Cold-formed steel sloped and mansard wall
A C-stud of a sloped wall or mansard, from the floor up its slope to the roof, optionally propped by a horizontal kicker to the building: the stud as a beam-column under dead, snow, roof live and wind loads, the kicker, and the screws at the roof, the floor and the kicker. To AISI S100-16 (with S2-20), with the ASCE 7-22 combinations.
Inputs of the sloped stud #
- Stud: an SSMA designation or custom dimensions, Fy and Fu, the spacing, the slope θ from the horizontal (15° to 90°) and the length along the slope from the floor to the roof; the flange bracing (sheathing on both flanges, or discrete braces at a spacing) and the weak-axis and torsional length for compression (your call, S240 B1.2.2).
- Kicker (optional): its position along the stud from the floor, its SSMA section, Fy, horizontal length and K (1.0 for pinned ends).
- Loads: dead load on the sloped surface; snow and roof live on the horizontal projection (ps from ASCE 7-22 Chapter 7 with the slope factor, drifts and sliding snow being yours); wind normal to the surface toward it and away from it at the strength level (components and cladding of ASCE 7-22 Chapter 30; which zone fits a steep mansard is your call).
- Connections: the screw size, the counts at the roof, the floor and each kicker end, and the supporting framing's thickness and Fu.
- Deflection: the wind factor (0.42, S240 B1.1.2 and the IBC Table 1604.3 footnote) and the span limits for wind and for snow or roof live.
Auto-design varies the stud and the kicker (SSMA designations, lightest first) and the screws at the floor, the roof and the kicker. The slope, lengths, the kicker's position, the loads and the limits are kept; Fy when unlocked.
Checks performed #
| Check | Basis |
|---|---|
| Stud flexure, shear, bending and shear | S100 F2, F3, G2, H2 |
| Stud compression and bending (B1 over the span of the station) | S100 E2, E3, H1.2, C1.2.1.1 |
| Kicker compression and tension | S100 E2, E3, D2 |
| Screws at the roof, the floor and the kicker ends | S100 J4.3.1, J4.3.2 |
| Deflection normal to the stud, wind and snow or roof live | IBC Table 1604.3 (limits entered), S100 L1 |
The loads split into a part normal to the stud and a part along it. Dead load acts on the sloped area: w cos θ normal, w sin θ along. Snow and roof live act on the horizontal projection, cos θ of each unit length, then split the same way. Wind is normal. The stud is pinned at the floor (which takes the force along the stud) and at the roof (normal only), with the kicker as a third support. A horizontal kicker's force is H = Rn / sin θ from the normal reaction Rn; its part H cos θ along the stud loads the stud below the kicker. The floor screws carry the resultant of the normal reaction and the axial force.
Limitations #
- The roof connection is taken to carry no load along the stud; a detail that does needs its own model.
- One horizontal kicker, pinned at both ends. An inclined kicker is not modelled.
- The roof and floor framing, track or clip details beyond their screws, web crippling at the supports, bridging and the finish are not designed.
Verification examples #
Verification status: 9 values compared in 3 examples (0 published, 3 hand calculations from the cited equations): 9 within tolerance, 0 recorded deviations. No published example: every value is a hand calculation. That checks the program against this reading of the code, not the reading itself. Code basis: not yet recorded for this module.
No published sloped or mansard stud example is in the free library. The values are hand calculations of the load split, the axial force at the floor, the simple-span moment (LRFD and ASD), and the two-span kicker reaction and force.