CSA S136 Cold-Formed Steel — CFS Design Guide

Complete reference for CSA S136:16 (North American Specification for Cold-Formed Steel Structural Members) — the Canadian cold-formed steel design standard. Covers the effective width method for local buckling, distortional buckling (P-DST method), CFS section properties for C/Z studs and tracks, screw connection capacity, welded connections, and a design example for a CFS stud wall under axial load.

Quick access: CSA S16 Guide | CISC Handbook | Steel Grades

CSA S136 — Canadian Cold-Formed Steel Standard

CSA S136:16, also known as the North American Specification for Cold-Formed Steel Structural Members, is harmonised with AISI S100-16 (North American Specification). The standard covers the design of cold-formed steel sections with thicknesses up to 12.7 mm (1/2 inch) — beyond this thickness, CSA S16 governs.

Cold-formed steel differs fundamentally from hot-rolled steel design:

Cold-formed steel is widely used in Canadian light commercial and residential construction for load-bearing stud walls, roof trusses, floor joists, curtain walls, and metal building secondary framing.

Effective Width Method (CSA S136 Clause C2)

Cold-formed steel sections have thin walls that buckle locally at stresses below the yield point. The effective width method accounts for this by reducing the width of slender compression elements to an effective width that, when stressed to the yield strength, carries the same load as the actual element in its post-buckled range.

Effective Width for Stiffened Elements (Clause C2.3)

For stiffened compression elements (webs, flanges with edge stiffeners):

b = w              when λ ≤ 0.673

b = ρ × w          when λ > 0.673

where:
  ρ = (1 - 0.22/λ) / λ   (reduction factor)
  λ = 1.052 × (w/t) × √(f / (E × k))   (slenderness parameter)

  w = flat width of element (mm)
  t = thickness (mm)
  f = design stress (MPa)
  E = modulus of elasticity (200,000 MPa)
  k = plate buckling coefficient (4.0 for stiffened elements)

Effective Width for Unstiffened Elements (Clause C2.4)

For unstiffened compression elements (open flanges, lips):

k = 0.43 (for unstiffened elements)
λ = 1.052 × (w/t) × √(f / (E × 0.43))
ρ = (1 - 0.22/λ) / λ   when λ > 0.673

Effective Width for Edge-Stiffened Elements (Clause C2.5)

For edge-stiffened elements (lipped flanges of C and Z sections), the buckling coefficient k depends on the stiffener dimensions. The effective width iteration involves checking the stiffener adequacy:

Stiffener adequacy criteria:
d/w ≤ 0.8 (lip depth to flange width ratio)
0.8 ≤ D/t ≤ 12 (lip depth ratio)
θ ≥ 45° (lip angle)

Distortional Buckling — P-DST Method (CSA S136 Clause C3.3)

Distortional buckling is a unique cold-formed steel buckling mode where the flange and lip rotate about the flange-web junction, distorting the cross-section. It is typically the critical buckling mode for C and Z sections with relatively deep lips and thin webs.

The distortional buckling resistance is calculated using the P-DST (Direct Strength for Distortional Buckling) method:

Pnd = Pne                   when λd ≤ 0.561

Pnd = Pne × (1 - 0.25 × (Pcrd / Pne)^0.6) × (Pcrd / Pne)^0.6
                            when λd > 0.561

where:
  λd  √(Pne / Pcrd)         (distortional slenderness)
  Pne = nominal global buckling resistance (N)
  Pcrd = elastic distortional buckling load (N)

The elastic distortional buckling load Pcrd is typically computed using finite strip analysis (software like CUFSM, GBTUL, or CFSEI). Canadian CFS design practice commonly uses the Direct Strength Method (DSM) for C and Z stud sections, with software tools for the elastic buckling analysis.

Approximate Distortional Buckling Stress

For simple C-section studs, the elastic distortional buckling stress can be approximated:

fcrd = 0.5 × (fcrl × t × E / (b_f × w))^0.5

where:
  fcrl = local buckling stress (MPa)
  b_f  = flange width (mm)
  w    = web depth (mm)

This approximation is suitable for preliminary sizing. For final design, finite strip analysis is recommended.

