Why does wind uplift govern cold-formed purlin design?

Wind uplift reverses bending moment, placing the unsupported bottom flange in compression. Cold-formed C-sections have very low LTB resistance. Under uplift, bottom flange LTB capacity can drop to less than 12 percent of gravity capacity without bridging. The worked example shows that a C20015 purlin with one row of bridging at midspan has an LTB capacity of only 9.81 kip-in. versus a gravity moment capacity of 90.5 kip-in. — a 9:1 reduction.

How is biaxial bending handled for cold-formed roof purlins?

On sloped roofs, the vertical gravity load resolves into components parallel and perpendicular to the purlin web. For a 4.76-degree roof slope, the major-axis component is 99.7 percent and the minor-axis component is 8.3 percent. Combined bending per AISI S100 H2 requires Mx/Mnx + My/Mny <= 1.0.

How many rows of bridging are needed for cold-formed purlins?

Typical practice is one row at midspan for spans 15 to 25 ft, two rows at third points for 25 to 35 ft, and three rows for spans over 35 ft. For the 20 ft example in Exposure C with 130 mph wind, even two rows of bridging increased LTB capacity to only 20.4 kip-in. — far below the required 255.6 kip-in. The final design used C25024 at 4 ft spacing with two bridging rows.

Purlin Design Worked Example — C20015 Cold-Formed Uplift Biaxial Bending

Q: How many rows of bridging are needed for cold-formed purlins?

Typical practice is one row at midspan for spans 15 to 25 ft, two rows at third points for 25 to 35 ft, and three rows for spans over 35 ft. For the 20 ft example in Exposure C with 130 mph wind, even two rows of bridging increased LTB capacity to only 20.4 kip-in. — far below the required 255.6 kip-in. The final design used C25024 at 4 ft spacing with two bridging rows.

AISI S100 / ASCE 7-22 Cold-Formed Purlin Design — C20015 Worked Example

Complete step-by-step design of a cold-formed C-section roof purlin per AISI S100-16 (2020 Ed.). Covers gravity loading (DL + RLL), wind uplift (suction), biaxial bending on a sloped roof, bridging requirements, and combined bending checks per AISI S100.

Related pages: Cold-Formed Steel Guide | Wind Load Guide | Combined Loading Guide

Problem Statement

Design a 20 ft simple-span roof purlin for a metal building in Exposure C (open terrain). The roof slope is 1:12 (4.76 deg). Purlins are at 5 ft centres supporting 26-gauge through-fastened standing seam roof panels.

Design data:

Purlin: C20015 (C8x2.5) cold-formed C-section, ASTM A653 Grade 50
Depth: d = 8.00 in., Flange: bf = 2.50 in., Lip: 0.625 in., t = 0.060 in.
Fy = 50 ksi, Fu = 65 ksi
Span: L = 20 ft, spacing: s = 5 ft c/c
Bridging: 1 row at midspan (Lb = 10 ft under uplift)
Roof slope: 4.76 deg (1:12)
Dead load: 3.0 psf, purlin self-weight: 2.62 plf
Roof live load: 20 psf (ASCE 7-22 Table 4.3-1)
Wind: Exposure C, V = 130 mph, mean roof height 25 ft

Step 1 — Section Properties (C20015)

Property	Value	Unit
Area Ag	0.772	in^2
Ixx	7.23	in^4
Sxx	1.81	in^3
Iyy	0.647	in^4
Syy	0.206	in^3
J	0.000901	in^4
Cw	2.70	in^6
rx	3.06	in.
ry	0.916	in.
r0	3.55	in.

Step 2 — Gravity Load Case (DL + RLL)

Service loads: w_D = 3.0 x 5 + 2.62 = 17.62 plf, w_Lr = 20 x 5 = 100 plf

Factored: wu = 1.2 x 17.62 + 1.6 x 100 = 181.14 plf = 0.181 klf (governs)

Biaxial bending (theta = 4.76 deg): w_x = 0.181 x cos(4.76) = 0.1804 klf, w_y = 0.181 x sin(4.76) = 0.0150 klf

Mx* = 0.1804 x 20^2/8 = 9.02 kip-ft = 108.2 kip-in. My* = 0.0150 x 20^2/8 = 0.75 kip-ft = 9.00 kip-in.

Step 3 — Gravity Bending Capacity

Major-axis: Mnx = Sxx x Fy = 1.81 x 50 = 90.5 kip-in. phi_b x Mnx = 81.5 kip-in.

Mx* = 108.2 kip-in. > 81.5 kip-in. — section undersized.

Remedy: use C20019 (t = 0.075 in., Sxx ~ 2.25 in^3). phi x Mnx = 0.90 x 112.5 = 101.3 kip-in. Still borderline. Upgrade to C25024.

Minor-axis: Mny = 0.206 x 50 = 10.3 kip-in. phi x Mny = 9.27 kip-in. vs My* = 9.00 kip-in. — 97.1%

Step 4 — Wind Uplift Case

Wind pressure (ASCE 7-22 Chapter 30): qh = 37.6 psf, GCP = -2.4 (Zone 2, A = 100 ft^2). p_net = -88.3 psf (suction).

Factored uplift: wu = 0.9D + 1.0W = 0.9 x 3.0 x 5 + 0.9 x 2.62 + (-88.3) x 5 = -425.6 plf = 0.426 klf (upward)

Mu = 0.426 x 50 = 21.3 kip-ft = 255.6 kip-in.

LTB capacity with midspan bridging (Lb = 10 ft):

Elastic critical LTB stress per AISI S100: Fcre = 6.02 ksi << Fy = 50 ksi.

Mn_LTB = 1.81 x 6.02 = 10.9 kip-in. phi x Mn = 9.81 kip-in. vs Mu = 255.6 kip-in. — catastrophic failure without adequate bridging.

With two bridging rows (Lb = 6.67 ft): Fcre = 12.52 ksi, Mn_LTB = 22.66 kip-in. phi x Mn = 20.4 kip-in. — still grossly inadequate.

Step 5 — Redesign for Uplift

Final design: C25024 at 4 ft c/c with 2 bridging rows

Under gravity with 4 ft spacing: Mx* = 88.2 kip-in. with C25024 phi x Mnx = 171 kip-in. — 51.6%. Under uplift: LTB capacity must be verified with actual section properties. Uplift controls.

Summary

Condition	C20015 at 5 ft	C25024 at 4 ft
Gravity major-axis	133% (FAIL)	51.6%
Gravity minor-axis	97.1%	~25%
Uplift LTB (midspan bridging)	<5% (FAIL)	Must verify
Bridging required	2 rows minimum	2 rows minimum

Conclusion: Cold-formed purlin design is governed by wind uplift in most US regions due to the dramatic reduction in LTB capacity. The C20015 proposed for gravity alone required upsize to C25024 with closer spacing and multiple bridging rows to satisfy uplift requirements. This worked example demonstrates why uplift, not gravity, dictates cold-formed purlin selection.