Page 159 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch03.qxd 9/29/05 5:05 PM Page 3.91

CONNECTIONS

CONNECTIONS 3.91

Note that, in this Special Case 2, the calculations can be simplified as shown in the preceding.
The same results can be obtained formally with the uniform force method by setting β= β = 12.25 and
proceeding as follows. With tan θ= 0.8906,
α− 0.8906β= 12.05 × 0.8906 − 8.37 = 2.362 in
Setting β= β = 12.25 in, α= 13.27 in. Since α =15.0 in, there will be a couple, M b , on the gusset-
to-beam edge. Continuing,

+
r = (.327 + .837 ) 2 + (.225 1205 2 = 3254
1
. )
.
1
P
= 26 .27
r
α
H = P = 349 kips
b
r
H = e c P = 220 kips
c
r
V = e b P = 317 kips
b
r
β
V = P = 322 kips
c
r
− ) | 548 in kips
M = | V (αα = ⋅
b
b
This couple is clockwise on the gusset edge. Now, introducing Special Case 2, set ∆V B = V B = 317 kips.
This reduces the vertical force between the gusset and beam to zero, and increases the gusset-
to-column shear, V C , to 317 + 322 = 638 kips and creates a counterclockwise couple on the gusset-
α
to-beam edge of ∆V B = 317 × 15.0 = 4755 in⋅kips. The total couple on the gusset-to-beam edge is
thus M B = 4755 − 548 = 4207 in⋅kips. It can be seen that these gusset interface forces are the same
as those obtained from the simpler method.
Gusset-to-Column Connection. The loads are 638 kips shear and 220 kips axial.
GUSSET STRENGTH. Design strength for gross section shear is
φR gv =φ0.60A g F y = 0.90 × 0.60 × 1.5 × 24.5 × 36 = 714 kips > 638 kips OK
Design strength for gross section tension is
φR gt =φA g F y = 0.90 × 1.5 × 24.5 × 36 = 1190 kips > 220 kips OK
WELD OF GUSSET-TO-COLUMN FLANGE
P = 638 2 + 220 2 = 675 kips
u
−1
The angle from the longitudinal weld axis is tan (220/638) = 19°. From the AISC Manual, Table 8.5
1
for 15° with k = a = 0.0, C = 3.84. The weld size in / 16ths is
D = 675 125 = 120.
.
0 75 × 3 84 24 5. × .
.
3
Use a / 4-in fillet. The ductility factor of 1.25 is used because the weld is assumed to be uniformly
loaded, but research shows that the ratio of peak-to-average stresses is about 1.25 (Hewitt and
Thornton, 2004).
Column Web
WEB YIELDING (UNDER NORMAL LOAD H C )
3
φR wy = 1.0 × 50 × 1.290(24.5 + 5 × 2 / 4) = 2470 kips > 220 kips OK

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