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Designing a chevron bracing gusset

The Chevron bracing gusset (chevron effect) type (Wizard group Truss & bracing, mark prefix CV) checks the beam and the gusset where two braces meet a gusset welded to the beam: V-bracing with the gusset above the beam, or inverted-V (chevron) bracing with it below. It follows the chevron-effect section of AISC Manual 16th Ed. Part 13 (pp. 13-15 to 13-19), which is based on Sabelli and Saxey (2021) and Fortney and Thornton (2015, 2017).

The work point where the brace centre lines meet is usually on the beam centre line, half the beam depth away from the gusset. That offset puts a moment on the gusset-to-beam joint. Beam analysis that ignores the connection dimensions misses the local forces it causes; the beam shear is the one that matters most.

Chevron gusset inputs

  • Loads: the brace forces F1 (brace 1, on the left) and F2 (brace 2, on the right), tension positive, as required strengths, service D + L, ASCE 7 combinations or load cases. Brace forces reverse also checks both forces with the opposite sign. The common seismic or wind case has one brace in tension and the other in compression.
  • Beam and braces:
    • the beam and its material, and whether the gusset is below or above it;
    • the bevel of each brace as a vertical and a horizontal leg. γ, the angle from the beam axis, comes from it;
    • Work point offset toward the gusset (default 0, the beam centre line). Moving the work point toward the gusset reduces the moment (Manual p. 13-15); design the beam for the moment the offset causes;
    • Other beam shear at the gusset midpoint (default 0). For a symmetric, symmetrically loaded frame with one gusset, 2Mf/Lg is the only shear there (Manual p. 13-18). Enter gravity shear, or the shear from a gusset on the other flange (X-bracing: the shears add, p. 13-15), here.
  • Gusset and welds: the gusset length Lg along the beam, its depth dg at the midpoint, the thickness and material, the fillet size (welded on both faces), the electrode, and the weld ductility factor (default 1.25, Manual p. 13-15).
  • Stress distribution (default: the Uniform Stress Method, the Manual's base method). Choose the Concentrated Stress Method when the gusset cannot be as long as Eq. 13-32 asks (Manual p. 13-17, step 2). It then asks for the concentrated stress length z at each gusset end. The default, 0, lets ILX choose the shortest z (in ¼ in. steps) that passes gusset yielding, beam web local yielding and crippling, and the weld.

How the chevron forces are found

  • Forces at the gusset-to-beam joint (Manual p. 13-16, Fig. 13-7), at the midpoint of the interface:
    • FN = F1 sin γ1 + F2 sin γ2, normal to the beam;
    • FV = F1 cos γ1 + F2 cos γ2, along the beam;
    • Mf = FV em, with em = d/2 for a concentric work point (Eq. 13-31), or d/2 less the work point offset.
  • Uniform Stress Method (pp. 13-17 to 13-19). The moment is carried by two blocks of normal stress, one on each half of the gusset length (Fig. 13-8). ILX checks:
    • beam shear at the gusset midpoint, Vr = 2Mf/Lg (Eq. 13-30), plus any other shear you enter, against the beam's shear strength by AISC 360-22 G2.1. The steps also give the minimum gusset length Lg ≥ 2Mf/Vc (Eq. 13-32) and the web thickness this needs (Eq. 13-33a for LRFD, 13-33b for ASD). When the beam shear fails, ILX suggests the minimum length;
    • beam web local yielding (J10.2) and crippling (J10.3, Eq. J10-4) under two concentrated forces Rr = FN/2 ± 2Mf/Lg, each on a bearing length Lg/2 (Eq. 13-34). The larger magnitude is used for both, since the brace forces can reverse. The gusset is taken to be away from the beam ends;
    • the gusset horizontal section (the higher-stressed half of the interface): N = |FN/2| + |2Mf/Lg| and V = FV/2 (Eqs. 13-35, 13-36) on Lg/2 × t, by normal yielding, shear yielding and Manual Eq. 9-1;
    • the gusset vertical section at the midpoint: Ng (Eq. 13-37), Vg (Eq. 13-38) and Mg (Eq. 13-39) on dg × t, by shear yielding and Manual Eq. 9-1 (M/Mc + (N/Nc)² + (V/Vc)⁴ ≤ 1). ILX finds these forces by statics of the half-gusset (Fig. 13-8(b)), which is what the Manual's equations express;
    • the gusset-to-beam welds, with the stress of the Uniform Stress Method (step 5, p. 13-17): per inch of each weld line fa = (|FN|/2 ± 2|Mf|/Lg)/Lg on the two halves and fv = |FV|/(2 Lg). The design force is the larger of the peak and the ductility factor × the average (p. 13-15); the directional strength increase of J2-5 applies. The minimum fillet size of Table J2.4 is checked too.
  • Concentrated Stress Method (p. 13-19, Fig. 13-9). The moment is carried at the two ends of the gusset over lengths z, and the middle Lg − 2z carries FN. The lever arm is ez = Lg − z, longer than the Uniform Stress Method's Lg/2, so the force at each end is smaller: Rz = Mf/ez. ILX checks:
    • beam shear Rz plus any other shear you enter, against G2.1. The steps show 2Mf/Lg for comparison;
    • beam web local yielding and crippling under Rz on a bearing length z, and under |FN| on the middle length Lg − 2z;
    • the gusset in each end length (Rz on z × t with the shear FV z/Lg) and in the middle, by normal yielding and Manual Eq. 9-1, and shear yielding on half the length;
    • the gusset vertical section from statics of the half-gusset of Fig. 13-9(b): Vg = F1 sin γ1 − Mf/ez + FN/2 and Mg with FN/2 on the middle half;
    • the welds, with the end-length stress Rz/z as the peak and the length-weighted average of the end and middle stresses (the Manual asks for welds that develop this distribution, p. 13-15).