CFS Section Properties — C and Z Sections

Typical C-Stud Sections

Typical Track Sections

Track sections (U-shaped) serve as top and bottom chords for C-stud walls:

Screw Connection Capacity (CSA S136 Clause E2)

Self-drilling and self-tapping screws are the primary connection method for cold-formed steel. CSA S136 Clause E2 provides the design method for screw connections:

Screw Shear Capacity

For screws in shear (connecting two CFS members):

Vn = 4.2 × √(Fu2 × t²_min × d_s) × (1 - 0.03 × d_s) × (t1 / t2)^0.15

where:
  Vn    = nominal shear resistance per screw (N)
  Fu2   = tensile strength of the thinner connected part (MPa)
  t_min = thickness of thinner connected part (mm)
  d_s   = screw diameter (mm)
  t1/t2 = ratio of thicknesses (connected parts)

Limit: Vn ≤ 2.7 × t_min × d_s × Fu2 (ensures ductile bearing failure rather than screw shear failure).

Screw Tension Capacity

Nn = 0.85 × t_c × d_s × Fu_c × (1 - 0.08 × d_s)

where:
  t_c  = thickness of the part with the screw head in contact (mm)
  Fu_c = tensile strength of the part with the screw head (MPa)
  d_s  = screw diameter (mm)

Screw Spacing and Edge Distance

Screw connections must be installed perpendicular to the connected surface, with full thread engagement through all connected layers. Screws in tension or combined tension-shear require special consideration per CSA S136 Clause E2.8.

Welded Connections for CFS (CSA S136 Clause E3)

Welded connections for cold-formed steel follow CSA W59 but with reduced effective throat for thin base metal. Resistance welding (spot welding) is more common than arc welding for CFS:

Arc Welds (Fillet and Groove)

Vn = 0.60 × φ × Fy × t × L / √3    (shear)
Tn = φ × Fy × t × L                  (tension)

where:
  φ = 0.60 (CFS welded connections)
  t = base metal thickness (mm)
  L = weld length (mm)
  Fy = base metal yield strength (MPa)

The lower resistance factor φ = 0.60 (vs φ = 0.67 for hot-rolled) reflects the greater sensitivity of thin CFS sections to weld heat input and distortion.

Worked Example — CFS Stud Wall Under Axial Load

Problem: Design a cold-formed steel stud wall for a warehouse mezzanine. Studs at 600 mm centres, wall height = 4.0 m. Axial load per stud: Pf = 25 kN (factored). Steel grade: G40.21 Grade 230 (Fy = 230 MPa, Fu = 310 MPa). Sheathing: 15 mm gypsum board both sides, screw fastened at 300 mm spacing.

Step 1 — Select Preliminary Section

Try C200x2.0 (d = 200 mm, bf = 51 mm, D = 12 mm, t = 2.0 mm, A = 815 mm², Ixx = 4.18 × 10^6 mm⁴, ry = 15.6 mm)

Step 2 — Global Buckling Check (Clause C4)

Radius of gyration about weak axis: ry = 15.6 mm Effective length: Ly = 4.0 m (unbraced about weak axis — sheathing provides bracing at 600 mm spacing)

With sheathing bracing at 600 mm:

Ky × Ly = 1.0 × 600 = 600 mm
λy = Ky × Ly / ry = 600 / 15.6 = 38.5

Global buckling stress (flexural):

Fe = π² × E / λy² = π² × 200,000 / 38.5² = 1,330 MPa > Fy → inelastic buckling
Fne = Fy × (1 - Fy / (4 × Fe)) = 230 × (1 - 230 / (4 × 1,330)) = 230 × (1 - 0.043) = 220 MPa

Step 3 — Local Buckling Check (Effective Width Method)

Web element (stiffened, k = 4.0):

w = 200 - 2 × 2.0 - 2 × 3 = 190 mm (flat width)
w/t = 190 / 2.0 = 95

λ = 1.052 / √(4.0) × 95 × √(220 / 200,000)
λ = 0.526 × 95 × 0.0332 = 1.66

ρ = (1 - 0.22 / 1.66) / 1.66 = (1 - 0.133) / 1.66 = 0.867 / 1.66 = 0.522

be = 0.522 × 190 = 99.2 mm

Flange element (edge-stiffened, with lip):

Flange flat width: wf = 51 - 2.0 - 3 = 46 mm
wf/t = 46 / 2.0 = 23

Lip adequacy check: D/t = 12 / 2.0 = 6.0 OK (0.8 ≤ D/t ≤ 12)
d/w = 12 / 51 = 0.235 OK (≤ 0.8)

k factor for edge-stiffened flange (per Clause C2.5):
k ≈ 1.5 (depends on stiffener geometry)

λ = 1.052 / √(1.5) × 23 × √(220 / 200,000)
λ = 0.859 × 23 × 0.0332 = 0.656

ρ = (1 - 0.22 / 0.656) / 0.656 = (1 - 0.335) / 0.656 = 0.665 / 0.656 = 1.014 → ρ = 1.0
λ = 0.656 ≤ 0.673 → full flange effective

