Cold-formed steel stud

A lipped C-section (SSMA stud or joist) as a simply supported member: a wall stud in a gravity wall under axial load and out-of-plane wind or seismic load, alone or in a pack, or a floor or roof joist. AISI S240-20 gives the wall framing rules. AISI S100-16 (with Supplement S2-20), Effective Width Method, with ASCE 7-22 load combinations, LRFD or ASD. Every provision was checked against the AISI S100-16 text (with its Commentary) on 1 November 2026.

Inputs of the cold-formed steel stud #

• Section: an SSMA designation (for example 600S162-54: 6 in. web, 1-5/8 in. flange, 54 mil) or custom out-to-out dimensions D, B and lip d, the design thickness t (minimum base metal thickness / 0.95) and the inside bend radius R. The designations use the SSMA design thicknesses and radii (54 mil: t = 0.0566 in., R = 0.0849 in.) and lips of 1/2 in. (162 flanges) or 5/8 in. (200 flanges and wider). Fy is entered (33 ksi for 33 and 43 mil, 50 ksi for 54 mil and thicker are the usual ASTM A1003 grades). Web holes: unpunched, or punched with holes centred in the web (shape, depth, length, spacing, nearest distance to a bearing, and how they enter the distortional stress).
• Studs at each location: one stud; two back to back, which meet S100 I1.2 (connector spacing a; you confirm the end connections or the S240 B1.3.1 track exception, and the connector strength), or do not, and are then the sum of the two (S240 B1.3.2); or up to six side by side, the sum of the studs.
• Design basis: all steel (discrete bridging), or sheathing braced by S240 B1.2.2: identical sheathing on both flanges (or the weaker taken on both), studs at most 24 in. on center. Then Ly = Lt = twice the fastener spacing, K = 1 (B3.2.1(b)), the compression flange is braced (B3.2.2(b)), gypsum limits the stud load (Table B3.2-1, screws at most 12 in. on center), or you enter a limit for other sheathing. The stud is also checked without the sheathing, on the bridging you enter, under 1.2D + (0.5L or 0.2S) + 0.2W with LRFD factors in either method (Eq. B1.2.2-1).
• Member and bracing: the length L (simple span) and the spacing, which is the tributary width of the area loads. Kx (Kx Lx = Kx L). The bridging spacing sets Ky Ly = Ky × spacing and Kt Lt = Kt × spacing for the axial check (longest segment) and the unbraced segments for lateral-torsional buckling; 0 means no bridging. Tick Compression flange braced by sheathing only when the compression flange is attached to sheathing for every load direction (lateral-torsional buckling then does not apply). Cb is computed per segment by Eq. F2.1.1-2 from each combination's moment diagram, or entered. Distortional buckling is computed as prefilled (E4, F4). You may instead determine that it is restrained or not critical: the checks are then left out, as this calculation did before. Without restraint L = Lcrd. Braces restrict rotation of both flanges makes Lm the brace spacing (S240 B3.2.1(a)): strap bridging alone does not do that as a rule, and the choice is yours. kφ comes from sheathing (S240 Appendix 1, 0 is permitted; gypsum values there are for serviceability only).
• Loads (per member): concentric axial compression per stud by gravity load type (D, L, Lr, S, R); area loads perpendicular to the member by load type (psf, multiplied by the spacing); point loads perpendicular to the member. See Loads and combinations. Axial loads are per stud location: a pack shares them.
• Floor-to-floor load takedown: rows of level, load type, pressure and tributary length, each multiplied by the stud spacing and added to the axial loads. A wall weight is its psf and height. Live load reduction (ASCE 7-22 4.7) is an option with KLL. The tributary area is the floor assigned to this stud location (S240 B1.1.1), so below 400 ft² of KLL AT it does not reduce, which is the usual case.
• Bearing: end bearing on a support (one-flange end loading, web crippling checked with the bearing length N and whether the flange is fastened to the support) or Not checked when the reaction is taken through screws or clips. Point loads are checked for web crippling as one-flange interior loading (end loading when the bearing edge is within 1.5h of an end) when Web crippling at point loads is on; N is at least 3/4 in. (G5).
• Deflection limits: span / n for live load or wind and for total load. IBC 2021 Table 1604.3 limits for exterior walls are L/360 with plaster or stucco, L/240 with other brittle finishes and L/120 with flexible finishes; floors L/360 live and L/240 total. The wind load for deflection is W × the entered factor (0.42 × the component and cladding load, IBC Table 1604.3 note). 0 turns a check off.

Auto-design (editor toolbar) varies the SSMA C-section (lightest first) and spacing; the yield stress when unlocked. Objectives: least steel per foot of wall or floor; lightest member, then widest spacing; lowest cost index. Kept unless you select them: yield stress Fy. Every other input is kept; see Auto-design.

Checks performed #

The drawings (on screen, in the report and on the PDF / DXF drawing sheet) are the member elevation, drawn horizontal with the bottom or left end at the left (pin supports, the area loads on the tributary width and the point loads by load type, the axial load P at the top end with its values in the sheet notes, the bridging lines, the span), the lipped C section with its depth, flange width, lip and thickness, and the shear, moment and deflection diagrams of the governing combinations aligned under the elevation. End clips, track, bridging members and their anchorage and the sheathing attachment are not part of the calculation and are not drawn.

