Cold-formed steel header

A header over a wall opening, to AISI S240-20 Section B3.3 and the AISI S100-16 North American Specification with Supplement S2-20, with ASCE 7-22 load combinations. Two C-sections back to back or boxed, double and single L-headers, and inverted L assemblies, on a simple span.

Inputs of the cold-formed steel header #

• Header: back to back (webs together, S240 B3.3.1), box (webs outside, tracks top and bottom, B3.3.2), double L (B3.3.3), single L (B3.3.4), with or without inverted angles below the track (B3.3.5).
• Section: an SSMA designation or custom dimensions for the C-sections; a designation such as 800L150-54 (8 in. vertical leg, 1-1/2 in. top flange, 54 mils) or custom dimensions for the angles. The yield stress is yours. Nothing is added for cold work.
• Span and loads: the span, and tributary area loads (a pressure times a tributary width), line loads and point loads, each with its load type. Every ASCE 7-22 2.3.1 (LRFD) or 2.4.1 (ASD) combination of the types present is analysed. Downward is positive. Enter wind uplift as a W load: W acts in both directions.
• Web holes (C-sections): unpunched, or punched with holes centred in the web, their shape, size, spacing and nearest distance to a bearing.
• Web crippling (C-sections): end bearing on the jack studs with its length, or clips (not checked); whether the flanges are fastened; point loads and their bearing length. For a box: the track thickness and flange, and whether the track flanges sit over the C-sections. S240 Eq. B3.3.2.3-1 applies only then, and its thickness tt is fixed at 0.0346 in. in the Standard. You also choose S240 Eq. B3.3.2.5 or S100 Eq. H3-1 for bending with web crippling: S240 permits either.
• Load points (L-headers): that a cripple stud sits at every load point, the bearing length and the wall width. S240 limits them.
• Web connections (back to back): the connection spacing s, the distance g between the rows nearest the flanges, the screws at each connection, their size and the tensile strength (0 takes the ASTM A1003 minimum: 45 ksi for 33 ksi steel, 65 ksi for 50 ksi steel).
• Distortional buckling: S240 B3.3 evaluates bending by S100 F3 with the full yield stress, so F4 is off as prefilled. You may turn it on, with a rotational restraint kφ. The SSMA header tables do limit by F4, so with F4 off the result is higher than those tables where F4 governs.
• Deflection (C-sections): live load and total load limits as span / n. 0 turns a check off.

Auto-design proposes the lightest listed C-section or angle; the header kind stays, the yield stress stays locked unless you unlock it, and a custom section is kept as entered.

Checks performed #

L-header section. Mno is the effective section modulus with the extreme compression fiber at Fy times Fy (S240 Commentary Eq. C-B3.3.3-1): yielding of the tension fiber is not a limit state. The top flange is an unstiffened element. The vertical leg, with its free edge in tension, takes Appendix 1 Eqs. 1.1.2-3 to -5 whatever its depth, as the Commentary says.

Inverted double L, a reading. S240 B3.3.5.2 sums the gravity and uplift nominal strengths and names no factor for the sum. The calculation applies each part's own factor. It is stated in the check. Confirm it if you rely on it.

Web connections at a point load. S100 Eq. I1.1-2 asks the connection nearest a short-bearing point load to take Ps s m / (2 g). Screw pull-out in thin webs is small, so this check often fails at cripple stud loads with the S240 Figure C3.4.4-1 minimum screws. Add screws at the load or a reinforcing plate (I1.1(b)), or take the load through a distribution member and enter it as a line load if that is what your detail does. Turning the check off is your decision as engineer of record: S240 B1.3 sends built-up sections to I1.

The drawings show the elevation with the loads, the assembly section, and the shear, moment and deflection diagrams. Upward loads are in the diagrams but not on the elevation.

Limitations #

• Simple span, bending about the major axis. Out-of-plane load on the header is not covered.
• Bracing is the Standard's: F3 at the yield stress takes the header as braced by its tracks and cripple studs. Lateral-torsional buckling is not computed.
• Tracks add no strength or stiffness, except α. Jack, king and cripple studs, tracks and their screws are not designed (S240 Figures C3.4.4, C3.4.5).
• L-headers get no deflection number. The S240 Commentary says the procedure is undefined, because the header is an indeterminate assembly; tests measured less than L/240 at nominal load.
• L-headers get no shear or web crippling check, as S240 allows. The Commentary suggests considering shear below a span to depth of 3: an advisory says so.
• A single L-header has no uplift strength (S240 B3.3.4.1.2 is reserved): uplift on one without inverted angles is NOT FEASIBLE.
• Screw pull-over and screw tension are not computed for the web connections. Two-flange web crippling is not checked. Holes in angles are not covered.

Verification examples #

Verification status: 48 values compared in 38 examples (35 published, 3 hand calculations from the cited equations): 39 within tolerance, 9 recorded deviations. Code basis: the provisions it uses were read in the target edition.

No published worked example of a header to S240 was on hand (research/DOCUMENTS_NEEDED.md).

SSMA tables. They treat a back-to-back or box header as twice one C, and limit by F4; those rows run with the F4 option on. Their web crippling column is not compared: an "e" in the table means web stiffeners.

DG-8. The guide prints spans with no calculation. The comparison assumes a 14 ft tributary width and a roof snow load of 0.7 times ground snow, which the guide does not state. Spans for legs up to 8 in. come within 4 %. Spans for the 10 in. legs are about 15 to 18 % longer in the guide, which predates the S240 factor Ω = 2.25 for legs over 8 in. It supports the section modulus; it does not verify the L-header provisions.

Hand calculations, not publications. The box factor α, Eqs. H3-2 and B3.3.2.5 as applied, I1.1, the L-header effective section, the uplift factor, the inverted assembly and the back-to-back section properties.