Purlin Types — Z vs C Sections

Z-Sections (Zed Purlins)

Z-sections are the dominant purlin shape in European practice. The flanges are oriented in opposite directions, allowing overlapping at supports (sleeved or nested connections) to achieve continuity. Z-purlins are oriented with the top flange pointing up the roof slope, which aligns the principal axes close to the vertical and horizontal loading directions.

Advantages: Can be nested for lapped continuous spans (2+ spans from a single section), efficient for roof slopes 5-15 degrees, symmetric about the web centreline for balanced torsion.

C-Sections (Channel Purlins)

C-sections have both flanges on the same side of the web. They are typically used as simply supported single-span members or with bolted lap splices at supports. C-purlins are oriented with the open face up-slope or down-slope depending on the loading direction.

Advantages: Simpler detailing than Z-sections, no nesting required, easier to install bridging. Used for wall girts and low-load applications where the moment capacity of a C-section is adequate without continuity.

Gravity Load (UDL) Design

Bending About Major Axis

Under gravity load (dead + snow), the purlin bends about its major axis. For a simply supported purlin with uniformly distributed load w_Ed:

M_y,Ed = w_Ed × L² / 8

The design bending resistance about the major axis per EN 1993-1-3 Clause 6.1.4:

M_c,Rd = W_eff × f_yb / γ_M0

Where W_eff is the effective section modulus accounting for local buckling of slender flange and web elements per EN 1993-1-5, and f_yb is the basic yield strength of the cold-formed steel (typically 350-450 MPa for S350GD+Z to EN 10346).

For a Z 200 × 2.0 section in S350GD with f_yb = 350 MPa:

The effective section modulus (11.8/37.2 = 0.91 of gross) accounts for local buckling of the compression flange and the portion of the web in compression.

Wind Uplift Design

Uplift Load Combination

Per EN 1990 Eq. 6.10, the wind-uplift-dominant combination is:

w_Ed,uplift = 1.00 × g_k (stabilising dead load) + 1.50 × q_k,wind (uplift — suction)

The dead load is taken as 1.00 (not 1.35) because it is favourable (resists uplift). Self-weight of the purlin plus roof sheeting provides the stabilising dead load.

For a typical industrial roof with 6 m purlin span at 1.8 m spacing:

• Dead load: g_k = 0.15 kN/m² (sheeting + insulation + purlin self-weight)
• Wind uplift: q_k,wind = −0.80 kN/m² (suction on roof, corner/edge zone per EN 1991-1-4)

Design uplift line load: w_Ed,uplift = (1.00 × 0.15 + 1.50 × (−0.80)) × 1.8 = (0.15 − 1.20) × 1.8 = −1.89 kN/m (uplift)

Bottom Flange in Compression

Under wind uplift, the bending moment reverses and the bottom flange (the "free" flange not restrained by sheeting) goes into compression. Lateral-torsional buckling of the free flange becomes the critical design check:

M_y,Ed,uplift = 1.89 × 6.0² / 8 = 8.51 kN·m

The buckling resistance of the free flange is calculated using the EN 1993-1-3 Clause 10.1.4 method, which accounts for:

1. Rotational restraint from the sheeting (k_φ)
2. Lateral restraint from the sheeting at the top flange
3. Torsional stiffness of the purlin section
4. Bridging restraints at intermediate points

Sigma/Tau Interaction — Combined Bending + Shear

EN 1993-1-3 Clause 6.1.5 requires checking the interaction of bending moment and shear force in the web. The interaction is checked at the web-to-flange junction where both bending normal stress (σ_x,Ed) and shear stress (τ_Ed) are present:

(σ_x,Ed / f_yb/γ_M0)² + 3 × (τ_Ed / f_yb/γ_M0)² ≤ 1.0

Which is equivalent to the von Mises yield criterion:

sqrt(σ_x,Ed² + 3 × τ_Ed²) ≤ f_yb / γ_M0

Shear Buckling of the Web

For unstiffened webs, shear buckling must be checked per EN 1993-1-3 Clause 6.1.5(2) when:

h_w / t > 72 × ε / η

Where h_w is the web depth (flat portion between corner radii), t is the thickness, ε = sqrt(235/f_yb), and η = 1.20 for S350GD.

