AS/NZS 4600 Cold-Formed Steel Design — C & Z Purlins with Effective Width

Complete AS/NZS 4600:2018 cold-formed steel design walkthrough: effective width method for C15024 and Z20024 purlins, distortional buckling, screw connection capacities, and bracing requirements. Australian cold-formed steel design differs from AISI S100 (North America) in material grades, connection phi factors, and the treatment of nested Z-sections.

The Steel Calculator WASM engine performs cold-formed steel checks for the Direct Strength Method. This page covers Australian CFS design per AS/NZS 4600, which governs roof purlins, wall girts, and light-gauge framing in Australian construction.

PRELIMINARY — NOT FOR CONSTRUCTION. All results are for educational and reference use only. Must be independently verified by a Chartered Professional Engineer (CPEng) or RPEQ before use in any project.

Australian CFS Material Grades (AS 1397)

Australian cold-formed steel is manufactured from hot-dipped zinc-coated steel strip to AS 1397. Three structural grades dominate:

G550 is the dominant grade for Australian roof purlins. The near-unity f_u/f_y ratio of G550 (1.00-1.05) means the material has essentially no strain-hardening capacity — it yields and fractures at near-identical stress levels. AS/NZS 4600 Clause 1.5.2 addresses this by limiting the yield stress used in design to 0.75 x f_u for sections where f_u/f_y < 1.08. For G550, this effectively caps the design yield at 413 MPa for flexural members unless additional ductility provisions are satisfied.

C-Section Purlin Design — C15024 Worked Example

Design Problem

A C15024 purlin (150 mm deep, 2.4 mm thick, G550 steel per AS 1397) spans 4.5 m simply supported at 1.2 m centres on a roof with 7.5-degree pitch. The purlin supports metal roof sheeting fastened at every rib (approximately 200 mm centres), providing continuous lateral restraint to the compression flange.

Section Properties — C15024 (G550):

Step 1 — Effective Width of the Compression Flange (AS/NZS 4600 Clause 2.2.1.2)

The compression flange of the C15024 is a stiffened element with an edge stiffener (lip). First, determine if the lip is adequate to fully stiffen the flange.

Flange Flat Width

b_f_flat = b_f - t - r_c = 62.5 - 2.4 - 3.6 = 56.5 mm

b_f_flat / t = 56.5 / 2.4 = 23.54

Effective Width of the Lip (Edge Stiffener)

The lip is an unstiffened element with one longitudinal edge free. For the lip flat width:

b_l_flat = b_l - r_c = 16.5 - 3.6 = 12.9 mm

b_l_flat / t = 12.9 / 2.4 = 5.38

For an unstiffened element (k = 0.43) at stress f* = 550 MPa:

lambda_lip = (1.052 / sqrt(0.43)) x (5.38) x sqrt(550 / 200,000)

= (1.052 / 0.656) x 5.38 x sqrt(0.00275)

= 1.604 x 5.38 x 0.0524 = 0.453

Since lambda_lip = 0.453 < 0.673, the lip is fully effective (rho_lip = 1.0).

Effective Width of the Flange (Edge-Stiffened Element)

Per AS/NZS 4600 Clause 2.4, the effective width of an edge-stiffened element depends on the adequacy of the stiffener. The required stiffener moment of inertia:

I_a = (b_f_flat / t)^2 x t^4 / 50 for lambda <= 1.0

For b_f_flat/t = 23.54: I_a = (23.54)^2 x (2.4)^4 / 50 = 554.4 x 33.18 / 50 = 368 mm^4

The actual lip stiffener moment of inertia about its own centroidal axis parallel to the stiffened element:

I_s = (t x b_l_flat^3) / 12 = (2.4 x 12.9^3) / 12 = 2.4 x 2,147 / 12 = 429 mm^4

I_s / I_a = 429 / 368 = 1.166 > 1.0 — the lip provides full stiffening. The flange plate buckling coefficient is therefore k = 4.0 (fully stiffened).

Flange Effective Width Calculation

For a stiffened element (k = 4.0) at stress f* = 550 MPa:

lambda = (1.052 / sqrt(4.0)) x (23.54) x sqrt(550 / 200,000)

= (1.052 / 2.0) x 23.54 x sqrt(0.00275)

= 0.526 x 23.54 x 0.0524 = 0.649

Since lambda = 0.649 < 0.673, the flange is fully effective (rho = 1.0). The flange gross width contributes fully to the section properties.

