Cold-Formed Steel Calculator
Quick answer: A 6-inch Cee section (6CS2.5x059 -- 6" web, 2.5" flange, 0.059" thick, 33 ksi steel) as a simply-supported stud at 12 ft unbraced length has an axial capacity of approximately 12-15 kips depending on the governing buckling mode. For most CFS sections, distortional buckling (flange-lip rotation) controls at intermediate unbraced lengths, while global buckling controls at longer lengths. Use the calculator below to get exact capacities per AISI S100.
Common CFS Section Sizes and Capacities
| Designation | Web (in) | Flange (in) | Lip (in) | Thickness (mils) | Fy (ksi) | Approx. Compression (kips, 10 ft) |
|---|---|---|---|---|---|---|
| 3.5CS1.625x045 | 3.5 | 1.625 | 0.5 | 45 | 33 | 6-8 |
| 6CS1.625x059 | 6.0 | 1.625 | 0.5 | 59 | 33 | 14-17 |
| 6CS2.5x059 | 6.0 | 2.5 | 0.625 | 59 | 33 | 15-19 |
| 8CS2.5x059 | 8.0 | 2.5 | 0.625 | 59 | 33 | 13-16 |
| 10CS2.5x068 | 10.0 | 2.5 | 0.625 | 68 | 33 | 17-22 |
| 12CS2.5x097 | 12.0 | 2.5 | 0.625 | 97 | 50 | 38-48 |
Approximate ranges vary with unbraced length. Use the calculator for exact values.
Three Buckling Modes in CFS Design
1. Local buckling -- Individual plate elements (web, flange) buckle between fold lines. Short half-wavelength (typically 1-3x the plate width). Post-buckling strength is available; the effective width method or DSM local curve accounts for it.
2. Distortional buckling -- The flange-lip assembly rotates about the flange-web junction. Medium half-wavelength (typically 5-15x the section depth). This mode often controls for stud and purlin sections at practical unbraced lengths.
3. Global buckling -- The entire member buckles: flexural (Euler), torsional, or flexural-torsional. Long half-wavelength. Same theory as hot-rolled columns, but the thin-walled cross-section means torsional modes can be critical even for doubly-symmetric Cee sections.
Design Methods
Effective Width Method (EWM): Reduces each compressed plate element to an effective width based on its slenderness. The effective section properties (Ae, Se, Ie) are then used with standard column/beam formulas. Required for simple hand checks.
Direct Strength Method (DSM): Uses the elastic buckling load of the full cross-section for each mode (Pcrl for local, Pcrd for distortional, Pcre for global) and applies calibrated strength curves. Preferred in AISI S100 because it handles complex shapes without computing individual effective widths. The calculator uses DSM.
How the Calculator Works
The calculator evaluates three buckling limit states using the Direct Strength Method (DSM) from AISI S100. Elastic buckling loads are computed from closed-form expressions for standard Cee and Zee profiles. Nominal strength is determined from DSM strength curves that relate elastic buckling stress to post-buckling capacity.
Direct Strength Method (DSM) Formulas — AISI S100
The DSM evaluates the nominal axial capacity Pn as the minimum of three limit states:
Global (flexural, torsional, or flexural-torsional) buckling
Pne = Ae × Fne
Where:
Fne = Fy × (0.658^(Fy/Fe)) for Fe ≤ 0.44Fy (inelastic)
= 0.877 × Fe for Fe > 0.44Fy (elastic)
Fe = elastic global buckling stress (Euler or torsional)
Ae = gross area (for global mode, no local reduction)
Local buckling (interacting with global)
Pnl = Pne × (0.658^(Pne/Pcrl)) for Pcrl/Pne ≤ 0.776
= Pne × (1 - 0.15 × (Pcrl/Pne)^0.4) × (Pcrl/Pne)^0.4 for Pcrl/Pne > 0.776
Where Pcrl = elastic local buckling load of the full cross-section
Distortional buckling (interacting with global)
Pnd = Pne × (0.658^(Pne/Pcrd)) for Pcrd/Pne ≤ 0.561
= Pne × (1 - 0.25 × (Pcrd/Pne)^0.6) × (Pcrd/Pne)^0.6 for Pcrd/Pne > 0.561
Where Pcrd = elastic distortional buckling load of the full cross-section
Governing capacity
Pn = min(Pne, Pnl, Pnd)
φPn = 0.85 × Pn (compression)
Check: φPn ≥ Pu (factored axial demand)
Worked Example — CFS Stud Capacity
Problem: A 6CS2.5x059 (6" web, 2.5" flange, 0.625" lip, 0.059" thick) Cee section in 33 ksi steel serves as a wall stud at 12 ft unbraced length. Determine the axial capacity.