For a Z 200 × 2.0 section with h_w ≈ 175 mm and t = 2.0 mm:

h_w / t = 175/2.0 = 87.5

Limit = 72 × 0.819 / 1.20 = 49.1

87.5 > 49.1 — shear buckling must be checked. The shear buckling resistance V_b,Rd per Clause 6.1.5 is:

V_b,Rd = h_w × t × f_bv / γ_M1 where f_bv is the shear buckling strength from EN 1993-1-5 Annex A.

For a non-rigid end post (typical purlin without transverse stiffeners at supports), the shear buckling coefficient k_τ = 5.34. The slenderness:

λw = (h_w/t) / (37.4 × ε × sqrt(kτ)) = 87.5 / (37.4 × 0.819 × sqrt(5.34)) = 87.5 / (37.4 × 0.819 × 2.31) = 87.5 / 70.8 = 1.24

Contribution from the web: χ_w = 0.83 / λ_w = 0.83/1.24 = 0.669

f_bv = 0.669 × f_yb / (sqrt(3) × γ_M1) = 0.669 × 350 / (1.732 × 1.00) = 134.8 MPa

V_b,Rd = 175 × 2.0 × 134.8 × 10⁻³ = 47.2 kN

Bridging and Anti-Sag Rods

Purpose of Bridging

Bridging (also called sag rods or sag angles) provides lateral and torsional restraint to purlins. Without bridging, the free flange (typically the bottom flange under gravity load) can buckle laterally between supports. Per EN 1993-1-3 Clause 10.1.5, bridging should be provided at intervals not exceeding:

• L_b,max = 0.5 × L for single-span purlins (one row at mid-span)
• L_b,max = 0.33 × L for multi-span purlins (two rows at third points)

For a 6.0 m single-span Z-purlin, one row of bridging at mid-span (3.0 m from each support) is the minimum requirement. For spans > 8 m, two rows of bridging are recommended.

Bridging Sizing

The bridging member is designed as a compression strut taking 1-2% of the purlin flange force:

N_bridging,Ed = 0.02 × A_f × f_yb / γ_M0

For a Z 200 × 2.0 with flange area A_f ≈ 140 mm² (60 mm flange width × 2.0 mm with corner radius):

N_bridging,Ed = 0.02 × 140 × 350 / 1.00 = 0.98 kN

A 12 mm diameter threaded rod (Grade 4.6) with a tension capacity of approximately 8.3 kN is adequate for typical purlin bridging. For heavier purlins, 16 mm rods or 40×5 flat bars are used.

Worked Example — Z 200 × 2.0 at 6.0 m Span

Step 1 — Gravity ULS (Snow Dominant)

w_Ed,gravity = (1.35 × 0.15 + 1.50 × 0.60) × 1.8 = (0.203 + 0.900) × 1.8 = 1.98 kN/m

M_y,Ed = 1.98 × 6.0² / 8 = 8.91 kN·m

Major axis bending resistance (effective): M_c,Rd = 11.8 kN·m

Utilisation = 8.91 / 11.8 = 0.76 — OK

Step 2 — Wind Uplift ULS

w_Ed,uplift = (1.00 × 0.15 + 1.50 × (−0.80)) × 1.8 = −1.89 kN/m

M_y,Ed = 1.89 × 6.0² / 8 = 8.51 kN·m (reverse curvature)

Free flange buckling resistance (with mid-span bridging, Lb = 3.0 m): M_b,Rd = 9.2 kN·m (calculated per EN 1993-1-3 Clause 10.1.4 with kφ = 0.15 from trapezoidal sheeting)

Utilisation = 8.51 / 9.2 = 0.93 — OK (uplift is the governing condition)

Step 3 — Shear Check (at Support)

V_Ed = w_Ed,gravity × L / 2 = 1.98 × 6.0 / 2 = 5.94 kN

V_b,Rd = 47.2 kN (from shear buckling calculation above)

Utilisation = 5.94 / 47.2 = 0.13 — OK

Step 4 — Sigma/Tau Interaction

At the web-to-flange junction, 300 mm from the support (where moment and shear coexist):

σ_x,Ed = M_Ed / W_eff = (w × x × (L − x) / 2 × W_eff) — at x = 0.3 m from support:

