EN 1993-1-3 Cold-Formed Steel Design — C & Z Sections, Effective Widths & Buckling

Complete reference for EN 1993-1-3:2006 cold-formed steel structural member design. Covers the effective width method for Class 4 sections (Clause 5.5), distortional buckling of edge stiffeners (Clause 5.5.3.5), local and global buckling interaction, screwed and blind rivet connection design (Clause 8), and practical design of purlins, side rails, and framing from C and Z cold-formed sections (EN 10162). Includes a worked C-section beam example.

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Cold-Formed Steel Design — Overview

EN 1993-1-3 is the Eurocode part for cold-formed steel members and sheeting. It supplements EN 1993-1-1 with specific rules for thin-gauge (typically 0.5-8.0 mm) sections. Cold-formed steel is shaped by press-braking or roll-forming from galvanised strip to EN 10346, producing the familiar C (lipped channel) and Z (lipped Z) purlin shapes used in industrial building envelopes.

Key differences from hot-rolled EN 1993-1-1 design:

Material Properties for Cold-Formed Steel

Cold-formed steel sections are typically produced to EN 10162 from galvanised coil strip to EN 10346. Common grades:

The +Z designation indicates hot-dip zinc coating. Z275 = 275 g/m^2 total both sides, providing the standard corrosion protection for UK internal building envelope environments.

Cold Work Strength Increase (Clause 3.2.2)

Cold forming increases yield strength in the corner regions. The average increased yield strength fya may be used:

fya = fyb + (fu - fyb) * k * n * t^2 / Ag  but fya <= fu and fya <= (fyb + fu)/2

Where k = 7 for cold-rolling, n is the number of 90-degree bends, and t is the material thickness. For typical C-sections (4 bends, t = 2.0 mm, S350GD), the increase is 2-5% — usually ignored in practice.

Section Properties — Common C and Z Sections

Lipped C-Sections (to EN 10162 / BS EN 1993-1-3 Annex A)

Lipped Z-Sections (to EN 10162)

Note: Z-sections have principal axes rotated relative to the geometric axes. The section properties above are for the principal axes. For Z-sections used as purlins, the bending is about axes parallel to the roof plane — accurate calculation requires transformation of section properties.

Effective Width Method (EN 1993-1-3 Clause 5.5)

All cold-formed sections are Class 4 (slender) unless proven otherwise. The effective width method accounts for local buckling of the thin plate elements:

Unstiffened Elements (e.g., flange outstands)

beff = rho * bp
rho = (1 / lambda_p_bar) * (1 - 0.22 / lambda_p_bar)  for lambda_p_bar > 0.673
rho = 1.0  for lambda_p_bar <= 0.673
lambda_p_bar = (bp / t) / (28.4 * epsilon * sqrt(k_sigma))

Where:

• bp = flat width of the plate element (mm)
• k_sigma = buckling coefficient: 0.43 for unsupported outstand, 4.0 for internal element in pure compression, 23.9 for internal element in pure bending
• epsilon = sqrt(235/fy)
• t = material thickness

Internal Elements (e.g., webs)

For a web in pure bending (k_sigma = 23.9):

beff = rho * bc  (compression zone only)

For a web in combined bending and compression, the effective width is apportioned between the compression and tension zones.

Worked Effective Width — C202 Section

C202 purlin (D = 202 mm, B = 70 mm, C = 20 mm, t = 2.0 mm, S350GD: fy = 350 MPa) Web flat width: bp = 202 - 2 * (2.0 + 2.0) = 202 - 8 = 194 mm (subtracting corner radii r = t)

Web: k*sigma = 23.9 (pure bending), epsilon = sqrt(235/350) = 0.819 lambda_p_bar = (194/2.0) / (28.4 * 0.819 _ sqrt(23.9)) = 97 / (28.4 _ 0.819 _ 4.889) = 97 / 113.6 = 0.854 rho = (1/0.854) _ (1 - 0.22/0.854) = 1.171 _ (1 - 0.258) = 1.171 * 0.742 = 0.869

Effective web depth in compression zone (half the web for pure bending): beff = 0.869 * 97 = 84.3 mm (reduced from 97 mm)

Flange outstand (compression): bp = 70 - 20 - 2*(2.0+2.0) = 50 - 8 = 42 mm (approximately, the flat portion) k_sigma = 0.43 (unstiffened outstand) lambda_p_bar = (42/2.0) / (28.4 * 0.819 _ sqrt(0.43)) = 21 / (28.4 _ 0.819 _ 0.656) = 21 / 15.24 = 1.378 > 0.673 rho = (1/1.378) _ (1 - 0.22/1.378) = 0.726 _ (1 - 0.160) = 0.726 _ 0.840 = 0.610

Effective flange outstand: beff = 0.610 * 42 = 25.6 mm (reduced from 42 mm)

The effective section modulus Ieff would be computed from the reduced section geometry. In practice, manufacturers such as Albion, Ayrshire, and Metsec provide tabulated effective properties for their standard sections.

