Cold-Formed Steel Design Guide — AISI S100

Effective Width Method, Local/Distortional/Global Buckling, and Direct Strength Method

Cold-formed steel (CFS) members are manufactured by bending thin steel sheet (typically 18 to 97 mil, or 0.018" to 0.097") 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 the Design of Cold-Formed Steel Structural Members) and its companion framing standard AISI S240. The fundamental challenge in CFS design is that the thin elements buckle locally at stresses well below the yield strength, requiring post-buckling strength to be accounted for — a concept foreign to hot-rolled steel design where sections are compact enough to reach full yield.

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

Key CFS Section Types

Five primary CFS section types are used in structural framing per AISI S100 and AISI S240. Each has distinct buckling behavior and applications.

C-Stud Designation System

C-stud designations follow the format XXXSYYY-ZZ, where XXX = out-to-out depth in inches x 100, YYY = flange width in inches x 100, and ZZ = thickness in mils x 1000. For example, 600S162-54 = 6.00" depth, 1.625" flange width, 0.054" (54 mil) design thickness.

Three Distinct Buckling Modes

Cold-formed steel members can buckle in three fundamentally different modes. Unlike hot-rolled steel where only global buckling (flexural, torsional, or flexural-torsional) controls the design, CFS design must check all three modes and consider their possible interaction.

1. Local Buckling

Local buckling involves individual plate elements (web, flange, lip) buckling between their supported edges at a short half-wavelength, typically 2-3 times the element width. The element does not fail when local buckling occurs — it continues to carry load through a post-buckling stress redistribution mechanism whereby stress migrates from the buckled center of the plate to the stiffer edge regions. The effective width method quantifies this redistribution.

Critical elastic local buckling stress: F*cr_local = k * (pi^2 _ E) / (12 _ (1-nu^2)) _ (t/w)^2

Where:

• k = buckling coefficient: 4.0 for stiffened elements (web between flanges), 0.43 for unstiffened elements (track flange without lip)
• E = 29,500 ksi (203,000 MPa) — modulus of elasticity of steel
• nu = 0.30 — Poisson's ratio
• t = base steel thickness (excluding coating)
• w = flat width of the element (between fillets or stiffeners)

Local buckling slenderness: lambda = sqrt(F_y / F_cr_local)

Effective width:

• When lambda <= 0.673: be = w (full width, no reduction)
• When lambda > 0.673: be = rho * w, where rho = (1 - 0.22/lambda) / lambda

2. Distortional Buckling

Distortional buckling is unique to cold-formed steel. It involves rotation of the flange about the flange-web junction, causing the lip stiffener to move laterally while the web remains relatively stationary. This mode has an intermediate half-wavelength between local and global buckling, typically 4-8 times the flange width.

Critical elastic distortional buckling stress (per AISI S100 Appendix 2, simplified method for lipped channels):

F_cr_dist = (k_phi_fe + k_phi_we + k_phi) / (k_phi_tilde_fe + k_phi_tilde_we)

The distortional buckling slenderness and strength are computed using the Direct Strength Method:

lambda_d = sqrt(F_y / F_cr_dist)

• When lambda_d <= 0.561: P_nd = F_y * A_g (yield controls, no reduction)
• When lambdad > 0.561: P_nd = [1 - 0.25 * (F_cr_dist / F_y)^0.6] * (Fcr_dist / F_y)^0.6 * F_y * A_g

3. Global Buckling

Global buckling is the same concept as in hot-rolled steel — the entire member buckles as a rigid body (no cross-section distortion). Three types:

• Flexural buckling: Bending about the weak axis (governs for singly-symmetric C-sections)
• Torsional buckling: Twisting about the shear center (relevant for point-symmetric Z-sections)
• Flexural-torsional buckling: Combined bending and twisting (governs for singly-symmetric sections under axial load)

Global buckling capacity follows AISI S100 Chapter C using the column curve:

• When lambda_c <= 1.5: F_n = (0.658^(lambda_c^2)) * F_y
• When lambda_c > 1.5: F_n = (0.877 / lambda_c^2) * F_y

where lambda_c = sqrt(F_y / F_e) and F_e is the minimum elastic buckling stress (flexural, torsional, or flexural-torsional, whichever is lowest).