Step 1 — Section properties
Gross area: Ag = 0.059 × (6 + 2×2.5 + 2×0.625) = 0.059 × 12.25 = 0.723 in²
(Simplified — actual area accounts for corner radii)
Actual Ag ≈ 0.740 in² (from manufacturer table)
Radius of gyration: rx ≈ 2.25 in, ry ≈ 0.90 in (typical for this section)
Step 2 — Global buckling
Fe = π² × E / (Ky × L/r)²
Fe = π² × 29,500 / (1.0 × 144/0.90)²
Fe = 290,887 / 25,600 = 11.36 ksi
Fy/Fe = 33/11.36 = 2.91 > 0.44 → elastic buckling
Fne = 0.877 × 11.36 = 9.96 ksi
Pne = 0.740 × 9.96 = 7.37 kips
Step 3 — Local buckling
Pcrl ≈ 18 kips (from CUFSM or analytical expression for this section)
Pcrl/Pne = 18/7.37 = 2.44 > 0.776
Pnl = Pne × (1 - 0.15 × (Pcrl/Pne)^0.4) × (Pcrl/Pne)^0.4
Pnl = 7.37 × (1 - 0.15 × 2.44^0.4) × 2.44^0.4
2.44^0.4 = 1.44
Pnl = 7.37 × (1 - 0.15 × 1.44) × 1.44 = 7.37 × 0.784 × 1.44 = 8.32 kips
Pnl > Pne → local buckling does NOT reduce global capacity
Step 4 — Distortional buckling
Pcrd ≈ 10 kips (from CUFSM for this section geometry)
Pcrd/Pne = 10/7.37 = 1.36 > 0.561
Pnd = Pne × (1 - 0.25 × (Pcrd/Pne)^0.6) × (Pcrd/Pne)^0.6
1.36^0.6 = 1.20
Pnd = 7.37 × (1 - 0.25 × 1.20) × 1.20 = 7.37 × 0.70 × 1.20 = 6.19 kips
Step 5 — Governing capacity
Pn = min(7.37, 8.32, 6.19) = 6.19 kips (distortional buckling governs)
φPn = 0.85 × 6.19 = 5.26 kips
At 12 ft unbraced length, this 6" Cee section can carry approximately 5.3 kips
in axial compression. Distortional buckling is the governing mode.
CFS vs Hot-Rolled Steel — Key Differences
| Property | Hot-Rolled (A992) | Cold-Formed (AISI S100) |
|---|---|---|
| Typical thickness | 1/4" to 4" | 0.018" to 0.125" |
| Yield strength | 50 ksi | 33-55 ksi |
| Local buckling | Rare (thick elements) | Common (thin elements) |
| Distortional buckling | Not applicable | Often governs |
| Design method | AISC 360 | AISI S100 |
| Connection types | Bolted, welded | Screwed, welded, clinched |
| Galvanizing | Shop-applied | Pre-galvanized coil |
| Typical use | Beams, columns, frames | Wall studs, purlins, girts |
Common CFS Applications and Span Ranges
| Application | Typical Section | Span Range | Typical Load |
|---|---|---|---|
| Wall studs (bearing) | 3.5CS or 6CS, 33-54 mil | 8-12 ft floor-to-floor | 1-5 kips axial |
| Wall studs (curtain) | 3.5CS, 33-43 mil | 10-16 ft | Wind lateral only |
| Roof purlins | 8ZS or 10ZS, 54-97 mil | 20-30 ft | Snow + dead load |
| Wall girts | 6CS or 8CS, 33-54 mil | 20-30 ft | Wind lateral |
| Floor joists | 6CS to 12CS, 54-97 mil | 12-24 ft | Floor live load |
| Header beams | Built-up box, 2×Cee | 6-12 ft opening | Floor/roof load |
Frequently Asked Questions
What is the difference between hot-rolled and cold-formed steel design? Hot-rolled shapes are thick enough that local buckling of individual plate elements rarely governs. Cold-formed sections have high width-to-thickness ratios, so local and distortional buckling interact with global buckling and often control the capacity. CFS design uses either the effective width method or the direct strength method to account for these thin-plate effects.
What is the Direct Strength Method (DSM)? DSM is an alternative to the effective width method introduced in AISI S100. Instead of computing effective widths for each element, DSM uses the elastic buckling load of the full cross-section (local, distortional, global) and applies strength curves calibrated to test data. It is generally simpler for complex cross-sections and is the preferred method in current editions of AISI S100.
Why does cold-formed steel have three buckling modes instead of one? Thin-walled open sections can buckle locally (plate elements buckle between fold lines), distortionally (the flange-lip assembly rotates about the flange-web junction), or globally (the entire member buckles as a column or beam). Each mode has a different half-wavelength and interacts differently with material yielding, so all three must be checked.
What steel grades are used for cold-formed framing? ASTM A653 (galvanized) Grade 33 (Fy = 33 ksi) is the most common for wall studs and curtain wall framing. Grade 50 (Fy = 50 ksi) is used for higher-load applications like bearing walls and floor joists. ASTM A1003 (non-galvanized) Grade 50 is used where galvanizing is not required. The mill-certified yield strength must be used for design; the "grade" number directly represents the minimum yield stress in ksi.
