Page 154 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch03.qxd 9/29/05 5:05 PM Page 3.86

CONNECTIONS

3.86 CHAPTER THREE

the member interfaces, four control points must be established: the work point, the beam control
point, the column control point, and the gusset control point.
The intersection of the centers of gravity of the beam, the column, and the brace at the work point
ensures that a force distribution exists that will produce no moments in any of the members. The inter-
section of the brace line, the gusset-to-beam line, and the gusset-to-column line at the gusset control
point ensure that the force distribution chosen is the one required to eliminate moments for the system.
The work point, the beam control point, and the column control point are established by the
geometry of the given situation. The position of the fourth, the gusset control point, must be calcu-
lated. The uniform force method uses the following relationship to determine the location of the
fourth control point. (Since the location of the gusset control point is not required in the determina-
tion of the force distribution, it is usually not calculated.)
3.7.1 Control Points

Refer to Fig. 3.48 for definition of dimensional terms and forces. From geometry, the angle of the
force P from the vertical θ is related to the key dimensions by α−β tan θ= e b tan θ− e c . With θ
determined, the interface forces are then calculated using
β e e α
V = P H = c P V = b P H = P
c
r c r b r b r
where r = (α + e ) 2 + (β + e ) 2
b
c
Note that for every choice of α or β, there will be a different location for the gusset control point
and a different force distribution at the interfaces. In this way, distribution of the forces can be
manipulated to the extent that the geometry of the gusset plate will allow.

3.7.2 Conditions with High Beam Reactions: ∆V b and Special Case 2

Problems can arise when the beam reaction is high and the additional vertical load V b delivered by the
bracing connection to the beam flange would overstress the member. Rather than reinforcing the beam
web, it is usually more economical to reduce V b . This is done by introducing a force ∆V b , which acts
opposite V b . Obviously, this will change the force distribution assumed in the uniform force method,
and moments in both the beam-to-gusset interface and locally within the column will have to be intro-
duced to maintain equilibrium. AISC recommends calculating the moment introduced at the beam-to-
gusset interface as ∆V b (α). A more direct and versatile method is to calculate the moment caused by
the gusset-to-beam force about the beam control point. This results in the equation
V −
(
M = α() e H ) (3.70)
b
b
b
b
where V = V − ∆ V b
b
b
α= actual distance from face of support to centroid of gusset-to-beam connection
AISC does not address the moment in the column at this section containing the column control point,
though one will exist. However, it can be found by calculating the moment caused by the gusset-to-
column force about the column control point, which results in
M = e V − ( H ) (3.71)
β
()
c c c c
where V = V + ∆ V b
c
c
β= actual distance from face of beam flange to centroid of gusset-to-column connection
The moment M c occurs in the column cross section that contains the column control point. If there
is a connection at this cross section (see Art. 3.7.4), M c needs to be considered in the design of this
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