## 536 Connections For Bracing

The lateral force-resisting system of large buildings is sometimes provided by a vertical truss with connections such as that in Fig. 5.63. The design of this connection is demonstrated in the following example by a method adopted by the AISC, the uniform-force method, the force distributions of which are indicated in Fig. 5.64. The method requires that only uniform forces, no moments, exist along the edges of the gusset plate used for the connection.

Example—AISC LRFD. Design the bracing connection of Fig. 5.63 for the factored loads shown. The column is to be made of grade 50 steel and other steel components of A36 steel. This connection comprises four connection interfaces: diagonal brace to gusset plate, gusset plate to column, gusset plate to beam, and beam to column. Use the AISC LRFD specification.

Brace to Gusset. The diagonal brace is a tube, slotted to accept the gusset plate and is field welded to the gusset with four %-in fillet welds. For a design stress of 0.75 X 0.60 X 70 = 31.5 ksi, a Vi6-in fillet weld has a capacity of 1.392 kips per in of length. Hence the weld length required for the 300-kip load is 300/(1.397 X 4 X 4) = 13.9 in. Use 16 in of V4-in fillet weld. The z/2-in tube wall is more than sufficient to support this weld.

Tearout. Next, the gusset is checked for tearout. The shear tearout area is = 2 X 16i, where t is the gusset thickness. The nominal shear fracture strength is

0.6FuAv = 0.6 X 58 X 32t = 1114t and the nominal tension fracture strength is

FIGURE 5.63 Details of the connection of a tubular brace to a tubular beam at a column. (a) A gusset plate is welded to the brace, to a plate welded to the top of the beam, and to end plates, which are field bolted to the column. (b) Section A-A through the tubular beam.

FIGURE 5.63 Details of the connection of a tubular brace to a tubular beam at a column. (a) A gusset plate is welded to the brace, to a plate welded to the top of the beam, and to end plates, which are field bolted to the column. (b) Section A-A through the tubular beam.

Because 1114t > 464t, the controlling limit state is shear fracture and tension yielding. The design strength for tearout is thus faRto = 0.75(1114t + 8t x 36) = 1052t > 300

Solution of this inequality gives t > 0.285 in. Try a gusset thickness of 5/16 in.

Buckling. For a check for gusset buckling, the critical or ''Whitmore section'' has a width lw = 15 in, and the gusset column length l = 12 in (Fig. 5.63a). The slenderness ratio of the gusset column is kl/r = 0.5 x 12V12/0.3125 = 66.4

For the yield stress Fy = 36 ksi, the design compressive stress on the Whitmore section (from the AISC LRFD manual, Table 3.36) is faFcr = 24.1. The actual stress is fa = 300/(15 x 0.3125) = 64.0 ksi > 24.1 ksi—NG

Recalculation indicates that a 3/4-in plate has sufficient strength. For 3/4-in plate, the slender-ness ratio and design compression strength are

FIGURE 5.63 Continued.

kl/r = 0.5 X 12V12/0.75 = 27.7 4>Fcr = 29.4 ksi and the actual stress is fa = 300/(15 X 0.75) = 26.7 ksi < 29.4 ksi—OK

Stress Components. The forces at the gusset-to-column and gusset-to-beam interfaces are determined from the geometry of the connection. As shown in Figs. 5.63a and 5.64, for the beam, eb = 6 in; for the column, ec = 8 in, and tan 6 = 12/5.875 = 2.0426. The parameters a and (3 determine the location of the centroids of the horizontal and vertical edge connections of the gusset plate:

This constraint must be satisfied for no moments to exist along the edges of the gusset, only uniform forces. Try a = 16 in, estimated, based on the 32-in length of the horizontal connection plate B (Fig. 5.65a), which is dictated by geometry. By Eq. (5.30),

For 3 = 6, three rows of bolts can be used for the connection of the gusset to the column.

FIGURE 5.64 Determination of forces in a connection of a brace to a beam at a column through a gusset plate, by the uniform force method. (a) Lines of action of forces when no moments exist along the edges of the gusset plate. (b) Horizontal and vertical forces act at the top of the beam and along the face of the column. (c) Location of connection interfaces are related as indicated by Eq. (5.30). (d) For an axial force P acting on the brace, the force components in (b) are given by: Hb = aP / r, VB = eBP / r, HC = eCP / r, and VC = fiP/ r, where r = V(a + ec)2 + (3 + eBf.

FIGURE 5.64 Determination of forces in a connection of a brace to a beam at a column through a gusset plate, by the uniform force method. (a) Lines of action of forces when no moments exist along the edges of the gusset plate. (b) Horizontal and vertical forces act at the top of the beam and along the face of the column. (c) Location of connection interfaces are related as indicated by Eq. (5.30). (d) For an axial force P acting on the brace, the force components in (b) are given by: Hb = aP / r, VB = eBP / r, HC = eCP / r, and VC = fiP/ r, where r = V(a + ec)2 + (3 + eBf.

FIGURE 5.65 Gusset plate in Fig. 5.63a. (a) Force distribution on the gusset. (b) Bolt arrangement in plate A. (c) Attachment of gusset plate B.

The distance from the working point WP, the intersection of the axes of the brace, beam, and column, to X (Fig. 5.64a) is r = V(16 + 8)2 + (5.75 + 6)2 = 26.72 in

The force components are

Hb = 300 X 16/26.72 = 180 kips VB = 300 X 6/26.72 = 67.4 kips

VC = 300 X 5.75/26.72 = 64.6 kips HC = 300 X 8/26.72 = 89.8 kips

These forces are shown in Fig. 5.65.

Gusset to Column. Try six A325N 7/8-in-diameter bolts. For a nominal strength of 48 ksi, the shear capacity per bolt is

These bolts are subjected to a shear VC = 64.6 kips and a tension (or compression if the brace force reverses) HC = 89.8 kips. The required shear capacity per bolt is 64.6/6 = 10.8 kips < 21.6 kips—OK.

The allowable bolt tension when combined with shear is

Therefore <f)B = 32.5 kips. The applied tension per bolt is 89.8/6 = 14.9 kips < 32.5 kips— OK.

Prying Action on Plate A. Check the end plate (Plate A in Fig. 5.65) for an assumed thickness of 1 in. Equations (5.2) and (5.3) are used to compute the allowable stress in the plate. As shown in section A-A (Fig. 5.65b), the bolts are positioned on 5!/2-in cross centers. Since the gusset is 3/4 in thick the distance from the center of a bolt to the face of the gusset is b = (5.5 - 0.75)/2 = 2.375 in and b' = b - d/2 = 2.375 - 0.875/2 = 1.9375 in. The distance from the center of a bolt to the edge of the plate is a = 1.50 in < (1.25b = 2.9969). For a = 1.50, a' = a + d/2 = 1.50 + 0.875/2 = 1.9375 in; p = b'/a' = 1.9375/1.9375 = 1.0; p = 3 in; and S = 1 - d'/p = 1 - 0.9375/3 = 0.6875.

For use in Eqs. (5.2) and (5.3), and converting to LRFD format,

Substitution in Eq. (5.2) yields 1

4.444>Bb' 4.44 X 32.5 X 1.9375 , _ tc = J-£-= J--= 1.609 in

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