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As before, the value of a' should be limited to the range 0 < a' < 1. This new value of a' is to be used in Equation 4.110 to recalculate freq>d.

### 4.11.1.10 Bolted Bracket-Type Connections

Figure 4.16 shows three commonly used bracket-type connections. The bracing connection shown in Figure 4.16a should preferably be designed so that the line of action of the force will pass through the centroid of the bolt group. It is apparent that the bolts connecting the bracket to the column flange are subjected to combined tension and shear. As a result, the combined tensile-shear capacities of the bolts should be checked in accordance with Equation 4.107 in ASD or Equation 4.108 in LRFD. For simplicity, fv and f are to be computed assuming that both the tensile and shear components of the force are distributed evenly to all bolts. In addition to checking for the bolt capacities, the bearing capacities of the column flange and the bracket should also be checked. If the axial component of the force is significant, the effect of prying should also be considered.

In the design of the eccentrically loaded connections shown in Figure 4.16b, it is assumed that the neutral axis of the connection lies at the center of gravity of the bolt group. As a result, the bolts above the neutral axis will be subjected to combined tension and shear and so Equation 4.107 or 4.108 needs to be checked. The bolts below the neutral axis are subjected to shear only and so Equation 4.104 or 4.105 applies. In calculating fv, one can assume that all bolts in the bolt group carry an equal share of the shear force. In calculating ft, one can assume that the tensile force varies linearly from a value of zero at the neutral axis to a maximum value at the bolt farthest away from the neutral axis. Using this assumption, f can be calculated from the equation Pey/I where y is the distance from the neutral axis to the location of the bolt above the neutral axis and I = X!Ay2 is the moment of inertia of the bolt areas where Ab is the cross-sectional area of each bolt. The capacity of the connection is determined by the capacities of the bolts and the bearing capacity of the connected parts.

For the eccentrically loaded bracket connection shown in Figure 4.16c, the bolts are subjected to shear. The shear force in each bolt can be obtained by adding vectorally the shear caused by the applied

load P and the moment Py0. The design of this type of connections is facilitated by the use of tables contained in the AISC Manuals for Allowable Stress Design and Load and Resistance Factor Design (AISC 1986, 2001).

In addition to checking for bolt shear capacity, one needs to check the bearing and shear rupture capacities of the bracket plate to ensure that failure will not occur in the plate.

### 4.11.1.11 Bolted Shear Connections

Shear connections are connections designed to resist shear force only. They are used in Type 2 or Type 3 construction in ASD, and Type PR construction in LRFD. These connections are not expected to provide appreciable moment restraint to the connection members. Examples of these connections are shown in Figure 4.17. The framed beam connection shown in Figure 4.17a consists of two web angles that are often

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