Step 4 — Distortional Buckling Check (P-DST Method)

C200x2.0 distortional buckling load (finite strip analysis approximation):

Pcrd ≈ 0.5 × π² × E / (h²) × (I_xf + I_web)
Pcrd ≈ 35 kN (conservative estimate for C200x2.0, typical per CFSEI design guide)

λd = √(Pne / Pcrd) = √(179.3 / 35) = √5.12 = 2.26 > 0.561

Pnd = Pne × (1 - 0.25 × (1/2.26)^0.6) × (1/2.26)^0.6
Pnd = 179.3 × (1 - 0.25 × 0.625) × 0.625
Pnd = 179.3 × (1 - 0.156) × 0.625
Pnd = 179.3 × 0.844 × 0.625
Pnd = 94.6 kN

Step 5 — Factored Compressive Resistance

Pr = φ × Pnd = 0.85 × 94.6 = 80.4 kN
Pf = 25 kN ≤ Pr = 80.4 kN OK, D/C = 0.31

Step 6 — Local Capacity Check at Connections

Screws at 300 mm spacing in tension flange:

Per screw shear (from wind or eccentricity): Vf ≈ 0 (pure axial — neglect for this example)

Butt joint at stud splice (if required):

4 × #12 screws at each flange, shear capacity per screw:
Vn = 4.2 × √(310 × 2.0² × 5.5) = 4.2 × √(6,820) = 4.2 × 82.6 = 347 N

Vr = φ × Vn = 0.60 × 347 = 208 N per screw
4 screws × 208 N = 832 N per flange → splice capacity ≈ 1.66 kN for axial

Splices require more screws or a sleeve connection. Consider continuous studs for full height if axial loads are large.

Step 7 — Summary

The C200x2.0 stud at 600 mm spacing is adequate for a 25 kN factored axial load over a 4.0 m height. Distortional buckling governs at D/C = 0.31. For higher loads, consider reducing spacing to 400 mm or increasing to C200x2.5.

Frequently Asked Questions

What is the difference between CSA S136 and CSA S16 for steel design? CSA S136 governs cold-formed steel (thickness ≤ 12.7 mm) and uses the effective width method or direct strength method for local buckling, while CSA S16 governs hot-rolled steel using element classification. The resistance factors also differ: CSA S136 uses φ = 0.85 (general) vs CSA S16 φ = 0.90. CSA S136 screw connections, distortional buckling, and thin-wall effects are not covered in CSA S16.

What is distortional buckling in cold-formed steel? Distortional buckling (CSA S136 Clause C3.3) is a buckling mode unique to cold-formed sections where the flange and lip rotate together about the flange-web junction. It affects C and Z sections with thin webs and relatively deep lips. The Direct Strength Method (P-DST) uses the elastic distortional buckling load Pcrd to calculate the nominal capacity. For Canadian CFS construction, distortional buckling often governs stud and joist design, particularly for mid-range slenderness (stud heights of 3-5 m).

How do you calculate the effective width of a CFS compression element? The effective width method reduces the flat width of compression elements to account for local buckling. For stiffened elements (webs), b = ρ × w when λ > 0.673, where ρ = (1 - 0.22/λ)/λ and λ depends on the width-to-thickness ratio, design stress, and plate buckling coefficient. Unstiffened elements (open flanges) use k = 0.43, and edge-stiffened elements (lipped flanges) use k based on stiffener dimensions.

What screw sizes are standard for Canadian CFS construction? #10 (4.8 mm) and #12 (5.5 mm) self-drilling screws are most common in Canadian light-gauge steel construction. #10 screws are used for sheathing attachment and secondary connections, while #12 screws are used for structural connections (stud-to-track, joist-to-bearing). Minimum edge distance is 10 mm for #10 screws and 12 mm for #12 screws. Maximum spacing for structural connections is 300 mm.

Related Pages

• Canada CSA S16 Guide — Full CSA S16:19 steel design reference
• Canadian Steel Beam Sizes — W, WWF, HSS sections per CISC
• Canadian Steel Grades — G40.21 230 to 550 MPa grades
• CSA S16 Beam Design — Hot-rolled beam flexure, LTB, shear
• CSA S16 Connection Design — Bolted and welded connections
• Fillet Weld Size Chart — Weld capacities per CSA W59
• HSS Section Properties — RHS and CHS section tables

This page is for educational reference. CSA S136:16 cold-formed steel design must comply with the current edition of CSA S136, CSA W59, and NBCC 2020. All results are PRELIMINARY — NOT FOR CONSTRUCTION without independent verification by a licensed Professional Engineer (P.Eng.).