Page 60 - Handbook of Structural Steel Connection Design and Details

Design of Connections for Axial, Moment, and Shear Forces

Design of Connections for Axial, Moment, and Shear Forces 45

gusset to the beam flange, this part of the Whitmore section is
not ineffective, that is, load can be passed through the weld to
be carried on this part of the Whitmore section. The effective
length of the Whitmore section is thus
0.510 50
l we 5s37.7 210.4d 1 10.4 3 3 5 27.3 1 9.8 5 37.1 in
0.75 36
The gusset buckling length is, from Fig. 2.1, l 9.5 in, and the
b
slenderness ratio is
Kl b 5 0.5 3 9.5 3 212 5 21.9
r 0.75
In this formula, the theoretical fixed-fixed factor of 0.5 is used
rather than the usually recommended value of 0.65 for
columns, because of the conservatism of this buckling check as
determined by Gross (1990) from full-scale tests. From the
AISC 2005 Specification Section J4.4, since Kl /r 25, the
b
design buckling strength is
F 0.9 36 32.4 ksi
cr
and the Whitmore section buckling strength is thus

R 32.4 37.1 0.75 902 kips > 855 kips, ok
wb
d. Brace-to-gusset connection angles:
(1) Gross and net area: The gross area required is 855/(0.9
36) 26.4 in 2
2
3
Try 4 Ls 5 5 / , A 6.94 4 27.8 in , ok
4 gt
The net area is A 27.8 4 0.75 1.25 24.1 in 2
nt
The effective net area is the lesser of 0.85 A or UA ,
gt nt
1.51
where U 5 1 2 5 0.944. Thus 0.85 A 0.85 27.8
27 gt
23.6 and UA 0.944 24.1 22.8 and then A 22.8.
nt e
Therefore, the net tensile design strength is R 0.75 58
t
22.8 992 kips > 855 kips ok.
3
(2) Bearing and tearout: Comparing the strength of two /
angles
4
3
to the /
gusset, it is clear that bolt bearing and tearout on the
4
angles will not control.
(3) Block shear rupture: The length of the connection on the gusset
side is the shorter of the two and is, therefore, the more criti-
cal. Per angle,
A 29.0 0.75 21.75 in 2
gv
A (29.0 6.5 1.25) 0.75 15.66 in 2
nv
A (2.0 0.5 1.25) 0.75 1.03 in 2
nt
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