Distortional Buckling of Edge Stiffeners (Clause 5.5.3.5)

Edge stiffeners (lips) in C and Z sections can buckle distortional (the lip rotates about the flange-web junction). The stiffener check:

Step 1 — Spring Stiffness K

The rotational spring stiffness per unit length provided by the flange to the lip:

K = E * t^3 / (4 * (1 - nu^2)) * (1 / (b1 + 0.5*b2))

Where b1 is the flange flat width from web to stiffener centreline, b2 is the stiffener development length.

Step 2 — Elastic Critical Stress

The critical stress for the stiffener treated as a strut on an elastic foundation:

sigma_cr,s = 2 * sqrt(K * E * Is) / As

Where Is is the second moment of area of the stiffener about its own centroidal axis parallel to the stiffened element, and As is the stiffener cross-sectional area.

Step 3 — Reduction Factor chi_d

lambda_d_bar = sqrt(fyb / sigma_cr,s)
chi_d = 1.0  for lambda_d_bar <= 0.65
chi_d = 1.47 - 0.723 * lambda_d_bar  for 0.65 < lambda_d_bar < 1.38
chi_d = 0.66 / lambda_d_bar  for lambda_d_bar >= 1.38

Step 4 — Reduced Stiffener Thickness:

t_red = chi_d * t

The reduced stiffener thickness is then used in the effective width calculation for the stiffened element, potentially reducing rho further.

For a C202 section (lip 20 mm, flange flat 42 mm, t = 2.0 mm), the lip is usually adequate — chi_d ~ 0.95-1.0. Distortional buckling becomes critical for deep, thin sections with short lips (high D/t, low C/B ratios).

Member Buckling Resistance (Clause 6.2)

The overall buckling check for cold-formed members uses the same EN 1993-1-1 buckling curves but with the effective cross-section properties (Aeff, Weff):

N_b,Rd = chi * Aeff * fy / gamma_M0  (columns)
M_b,Rd = chi_LT * Weff * fy / gamma_M0  (beams)

For combined bending and compression (Clause 6.2.5):

N_Ed / N_b,Rd + k_yy * M_y,Ed / M_y,Rd + k_yz * M_z,Ed / M_z,Rd <= 1.0

The interaction factors k_yy, k_yz, k_zy, k_zz follow Annex B of EN 1993-1-1 but use effective section properties. For C-sections, lateral-torsional buckling is usually the critical beam failure mode because of the low torsional stiffness (It small) and the fact that the shear centre is outside the section.

Torsional-flexural buckling (Clause 6.2.3.5) must be checked for cold-formed columns. Because the shear centre and centroid do not coincide in C and Z sections, pure axial compression produces twisting. The elastic critical load Ncr,TF is the lowest root of the cubic stability equation, and the reduction factor chi_T is calculated using buckling curve b.

Connection Design — Screws and Blind Rivets (Clause 8)

Cold-formed steel connections use self-drilling/tapping screws, blind rivets, and occasionally cartridge-fired pins. EN 1993-1-3 Clause 8 covers these:

Screw Connections

Where:

• d = screw nominal diameter (mm)
• t = connected sheet thickness (mm, thinnest ply)
• fu = ultimate tensile strength of the sheet (MPa)
• alpha = bearing coefficient (typically 2.1 for screws with washers, 2.5 for bolts in standard holes)
• gamma_M2 = 1.25

Typical Screw Capacities — Steel-to-Steel, S350GD, t = 2.0 mm

Self-drilling screws (TEK screws) are the standard UK practice. For critical connections, the manufacturer's declared values from the CE marking or UKCA marking should be used rather than the simplified code formulae.

