Steel Purlins & Girts — Z vs C Sections, Sag Rod Bracing & Span Tables
Purlins and girts are secondary framing members in metal building systems. Purlins support the roof sheeting and span between primary frames (rafters or trusses); girts support the wall sheeting and span between columns. Both are typically cold-formed Z-sections or C-sections made from high-strength galvanized sheet steel (ASTM A653 Gr 55, Fy = 55 ksi). Their design is governed by AISI S100-16 (cold-formed steel) rather than AISC 360.
Z-section vs C-section
| Feature — Z-section — C-section | | ----------------------- — ----------------------------------------------------------------------------- — -------------------------------------------------------- | | Shape — Equal flanges angled in opposite directions — Standard channel shape | | Biaxial bending — Principal axes inclined ~17 degrees to web — bends in both axes under gravity — Principal axes align with web — simpler bending behavior | | Continuous span lapping — Excellent — Z's nest together at laps — Poor — C's cannot nest, require specialized clips | | Shear center — Away from web, outside section — Away from web, outside section | | Lateral stability — Requires bridging/sag rods — Requires bridging/sag rods | | Common use — Roof purlins (lapped continuous spans) — Wall girts, simple span purlins |
Key Z-section issue: Because the principal axes are inclined, a gravity load on a Z-purlin creates both downslope (weak-axis) and normal (strong-axis) bending components. The downslope component must be resisted by bridging, sheeting restraint, or sag rods. Without these, the purlin rolls and deflects laterally.
Common purlin sizes
| Designation — Depth (in) — Flange (in) — Thickness (ga/mil) — Weight (plf) — Ix (in4) — Sx (in3) | | ------------ — ---------- — ----------- — ------------------ — ------------ — -------- — -------- | | Z8x2.5-14ga — 8.0 — 2.5 — 14 ga (0.075") — 3.14 — 10.1 — 2.53 | | Z8x2.5-12ga — 8.0 — 2.5 — 12 ga (0.105") — 4.37 — 13.7 — 3.43 | | Z10x3-14ga — 10.0 — 3.0 — 14 ga (0.075") — 3.78 — 18.1 — 3.63 | | Z10x3-12ga — 10.0 — 3.0 — 12 ga (0.105") — 5.28 — 24.8 — 4.96 | | Z12x3.5-14ga — 12.0 — 3.5 — 14 ga (0.075") — 4.55 — 29.0 — 4.83 | | Z12x3.5-12ga — 12.0 — 3.5 — 12 ga (0.105") — 6.35 — 40.0 — 6.67 |
Design method — purlin flexural capacity
Per AISI S100-16, the flexural capacity of a Z-purlin is:
phi_b × Mn = phi_b × Se × Fy (for yielding-controlled sections)
Where phi_b = 0.90 (LRFD) and Se = effective section modulus accounting for local buckling of compressed elements. For most standard purlin sizes at Fy = 55 ksi, local buckling of the compression flange lip reduces Se below the full Sx. Distortional buckling may further reduce capacity for deeper sections with small lips.
Lateral-torsional buckling is typically prevented by the roof sheeting on the compression flange (through-fastened or standing seam). Through-fastened sheeting provides full lateral bracing of the connected flange per AISI S100 Section I6.4.1. Standing seam sheeting provides partial bracing that must be quantified by the base test method (AISI S100 Section I6.2).
Worked example — roof purlin design
Given: Z10x3-14ga purlin (Fy = 55 ksi), simple span 25 ft, tributary width 5 ft, roof dead load = 5 psf, roof live load = 20 psf, roof slope = 1:12. Through-fastened metal sheeting on compression (top) flange.
Step 1 — Loading: wD = 5 × 5 = 25 plf. wL = 20 × 5 = 100 plf. wu = 1.2 × 25 + 1.6 × 100 = 190 plf = 0.190 klf. Mu = 0.190 × 25² / 8 = 14.84 kip-ft = 178 kip-in.
Step 2 — Effective section modulus: For Z10x3-14ga with through-fastened sheeting: Se ≈ 3.35 in³ (reduced from Sx = 3.63 due to effective width reduction in compression flange and lip).
Step 3 — Flexural capacity: phi_b × Mn = 0.90 × 3.35 × 55 = 165.8 kip-in.
