## 3347 Design of Stud Shear Connectors

The Vierendeel girder shear force diagram gives the shear forces that must be transferred between the slab and the stubs. These are the factored shear force values that are to be resisted by the connectors. The example shown in Figure 33.7 indicates the individual shear forces for the stub verticals, as listed in the preceding section. However, in the design of the overall shear connection, the total shear force that is to be transmitted to the stub is used, and the stud connectors are then distributed uniformly along the stub. The design strength of each connector is determined in accordance with the LRFD Specification [3], including any deck profile reduction factor.

Analyzing the girder whose data are given in Figure 33.7, the following is known:

Exterior stub:

Interior stub:

The nominal strength, Qn, of the stud shear connectors is given by the LRFD Specification; thus

where Asc is the cross-sectional area of the stud shear connector, f' and Ec are the compressive strength and modulus of elasticity of the concrete, respectively, and Fu is the specified minimum tensile strength of the stud shear connector steel (60 ksi) (ASTM A108).

In the equation for Qn, the left-hand side reflects the ultimate limit state of shear yield failure of the connector; the right-hand side gives the ultimate limit state of tension fracture of the stud. Although shear almost always governs, and is the desirable mode of behavior, a check has to be made to ensure that tension fracture will not take place. This is achieved by the appropriate value of Ec, setting Fu = 60 ksi, and solving for f' from the Equation 33.2. The requirement that must be satisfied in order for the stud shear limit state to govern is given by Equation 33.3:

57,000

This gives the limiting values for concrete strength as related to the density (Table 33.1).

For concrete with wc = 120 pcf and f' = 4000 psi, as used in the design example, Ec = 2,629,000 psi. Using 3-in. diameter studs, the nominal shear capacity is

Qn = 0.5[n(0.75)2/4]^/(4.2,629) < [n(0.75)2/4]60

TABLE 33.1 Concrete Strength Limitations for Ductile Shear Connector Failure

Concrete density Wc (pcf)

0 0