Page 240 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch05.qxd 9/29/05 5:12 PM Page 5.20

CRITERIA FOR BUILDING DESIGN

5.20 CHAPTER FIVE

For compression flange yielding,
(5.55)
M n = R pg F y S xc
For lateral-torsional buckling,
(5.56)
M n = R pg F cr S xc
When L b ≤ L p , the limit state of lateral-torsional buckling does not apply.
When L p < L b ≤ L r ,
  L − L  
F = C F − (.03 F ) b p   ≤ F (5.57)
cr b  y y   L − L   y
  r p 
When L b > L r ,
C π 2 E
F = b ≤ F (5.58)
cr
( Lr / ) 2 y
b t
where L p is defined by Eq. (5.44) and
L =π r t E (5.59)
r
.
07 F y
R pg = bending strength reduction factor

1
R pg =− a w   h c − 57. E   ≤10. (5.60)
1200 + 300 a  t w F 
cr
w
and a w = ratio of two times the web area in compression, due to application of major axis bending
moment alone, to the area of the compression flange components, but no more than 10. For I-shapes
with a rectangular compression flange,
a = ht (5.61)
cw
w
bt
fc fc
For I-shapes with a rectangular compression flange, the effective radius of gyration for lateral-
torsional buckling, r t , is
r = b fc (5.62)
t
2
12[( hd + 1 6/ ) ( / ) a h h d)]
( /
w
o
o
where b fc = width of compression flange
h = clear distance between flanges
d = total member depth
For I-shapes with channel caps or cover plates attached to the compression flange, r t = radius of
gyration of the flange components in flexural compression plus one-third of the web area in
compression due to application of major axis bending moment alone.
For compression flange local buckling,
(5.63)
M n = R pg F cr S c
For compact flange sections,
(5.64)
F cr = F y

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