Building Design and Construction Handbook - Merritt - Ventech!

7.98 SECTION SEVEN
FIGURE 7.41 Eccentrically loaded fastener groups: (a) with bolts in shear only; (b)
with bolts in combined tension and shear.
1 � n
leff � l � (7.79)
2
when n is the number of fasteners per gage line. For the bracket in Fig. 7.41a, the
reduction is (1 � 4)/2 � 2.5 in.
In Fig. 7.41a, the load P can be resolved into an axial force and a moment:
Assume two equal and opposite forces acting through the center of gravity of the
fasteners, both forces being equal to and parallel to P. Then, for equal distribution
on the fasteners, the shear on each fastener caused by the force acting in the direction
of P is ƒ v � P/n, where n is the number of fasteners.
The other force forms a couple with P. The shear stress ƒ e due to the couple is
proportional to the distance from the center of gravity and acts perpendicular to the
line from the fastener to the center. In determining ƒ e, it is convenient to first express
it in terms of x, the force due to the moment Pl eff on an imaginary fastener at unit
distance from the center. For a fastener at a distance a from the center, ƒ e � ax,
and the resisting moment is ƒ ea � a 2 x. The sum of the moments equals Pl eff. This