Cold-formed steel special bolted moment frame

A one-story cold-formed steel special bolted moment frame (CFS-SBMF): lipped C beams bolted to HSS columns with the Standard's 8-bolt groups, designed so that slip and bearing at the bolted connections dissipate the energy and the beams and columns stay elastic. To AISI S400-20 Section E4, with the members to AISI S100-16 (with S2-20) and the combinations of ASCE 7-22. The Standard gives this system for the United States and Mexico only, and in LRFD only.

Inputs of the moment frame #

• Frame: the height from the column base to the beam centerline h, the beam span between column centerlines, the number of columns in the frame line n, and the unfactored gravity loads on the beam (D, Lr, S as line loads).
• Seismic: the design story drift Δ and the elastic lateral stiffness K of the frame line, both from your analysis (Δ = Cd δxe / Ie, ASCE 7-22 12.8.6); the code-level seismic shear of the frame line Eh, which caps the design shear at Ω0 Eh (S400 E4.3.1; 0 removes the cap); Ω0 (3.0) and Cd (3.5) of ASCE 7-22 Table 12.2-1 line C.12; Ie; SDS for the vertical effect Ev = 0.2 SDS D; and the allowable drift ratio (0.025 prefilled, Table 12.12-1; 0 when the one-story footnote applies).
• Bolted connection: the 8-bolt configuration of Table E4.3.3-1 (spacings a, b and c), one or two channels (N), the snug-tight bolt tension T (10 kips for 1 in. bolts unless a higher value is approved), the hole oversize (1/16 in. for standard holes), whether you specify another hole type, the bolt grade and threads, the edge distance, and an optional bolt bearing plate welded to the beam web with its welds.
• Beam: the lipped C dimensions, Fy, Fu, Rt (1.1 for sheet of Fy ≥ 50 ksi, S400 Table A3.2-1), the A653 Grade 55 confirmation, the brace spacing and Cb.
• Column: the tube's depth, width, design wall thickness and outside corner radius, the steel (A500 B or C, A1085), Fy, Fu, Rt, and the effective length factors in and out of the frame plane (Kx = 2.0 prefilled for a pin-based sway frame: your call).
• System limits: one story without column splices, all columns engaged, pin-based columns, one size and detail of beam, column and connection, level support. These are requirements of E4.4.1, on by default; a condition you clear makes the frame not feasible.

Auto-design varies the beam thickness, the column wall (with an outside corner radius of 2t) and the bolt grade, lightest frame first. The frame, loads, drift, stiffness, bolt configuration and member depths are kept. A thicker beam web raises the connection's expected strength, so a thicker beam is not always better.

Checks performed #

How the expected strength is found: the slip component VS and the slip drift ΔS follow directly. The bearing component needs the bearing drift ΔB = Δ − ΔS − n Me/(h K), and Me itself depends on VB, so the calculation solves Eq. E4.3.3-3 for VB by bisection. Below the slip drift there is no bearing (VB = 0); beyond ΔB,max, VB stays at VB,max. CDB is interpolated linearly between the points of Table E4.3.3-2. R0 and the relative bearing strength use the beam web (with any bearing plate, whose thickness adds to the web when the holes are drilled through both, Commentary C-E4.3.1.2) and one column wall.

The gravity moment at the connection is taken as the fixed-end moment w L²/12, the upper bound for the semi-rigid connection. At midspan the gravity moment is w L²/8. The column axial load at an exterior column is its gravity share plus 2 Md / L.

Limitations #

• The design story drift and the frame stiffness come from your analysis; this calculation does not analyse the frame.
• Base plates and anchorage, the roof diaphragm and collectors are not designed.
• With one channel per side, torsion of the C beam must be accounted for (E4.4.2(e)); this calculation says so and does not compute it.
• The column model is a cold-formed tube with its webs fully effective, which the S400 flat-ratio limit guarantees.
• The ductile-hierarchy check of the bolts (bolt shear against the expected bearing strength) is this calculation's reading of E4.4.4, which requires that a ductile limit state controls without giving an equation.
• Canada: S400 has no CFS-SBMF provisions for Canada.

Verification examples #

Verification status: 11 values compared in 2 examples (0 published, 2 hand calculations from the cited equations): 11 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 CFS-SBMF design example is in the free library. The values are hand calculations from S400-20 E4.3.3 (Eqs. E4.3.3-1 to -7 and both tables) with a very stiff frame, so that the elastic drift is negligible and the bearing drift is known in closed form, and one case of the Ω0 Eh cap. A published example (AISI D110, a CFSEI design example) would replace them.