Designing a horizontal bracing wrap-around gusset
The Horizontal bracing wrap-around gusset type (Wizard group Truss & bracing, mark prefix HB) designs a horizontal brace connected by a gusset plate where two beams frame into a column at right angles. The gusset is cut out around the column, so it has two legs: leg 1 along beam 1 and leg 2 along beam 2 (AISC Manual 16th Ed. Part 13, "Wrap-Around Gusset Plates", Fig. 13-10). Each leg is lapped on its beam's top flange and bolted or welded to it.
Wrap-around gusset inputs #
- Loads: the brace force P (tension positive), as a required strength (the default), service loads, ASCE 7 combinations or load cases. Tick Brace force reverses to check tension and compression.
- Minimum connection strength: on by default. When no brace force is defined (P = 0), the connection is designed for 10 kips (LRFD) or 6 kips (ASD), Manual p. 13-24 and Specification Commentary J1.1. Enter a smaller value for small elements ("a required strength more appropriate to the size and use of the part").
- Beams and column: beam 1 and beam 2 (W shapes) and their material, the column, and whether beam 1 frames to the column flange (beam 2 then frames to the web, as in Fig. 13-10(a)) or to the web.
- Brace: double angle, single angle, WT, or a slotted rectangular or round HSS, its material and the bevel as a run along beam 1 and a run along beam 2. The angle θ is measured from beam 1. The brace end is placed clear of the cutout by the Brace clearance to the cutout, unless you enter the distance from the work point.
- Brace connection: bolted (lines, bolts per line, pitch, gage, end distances) or welded (fillet and length).
- Wrap-around gusset: thickness and material, the cutout e1 (along beam 1) and e2 (along beam 2), the leg lengths d1 and d2, the clearance from the cutout to the column, the leg buckling method and Cb (see below), the Whitmore buckling K, an optional chamfer of the outer corner square to the brace (the "optional cuts" of Fig. 13-10(a)), and an optional diagonal cut at the reentrant corner: its length along beam 2 (along leg 1's inner edge, back from leg 2) and along beam 1 (down leg 2's inner edge, back from leg 1).
- Gusset to the beams: Bolted (one bolt line along each beam, centred on the leg; bolt grade, diameter, threads, joint type, holes, bolts per leg, spacing, and the distance from the beam centreline to the bolt line) or Welded (fillet per leg, one line along the gusset edge or two lines adding the flange tip, and the weld ductility factor).
The gusset edges lie on the beam centrelines, as in the Manual's free-body diagram (Fig. 13-10(b)).
What is checked #
The brace force splits into Pr1 = Pr cos θ, delivered by leg 1 to beam 1, and Pr2 = Pr sin θ, delivered by leg 2 to beam 2. Each leg is a rectangular beam with its largest moment at the reentrant corner:
| Check | Basis |
|---|---|
| Leg 1 flexure, Mr1 = Pr1 e2 | Manual Eq. 13-40; Specification F11 |
| Leg 2 flexure, Mr2 = Pr2 e1 | Manual Eq. 13-41; Specification F11 |
| Leg lateral-torsional buckling, general method: tension Lb1 = e2, Lb2 = e1, Cb = 1.84; compression Lb1 = e2 + d2/2, Lb2 = e1 + d1/2, Cb = 1.84 when the critical load ratio α is above 1.6 or below 1/1.6, else 1.00 | Dowswell et al. (2017) pp. 161-162, Eq. 2; Manual Eqs. 13-42, 13-43; Spec. F11 |
| Simplified method (default): tension legs fully braced, Mn = Mp = Fy Z ≤ 1.5 Fy Sx; compression as above with Cb = 1.00 | Manual p. 13-21; Dowswell et al. (2017) p. 162; Spec. Eq. F11-1 |
| Diagonal cut: buckling moment at the midpoint of the cut, Mr1 = Pr1 em2 and Mr2 = Pr2 em1 (em = work point to the cut's midpoint), with the square-cutout Lb, Cb and leg depths; plastic moment at both ends of the cut (the leg depth there, the moment to that section) | Dowswell et al. (2017) pp. 160, 162, Fig. 10, Example 3 |