How are CFS connections designed? CFS members are typically connected using self-drilling screws (#8 to #14), welds ( Resistance welds or MIG fillet), or mechanical clinching. Screw connections are designed per AISI S100 Section J4: the nominal shear strength per screw depends on the screw diameter, the connected ply thickness, and the steel grade. For #12 screws connecting two 54-mil plies of 33 ksi steel, the typical shear capacity per screw is 250-350 lb. Minimum edge distance is 3× screw diameter, and minimum spacing is 3× screw diameter.
What is the difference between Cee and Zee sections? Cee (C) sections have a symmetric cross-section with equal flanges and are used for wall studs, floor joists, and columns. Zee (Z) sections have flanges that point in the same direction (asymmetric about the web) and are used for roof purlins and wall girts where they nest efficiently for shipping and can be lapped at supports for continuity. Zees develop negative moment capacity at interior supports through lapped connections, which is more efficient than simple-span Cee sections.
What is bridging and why is it required for CFS framing? Bridging (also called bracing) consists of horizontal straps, channels, or angles that connect adjacent CFS studs or joists at regular intervals. It prevents three failure modes: weak-axis buckling under compression, lateral-torsional buckling under bending, and rotation during construction. AISI S100 requires bridging at a spacing that limits the unbraced length to prevent these modes. For wall studs, bridging is typically provided at 4-5 ft spacing. For floor joists, bridging at 6-8 ft is common. The bridging must have adequate strength and stiffness to resist the accumulated bracing force from all connected members.
How do I read CFS section designations? CFS sections are designated by web depth, section type, flange width, and thickness in mils. For example, 600S162-54 means: 600 = 6.00 inch web depth, S = stud (Cee section), 162 = 1.625 inch flange width, 54 = 54 mils (0.054 inch) thickness. The SSMA naming convention uses S for studs and T for track. A designation of 8CS2.5x059 means: 8-inch web, Cee section, 2.5-inch flange, 0.059-inch thickness. Older gage designations (12 gage, 14 gage, 16 gage, 18 gage, 20 gage) are still used informally but mil designations are preferred because they are unambiguous.
What corrosion protection is used for CFS framing? CFS framing members are typically protected by hot-dip galvanizing per ASTM A653 (G40 to G90 coating designations, where the number represents the total coating weight in hundredths of oz/ft^2). G40 is minimum for interior dry locations, G60 for interior humid or exterior sheltered, and G90 for exterior exposed. For highly corrosive environments, additional coatings (paint systems, zinc-aluminum-magnesium alloys) or stainless steel (ASTM A240 Type 304 or 316) may be required. The galvanized coating provides both barrier protection and sacrificial (cathodic) protection at cut edges and scratches.
What is web crippling and when does it govern in CFS design? Web crippling is a local buckling failure that occurs at concentrated loads or reactions where the web is compressed transversely. It is critical for CFS members because the thin web (typically 0.033-0.097 inches) has limited capacity to resist transverse compression. AISI S100 Section G5 provides web crippling strength formulas that depend on the bearing length, the web slenderness h/t, the inside bend radius, and the section geometry. Web crippling often governs at interior supports of CFS floor joists and at stud-to-track connections where reaction forces are concentrated. Bearing stiffeners (clip angles or web stiffeners) can be added to increase the web crippling capacity.
What software is available for CFS analysis beyond simple calculators? For detailed CFS analysis beyond simplified hand checks, CUFSM (Cornell University Finite Strip Method) is a free open-source tool that computes elastic buckling stresses for any CFS cross-section, providing the Pcrl and Pcrd values needed for DSM design. AISIWin (AISI Design Software) automates the full AISI S100 design checks. Commercial FEA software (ABAQUS, ANSYS) can model CFS members with full geometric and material nonlinearity. For practical design, most CFS manufacturers provide free software (ClarkDietrich's SteelSmart System, Marino/WARE's CFS Designer) that includes their specific section libraries and automates AISI S100 checks.
What is the minimum bearing length for CFS members? AISI S100 requires a minimum bearing length of 3.5 inches for CFS joists and studs at supports (Section G5 web crippling check). For concentrated loads, the bearing length must be sufficient to prevent web crippling failure. The actual required bearing length depends on the section geometry, thickness, and applied load, and is computed using the AISI web crippling formulas. In practice, a minimum bearing of 1.5 inches is used for end reactions and 3 inches for interior reactions, but heavier loads may require longer bearing lengths or bearing stiffeners.
Related pages
- CFS wall stud calculator
- Steel deck calculator
- Column capacity calculator
- Section properties database
- Steel grades reference
- Tools directory
- How to verify calculator results
- Disclaimer (educational use only)
- Steel weight calculator
- Steel channel sizes
Disclaimer (educational use only)
This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.
All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.
The site operator provides the content "as is" and "as available" without warranties of any kind. To the maximum extent permitted by law, the operator disclaims liability for any loss or damage arising from the use of, or reliance on, this page or any linked tools.