Building Design and Construction Handbook - Merritt - Ventech!

STRUCTURAL STEEL CONSTRUCTION 7.65
�
rX y 1 2
Lr � 1 � �1 � X 2(Fyw � F r)
(7.14)
(F � F )
yw r
where F yw � specified minimum yield stress of web, ksi
F r � compressive residual stress in flange � 10 ksi for rolled shapes, 16.5
ksi for welded sections
X 1 � (�/S x) �EGJA/2
X 2 � (4C w/I y)(S x/GJ) 2
E � elastic modulus of the steel � 29,000 ksi
G � shear modulus of elasticity � 11,200 ksi
S x � section modulus about major axis, in 3 (with respect to the compression
flange if that flange is larger than the tension flange)
C w � warping constant, in 6 (see AISC Manual—LRFD)
I y � moment of inertia about minor axis, in 4
7.20.3 Limit-State Moments
For the aforementioned shapes, the limiting buckling moment M r, ksi, may be
computed from
M � (F � F )S (7.15)
r yw r x
For compact beams with L b � L r, bent about the major axis,
� �
Lb � Lp
Mn � Cb Mp � (Mp � M r) � M p
(7.16)
L � L
r p
where C b � 1.75 � 1.05(M 1/M 2) � 0.3(M 1/M 2) 2 � 2.3, where M 1 is the smaller
and M 2 the larger end moment in the unbraced segment of the beam;
M 1/M 2 is positive for reverse curvature
� 1.0 for unbraced cantilevers and beams with moment over much of
the unbraced segment equal to or greater than the larger of the segment
end moments (see T. V. Galambos ‘‘Guide to Stability Design Criteria
for Metal Structures,’’ 4th ed., John Wiley & Sons, Inc., New York,
for use of larger values of C b)
For solid rectangular bars bent about the major axis,
and the limiting buckling moment is given by
L � 57,000(r /M ) �JA (7.17)
r y r
M � FS (7.18)
r y x
For symmetric box sections loaded in the plane of symmetry and bent about the
major axis, M r should be determined from Eq. (7.15) and L r from Eq. (7.17).
For compact beams with L b � L r, bent about the major axis,
M � M � CM (7.19)
n cr b r
where M cr � critical elastic moments, kip-in. For shapes to which Eq. (17.11)
applies,