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CONNECTIONS

3.4 CHAPTER THREE

than, or at most equal to, the applied external force that would cause failure, provided that all the limit
states are satisfied and sufficient ductility exists to allow redistribution of the forces.

3.1.4 Limit States for Connection Design
Limit states for connection elements are arrived at in a similar fashion as those for main-member
design. Limit states that could result in sudden, fracture-type failures are required to have greater
safety factors, or greater reliabilities, than limit states associated with yielding. Bolt and weld fail-
ures are treated as fracture-type failures, and are therefore required to be designed at the higher reli-
ability level. Plates, angles, and other connection elements are designed to reliabilities based on the
individual modes of failure in the same way that main members are designed. Generally, connections
are not required to be designed to a higher reliability than the members they connect.

3.1.5 Ductility of “Pinned” Connections
In theory, a pinned connection will have no rotational stiffness. In reality, simple shear connections,
which have been modeled as pinned during the structural analysis, will have varying degrees of rota-
tional stiffness. The key, then, is to allow sufficient rotation to develop the simple end-beam rotations
without fracturing the connection. This is accomplished through various means.
For double-angle, single-angle, end-plate, and tee shear connections, flexing of the connecting
element accommodates the simple beam-end rotation. For seated connections, the top or side stabil-
ity angle should be sized such that the simple beam-end rotation can be accommodated. For single-
plate shear connections with either one or two vertical rows of bolts, bolt plowing at the plate can
accommodate the simple beam-end rotation. For other types of single-plate shear connections, sim-
ple beam-end rotation is accommodated by flexing of the plate.
For tees cut from wide flange sections, double angles, and end plates, the thickness of the con-
nection material at the support can be related to the minimum bolt diameter required to develop the
simple beam-end rotation by the equation presented by Thornton (1996, 1995a)

y 
Fs b 2 
.
d = 0 892 t  +  2 (3.1)

b
Fb L 2 
t
where t = thickness of end plate, tee flange, or angle leg, in
F y = yield stress of endplate, tee, or angle, ksi
F t = tensile strength of bolt, ksi
s = bolt spacing, in
b = flexible width of connection element, in
L = depth of connection element, in
Assuming A325 bolts (F t = 90 ksi) and s = 3 in, the equation reduces to the relationship in the
AISC Manual:
F  b 2 
y
.
d = 0 163 t b   L 2 +  2  (3.2)
b
When connections are welded to the support, the 70-ksi weld size, w, must be such that
2
Ft  b 2 
y f
w = 0 0158  +  2 (3.3)
.
b  L 2 
All of the above minimums are calculated assuming an end rotation of 0.03 rad, which exceeds the
beam-end rotation of most beams when a plastic hinge forms at the center.

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