common UK construction features not fully addressed in EN 1993-1-3. The UK NA also includes supplementary guidance on fastener spacing and edge distances specific to UK roofing practice.

What is the role of anti-sag bars in UK purlin design?

Anti-sag bars (or sag rods) are tension members installed between adjacent purlins at midspan or third points to provide lateral restraint to the purlin bottom flange during wind uplift conditions. Without anti-sag bars, the effective length for LTB under uplift is the full span (6-8 m), and the uplift capacity is severely reduced. With anti-sag bars at midspan, the effective length halves, significantly improving uplift capacity. UK practice typically provides anti-sag bars at 2.5-3.5 m centres, aligned with the purlin manufacturer's standard design assumptions.

Educational reference only. All design values are per BS EN 1993-1-3:2006 + UK National Annex and BS EN 10346:2015. Verify all values against the current editions of the standards and the applicable National Annex for your project jurisdiction. Designs must be independently verified by a Chartered Structural Engineer registered with the Institution of Structural Engineers (IStructE) or the Institution of Civil Engineers (ICE). Results are PRELIMINARY -- NOT FOR CONSTRUCTION without independent professional verification.