----------------- | :---------------------- | :-------------------------- | | Thickness t | ≥ 4.5 mm typical | 0.84-6.0 mm | | Fy | 350 MPa typical | 230-550 MPa | | Design approach | Plastic/elastic section | Effective width method | | Buckling modes | LTB, LB, FB | Local, distortional, global | | Resistance factor phi | 0.90 (members) | 0.90 (members) |

Material Grades

Grade 340 MPa is the most common for cold-formed structural members in Canada.

Effective Width Method

Per CSA S136 Clause B2, the effective width of a uniformly compressed stiffened element:

b_e = w × (1 - 0.22/lambda_p) / lambda_p when lambda_p > 0.673 b_e = w when lambda_p ≤ 0.673

Where:

• lambda_p = sqrt(Fy / F_cr) = (w/t) × sqrt(Fy / (k × pi^2 × E / (12 × (1 - nu^2))))
• k = plate buckling coefficient (4.0 for stiffened elements)
• w = flat width of element

Section Types

Distortional Buckling

Per CSA S136 Clause B3.2, distortional buckling is a critical limit state for cold-formed sections with edge stiffeners:

Mn_dist = Sc × Fd (nominal moment capacity for distortional buckling)

Where:

• Sc = section modulus of effective section about compression fibre
• Fd = distortional buckling stress

Distortional buckling is unique to cold-formed steel — it occurs when the lip-stiffened flange rotates about the flange-web junction.

Distortional Buckling Stress

Fd = (k_d × pi^2 × E) / (12 × (1 - nu^2)) × (t/b_f)^2

For C-sections, k_d depends on the lip depth to flange width ratio d/b_f:

• For d/b_f = 0.05-0.15: k_d = 0.5-2.0 (typical range)

For most C-sections, distortional buckling governs when the flange width-to-thickness ratio b_f/t > 70/sqrt(Fy/340).

C-Section Properties

Standard C-Section (CS) Dimensions

C-Section Flexural Capacity (340 MPa)

Z-Section Properties

Standard Z-Section (ZS) Dimensions

Z-sections have better bending capacity than C-sections of the same dimensions due to the offset web, which increases the weak-axis section modulus.

Worked Example — Purlin Design

Given: CS200×50×15×1.9 purlin at roof slope 2:12. Span = 6.0 m, continuous over two spans. Purlin spacing = 1.5 m. Loads: dead = 0.5 kPa, snow = 1.0 kPa (NBCC 2020). Grade 340 MPa steel.

Step 1 — Section Properties: CS200×50×15×1.9: mass = 4.68 kg/m, Sx_eff = 42.1 × 10^3 mm^3 Ix_eff = 4.21 × 10^6 mm^4 (approximate — depends on effective width calculation)

Step 2 — Factored Loads: Dead load: 0.5 kPa × 1.5 m = 0.75 kN/m (purlin self-weight: 0.046 kN/m — included) Snow load: 1.0 kPa × 1.5 m = 1.50 kN/m

Load combination (NBCC 2020): 1.25D + 1.5S = 1.25 × 0.80 + 1.5 × 1.50 = 1.0 + 2.25 = 3.25 kN/m

Step 3 — Moment (continuous two-span): Maximum positive moment: M_pos = 0.096 × w × L^2 = 0.096 × 3.25 × 6.0^2 = 11.2 kN·m Maximum negative moment (at interior support): M_neg = 0.063 × w × L^2 = 0.063 × 3.25 × 6.0^2 = 7.4 kN·m

Step 4 — Flexural Capacity: Sx_eff = 42.1 × 10^3 mm^3 (positive bending, compression flange on lip side) Mr = phi × Sx_eff × Fy = 0.90 × 42,100 × 340 / 10^6 = 12.9 kN·m

Step 5 — Check: Mf = 11.2 kN·m ≤ Mr = 12.9 kN·m. Ratio = 0.87. OK.

Step 6 — Deflection (Serviceability): Live load deflection: delta = 0.0069 × w_S × L^4 / (E × Ix_eff) = 0.0069 × 1.50 × 6000^4 / (200,000 × 4.21 × 10^6) = 15.9 mm L/240 = 6000/240 = 25.0 mm. 15.9 < 25.0. OK.

Result: CS200×50×15×1.9 Grade 340 MPa purlin at 1.5 m spacing, spanning 6.0 m continuous over 2 spans. Adequate for factored loads and serviceability.

Connections in Cold-Formed Steel

Per CSA S136 Clause E:

Screw Spacing and Edge Distance

• Minimum edge distance: 3 × screw diameter (typically 12 mm for No. 12 screws)
• Minimum centre-to-centre spacing: 3 × screw diameter
• Minimum end distance: 3 × screw diameter

Frequently Asked Questions

What is the difference between CSA S136 and CSA S16 for steel design? CSA S136 (cold-formed steel) is used for light-gauge members (t = 0.84-6.0 mm) that are formed at room temperature. Design uses the effective width method to account for local and distortional buckling. CSA S16 (hot-rolled steel) is used for heavier sections and uses plastic/elastic section properties with section classification (Class 1-4). CSA S136 addresses distortional buckling (unique to cold-formed sections with lip stiffeners), which CSA S16 does not cover.

What is the effective width method in cold-formed steel design? The effective width method accounts for local buckling by reducing the width of compression elements. Per CSA S136 Clause B2, the effective width be = w × (1 - 0.22/lambda_p)/lambda_p when lambda_p > 0.673. This means the centre portion of a slender compression element is assumed to buckle and carry no stress, while the edges near the supports carry stress up to Fy. The reduced section properties are calculated using the effective widths of all compression elements.

What is distortional buckling in cold-formed steel? Distortional buckling is a buckling mode unique to cold-formed sections with edge stiffeners (lips). The compression flange and lip rotate about the flange-web junction, while the web remains straight. Unlike local buckling (where the flange buckles between lip and web), distortional buckling involves the whole flange-lip assembly. CSA S136 Clause B3.2 provides the distortional buckling check, which often governs for intermediate flange slenderness.

What fasteners are used in cold-formed steel construction in Canada? Self-drilling screws are the most common fasteners (Nos. 8-14, with No. 12 being standard for structural connections). Power-actuated fasteners (powder-actuated or gas-actuated) are used for connections to concrete or steel supports. Bolted connections (M6-M12) are used for heavy connections with thicker material. Welding is less common in cold-formed construction due to the thin material but is permitted per CSA W59 for t ≥ 1.5 mm.

Related Pages

• Canadian Steel Grades — G40.21 Reference
• CSA S16 Beam Design
• Canadian HSS Section Properties
• CSA S16 Column Design
• Canadian Composite Column
• Beam Capacity Calculator
• All Canadian References

This page is for educational reference. Cold-formed steel design per CSA S136-19. Verify effective width calculations and buckling modes with analysis software. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent PE/SE verification.

Design Resources

Calculator tools

• Cold-Formed Steel Calculator
• CFS Wall Stud Calculator

Reference pages

• CA Cold Formed