178 > 165.8 — FAILS. Increase to Z10x3-12ga: Se ≈ 4.70 in³. phi_b × Mn = 0.90 × 4.70 × 55 = 232.7 kip-in > 178 — OK.
Step 4 — Deflection check (L/180 for roof live load): delta_allow = 25 × 12 / 180 = 1.67 in. delta_L = 5 × wL × L^4 / (384 × E × I) = 5 × 0.100 × (300)^4 / (384 × 29500 × 24.8) = 5 × 0.100 × 8.1 × 10^9 / (2.81 × 10^8) = 4.05 × 10^9 / 2.81 × 10^8 = 14.4 in — FAILS badly.
This illustrates a critical purlin design reality: deflection almost always governs over strength for simple spans above 20 ft. The solution is to use continuous spans (lapped at supports), which reduce midspan deflection by 60-75%.
Sag rods and bridging
Sag rods are tension rods (typically 1/2" or 5/8" diameter) that span between adjacent purlins at one or more points along the span to resist the downslope component of loading and provide lateral bracing.
Sag rod spacing rules of thumb:
- One row at midspan for spans up to 25 ft
- Two rows at third points for spans 25–35 ft
- Three rows at quarter points for spans over 35 ft
Bridging (diagonal angles connecting adjacent purlins) is an alternative to sag rods that provides both lateral bracing and torsional restraint. Required per AISI S100 Section C2 when sheeting bracing alone is insufficient (common for standing seam roofs).
Continuous span design
Most metal building purlins are designed as 2-span, 3-span, or multi-span continuous members with lapped connections at interior supports. Lapping (overlapping the top and bottom Z-sections by 2–4 ft at the support) creates a built-up section with approximately double the moment of inertia at the high-moment support region.
Benefits of continuous spans:
- Interior support negative moment = wL²/10 (vs wL²/8 for simple spans)
- Midspan positive moment = wL²/14 to wL²/16 (depending on lap length)
- Deflection reduced by 60–75% compared to simple spans
- Total purlin weight reduced by 20–30% for the same span and load
Code comparison
AISI S100-16 (USA/Canada): Primary standard for CFS purlins. Effective width method or Direct Strength Method (DSM). Through-fastened sheeting bracing per Section I6.4.1. Standing seam bracing per base test method (Section I6.2). phi_b = 0.90 for flexure.
AS/NZS 4600:2018 (Australia/NZ): Closely aligned with AISI S100. Purlin design per Section 3.3 (flexural members). Through-fastened sheeting restraint provisions. Australian practice commonly uses Lysaght or Stramit proprietary purlin systems with manufacturer-published span tables based on AS/NZS 4600.
EN 1993-1-3 (Eurocode 3): Cold-formed members per Part 1-3. Effective cross-section properties per Section 5.5. Lateral restraint from sheeting per EN 1993-1-3 Section 10. Eurocode uses a more complex interaction formula for combined bending and axial force in purlins on sloped roofs, explicitly accounting for the biaxial bending in Z-sections.
Common mistakes engineers make
Designing Z-purlins as simple spans when continuous spans are feasible. Simple span Z-purlins are grossly inefficient for spans above 20 ft — deflection governs and requires oversized sections. Continuous spans with laps at supports are standard practice in metal building design.
Ignoring the downslope bending component in Z-sections. On a 4:12 roof slope, approximately 15% of the gravity load acts as a downslope (weak-axis) force. Without sag rods or bridging, this force causes the purlin to twist and deflect laterally, reducing strong-axis capacity and causing visible deformation.
Assuming through-fastened sheeting always provides full bracing. Through-fastened (screw-attached) sheeting braces the connected flange effectively, but standing seam sheeting provides only partial restraint because the clips allow the panel to slide. Using full bracing capacity with standing seam sheeting unconservatively overestimates purlin capacity by 15–30%.
Using AISC 360 for purlin design. Purlins are cold-formed members — their thin elements buckle locally and distortionally in ways that AISC 360 does not address. Using AISC column curves or beam flexure equations for CFS purlins produces incorrect capacities. AISI S100 must be used.
