Page 168 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch03.qxd 9/29/05 5:05 PM Page 3.100

CONNECTIONS

3.100 CHAPTER THREE

=
⋅
M = e V − H β 108 347) − 900 414) = 0 in kips
.
.(
(
.
.
c c
c
c
−
−
M =−β H + α( V V + e V e H =−9 00 41 4) + 9 00 10 2) +10 75 44 8) − 8 995 76 9)
.
(
.
.
)
.
(
.
.
(
(
.
.
b
c
c
c
g
⋅
= 491 in kips
Determine Interface Forces for Bottom Bracket
θ
H = sin( ) P = sin(59 .74 )140 = 121 kips
θ
.5
V = cos( ) P = cos(59 .74 )140 = 70 kips
θ
β
θ
=
α = e tan( ) − e + tan( ) ( .900 )tan(5974 ) −108 + ( . )tan(5974 ) = 227 in
.
.
.
1
05
.
b
c
r = (α + e ) 2 + (β + e ) 2 = (22 .7 +10 . ) 2 + ( .5 9900. ) = 387 in
+
2
8
10
.
b
c
β
   10 5 . 
V c = P = 140 = 38 0 . kips
  r  38 7 . 
 e c   10 8 . 
H c = P  = 140  = 39 1 . kips
 r 38 7 . 
.
 e b   900 
V b = P = 140 = 32 6 . kips
 r   38 7 . 
α
   22 7 . 
.
H b = P   = 140  38 7 .   = 82 1 kips
r
Distribute Half of Beam Reaction to Top Gusset
. ( . ) 8
R )
.6
H c ′ = (/2 e c = 24 5 10 = 13 kips
e b + β . 900 +105
.
R )β
. ( . ) 5
V c ′ = (/2 = 24 5 10 = 13 .2 kips
e b + β . 900 +105
.
. ( . 900
R )
V b ′ = (/2 e b = 245 ) = 11 kips
.3
.
e + β . 900 +105
b
∆
+ V
V b = V b − V + ′ = 32 6 . − +11 3 . = 43 9 . kips
0
b
b
∆
0
V
V c = V c − V b + ′ = 38 0 . + +13 2 . = 51 2 . kips
c
+
.
H c = H c + H ′ = 39 1 13 6 . = 52 7 . kips
c
R
−
⋅
(
(
.
.
8
.
5
M b = α   V b − R   − eH b − e c   = 9 00 43 9 24 5 . ) − 9 00 68.. )5 − 10 . (24 . ) = 707 in kips
 
b
2
2
⋅
−
M c = e V − H β = 10 .(51 . ) 10 .(52 . ) = 0 in kips
8
2
5
7
c c
c
+
−
+
−
β
M g =− H c + α ( − V c ) + e V e H =− 10 . (52 . ) 9 .00 ( . ) 10 . (70 . ) 8 .995 (121 )
19
7
8
5
3
V
5
c
b
= 707 in kips
⋅
Nonorthogonal Trusses. The uniform force method as originally formulated can be applied to
trusses as well as to bracing connections. After all, a vertical bracing system is just a truss, as can be
seen in Fig. 3.55, which shows various arrangements. However, bracing systems generally involve
orthogonal members whereas trusses, especially roof trusses, often have a sloping top chord. To han-
dle this situation, the uniform force method has been generalized as shown in Fig. 3.55 to include
nonorthogonal members. As before, α and β locate the centroids of the gusset-edge connections
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