Cold-Formed Steel Design — AISI S100, Effective Width & Buckling Modes

Cold-formed steel (CFS) members are manufactured by bending thin steel sheet (typically 18 to 54 mil / 0.018" to 0.054") at room temperature into C-shapes, Z-shapes, tracks, angles, and hat sections. Unlike hot-rolled structural steel governed by AISC 360, CFS design follows AISI S100-16 (North American Specification for Cold-Formed Steel) and its specialized framing standard AISI S240. The thin elements of CFS sections create buckling modes that do not occur in hot-rolled shapes, making the design methodology fundamentally different.

Key CFS section types

Three buckling modes in CFS

The fundamental difference between CFS and hot-rolled design is that CFS elements are slender enough to buckle locally before the full section yields. AISI S100 addresses three distinct buckling modes:

1. Local buckling — individual flat elements (flanges, webs, lips) buckle in short half-waves between restraint points. Controlled by the effective width method (AISI S100 Section 1.1) where the effective width be of a compression element is:

be = rho × w    where rho = (1 - 0.22/lambda) / lambda ≤ 1.0
lambda = (1.052/sqrt(k)) × (w/t) × sqrt(f/E)

k = plate buckling coefficient (4.0 for stiffened elements, 0.43 for unstiffened edges).

2. Distortional buckling — the compression flange and lip rotate as a unit about the flange-web junction. This mode has a half-wavelength between local and global buckling (typically 200–800 mm). AISI S100 Section 1.4 provides the distortional buckling stress Fd based on the elastic distortional buckling stress Fcrd.

3. Global buckling — the entire cross-section buckles in flexural, torsional, or flexural-torsional mode. For C-studs loaded in compression, flexural-torsional buckling almost always governs over pure flexural buckling because the shear center does not coincide with the centroid.

Worked example — CFS stud axial capacity

Given: 600S162-54 stud (6" deep, 1-5/8" flange, 54 mil = 0.054"), Fy = 50 ksi, KL = 10 ft (braced at midheight by sheathing, effective KL = 5 ft for weak axis).

Step 1 — Section properties (from AISI S200 tables): Ag = 0.840 in², Ix = 5.18 in4, Iy = 0.596 in4, rx = 2.48 in, ry = 0.842 in, J = 0.000815 in4, Cw = 2.47 in6.

Step 2 — Global buckling (flexural-torsional): Fe,x = pi² × E / (KxLx/rx)² = pi² × 29500 / (120/2.48)² = 124.5 ksi (strong axis) Fe,y = pi² × E / (KyLy/ry)² = pi² × 29500 / (60/0.842)² = 57.3 ksi (weak axis) Fe,t = [GJ + pi²ECw/(KtLt)²] / (Ag × ro²) — torsional buckling stress.

Flexural-torsional: Fe,FT controls for singly-symmetric C-sections. Typically Fe,FT ≈ 35–45 ksi for this configuration.

Step 3 — Nominal axial capacity: Fn = 0.658^(Fy/Fe,FT) × Fy (if lambda_c ≤ 1.5) with phi_c = 0.85 (LRFD). Assuming Fe,FT = 40 ksi: Fn = 0.658^(50/40) × 50 = 0.658^1.25 × 50 = 0.583 × 50 = 29.2 ksi.

Step 4 — Effective area: Local and distortional buckling reduce the effective area. Ae ≈ 0.72 in² (typical reduction for 54-mil studs at this stress level).

phi_c × Pn = 0.85 × 29.2 × 0.72 = 17.9 kips per stud.

Code comparison

AISI S100-16 / CSA S136 (North America): Unified North American standard. Uses effective width method for local buckling and the Direct Strength Method (DSM) as an alternative for all three modes. LRFD phi_c = 0.85 for compression, phi_b = 0.90 for flexure. CFS modulus of elasticity E = 29,500 ksi (slightly higher than hot-rolled 29,000 ksi due to cold working).

AS/NZS 4600:2018 (Australia/NZ): Closely harmonized with AISI S100. Uses the same effective width and DSM approaches with capacity reduction factors phi = 0.85 for columns, phi = 0.90 for beams. Material grades per AS 1397 (G250, G300, G450, G550). G550 (Fy = 550 MPa) ultra-thin sheet is permitted with restrictions on ductility.

EN 1993-1-3 (Eurocode 3): Uses effective width but with a different buckling curve formulation. Partial safety factor gamma_M0 = 1.00 for cross-section resistance, gamma_M1 = 1.00 for buckling. Distortional buckling is addressed through reduced effective thickness in EN 1993-1-3 Section 5.5.3, rather than the explicit DSM approach used in AISI. Eurocode permits higher steel grades (S350, S450) for CFS without the ductility restrictions found in AISI.

Common mistakes engineers make

1. Treating CFS studs like hot-rolled columns. AISC 360 column curves assume the full gross section yields before buckling. CFS elements buckle locally at stresses well below Fy, so the effective area is always less than the gross area. Using Ag instead of Ae overestimates capacity by 15–30%.

2. Ignoring flexural-torsional buckling for C-studs. Because the shear center of a C-section is outside the web, compression loads always trigger flexural-torsional buckling before weak-axis flexural buckling. Using weak-axis Euler buckling alone overestimates the critical load.

3. Assuming sheathing bracing is always effective. Gypsum board and OSB sheathing provide lateral and rotational bracing to studs, but only if the fastener spacing, edge distance, and panel stiffness meet AISI S240 requirements. Bracing capacity must be explicitly checked — it is not automatic.

4. Using Fy = 33 ksi for all CFS. Modern structural studs commonly use 50 ksi material (ASTM A1003 Structural Grade 50). Specifying 33 ksi when the project requires 50 ksi — or vice versa — leads to either overweight designs or under-capacity members.

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Related references

• How to Verify Calculations
• Steel Tension Members
• Steel Framed Walls
• steel member weight calculator

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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.