Fm

Fastener i

(b) Fastener i

(a) Connection

Fig. 12.5. Shear force analysis of member 1 subjected to moment Md per shear plane.

x grain within the boundary area of the connection will occur to the left of the centre of rotation and will envelope the fasteners within the shear zone area shown in the figure.

Consider each shear plane in the connection subjected to moment Md and lateral forces Vd and Hd. Under the action of the design moment only, lateral forces will be induced in the fasteners and the force in fastener i in the shear zone area will be as shown in Figure 12.5a. The radius of the fastener from the centroid of the connection is ri and is at an angle fa to the horizontal. The vertical design force per shear plane in the fastener, FM,v,;,d, shown in Figure 12.5b, can be written as:

rmax ri rmax where \xi | is the absolute value of the x coordinate of fastener i. The origin of the coordinate system is the centre of rotation of the fastener configuration in the connection.

The summation of the vertical component of the forces in the fasteners in each line j to the left side of the centre of rotation arising from the design moment, Md, will be:

rmax rmax where the functions are as previously defined, and FM v d, j is the vertical shear force per shear plane in each line j in the zone arising from the applied moment Md and nj is the number of fasteners in the shear plane in line j .

If the connection is now subjected to the vertical design force, Vd, in accordance with the assumption in 12.5.1(b), the vertical lateral force taken by each fastener in the shear plane, Fy,v,;,d, shown in Figure 12.6, will be:

n where n is the number of fasteners in the shear plane.

Fastener i

Fastener i Member 2

Member 1

Fig. 12.6. Shear force in each fastener due to vertical force, Vd, per shear plane.

Member 2

Member 1

Fig. 12.6. Shear force in each fastener due to vertical force, Vd, per shear plane.

When the connection is subjected to the horizontal design force, Hd, the horizontal lateral force taken by each fastener in the shear plane, fH,h,,-,d, shown in Figure 12.7, will be

When considering only member 1, the forces contributing to the vertical shear force in the member will be those arising from the application of the design moment, Md, and the vertical design shear force, Vd.

The vertical design shear force per shear plane on member 1, FVjVjd, will be the maximum shear force in the shear zone. This is obtained by starting at the left side of the zone and evaluating the cumulated shear force across the zone. The maximum value will depend on the fastener configuration and the value of the vertical shear design force, Vd. For the case shown in Figure 12.5 the maximum value, FV v d, will be as follows:

0 0