Step 2 — Effective Width of the Web (Stiffened Element in Bending)

The web of the C15024 in bending is a stiffened element with one edge in compression and one in tension (k = 24.0 for webs in bending per AS/NZS 4600 Table 2.2.1a).

Web Flat Width

d_1 = d - 2 x (t + r_c) = 150 - 2 x (2.4 + 3.6) = 150 - 12 = 138 mm

d_1 / t = 138 / 2.4 = 57.5

Web Slenderness

lambda_web = (1.052 / sqrt(24.0)) x (57.5) x sqrt(550 / 200,000)

= (1.052 / 4.899) x 57.5 x 0.0524

= 0.2147 x 57.5 x 0.0524 = 0.647

Since lambda_web = 0.647 < 0.673, the web is fully effective in bending at the yield stress.

For this relatively stocky C15024 purlin, all elements are fully effective at the yield stress — no reduction to the section modulus is required. This is typical for purlins with b/t ratios under 30 and G550 steel.

Step 3 — Section Moment Capacity (AS/NZS 4600 Clause 3.3.3)

Since all elements are fully effective, the section moment capacity is based on the gross section:

Initiation of Yielding

M_y = Z_fx x f_y = 28.3 x 10^3 x 550 = 15.6 kN.m

With the capacity factor for flexure (laterally braced): phi_b = 0.90 (AS/NZS 4600 Table 1.6)

phi x M_y = 0.90 x 15.6 = 14.0 kN.m

Load Check

Dead load: roof sheeting 0.05 kPa + purlin self-weight 0.04 kPa = 0.09 kPa Live load: 0.25 kPa (roof live, AS 1170.1 Table 3.3) Wind uplift: -0.90 x 0.95 kPa (region A2, roof suction) = -0.86 kPa (net uplift, including internal pressure)

ULS downward: w* = 1.2 x 0.09 + 1.5 x 0.25 = 0.108 + 0.375 = 0.483 kPa

Line load on purlin: w* x spacing = 0.483 x 1.2 = 0.580 kN/m

M* = w* x L^2 / 8 = 0.580 x 4.5^2 / 8 = 1.47 kN.m

Utilisation = 1.47 / 14.0 = 0.105 — the purlin is very lightly loaded in downward bending. Wind uplift governs — the wind suction load produces a reversal moment on the purlin.

ULS uplift: w*_up = 1.0 x 0.09 + 1.0 x (-0.86) = -0.77 kPa (net uplift)

Line load uplift: w*_up x 1.2 = 0.924 kN/m

M*_up = 0.924 x 4.5^2 / 8 = 2.34 kN.m

The bottom flange is now in compression. With roof sheeting attached only to the top flange, the bottom flange is unbraced between bridging rows.

Step 4 — Lateral-Torsional Buckling of C15024 Purlin Under Uplift

Under wind uplift, the bottom flange is in compression with no continuous lateral restraint. Bridging is provided at L/3 points (1.5 m spacing).

Elastic LTB Stress (AS/NZS 4600 Clause 3.3.3.2)

For a C-section under uniform moment with the compression flange unbraced:

f_oc = (pi^2 x E) / (L_ey / r_y)^2

For the segment between bridging rows: L_ey = 1,500 mm, r_y = 18.6 mm.

f_oc = (pi^2 x 200,000) / (1,500 / 18.6)^2 = 1,973,900 / 6,496 = 303.9 MPa

Slenderness for LTB

lambda_c = sqrt(f_y / f_oc) = sqrt(550 / 303.9) = sqrt(1.810) = 1.345

Since lambda_c = 1.345 > 1.5? No, 1.345 < 1.5.

For lambda_c <= 1.5: f_c = (0.658^(lambda_c^2)) x f_y = (0.658^1.810) x 550 = 0.476 x 550 = 261.8 MPa

Member Moment Capacity

M_c = Z_fx x f_c = 28.3 x 10^3 x 261.8 = 7.41 kN.m

phi_b x M_c = 0.90 x 7.41 = 6.67 kN.m

M*_up = 2.34 kN.m < 6.67 kN.m — the purlin is adequate for uplift with bridging at 1.5 m centres. Without bridging (L_ey = 4,500 mm), f_oc = 33.8 MPa, lambda_c = 4.03, f_c = 0.877 x 33.8 = 29.6 MPa, and M_c = 0.84 kN.m — the purlin would fail.