Cold-formed steel purlin design per AISI S100 — detailed procedure
The AISI S100 specification provides two methods for determining the flexural capacity of cold-formed steel purlins:
Effective Width Method (EWM) — AISI S100 Section B2:
- Calculate full (gross) section properties (Ix, Sx, Zx)
- Determine the effective width of each compression element using the plate buckling coefficient k and the slenderness ratio lambda = 1.052 × sqrt(f/b/t)
- Reduce the compression flange and lip to their effective widths
- Recalculate section properties using the effective section (Se = effective section modulus)
- phi × Mn = phi × Se × Fy (with appropriate checks for local buckling interaction)
Direct Strength Method (DSM) — AISI S100 Appendix 2:
- Calculate full section properties
- Determine elastic buckling loads for each mode using a finite strip analysis (e.g., CUFSM software): Mcr (global), Ml (local), Md (distortional)
- Calculate nominal capacity for each mode using DSM formulas:
- Global: Mn = Mcr (if lambda <= 0.60) or 1 - 0.15(My/Mcr)^0.4^0.4 × Mcr^0.6
- Local: Mn = My (if lambda_l <= 0.776) or 1 - 0.15(Mcr/Ml)^0.4^0.4 × Ml^0.6
- Distortional: Mn = My (if lambda_d <= 0.673) or 1 - 0.25(Mcr/Md)^0.6^0.6 × Md^0.4
- phi × Mn = min(phi × Mn_global, phi × Mn_local, phi × Mn_distortional)
The DSM is increasingly preferred because it captures all three buckling modes explicitly and does not require iterative effective width calculations.
Z-section vs C-section detailed comparison
| Property | Z-Section | C-Section |
|---|---|---|
| Flange orientation | Equal flanges, opposite direction | One flange has lip, channel shape |
| Principal axis inclination | ~17° from web (biaxial bending under load) | Aligned with web (simpler analysis) |
| Nesting at laps | Excellent — flanges interlock | Poor — flanges do not nest naturally |
| Section efficiency | Higher (symmetric about strong axis) | Lower (asymmetric section) |
| Shear center location | Outside section, eccentric from web | Outside section, eccentric from web |
| Torsional stiffness | Moderate | Moderate |
| Optimal use | Roof purlins (continuous, lapped) | Wall girts (simple span), short purlins |
| Connection at supports | Nest in pairs at laps, creating built-up section | Individual clips or brackets needed |
| Economy for long spans | Better (lap creates composite action) | Worse (no lapping benefit) |
| Manufacturer availability | Wide (Butler, Varco-Pruden, Nucor) | Wide (all manufacturers) |
Purlin span tables by roof load
Approximate maximum simple spans for Z-section purlins (Fy = 55 ksi) with through-fastened sheeting, L/180 deflection limit under live load:
| Purlin Section | 15 psf LL | 20 psf LL | 25 psf LL | 30 psf LL |
|---|---|---|---|---|
| Z8x2.5-14ga | 21 ft | 19 ft | 17 ft | 16 ft |
| Z8x2.5-12ga | 25 ft | 23 ft | 21 ft | 20 ft |
| Z10x3.0-14ga | 26 ft | 24 ft | 22 ft | 20 ft |
| Z10x3.0-12ga | 31 ft | 28 ft | 26 ft | 24 ft |
| Z12x3.5-14ga | 31 ft | 28 ft | 26 ft | 24 ft |
| Z12x3.5-12ga | 36 ft | 33 ft | 31 ft | 29 ft |
For continuous spans (2-span or 3-span), the above spans can be increased by approximately 30-40% because the continuous moment distribution reduces both the maximum moment and deflection.
Sag rod and bracing requirements
Sag rods serve two purposes: they resist the downslope component of gravity loading on sloped purlins, and they provide lateral bracing to the purlin compression flange (or tension flange for uplift).
Sag rod design loads: For a roof slope of angle theta, the downslope force per purlin per sag rod:
F_downslope = w_gravity × sin(theta) × tributary_width × sag_rod_spacing / number_of_purlins_between_anchorage
Typical sag rod sizes:
- 1/2" diameter rod for purlin spans up to 25 ft and slopes up to 4:12
- 5/8" diameter rod for spans 25-35 ft or slopes up to 6:12
- 3/4" diameter rod for spans over 35 ft or slopes over 6:12
Sag rod anchorage: Sag rods must be anchored at the ridge or eave to transfer the accumulated downslope forces to the primary structure. The ridge purlin is typically the anchor point, with all sag rods spanning downslope to it. The ridge connection must resist the total downslope force from all purlins on one side of the roof.