Buckling Mode Interaction

A critical aspect of CFS design is that the three buckling modes can interact. Local-global interaction occurs when the critical local buckling stress is close to the global buckling stress — the combined failure load is lower than either mode individually. The AISI S100 Direct Strength Method handles this via a two-step reduction: first apply the global buckling reduction, then apply the local buckling reduction to the already-reduced global capacity.

Effective Width Method — Detailed Procedure

The Effective Width Method (EWM) is the traditional and most widely used approach in AISI S100. It works element-by-element: for each flat element in the cross-section, calculate the effective width, then assemble an effective cross-section with reduced element widths. The procedure:

1. Identify each flat element: Web (stiffened, both edges supported by flanges), flange (stiffened by web and lip), and lip (unstiffened, one free edge).

2. Determine the stress in each element: For members in pure compression, f = F_n (the nominal global buckling stress). For members in bending, f varies linearly across the depth.

3. Calculate plate buckling coefficient k: From AISI S100 Table B4-1 for different support conditions. k = 4.0 for stiffened elements with both longitudinal edges supported. k = 0.43 for unstiffened elements with one free edge.

4. Calculate slenderness lambda: lambda = (1.052 / sqrt(k)) _ (w/t) _ sqrt(f/E) per AISI S100 Section B2.1.

5. Determine effective width be: be = w when lambda <= 0.673. be = rho * w when lambda > 0.673, where rho = (1 - 0.22/lambda) / lambda. The reduction accounts for post-buckling strength — the center of the buckled plate sheds load to the stiffer edge regions.

6. Assemble effective section: Replace each full-width element with its effective width, centering the effective width on the original element for stiffened elements or locating it at the supported edge for unstiffened elements.

7. Compute effective section properties: A_e, I_xe, S_xe, etc. from the effective section geometry.

8. Check iterations: Because the effective width depends on the stress f, and the stress depends on the effective section properties, iterations may be required until convergence (typically 2-3 iterations sufficient).

Worked Example: C-Stud in Compression

Design a 600S162-54 C-stud (6.00" deep, 1.625" flange, 0.50" lip, t = 0.0566") as a 10 ft tall wall stud in compression, ASTM A1003 Grade 50, F_y = 50 ksi, fully braced against weak-axis and torsional buckling.

Step 1 — Section geometry (gross):

• Web: h = 6.00", flat width w_web (inside-to-inside of bends) = 6.00 - 2*(R + t) = 6.00 - 2*(0.0849 + 0.0566) = 5.717"
• Flange: b = 1.625", w_flange = 1.625 - (R + t) - (R + t) = 1.625 - 2*(0.0849 + 0.0566) = 1.342"
• Lip: d = 0.50", w_lip = 0.50 - (R + t/2) = 0.50 - (0.0849 + 0.0283) = 0.387"
• R = bend radius = 1.5*t = 0.0849" (typical for 54 mil)
• Gross area A_g = 0.872 in^2 (from manufacturer table)

Step 2 — Effective width of web (stiffened element, k = 4.0):

• lambda*web = (1.052/sqrt(4.0)) * (5.717/0.0566) _ sqrt(50/29500) = 0.526 _ 101.0 _ 0.0412 = 2.19
• lambda_web = 2.19 > 0.673 → effective width required
• rho_web = (1 - 0.22/2.19) / 2.19 = (1 - 0.100) / 2.19 = 0.411
• b_e_web = 0.411 * 5.717 = 2.35" (only 41% of the web is effective!)

Step 3 — Effective width of flange (stiffened element, k = 4.0):

• lambda*flange = (1.052/sqrt(4.0)) * (1.342/0.0566) _ sqrt(50/29500) = 0.526 _ 23.71 _ 0.0412 = 0.514
• lambda_flange = 0.514 <= 0.673 → fully effective
• b_e_flange = 1.342" (no reduction)

Step 4 — Effective width of lip (unstiffened element, k = 0.43):