Worked Example — C202 Purlin in Bending

Problem: Check a C202 x 2.0 purlin (S350GD) spanning 6.0 m as a simply supported roof purlin. The purlin supports a roof dead load of 0.15 kN/m^2 and imposed load of 0.60 kN/m^2, with purlins at 1.8 m centres. Lateral restraint from the roof profile attached to the top flange (gravity loading — stabilising). Assume the roof profile provides full lateral restraint to the top flange at each screw line (300 mm spacing).

Step 1 — Design Loads

ULS vertical load w*Ed = 1.35 * 0.15 _ 1.8 + 1.5 _ 0.60 _ 1.8 = 0.365 + 1.620 = 1.985 kN/m

M_y,Ed = 1.985 * 6.0^2 / 8 = 8.93 kN.m

Step 2 — Section Properties (C202 x 2.0, S350GD)

Gross: Iy = 634 cm^4, Wel,y = 60.8 cm^3, fy = 350 MPa Effective (considering local buckling of web and compression flange — use manufacturer data or compute as above): Weff,y ~ 52.5 cm^3 (approximate, 86% of gross for this slenderness)

Step 3 — Cross-Section Resistance

Mc,Rd = Weff,y _ fy / gamma_M0 = 52.5 _ 10^3 _ 350 / 1.00 = 18.38 _ 10^6 N.mm = 18.38 kN.m Utilisation: 8.93 / 18.38 = 0.486 — OK.

Step 4 — Lateral-Torsional Buckling

Because the top flange is laterally restrained by the roof sheeting, LTB may not govern. However, if the loading is uplift (wind suction), the unrestrained bottom flange is in compression and LTB must be checked.

For gravity loading with top flange restraint, the LTB slenderness between restraints is taken as the purlin depth between sheeting screw lines over the unrestrained length:

Mcr for L = 6.0 m, top flange restraint at 300 mm intervals: assume buckling between purlin supports for the unrestrained bottom flange (top flange in tension). For gravity loading, C1 = 1.13 (simply supported, UDL). For the approximate C202 section:

Iz = 29.5 cm^4 (approx.), It = 0.079 cm^4, Iw = 1,120 cm^6

Mcr (LTB, bottom flange unrestrained): Mcr = C1 _ pi^2 _ E _ Iz / (L^2) _ sqrt(Iw/Iz + L^2GIt/(pi^2EIz)) L = 6,000 mm Mcr = 1.13 _ pi^2 _ 210,000 _ 29.5e4 / (6,000^2) _ sqrt(1,120e6/29.5e4 + (6,000^2 _ 81,000 _ 0.079e4)/(pi^2 _ 210,000 _ 29.5e4)) = 1.13 _ 2,045e9 / 36e6 _ sqrt(3,797 + (5,916e9)/(6,122e10)) = 64.2e3 _ sqrt(3,797 + 0.0967) = 64.2e3 _ 61.6 = 3,955,000 N.mm = 3.96 kN.m

lambda*LT_bar = sqrt(Weff,y * fy / Mcr) = sqrt(52.5e3 _ 350 / 3.96e6) = sqrt(18.38e6 / 3.96e6) = sqrt(4.64) = 2.15

For buckling curve b (alpha*LT = 0.34): Phi_LT = 0.5 * (1 + 0.34_(2.15 - 0.2) + 2.15^2) = 0.5 * (1 + 0.663 + 4.62) = 3.14 chi_LT = 1 / (3.14 + sqrt(3.14^2 - 2.15^2)) = 1 / (3.14 + sqrt(9.86 - 4.62)) = 1 / (3.14 + 2.29) = 1 / 5.43 = 0.184

Mb,Rd = 0.184 * 18.38 = 3.38 kN.m (for uplift without restraint)

Under gravity (top flange restrained): Mb,Rd >= Mc,Rd — treat as fully restrained. OK.

Step 5 — Serviceability Deflection

SLS load (imposed only): w = 0.60 _ 1.8 = 1.08 kN/m delta = 5 _ 1.08 _ 6,000^4 / (384 _ 210,000 _ 634e4) = 5 _ 1.08 _ 1.296e15 / (384 _ 210,000 * 6.34e6) = 7.00e15 / 5.12e14 = 13.7 mm Limit (L/200): 6,000/200 = 30 mm. OK (46% utilisation).

Step 6 — Uplift Check (Wind Suction)

Wind uplift: w*uplift = -0.8 kN/m^2 (net suction), gamma_Q = 1.5 ULS upward: w_Ed,up = -1.5 * 0.8 _ 1.8 = -2.16 kN/m

M_Ed,up = 2.16 * 6.0^2 / 8 = 9.72 kN.m

Without bottom flange restraint: Mb,Rd = 3.38 kN.m (from above) — FAIL.

