Cold-formed steel rafter

A sloped lipped C-section rafter with the thrust at its heel and the ceiling joist or tie that resists it, to AISI S240-20 Section B4.2 and the AISI S100-16 North American Specification with Supplement S2-20, with ASCE 7-22 load combinations.

Inputs of the cold-formed steel rafter #

• Section: an SSMA designation or custom dimensions. Fy and Fu are yours. Nothing is added for cold work.
• Roof geometry: horizontal span from plate to ridge, slope as rise in 12, a horizontal overhang, and the rafter spacing.
• Ridge: a ridge board with a tie at the heel makes a three-hinged frame, and the tie takes the thrust. A structural ridge beam or bearing wall holds the ridge up, with no thrust.
• Area loads: by load type, each on the slope, on the horizontal projection or normal to the roof. Normal is positive toward the roof, negative for suction. Both rafters of a pair take the same load, so enter the heavier side.
• Point loads: vertical, placed horizontally from the plate.
• Bracing: each flange braced by sheathing or at a spacing you enter. S240 B4.5(b) states what sheathing counts. The rotational restraint kφ is yours, from S240 Appendix 1; 0 means none.
• Compression basis: continuously braced (S240 B4.2.2(b): Fn = Fy with E3, and distortional buckling) or discretely braced (Chapter E at your brace spacing). Tick the box when your braces also restrict flange rotation, which makes Lm the spacing.
• Kx: on the sloped length from plate to ridge. It enters E2 and the amplifier B1.
• Bearing: flange bearing with its length N, or a clip, which turns web crippling off.
• Tie: section, steel, the net area ratio An/Ag (your judgment; 0.85 is prefilled and is not a code value), and the screws at the heel.
• Deflection limits: span / n, on the length along the slope and on twice an overhang. 0 turns a check off.

Auto-design varies the section (lightest first) and the screws at the heel, and the yield stress when unlocked. Spacing, tie and loads are kept.

Checks performed #

The perpendicular load components bend the rafter as a simple span along the slope. The parallel components and the end reactions give the axial force by statics at every station. With a ridge board, moments about the heel give the thrust H = R / sin(slope), where R is the perpendicular reaction at the ridge.

Limitations #

• The tie is at the heel. A raised tie is not built.
• Both rafters take the same load. Unbalanced snow and wind on one side are your entry on the heavier side.
• Web holes, bearing stiffeners and clips are not designed. The tie's bending under a ceiling load is a job for the cold-formed joist type.
• Under net uplift the tie goes into compression and the ridge pulls apart: the force is reported, and its check is yours.
• The rafter's net section is taken as the gross section in D3.
• S240 B4.2.2(b) prints F4 (a flexure section) for the compression distortional check. This calculation reads it as E4, the compression section, and says so in its note.
• The tie net area ratio is your judgment. The module does not derive it from the screw pattern.

Verification examples #

Verification status: 17 values compared in 6 examples (3 published, 3 hand calculations from the cited equations): 17 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.

No published worked example of a cold-formed rafter is on disk. The AISI Framing Design Guide D110 would give one; it is on the list to buy.

• Published section strengths: the SSMA Guide (2022) p. 11, Mal, Mad and Vag of three sections, read back through the module. They confirm the section strengths, not the rafter's statics or combined checks.
• Hand calculations: three cases of statics, closed form: thrust, moment and axial force of a ridge board frame and a ridge beam rafter under plan and normal loads. No published value checks these.