• Check lip stiffener adequacy per AISI S100 Section B5.1: The lip acts as an edge stiffener for the flange. Its effectiveness depends on its moment of inertia I_s compared to the adequate stiffener inertia I_a.
• I*s = (d^3 * t) / 12 = (0.387^3 _ 0.0566) / 12 = 2.73 x 10^-4 in^4
• I*a = 399 * t^4 _ [(w_flange/t)/28 - 0.328]^3 = 399 _ (0.0566^4) _ [(1.342/0.0566)/28 - 0.328]^3 = 399 _ 1.027e-5 _ [0.846 - 0.328]^3 = 5.72e-4 in^4
• I_s / I_a = 2.73e-4 / 5.72e-4 = 0.477 < 1.0 → lip is not fully adequate, flange must be treated as partially stiffened
• Revised k for flange with inadequate lip: k = 4.0 - (4.0 - 0.43) _ (1 - I_s/I_a) = 4.0 - 3.57 _ (1 - 0.477) = 4.0 - 1.867 = 2.13
• lambda*flange_revised = (1.052/sqrt(2.13)) * (1.342/0.0566) _ 0.0412 = 0.721 _ 23.71 _ 0.0412 = 0.705
• lambda_flange_revised = 0.705 > 0.673 → effective width required
• rho_flange = (1 - 0.22/0.705) / 0.705 = (1 - 0.312) / 0.705 = 0.976
• b_e_flange = 0.976 * 1.342 = 1.310" (4% reduction)

Step 5 — Effective section properties:

• Effective web: 2.35" centered on original web location
• Effective flanges: 2 x 1.310 = 2.620" (both flanges reduced)
• Lip is fully effective for length
• Compute Ae = (2.35 + 21.310 + 2*0.387) * 0.0566 = 5.744 _ 0.0566 = 0.325 in^2
• Effective area ratio: A_e / A_g = 0.325 / 0.872 = 0.373

Step 6 — Global buckling check:

• Length L = 10 ft = 120 in, K = 1.0 (pinned-pinned)
• Weak-axis radius of gyration r_y = 0.698 in (from manufacturer)
• KL/r_y = 120 / 0.698 = 172
• F*e = pi^2 * E / (KL/r)^2 = pi^2 _ 29500 / 172^2 = 9.87 * 29500 / 29584 = 9.84 ksi
• lambda_c = sqrt(50 / 9.84) = 2.26 > 1.5
• F*n = 0.877 / 2.26^2 * 50 = 0.172 _ 50 = 8.58 ksi (global buckling stress)

Step 7 — Nominal axial capacity with effective section:

• Pn = A_e * Fn = 0.325 * 8.58 = 2.79 kips
• phi_c = 0.85 (AISI S100 Chapter C for compression)
• phic * Pn = 0.85 * 2.79 = 2.37 kips

This is the maximum factored axial load this stud can carry. Note the dramatic reduction from the gross section yield load (Ag * Fy = 0.872 * 50 = 43.6 kips) — the effective width method and global buckling together reduce capacity by 94% due to the extreme slenderness of thin CFS elements.

Direct Strength Method (DSM)

The Direct Strength Method (DSM) per AISI S100 Appendix 1 is an alternative to the Effective Width Method. Instead of reducing element widths, DSM uses the full gross section properties and applies reduction factors at the member level.

DSM Procedure for Columns

1. Determine the elastic buckling loads: P_cr_local (local), P_cr_dist (distortional), P_cr_global (flexural/torsional) — typically from finite strip analysis (e.g., CUFSM) or closed-form solutions.

2. Global buckling strength P_ne: Using the AISI column curve with lambda_c = sqrt(P_y / P_cr_global), where P_y = A_g * F_y.

3. Local buckling strength P_nl: lambdal = sqrt(P_ne / P_cr_local). When lambda_l <= 0.776: P_nl = P_ne. When lambda_l > 0.776: P_nl = [1 - 0.15 * (P_cr_local / P_ne)^0.4] * (Pcr_local / P_ne)^0.4 * P_ne.

4. Distortional buckling strength P_nd: lambdad = sqrt(P_y / P_cr_dist). When lambda_d <= 0.561: P_nd = P_y. When lambda_d > 0.561: P_nd = [1 - 0.25 * (P_cr_dist / P_y)^0.6] * (Pcr_dist / P_y)^0.6 * P_y.