M_Ed = 1.98 × 0.3 × (6.0 − 0.3) / 2 = 1.98 × 0.3 × 2.85 = 1.69 kN·m

σ_x,Ed = 1.69 × 10⁶ / (33.8 × 10³) = 50.0 MPa

τ_Ed = V_Ed / (h_w × t) = (5.94 − 1.98 × 0.3) × 10³ / (175 × 2.0) = 5.35 × 10³ / 350 = 15.3 MPa

Interaction: (50.0/350)² + 3 × (15.3/350)² = 0.0204 + 3 × 0.00191 = 0.0204 + 0.00573 = 0.0261 ≤ 1.0 — OK

Step 5 — Serviceability Deflection

Deflection under frequent combination (G + ψ_1 × S, ψ_1 = 0.2 for snow, Category H roof per EN 1991-1-1 Table A1.1):

I_eff ≈ 3.72 × 10⁶ mm⁴

w_ser = (0.15 + 0.2 × 0.60) × 1.8 = 0.486 kN/m

δ = 5 × 0.486 × 6,000⁴ / (384 × 210,000 × 3.72 × 10⁶) = 5 × 0.486 × 1.296 × 10¹⁵ / (384 × 210,000 × 3.72 × 10⁶)

δ = 3.15 × 10¹⁵ / 3.00 × 10¹⁴ = 10.5 mm

Limit = L/200 = 6,000/200 = 30 mm. Utilisation = 10.5/30 = 0.35 — OK.

Frequently Asked Questions

Why do Z-purlins overlap at supports and how does the overlap affect design?

Z-purlin overlaps (sleeved connections) achieve continuity over internal supports. The overlap length is typically 10-15% of the span, creating a reinforced section with double thickness at the maximum negative moment region. Per EN 1993-1-3 Clause 10.1.4(6), the overlap zone is designed as a compound section with combined section properties. The overlap transforms the purlin from a series of simply supported spans into a quasi-continuous beam, reducing the maximum positive moment by approximately 20-30% compared to simply supported single spans, and introducing a negative moment at the support that must be verified.

How does trapezoidal roof sheeting provide lateral-torsional restraint to purlins?

Trapezoidal steel sheeting fastened to the top flange of the purlin with self-drilling screws at regular centres (typically 333 mm every other trough) provides: (1) lateral restraint — the sheeting acts as a diaphragm preventing lateral displacement of the top flange; (2) rotational restraint kφ — the sheeting stiffness resists rotation of the purlin cross-section. The rotational stiffness depends on the sheeting profile, thickness, fastener spacing, and the presence of insulation. Typical kφ values per EN 1993-1-3 Table 10.1 range from 0.05 (soft insulation layer) to 0.30 (direct steel-to-steel contact). Conservative design often assumes k_φ = 0, relying on bridging alone for stability.

When is shear buckling critical in cold-formed purlin webs?

Shear buckling governs when the web slenderness h_w/t exceeds 72 ε/η. For S350GD (ε = 0.819, η = 1.20), this occurs at h_w/t > 49. For typical Z/C purlins with a 2.0 mm web and flat depth 150-200 mm, h_w/t = 75-100, placing most purlins in the shear-buckling range. However, shear buckling rarely governs the design because the shear demand at the support (V_Ed) is typically far less than V_b,Rd for practical span-to-depth ratios. Shear buckling becomes critical only for very deep purlins (h > 300 mm) with thin webs (t ≤ 1.5 mm) under high shear near supports.

Design Resources

• EN 1993 Cold-Formed Steel — General Design per Part 1-3
• EN 1993 Beam Design — Flexure and LTB for Hot-Rolled Sections
• EN 1993 Lateral-Torsional Buckling — M_cr and χ_LT per Clause 6.3.2
• EN 1993 Load Combinations — EN 1990 ULS and SLS Expressions
• EN 1993 Deflection Limits — Serviceability per Clause 7.2
• All European Reference Guides →

Reference only. Purlin design must be verified against the current edition of EN 1993-1-3:2006 and the applicable National Annex. Section properties from manufacturer's load/span tables should be used in preference to generic calculations. Z-purlin overlap and bridging details must be specified by the purlin system manufacturer. All designs must be independently verified by a licensed Structural Engineer. This guide is for educational purposes only and does not constitute professional engineering advice.