Bridging requirements: Diagonal bridging (angles or channels) is required in addition to sag rods when:
- Standing seam roofing is used (reduced diaphragm stiffness)
- Purlin spans exceed 30 ft (simple span) or 40 ft (continuous)
- The roof slope exceeds 4:12
- Heavy concentrated loads are present (HVAC units, rooftop equipment)
Girt design for wind loads
Girts are the wall-framing equivalent of purlins, spanning between columns to support wall cladding. They are designed for wind pressure and suction (out-of-plane bending) and are typically C-sections for simplicity.
Wind load determination per ASCE 7-22:
- Wind pressure q = 0.00256 × Kz × Kzt × Kd × V² × G × Cp (analytical procedure)
- For a typical metal building wall: Cp = +0.80 (pressure) or -0.70 / -1.0 (suction at corners)
- The controlling load case is often wind suction (uplift on the girt, compression flange unbraced)
Girt design example: Given: 8" C-section girt (C8x2.5-14ga), 25 ft span, 6 ft tributary width, wind pressure = 20 psf. Mu = 1.0 × 20 × 6 × 25² / 8 = 9,375 lb-ft = 9.38 kip-ft = 112.5 kip-in. Required Se = 112.5 / (0.90 × 55) = 2.27 in³. C8x2.5-14ga Se (effective) ≈ 2.0 in³ — slightly short. Use 12ga or reduce span.
Key girt design considerations:
- Wind suction reverses the compression flange from the sheeting-connected side to the interior side, requiring bridging or brace points for the unbraced flange
- Girts at building corners and edges experience higher wind suction (Cp = -1.4 per ASCE 7 Fig. 30.4-1 for Zone 5)
- Deflection limits are often L/120 for metal wall panels and L/180 for masonry veneer
Bridging and tie requirements
| Requirement | Specification | Purpose |
|---|---|---|
| Flange brace (purlin) | At each support and at midspan | Prevent lateral buckling of bottom flange |
| Anti-roll device | At each rafter for Z-purlins | Prevent rotation at supports |
| Flange brace (girt) | At midspan for suction loading | Brace interior flange under uplift |
| Sag rod spacing | Per span length table above | Resist downslope forces, provide lateral bracing |
| Diagonal bridging | As required per AISI S100 Section C2 | Torsional restraint at discrete points |
| Eave strut tie | At eave connecting purlins to column | Transfer horizontal thrust |
| Ridge tie | At ridge connecting purlins across peak | Prevent ridge separation under load |
Typical purlin/girt sizes by span
| Span (ft) | Typical Purlin (roof, 20 psf LL) | Typical Girt (wall, 20 psf wind) |
|---|---|---|
| 15 | Z8x2.5-14ga | C6x2.0-14ga |
| 20 | Z8x2.5-12ga | C8x2.5-14ga |
| 25 | Z10x3.0-14ga | C8x2.5-12ga |
| 30 | Z10x3.0-12ga | C10x3.0-12ga |
| 35 | Z12x3.5-12ga | C10x3.0-10ga |
| 40 | Z12x3.5-10ga (continuous) | C12x3.5-10ga (continuous) |
These are preliminary selections for typical metal building loads. Final sizing requires a full AISI S100 check including local buckling, distortional buckling, and combined loading effects.
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Related references
- How to Verify Calculations
- roof load combinations
- portal frame primary members
- cold-formed steel design
- steel member weight calculator
- Cold Formed Sections
- Roof Framing
Disclaimer
This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.
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Frequently Asked Questions
What is the recommended design procedure for this structural element?
The standard design procedure follows: (1) establish design criteria including applicable code, material grade, and loading; (2) determine loads and applicable load combinations; (3) analyze the structure for internal forces; (4) check member strength for all applicable limit states; (5) verify serviceability requirements; and (6) detail connections. Computer analysis is recommended for complex structures, but hand calculations should be used for verification of critical elements.
How do different design codes compare for this calculation?
AISC 360 (US), EN 1993 (Eurocode), AS 4100 (Australia), and CSA S16 (Canada) follow similar limit states design philosophy but differ in specific resistance factors, slenderness limits, and partial safety factors. Generally, EN 1993 uses partial factors on both load and resistance sides (γM0 = 1.0, γM1 = 1.0, γM2 = 1.25), while AISC 360 uses a single resistance factor (φ). Engineers should verify which code is adopted in their jurisdiction.