Limitations #

• The Direct Strength Method is not used. Distortional buckling uses the Appendix 2 closed form with β = 1.0.
• The hole conditions the inputs cannot express are yours: holes centred in the web, noncircular corner radii at least 2t, at least 10 in. clear from the end (Appendix 1 1.1.1) and the section depth from a hole to the member end (G3, G6). Hole limits are NOT FEASIBLE when exceeded.
• Sheathing strength other than the gypsum table is your entered limit. S240 Appendix 1 kφ is not computed: you enter it. Force accumulation along bridging and the anchorage are not computed; a note gives the 2 % brace force of B3.4.1.
• Packs: the connectors and end connections of I1.2 are confirmed by you, not designed. Box-type packs are not covered.
• The takedown does not place walls or check load path alignment (in-line framing, S240 B1.2.3) or the track.
• Simply supported members only; concentric axial load (no eccentricity), bending about the strong axis only (no weak-axis bending, torsion from eccentric loads, or axial tension).
• Inelastic reserve capacity (F2.4) is not used. The shift of the effective centroid under axial load is not considered. The member is taken as loaded through the shear center or restrained against twisting by the sheathing (Chapter F scope; H4 torsion is not checked). Combined bending and web crippling (H3) is checked at interior point loads; end reactions of a simple span carry no moment.
• Bridging, its anchorage and the track (AISI S240) are designed separately.
• Checked against AISI S100-16 (1 November 2026): E = 29,500 ksi, G = 11,300 ksi; Appendix 1 1.1, 1.1.2, 1.2.1, 1.2.2 and 1.3 with Table 1.3-1; E2, E2.1, E2.2; E3.1; F2.1, F2.1.1; F3.1; G2.1, G2.3; G5 and Table G5-2; H1.2, H2, H3; C1.2.1.1 (B1); Table B4.1-1. Corrections made: Table 1.3-1 now uses 3.57 RI^n + 0.43 for D/w ≤ 0.25; the lip under stress gradient by 1.2.2 (was uniform at its largest stress); Mnℓ limited by Set Fy and Se always at the compression fiber (Eq. F3.1-1); shear written in the S100-16 form (same values); web crippling cites Table G5-2 (the C-section table; Table G5-3 is for Z-sections; the coefficients were already those of G5-2), N ≥ 3/4 in. and end loading measured from the bearing edge; the B4.1 limits completed (R/t, do/bo, Fy < 80 ksi, b/t 90 when Is ≥ Ia); the H3 check added.
• Checked against the SSMA Product Technical Guide (2022), p. 5: the SSMA design thicknesses, inside radii and lip lengths of the designations (equal to its Steel Thickness and Stiffening Lip Length tables).
• Still to verify: the IBC 2021 Table 1604.3 note for the 0.42 wind factor.

Verification examples #

Verification status: 93 values compared in 33 examples (27 published, 6 hand calculations from the cited equations): 91 within tolerance, 2 recorded deviations. Code basis: the provisions it uses were read in the target edition.

Published values: the SSMA Product Technical Guide (Steel Stud Manufacturers Association, 2022, free from ssma.com; computed to AISI S100-07/S2-10 and S100-12, ASD) tabulates the gross and torsional properties, the effective section modulus Sxe and allowable moment Mal for local buckling, the allowable shear Vag, the effective moment of inertia Ixe for deflection (at the allowable moment) and the allowable web crippling loads of the SSMA studs. The SSMA examples run a 10 ft member with the compression flange braced (Fn = Fy, local buckling only, as Mal is defined), ASD; for Ixe the wind service moment is set equal to Mal.

Deviations (docs/verification/deviations.json): SSMA-COLD-WORK, the SSMA allowable moments marked with footnote 2 include the cold work of forming (S100 A7.2), which ILX does not use; SSMA-SXE, the SSMA Sxe of the 600S162-54 at 50 ksi is 1.4 % below the S100 effective section that ILX and the independent hand calculation CS-4 both give. The narrow 362S162 sections of the guide also list Sxe below the S100 effective section (0.444 against 0.468 in.³ at 50 ksi) and are not used as examples.

Compression and combined load. The SSMA Combined Axial and Lateral Loads tables reproduce only with the standard 1-1/2 × 4-1/2 in. punchout in the effective area (Appendix 1 1.1.1) and the H1.2 interaction with the B1 amplifier, so they verify the hole provisions and H1.2 together. Distortional buckling did not govern any of these rows.

Not published, hand calculations only: E4 and E4.2 (hand values in the test suite), kφ, sheathing braced design, Eq. B1.2.2-1, stud packs (I1.2, the built-up Cw), takedown and live load reduction. The AISI Cold-Formed Steel Design Manual (D100) and Framing Design Guide (D110) would close that (research/DOCUMENTS_NEEDED.md).

The S100-16 Commentary gives the yield load and yield moment of the Manual's 9CS2.5x059 (Figure C-2.2.2-2(a), Commentary p. 2-5). The strengths are also verified by hand calculations in closed form (backend/tests/test_verify_cfs_stud.py): the section properties by the Manual's linear-method formulas (u = 1.57r, centroid 0.637r, own inertia 0.149r³) and its square-corner formulas for m and Cw, and the strengths by the S100-16 equations, independent of the engine. 600S162-54, Fy = 50 ksi, 12 ft, 16 in. on center, bridging at 48 in.:

The hand calculations agree within 0.1 %. The published 9CS2.5x059 values come from a finite strip (centerline) model; ILX uses the linear method with rounded corners and agrees within 0.2 % (Py) and 0.6 % (My).