Z20024 Purlin — Continuous Span System

Z-section purlins are roll-formed from G550 steel and nested (overlapped) at internal supports to create a continuous multi-span system. The nesting provides rotational restraint at the support, approximating a fixed-end condition.

Z20024 Properties

Effective Width at Support (Negative Moment)

At the internal support of a continuous Z-purlin, the web is in bending with the compression zone at the bottom (the free flange). For a two-span continuous purlin with equal spans:

Negative moment at interior support: M*_support approximately w* x L^2 / 8 (conservative for two-span case).

For Z20024 at 1.5 m spacing over 7.2 m span: w*_down = 0.58 kN/m (same roof loading).

M*_support = 0.58 x 7.2^2 / 8 = 3.76 kN.m

At this stress level, the compression flange effective width is recalculated. Since the stress is significantly below yield (M* / M_y = 3.76 / 27.3 = 0.138), all elements remain fully effective and no reduction to Z_x is needed.

M_y = Z_fx x f_y = 49.6 x 10^3 x 550 = 27.3 kN.m phi x M_y = 0.90 x 27.3 = 24.6 kN.m

Utilisation = 3.76 / 24.6 = 0.153 — the purlin has significant reserve capacity.

Distortional Buckling Check (AS/NZS 4600 Clause 2.3.2)

Distortional buckling involves rotation of the compression flange and lip about the flange-web junction. For the Z20024 purlin:

Flange flat width: b_f_flat = 71 - 2.4 - 3.6 = 65.0 mm, b_f_flat / t = 27.1

Lip flat width: b_l_flat = 20 - 3.6 = 16.4 mm, b_l_flat / t = 6.83

The elastic distortional buckling stress for a lipped channel with compression flange in compression can be estimated from the simplified AS/NZS 4600 approach. For sections with b_f_flat / t > 25 and G550 steel, the distortional buckling stress typically falls in the range:

f_od approximately 280 to 350 MPa for Australian C-sections with lips of 15-20 mm.

For the Z20024 with b_l_flat / b_f_flat = 16.4 / 65.0 = 0.252 (within the optimal range of 0.25-0.33), the distortional buckling stress is approximately 310 MPa.

lambda_d = sqrt(f_y / f_od) = sqrt(550 / 310) = sqrt(1.774) = 1.332

For lambda_d > 0.561: f_d = (1 - 0.22 / lambda_d) x f_y / lambda_d

f_d = (1 - 0.22/1.332) x 550 / 1.332 = (1 - 0.165) x 413.1 = 0.835 x 413.1 = 344.8 MPa

The distortional buckling effective section modulus:

Z_d = Z_fx x (f_d / f_y) = 49.6 x 10^3 x (344.8 / 550) = 49.6 x 10^3 x 0.627 = 31.1 x 10^3 mm^3

M_d = Z_d x f_y = 31.1 x 10^3 x 550 = 17.1 kN.m phi x M_d = 0.90 x 17.1 = 15.4 kN.m

Even with the distortional buckling reduction (37% reduction in Z_x), the Z20024 has adequate capacity for the 3.76 kN.m support moment.

Screw Connection Design for Purlins (AS/NZS 4600 Clause 5.4)

Australian purlin-to-cleat connections use self-drilling screws (typically No. 12 or No. 14 gauge) conforming to AS 3566. For a C15024 purlin connected to a 6 mm thick hot-rolled steel cleat with two No. 12 screws through the web:

Screw Shear Capacity

No. 12 screw: d = 5.5 mm, f_u_screw = 900 MPa (minimum per AS 3566 Class 3)

Threads in the shear plane: screw shear capacity per AS/NZS 4600 Clause 5.4.2.2:

V_fv = 0.62 x f_u_screw x A_c where A_c = net area at thread root.

For No. 12 screw with thread root diameter 4.2 mm: A_c = pi x 4.2^2 / 4 = 13.85 mm^2

V_fv = 0.62 x 900 x 13.85 = 7,728 N = 7.73 kN

phi = 0.65 for screw shear: phi x V_fv = 0.65 x 7.73 = 5.02 kN per screw

Bearing/Tearout in the CFS Web (2.4 mm G550 sheet)

V_b = 2.7 x t x d x f_u = 2.7 x 2.4 x 5.5 x 550 = 19,602 N = 19.6 kN

phi x V_b = 0.65 x 19.6 = 12.7 kN per screw

The screw shear governs at 5.02 kN per screw. For two screws: 2 x 5.02 = 10.0 kN design capacity.

