Page 115 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch03.qxd 9/29/05 5:05 PM Page 3.47

CONNECTIONS

CONNECTIONS 3.47

 ab  Tab  
+
P = 2 M   4 + L  (3.48)

p
u
+
  ab  ab   
2
For a hollow structural section, substitution of B = T, N = L, a = b, t 1 = T – a – b, and 0.25t w F y = M p
results in
2
tF  t 2 N 
P = wy  41 − 1 +  (3.49)
u
tB 
1 [ − ( / )] B B 
1
This is the equation given in the AISC “Hollow Structural Sections Connection Manual.”
Axial Load Effect. When members are subjected to a concentrically applied axial load as well
as the transverse load, the strength derived by the yield line equations should be reduced by a factor,
Q, defined as
 f   f  2
10.
Q =− 3   − 0 3 .   (3.50)
 F   F 
y
y
where f is the magnitude of the compressive stress.
3.3.5 Stability
In addition to satisfying the limit states of yielding and fracture, connections must also be checked
for limit states of stability, the resistance of the connecting elements to buckling. Buckling can occur
in plates loaded in pure compression, plates in bending, or plates subjected to both compression and
bending forces.
Plates in Uniform Compression. Oftentimes plates are checked to resist buckling in a manner sim-
ilar to columns. As with columns, the end restraint is important in determining the plate’s resistance
to buckling. This is reflected in the effective length factor K. Several conditions can exist, as illus-
trated in Fig. 3.29.
A gusset connected to only one supporting member and supporting a single brace is free to trans-
late out of plane. The welded connection of the gusset to the support, and the welded or bolted con-
nection of the brace to the gusset, are both assumed fixed, since considerable rotational stiffness is
present relative to the stiffness of the plate. Therefore, K = 1.2 is assumed.
The behavior of a gusset connected to only one supporting member and supporting two or more
braces depends on the loads in the braces. If all the braces act in compression simultaneously, then
the gusset should be considered free to translate out of plane, and K = 1.2 is assumed. However, if
one of the braces acts in tension, this brace will tend to resist movement out of plane, and K = 0.65
can be assumed. Of course, some engineering judgment must be used in determining if the tension
force is sufficient to resist the out-of-plane movement. If the tension force counteracts the compres-
sion force, the most common case, the tension will be sufficient.
It is typically assumed that a gusset attached to a beam and a column, as is the usual case for ver-
tical bracing, is retrained against both rotation and translation. For this case the recommended K
value is 0.65. However, test data support the use of the theoretical K value of 0.5, so this has become
the accepted approach.
At the intersection of X bracing, the end of the plate connected to the compression brace is assumed
fixed. However, the connection to the tension brace is assumed pinned, because the tension brace often
has little torsional stiffness. Since out-of-plane translation can occur, K = 2.0 is assumed. If the tension
brace is deemed to have sufficient torsional stiffness, a less conservative K = 1.2 can be used.
Often a connection framing to another element can provide resistance to out-of-plane movement.
This is the case with a flange-plate moment connection where the shear connection to the web of the
member prevents the translation of flange plate. This allows a K = 0.65 to be assumed.
The last condition illustrated, that of a simple strut, is essentially the same condition as the sin-
gle brace, and therefore utilizes K = 1.2.

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