Page 238 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch05.qxd 9/29/05 5:12 PM Page 5.18

CRITERIA FOR BUILDING DESIGN

5.18 CHAPTER FIVE

The nominal flexural strength M n of the members discussed in this article is the lower of two limit
states: yielding (plastic moment) and lateral-torsional buckling. The nominal flexural strength for
yielding (plastic moment) is
(5.40)
M n = M p = F y Z x
where Z x is the plastic section modulus about the x axis.
The nominal flexural strength for lateral-torsional buckling depends on the length between lat-
eral braces L b as related to certain limiting lengths, L p and L r .
When L b ≤ L p , the limit state of lateral-torsional buckling does not apply.
When L p < L b ≤ L r ,
  L − L  
M = C M − ( M − .07 F S ) b p   ≤ M p (5.41)
b 
y x 
p
p
n
   L − L   
r
p
When L b > L r ,
(5.42)
M n = F cr S x ≤ M p
The following definitions apply: The lateral buckling stress F cr is given by
C π 2 E Jc  L  2
F = b 1 + 0 078  b  (5.43)
.
cr
( Lr / ) 2 Sh  r 
ts
b ts
x o
The limiting lengths are
E
L = 176 r y (5.44)
.
p
F y
E Jc  07. F Sh  2
+
y
.
.
L = 195 r 1 + 1 6 76  xo  (5.45)
r ts 
07 F y Sh E Jc 
.
x o
The term c in Eq. (5.45) is defined as follows:
For a doubly symmetric I-shape,
c = 1 (5.46)
For a channel,
c = h o I y (5.47)
2 C w
where h o = distance between flange centroids.
Conservatively, in lieu of Eq. (5.43), F cr may be taken simply as
C π 2 E
F = b (5.48)
cr
( Lr / )
b ts
and L r may be taken as
L =π r E (5.49)
r
ts
07 F y
.
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