5. Nominal strength P_n: minimum of P_nl and P_nd.

DSM Advantages Over EWM

• Works directly with any cross-section geometry without tedious element-by-element reduction
• Naturally accounts for element interaction (local buckling strength uses P_ne, not P_y, incorporating global-local interaction)
• Better agreement with test results for complex sections
• Easily automated — finite strip analysis gives all three elastic buckling values at once

DSM Limitations

• Requires elastic buckling analysis (finite strip or finite element)
• The buckling coefficient k is implicit in the FEA results rather than explicitly chosen
• Less familiar to engineers accustomed to element-by-element effective width calculations

CFS vs. Hot-Rolled Steel Design — Key Differences

Z-Purlin Design Considerations

Z-purlins present unique design challenges due to their point-symmetric shape and torsional flexibility:

• Restrained vs unrestrained: Z-purlins with through-fastened roof sheathing on the top flange are torsionally restrained. Without adequate rotational restraint, lateral-torsional buckling can govern.
• Continuity: Z-purlins are commonly lapped over supports to create continuous span action, reducing moments by 25-33% compared to simple spans. The lap length is typically 10-15% of the span.
• Base test method: AISI S100 Section I6.2 permits designing Z-purlins using the base test method, where capacity is determined from full-scale flexural tests rather than analytical calculations. This accounts for the complex torsional-flexural behavior that is difficult to capture analytically.
• Web crippling: Z-purlins are thin and susceptible to web crippling at supports. AISI S100 Section C3.4 provides web crippling equations that consider the bearing length, section depth, bend radius, and whether the load is applied to one flange or both.

Frequently Asked Questions

What is the minimum base steel thickness for structural CFS?

Per AISI S240, structural CFS members must have a minimum base steel thickness of 0.033" (33 mil, 20 ga). Thinner materials (18-30 mil, 25-22 ga) are classified as non-structural and can only be used for interior partition walls, furring, and cladding support where no structural loads are carried.

How does CFS perform in fire conditions?

Unprotected CFS loses strength rapidly above 400degC (750degF). For fire-rated assemblies, CFS walls and floors achieve fire resistance through gypsum board layers (Type X or Type C), mineral wool insulation in the cavity, and intumescent coatings. UL fire-rated assembly designs (e.g., U419 for 1-hour walls, V497 for 2-hour floor-ceiling) specify the required layers and stud spacing. CFS studs themselves are typically protected — the steel temperature must remain below the critical temperature (approximately 550degC for 50% of yield strength) for the required fire resistance period.

Can CFS be used for seismic lateral force-resisting systems?

Yes. CFS shear walls using flat strap X-bracing or sheet steel sheathing are common lateral systems for low-rise and mid-rise CFS buildings. AISI S400 (North American Standard for Seismic Design of Cold-Formed Steel Structural Systems) provides the design requirements. CFS strap-braced walls typically have R = 3.0-3.5 per ASCE 7 Table 12.2-1. CFS shear walls with steel sheet sheathing have R = 6.5. The limiting height is typically 65 ft for strap-braced and 160 ft for sheet-sheathed CFS walls. Overturning hold-downs, shear transfer at the base, and chord stud design for compression/tension couples are critical details.

What is the difference between AISI S100 and AISI S240?

AISI S100 is the base specification for designing individual CFS members — it covers the effective width method, buckling, connections, and member strength for any CFS structural member. AISI S240 is the framing standard that provides system-level requirements specific to CFS wall stud, floor joist, and roof truss assemblies: stud-to-track connections, bridging and bracing requirements, built-up sections, header design, web hole provisions, and installation tolerances. Both must be followed for CFS structural framing. AISI S100 = member design, AISI S240 = system assembly.

How do I determine the elastic buckling stresses for DSM without FEA software?

For common CFS sections (C-studs, Z-purlins, tracks), closed-form solutions exist: (1) Local buckling F_cr_local can be approximated using the plate buckling formula with k = 4.0 for web and flange elements. (2) Distortional buckling F_cr_dist for lipped channels can be computed using the equations in AISI S100 Appendix 2, which consider the rotational stiffness provided by the flange to the lip. (3) Global elastic buckling F_e uses the standard Euler column formula with appropriate effective length factors. For irregular or complex sections, CUFSM (Cornell University Finite Strip Method) is free software that computes all three elastic buckling values from a finite strip analysis — it is the de facto standard for DSM-based CFS design in engineering practice.

Related Pages

• Cold-Formed Steel Reference — CFS section properties tables and screw connection design
• Steel Beam Capacity Calculator — Hot-rolled steel beam design per AISC 360
• Steel Column Design Guide — Column buckling per AISC 360 Chapter E
• HSS Connection Design — Hollow structural section connections
• Steel Grades Reference — ASTM A1003, A653, A992 material properties

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