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:

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:

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

  1. 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.

  2. 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.

  3. 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%.

  4. 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:

  1. Calculate full (gross) section properties (Ix, Sx, Zx)
  2. 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)
  3. Reduce the compression flange and lip to their effective widths
  4. Recalculate section properties using the effective section (Se = effective section modulus)
  5. phi × Mn = phi × Se × Fy (with appropriate checks for local buckling interaction)

Direct Strength Method (DSM) — AISI S100 Appendix 2:

  1. Calculate full section properties
  2. Determine elastic buckling loads for each mode using a finite strip analysis (e.g., CUFSM software): Mcr (global), Ml (local), Md (distortional)
  3. Calculate nominal capacity for each mode using DSM formulas:
  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:

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:

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:

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:

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

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.