Eccentrically Loaded Welded Connections

Welds are of two general types, fillet (Fig. 7.43a) and groove (Fig. 7.43b), with allowable stresses dependent on grade of weld and base steels. Since all forces on a fillet weld are resisted as shear on the effective throat (Art. 7.31), the strength of connections resisting direct tension, compression and shear are easily computed on the basis that a kip of fillet shear resists a kip of the applied forces. Many connections, some of which are shown in Fig. 7.44, are not that simple because of eccentricity of applied force with respect to the fillets. In designing such joints it is customary to take into account the actual eccentricity.
The underlying design principles for eccentric welded connections are similar to those for eccentric bolted connections (Art. 7.32). Consider the welded bracket in Fig. 7.45. The first step is to compute the center of gravity of the weld group.
Then, the load P can be resolved into an equal and parallel load through the center of gravity and a couple. The load through the center of gravity is resisted by a uniform shear on the welds; for example, if the welds are all the same size, shear per linear inch is Æ’v = P/n where n is the total linear inches of weld. The moment Pl of the couple is resisted by the moment of the weld group. The maximum stress, which occurs on the weld element farthest from the center of gravity, may be expressed as Æ’e = Pl/S, where S is the polar section modulus of the weld group.
To find S, first compute the moments of inertia Ix of the welds about the XX axis and IY about the perpendicular YY axis. (If the welds are all the same size, their lengths, rather than their relative shear capacities, can be conveniently used in all moment calculations.) The polar moment of inertia J  IX  UY, and the polar section modulus S = J/a, where a is the distance from the center of gravity to the farthest weld element. The resultant R of Æ’v and Æ’e, which acts normal to the   line from the center of gravity to the weld element for which the stress is being determined, should not exceed the capacity of the weld element (Art. 7.31).

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