| Leg shear yielding, Rn = 0.60 Fy t d (with a diagonal cut, d on the plane just beyond the gusset-to-beam connection) | Specification J4.2(a) |
| Brace end: member yielding and rupture (shear lag), bolts or welds, block shear | Specification D2, D3, J3, J4 |
| Whitmore section in tension (yielding, and rupture when bolted) and in compression (K L / r with the length back to the cutout) | Manual Part 9, Fig. 9-1; Spec. J4.1, J4.4 |
| Legs to beams, bolted: bolt shear, bearing and tearout on the gusset and the flange, slip (slip-critical), block shear of the gusset strip at the beam, spacing and edge distances | Specification J3, J4.3 |
| Legs to beams, welded: fillet strength for the larger of the force and 1.25 × the average force, not more than the force that develops the leg in shear; base metal; fillet size limits | Manual p. 13-15; Spec. J2 |
When the plate is Fy = 50 ksi, 3/8 or 1/2 in. thick and a leg length is tabulated (6½, 9½, 12½, 15½ or 18½ in., and in compression an Lb from 8 to 30 in. with Cb = 1.0), the calculation also quotes the Manual Table 13-1 value. ILX reproduces every value of that table with the F11 calculation (see Verification).
The beams receive Pr1 and Pr2 as axial forces at the beam-to-column connections. ILX reports them; the beams, the column and the beam-to-column connections are designed separately.
Engineer inputs and their defaults #
The Manual and Dowswell et al. (2017) leave these to the engineer. Each is an input with a stated default, and the report states it:
- Leg buckling method: simplified (the method the Manual adopts, p. 13-21): tension legs fully braced, compression Cb = 1.0. You can choose the general method of Dowswell et al. (2017), the Manual's source, which takes Cb from the critical load ratio and can give a higher compression capacity; it matched the 15 tests better (mean test / calculated 1.40 at the maximum load). For 3/8 in. and thicker plates in tension both methods usually give Mp.
- Cb = 0, by the method: 1.84 or 1.00 as above. Enter a value to replace it.
- Weld ductility factor 1.25 (Manual p. 13-15).
- Minimum connection strength 10 kips (LRFD) / 6 kips (ASD) when no force is defined (Manual p. 13-24).
- Whitmore buckling K = 0.5 with the length from the Whitmore section back to the cutout. This check comes from Manual Part 9; Part 13 gives no Whitmore rule for wrap-around gussets.
Verification against Manual Table 13-1 #
Manual Table 13-1 (p. 13-31) is the golden data: all 400 tabulated values (two thicknesses, five leg lengths, the tension row and 19 compression rows, ASD and LRFD) are reproduced within the table's rounding by backend/tests/test_horizontal_bracing.py. The AISC Design Examples v16.0 have no wrap-around gusset example.
The three worked examples of Dowswell et al. (2017) are also golden tests, LRFD and ASD, tension and compression: Example 1 (simplified method), Example 2 (general method; α = 0.639, so Cb = 1.00 in compression) and Example 3 (diagonal cut; em1 = 4⅜ in., em2 = 10 in.). Every leg moment and available strength matches the paper within its three-figure rounding.
Limits #
- The Manual notes that Eqs. 13-40 and 13-41 "may be conservative for some gusset plate geometries".
- Neither the Manual nor Dowswell et al. (2017) give a flexure-shear interaction for the legs; flexure and shear are checked separately, as in the paper.
- In its Example 3 the paper takes the shear depth on the plane beyond a clip angle on the beam web. ILX laps the legs on the top flanges and takes the plane beyond its own connection (the bolt line, or the gusset edge or flange tip for welds).
- Gussets connected through angles to the beam webs (the detail of Fig. 13-10(a)) are not modelled; the legs are lapped on the top flanges.