Page 166 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch03.qxd 9/29/05 5:05 PM Page 3.98

CONNECTIONS

3.98 CHAPTER THREE

beam as the beam-to-column connection is, it is advantageous to resist the moment here. To accomplish
this, an H c ′ is calculated in a manner similar to the H c calculation in the uniform force method, as follows:

H c ′ = e c R (3.75)
e b + β
The beam reaction is then distributed between the beam-to-column connection and the gusset-to-
column connection so as to eliminate moments in the extended single-plate connection. This is done
as follows:
β
V c ′ = R (3.76)
e b + β
V b ′ = e b R (3.77)
e b + β

These forces can then be included in the equations used with the uniform force method so that
β
V = P + ∆ V + ′ (3.78)
V
c
r b c
H = e c PH′ (3.79)
+
c
r c
V = e b P − ∆ V + ′ b (3.80)
V
b
b
r
The moments at the interfaces can be calculated as
 R   R 
M = α  V − 2  − eH − e c   (3.81)
b
b
b
b
2
M = e V − H β (3.82)
c
c c
c
−
−
M =−β H + α( V V + e V e H (3.83)
)
c
c
g
c
b
Example of Extended Single-Plate Connection for Vertical Brace. The above formulation of the
uniform force method will be applied to the design of the connection shown in Figs. 3.54 and 3.55.
Determine Interface Forces
θ
.9
H = sin( ) P = sin(59 .74 )89 = 76 kips
θ
.8
V = cos( ) P = cos(59 .74 )89 = 44 kips
α = e tan ( ) − e + tan( ) ( .900 ) tan(5974 ) −108 + ( ) tan(5974 ) = 201 in
θ
θ
=
β

.

9
.
.
.
c
b
+
r = (α + e ) 2 + (β + e ) 2 = (20 .1 +10 . ) 2 + (9..00 900 ) = 357 in
2
.
8
.
c
b
β
   . 900 
V c = P = 89  = 22 .4 kips
  r 35 .7 
 e c   10 .8 
H c = P = 89 = 26 .8 kips
 r   35 .7 
 e b   . 900 
V b = P = 89 = 22 .4 kips
 r   35 .7 
α
    20 .1
.
H b = P   = 89  35 .7  = 50 1 kips
r
Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.