Reaction at the purlin support: R* = w* x L / 2 = 0.58 x 4.5 / 2 = 1.31 kN < 10.0 kN — connection is adequate.

AS/NZS 4600 vs AISI S100 Comparison

Frequently Asked Questions

How does AS/NZS 4600 calculate the effective width of a cold-formed steel element?

AS/NZS 4600 Clause 2.2.1.2 uses the Winter formula to calculate the effective width b_e = rho x b where rho = (1 - 0.22/lambda)/lambda for lambda > 0.673, and rho = 1.0 for lambda <= 0.673. The plate slenderness lambda = (1.052/sqrt(k)) x (b/t) x sqrt(f*/E) where k is the plate buckling coefficient (4.0 for stiffened elements, 0.43 for unstiffened). For a C15024 purlin web at G550 yield with b/t = 59.0, lambda = 1.27 and rho = 0.650, meaning the web effective width is only 65% of the gross width.

What is the difference between G250, G450, and G550 steel in Australian CFS design?

G250, G450, and G550 grades per AS 1397 refer to minimum yield strengths of 250, 450, and 550 MPa respectively for cold-formed steel strip. G550 is the most common grade for roof purlins and wall girts in Australia because its higher strength allows thinner sections and longer spans. However, G550 has reduced ductility — the yield-to-tensile ratio is typically 0.95-0.98, meaning the material yields almost immediately before fracture. AS/NZS 4600 Clause 1.5.2 limits G550 to sections with thickness >= 0.9 mm for structural applications and requires capacity reduction factors for connections. G450 offers a better balance of strength and ductility and is preferred for seismic applications.

How are screw connections designed in Australian cold-formed steel per AS/NZS 4600?

AS/NZS 4600 Clause 5.4 specifies screw connection design with phi = 0.65 for screws in shear and phi = 0.60 for screws in tension (pull-out and pull-over). For a No. 12 self-drilling screw (d = 5.5 mm) in 1.5 mm G550 sheet, the shear capacity per screw is approximately 3.2 kN. Minimum edge distance is 3d = 16.5 mm, and minimum spacing is 3d = 16.5 mm. Screws in tension (pull-over) are governed by the head diameter and sheet thickness: N_ov = 1.5 x t x f_u x d_w, which for a 1.5 mm sheet with 12 mm washer diameter gives approximately 5.0 kN. For purlin-to-cleat connections, two No. 12 screws per purlin flange are standard practice in Australian roof construction.

When does distortional buckling govern over local buckling in CFS purlins?

Distortional buckling per AS/NZS 4600 Clause 2.3.2 governs when the lip stiffener is insufficient to prevent rotation of the compression flange about the flange-web junction. For C-section purlins with standard Australian lip lengths (15-20 mm for C150-C300 sections), distortional buckling typically governs when the flange flat width-to-thickness ratio exceeds approximately 25 for G550 steel. For a C20024 purlin with flange b/t = 26.1, the distortional buckling stress f_od is typically 280-320 MPa, which is below the yield stress of 550 MPa — meaning distortional buckling reduces the effective section modulus by 15-25% at full yield. Australian manufacturers address this by providing larger lips (20-25 mm) on deeper purlins to elevate the distortional buckling stress above yield.

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Related Pages

• AS 4100 Steel Design Guide — Australia — Full Australian steel reference
• AS 4100 Beam Design — 310UB40.4 Worked Example — Hot-rolled beam design
• AS 4100 Column Design — 200UC46 Worked Example — Hot-rolled column design
• AS 4100 Bolt Design Guide — Bolted connections
• Cold-Formed Steel Design — AISI S100 — North American CFS design
• Australian Steel Grades Guide — Complete AU material grades
• Steel Material Properties Reference — Multi-code comparison

This page is for educational reference. All resistance formulae are per AS/NZS 4600:2018 with AS 1397 material grades. Verify the applicable edition of the National Construction Code for your project jurisdiction. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent review by a registered structural engineer (CPEng/RPEQ).