Cold-formed steel joist

A lipped C-section floor or roof joist on any supports, to the AISI S100-16 North American Specification with Supplement S2-20, by the Effective Width Method, with ASCE 7-22 load combinations. Simple spans, continuous spans, overhangs and cantilevers, an unpunched or punched web, flexure with distortional buckling, shear, web crippling at each bearing, the combined checks and deflection.

Inputs of the cold-formed steel joist #

• Section: an SSMA designation (800S162-54 is an 8 in. web, 1-5/8 in. flange, 54 mils) with its design thickness, inside radius and lip from the SSMA tables, or custom dimensions. The yield stress is yours: 33 ksi for 33 and 43 mils and 50 ksi for 54 mils and thicker are the usual values. Nothing is added for the cold work of forming (A3.3.2): if you take that increase, enter the raised value (see Verification).
• Web holes: unpunched, or punched with holes centred in the web: noncircular (depth and length, the SSMA standard punchout is 1-1/2 × 4-1/2 in.) or circular, their spacing, and the nearest distance from a hole to the edge of a bearing (for the web crippling factor). You also choose how the holes enter the distortional buckling stress (Appendix 2 2.3.4.3): patterned along the web (Eq. 2.3.4.3-2, prefilled because the input describes a regular pattern), or a hole within the buckling wavelength (Eq. 2.3.4.3-1, up to about 4 % lower on Mnd for short wavelengths).
• Length and supports: the joist length and a table of supports (position, pin or fixed, flange bearing or clip, bearing length N), and the joist spacing, which is the tributary width of the area loads.
• Loads: area loads (on the joist spacing, full length or part), line loads (uniform or linearly varying) and point loads, each with its load type (D, L, Lr, S, R, W, E), plus the optional self-weight. Every ASCE 7-22 2.3.1 (LRFD) or 2.4.1 (ASD) combination of the types present is analysed. On more than one span or overhang, Pattern live load places the live load L span by span (ASCE 7-22 4.3.3). See Loads and combinations.
• Flange bracing: for the top flange (in compression under positive moment) and the bottom flange (in compression over interior supports, on overhangs and under uplift): continuous bracing by sheathing, or bracing at a spacing you enter (0 = at the supports only). K applies to both Ky and Kt. Cb is computed from the moment diagram of each segment (1.0 on a segment with a free end) or entered.
• Distortional restraint: the rotational restraint kφ of each flange (0, prefilled, is the unrestrained value and the one the SSMA tables use; a higher value is your own, from the sheathing and its fastening), and the moment gradient factor β: 1.0, which the code permits, or Eq. 2.3.3.3-3 for segments between brace points. A brace point is taken as a distortional restraint too (Lm = the segment).
• Web crippling: whether the flanges are fastened to the supports, and whether to check point loads and their bearing length.
• Deflection: live load and total load limits as span / n (the IBC 2021 Table 1604.3 floor values 360 and 240 are prefilled; 0 turns a check off). Overhangs are checked on twice their length (note h of the table).

Auto-design proposes the lightest SSMA designation and, where it helps, a wider spacing; the yield stress stays locked unless you unlock it, and a custom section is kept as entered.

Checks performed #

End or interior loading. A bearing whose edge is within 1.5 h of the member end is end loading; otherwise interior. The overhang increase of Eq. G5-2, which the code permits as an alternative, is not taken.

Holes. For a hole depth below 0.38 h the web is taken without the hole in local buckling; at 0.38 h or more, the compression part of the web beside the hole is an unstiffened element at f1 (Appendix 1 1.1.3(a)). No reduction of the lateral-torsional buckling stress is needed within those hole limits (F2.2 exception). Deflection ignores holes (1.1.3(b)). The shear check and H2 take a hole at the point of largest shear, wherever the holes are.

Shear at a hole. S100-16 G3 reads "in accordance with Section G2, with Vcr computed using G2.3, multiplied by the reduction factor". The calculation multiplies the G2 nominal strength by qs, the wording of S100-12 C3.2.2 and what the SSMA Vanet values reproduce. Where the web is in the inelastic range of G2 this is the lower reading (a 600S162-68 at 50 ksi: 2,880 lb against 3,075 lb if qs multiplied Vcr alone).

What the calculation does not decide. You give the bracing and restraint values; the bridging, blocking and their anchorage (AISI S240), and the sheathing attachment behind kφ, are yours. The hole conditions the inputs cannot express are yours to confirm: holes centred in the web, noncircular corner radii at least 2t, and at least the section depth from the member end to a hole (G3, G6, Appendix 1 1.1.3). The calculation states them in a note.

The drawings show the joist elevation with its supports, loads and brace points, the C-section, and the shear, moment and deflection diagrams of the governing combinations. The notes give the web holes, which are not drawn.

Limitations #

• Single lipped C-sections bent about their major axis. Back-to-back or built-up joists, tracks, Z-sections and axial load are not covered. Inelastic reserve (F2.4, F3.1.3, F4.3) and the Direct Strength Method are not used.
• A bearing stiffener: hand calculations only, no published example on hand. Its bearing on the support, web holes beside it and H3 at a stiffened support are not checked. CFSEI F100 and F104 are not on disk. The stiffener's own screws take all of the reaction, on the conservative side. The joist's Fu for these screws is your entry, or 0 pairs it with Fy as the SSMA Guide does: 45 ksi with 33, 65 with 50.
• Two-flange web crippling is not checked. A point load within 1.5 h of a flange-bearing support gets a note saying so.
• Bearing stiffeners and clips are not designed: a support marked as a clip has no web crippling check, and a hole within the bearing needs a stiffener (G6), which you confirm by the hole distance you enter.
• Floor vibration is not checked, and the diaphragm role of the sheathing is not covered.

Verification examples #

Verification status: 71 values compared in 36 examples (36 published, 0 hand calculations from the cited equations): 69 within tolerance, 2 recorded deviations. Code basis: the provisions it uses were read in the target edition.

No published worked example of a joist to S100-16 was on hand (the AISI Cold-Formed Steel Design Manual is listed as a document needed). The calculation is compared with the published tables of the SSMA Product Technical Guide (2022), which are computed to S100-07 / S2-10 and S100-12, ASD; the provisions compared read the same in S100-16.

The full list is on the Verification page. Rows with footnote 2. Where the guide marks a section "includes cold work of forming", its Mal and Mad use a raised yield stress: for 600S162-54 at 50 ksi it prints 30.33 and 25.90 kip-in, the calculation at 50 ksi gives 27.80 and 24.23 (a listed deviation, the calculation is lower). With the raised value worked out from the same row (30.33 × 1.67 / 0.916 = 55.3 ksi) it gives 30.35 and 25.89.

Not compared. The double-span columns and the moment-governed rows of the span tables exceed the guide's own Mal by 10 to 14 % and cannot be reproduced from the section values, so they are not used.

Hand calculations. No published value covers kφ above 0, Lm below Lcrd, β, the hole terms of Appendix 2 2.3.4.3, F4.2, G6 or Appendix 1 1.1.3: those are checked in the test suite against hand calculations from the cited equations, not against a publication.