Page 158 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch03.qxd 9/29/05 5:05 PM Page 3.90

CONNECTIONS

3.90 CHAPTER THREE

The design tensile rupture strength of the toe of the MC flange under the fillet is

.
.
×
×= 28 kips
.
φR = 075 36  0 366 + 0 470   0 625 4
.

t
2
Thus the total strength of the load path in the channel flange is 834 + 28 = 862 kips > 855 kips; OK.
GUSSET-TO-BRACE RUPTURE. Design strength for limit state of shear rupture of gusset is
φR v = 0.75 × 0.6 × 58 × 1.5 × 17 × 2 = 1331 kips
Design strength for limit state of tension rupture of gusset is
φR t = 0.75 × 58 × 1.5 × 12 = 783 kips
Design strength for limit state of block shear rupture of gusset is
φR bs = 1331 + 0.75 × 36 × 1.5 × 12 = 1817 kips > 855 kips OK
WHITMORE SECTION. The theoretical length of the Whitmore section is (17 tan 30°)2 + 12 = 31.6 in.
The Whitmore section extends into the column by 5.40 in. The column web is stronger than the gus-
set since 1.29 × 50/36 = 1.79 > 1.5 in. The Whitmore also extends into the beam web by 6.80 in, but
since 0.470 × 50/36 = 0.653 < 1.5 in, the beam web is not as strong as the gusset. The effective
Whitmore section length is therefore taken as

l weff = (31 .6 − . 6 80 ) + . 6 80 × . 0 470 × 50 = 27 .8 in
. 15 36
The effective length is based on F y = 36 ksi and the gusset thickness of 1.5 in.
Since the brace force can be tension or compression, compression will control. The slenderness
ratio of the unsupported length of gusset is

.
Kl 05 . × 85 12
= = 98 .
r 15 .
From the AISC Specification, Sec. J4.4, the buckling strength is
φF a = 0.9 × 36 = 32.4 ksi

and the buckling strength of the gusset is
φR wb = 27.8 × 1.5 × 32.4 = 1350 > 855 kips OK
This completes the brace-to-gusset part of the design. Before proceeding, the distribution of
forces to the gusset edges must be determined. From Figs. 3.49 and 3.50,
.
e = 24 10 = 1205 in e = 837 in β = 1225 in α = 150 . in
.
.
.
b
2 c
.
θ = tan −1 10 6875 = 41 6 . °
12
=
V = P cos θ = 855 0 747 638 kips
× .
c
.
H = Ve = 638 × 8 37 = 220 kips
cc
c
e + β 12 05 +12 25
.
.
b
H = P sin θ − H = 855 0 665 220 = 349 kips
−
× .
c
b
M = H e = 349 ×12 05 = 4205 in ⋅kips
.
b
b b
b
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