Options: (1) Use anti-sag rods at mid-span to provide bottom flange lateral restraint — reduces L to 3.0 m → Mcr increases ~4x → chi_LT ~ 0.64 → Mb,Rd ~ 11.8 kN.m — OK. (2) Use a deeper section (C232 or C262). (3) Reduce purlin spacing to 1.2 m centres.

Result: C202 purlin at 1.8 m centres is adequate for gravity loading but requires anti-sag rods for uplift restraint. Standard UK practice fits anti-sag rods at third or quarter points for all purlin spans over 5 m.

Frequently Asked Questions

Why are all cold-formed sections Class 4 in EN 1993-1-3?

Cold-formed sections are manufactured from thin strip (0.5-8.0 mm), so the width-to-thickness ratios (c/t) of the plate elements exceed the Class 3 limit for almost all commercial sections. For example, a C202 web (flat width 194 mm at t = 2.0 mm) has c/t = 97, far exceeding the Class 3 limit of 42*epsilon = 34.4 for S350. The effective width method accounts for post-buckling reserve strength — the section does not fail at the onset of local buckling but continues to carry load with a reduced effective cross-section until the ultimate load is reached.

What is distortional buckling and how does it differ from local buckling?

Local buckling is the buckling of an individual plate element (web, flange) between its supported edges, with the corner junctions remaining straight. Distortional buckling (EN 1993-1-3 Clause 5.5.3.5) is buckling of the edge stiffener (lip) where the lip rotates about the flange-web junction — the corner junction moves. Distortional buckling is a longer-wavelength instability that involves both the lip and the adjacent flange. It is addressed by reducing the stiffener thickness (chi_d * t) and recalculating effective widths with the reduced stiffener.

How are screwed connections designed for cold-formed steel per EN 1993-1-3?

EN 1993-1-3 Clause 8 covers self-tapping screws, blind rivets, and cartridge-fired pins. Screw shear resistance Fv,Rd = 0.65 _ fu _ As. Pull-out resistance Ft,Rd = 0.65 _ d _ t _ fu,p (depends on the thinnest connected ply). Pull-through resistance checks the head pulling through the sheet. Bearing resistance uses alpha _ d _ t _ fu / gamma_M2 with alpha = 2.1 for screws with washers. For critical connections, use manufacturer-declared values from the UKCA/CE marking. The simplified code formulae are conservative lower bounds.

What are the practical differences between C and Z section purlins?

C-sections have the shear centre outside the flange (like channels), causing twisting under vertical load. Z-sections have the shear centre near the flange centroid, reducing twist but the principal axes are rotated relative to the roof plane — bending about the horizontal axis couples with lateral displacement. C-sections are symmetric about the web and simpler for single spans. Z-sections can be lapped (nested) over supports for continuity (sleeved Z purlins), providing higher stiffness and capacity than simple spans. UK practice typically uses Z purlins for spans over 6 m with sleeved systems (e.g., Metsec, Ayrshire).

Does cold forming increase the yield strength of the steel?

Yes. EN 1993-1-3 Clause 3.2.2 permits the use of an increased average yield strength fya to account for strain hardening at the cold-formed corners. fya = fyb + (fu - fyb) _ k _ n * t^2 / Ag. For a typical C-section with 4 bends, t = 2.0 mm, and S350GD (fyb = 350, fu = 420): the increase is typically 2-5%. Most UK manufacturers do not factor this increase into their published section tables because it is small and conservatism is preferred. For S390GD and S450GD grades with lower fu/fyb ratios, the increase is negligible.

Related Pages

• EN 1993-1-1 Beam Design — Flexure, Shear & LTB
• EN 1993 Column Buckling — Curves a0-d
• EN 1993-1-8 Connection Design — Bolts, Welds & Fin Plates
• EN 1993 Steel Grades — S235, S275, S355, S460
• EN 1994 Composite Beam Design
• Beam Capacity Calculator — Free Online Tool
• Column Capacity Calculator — Free Online Tool

Educational reference only. Verify all design values against the current EN 1993-1-3 and the applicable National Annex for your jurisdiction. Cold-formed steel section properties vary by manufacturer — always use the manufacturer's published data for final design. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent verification by a qualified structural engineer.