Cold-formed steel shear wall chord studs

The built-up boundary studs (chords) at the end of a stack of cold-formed steel shear walls, story by story from the top: the overturning accumulated down the stack with the gravity the chord collects, the chord in compression and tension, the hold-down at the base of each story and the anchorage at the bottom. To AISI S100-16 (with S2-20), with the ASCE 7-22 combinations.

Inputs of the chord studs #

• Wall stack: one wall length L for every story and the distance e from the wall end to the chord centroid (the chords are d = L − 2e apart).
• Stories, top first (up to 8): the story height; the story shear from wind and from seismic (Eh), at the strength level; the dead load on the wall at the top of the story (it resists overturning); the gravity loads the chord collects at that level (D, L, Lr, S); the chord stud designation of that story; the hold-down's strength in the method's terms (φRn for LRFD, Rn/Ω for ASD, from its evaluation report); and the hold-down screws into the chord (0 when the product's rating already covers them).
• Chord studs: one stud, studs side by side, two back to back (connector spacing a, S100 I1.2), or a box closed by its connections (your confirmation), Fy and Fu, the bracing length for the weak axis and torsion (your call, S240 B1.2.2), Kx over the story height, distortional buckling with an optional kφ, and the holes in one stud cross-section at the hold-down.
• Seismic: the amplification on the seismic effect for chords and hold-downs (Ω0 = 3.0 prefilled for walls with wood structural panels, ASCE 7-22 Table 12.2-1) and SDS for Ev = 0.2 SDS D.
• Hold-downs and anchorage: the screw size, the hold-down's thickness and Fu under the screw heads, the anchor rod diameter and Fu, and the concrete anchorage strength from ACI 318-19 Chapter 17 (0 = not checked here).

Auto-design is not offered: the studs are chosen story by story in the stories table.

Checks performed #

The overturning moment at the base of a story is the sum of V h over that story and the stories above. The tension is T = (M − fD ΣwD L (L/2 − e)) / d, with the dead load factor of each combination (0.9D, 0.6D, and less Ev in the seismic combinations); the compression is M/d plus the accumulated gravity on the chord. The seismic part of M is multiplied by your amplification. S400 E1.4 allows the shear wall's expected strength instead when it is smaller; this calculation does not compute it, so the amplified load is the safe side.

Limitations #

• One wall length for the whole stack, the walls stacked over one another. Walls of different lengths or offsets need their own calculation.
• The sheathing and its unit shear (the cold-formed shear wall type), the wall drift, the chord's bearing on the track and the hold-down-to-hold-down continuity between stories are not designed.
• Out-of-plane wind on an exterior chord is not combined here: use the jamb stud type for that.
• Screws into a built-up chord are checked against one stud's thickness, the safe side.

Verification examples #

Verification status: 5 values compared in 2 examples (0 published, 2 hand calculations from the cited equations): 5 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 multi-story chord stud example is in the free library. The values are hand calculations of the accumulated overturning and the chord forces for wind (LRFD and ASD) and for seismic with the amplification and Ev.