    With z = Lg/2 the Concentrated Stress Method gives the Uniform Stress Method's forces (for FN = 0); a test checks this. With FN ≠ 0, z must leave a middle length.

Chevron gusset drawings

The elevation shows the beam (broken at both ends), the gusset outline, the two brace work lines through the work point, the gusset-to-beam fillets with their symbol, the dimensions Lg (in halves), dg and em, the gusset callout, the brace forces and a note with FN, FV, Mf and the beam shear (2Mf/Lg, or Mf/(Lg − z) and z with the Concentrated Stress Method).

Chevron gusset verification

The forces are compared with two published chevron examples, LRFD and ASD:

  • AISC Design Guide 29, Example 5.9 (W27X114, two HSS8X8X1/2 at 45°, ±289 / ±193 kips, a 3/4 × 18 × 64 in. gusset): the interface shear 408 / 272 kips and moment 5,560 / 3,720 kip-in., and the vertical section forces N′ = 0, V′ = 30.3 / 19.8 kips, M′ = 0. ILX is within 0.5 % (the guide rounds each brace component to 204 / 136 kips). The beam's shear strength 467 / 311 kips matches Manual Table 3-2.
  • AISC Design Examples V14.1, Example II.C-5 (W18X35, two HSS6X6X1/2, ±158 / ±105 kips): the interface shear 234 / 156 kips and moment 2,080 / 1,380 kip-in., and V′ = 11.5 / 7.57 kips at the vertical section.

Neither example applies the Manual 16th Ed. beam-shear rule of Eq. 13-30 (both are older than it). That rule and Eqs. 13-32 to 13-34 are verified by hand calculations. No published example applies the Concentrated Stress Method: it is verified by hand against Fig. 13-9, by statics of both half-gussets, and by its limit z = Lg/2.

Chevron gusset limits

  • The Concentrated Stress Method follows the Manual's description and Fig. 13-9. The Manual refers to Sabelli and Saxey (2021) for the full design procedure; that paper is not yet on file, so the choice of z (auto: the shortest passing length) and the checks in the end lengths are ILX's reading of p. 13-19.
  • The brace-to-gusset connections, the Whitmore section and gusset buckling are not checked here: use the vertical bracing gusset or tension member types for them.
  • The beam's own flexure and axial force, and the moment from a work point offset, are designed separately.
  • The gusset is assumed away from the beam ends (interior J10 equations).