Page 279 - Civil Engineering Formulas

BUILDING AND STRUCTURES FORMULAS 213

where F yw specified minimum yield stress of web, ksi (MPa)
F compressive residual stress in flange
r
10 ksi (68.9 MPa) for rolled shapes, 16.5 ksi (113.6 MPa), for
welded sections
F smaller of F F or F yw
yf
r
L
F specified minimum yield stress of flange, ksi (MPa)
yf
X (
/S x ) 2 EGJA/2
1
X (4C /I ) (S /GJ) 2
2
x
w
y
E elastic modulus of the steel
G shear modulus of elasticity
3
3
S section modulus about major axis, in (mm ) (with respect to the
x
compression flange if that flange is larger than the tension flange)
6
6
C warping constant, in (mm ) (see AISC manual on LRFD)
w
4
4
I moment of inertia about minor axis, in (mm )
y
For the previously mentioned shapes, the limiting buckling moment M , ksi (MPa),
r
may be computed from
(9.20)
M r F L S x
For compact beams with L L , bent about the major axis,
b
r
M n C b M p (M p M r ) L b L p M p (9.21)
L r L p
where C 1.75 1.05(M /M ) 0.3(M /M ) 2.3, where M is the smaller
1
b
2
1
2
1
and M the larger end moment in the unbraced segment of the beam; M /M is
2
1
2
positive for reverse curvature and equals 1.0 for unbraced cantilevers and
beams with moments over much of the unbraced segment equal to or greater
than the larger of the segment end moments. (See Galambos, T. V., Guide to
Stability Design Criteria for Metal Structures, 4th ed., John Wiley & Sons, New
York, for use of larger values of C .)
b
For solid rectangular bars bent about the major axis,

r y
L r 57,000 JA (9.22)
M r
and the limiting buckling moment is given by:
(9.23)
M r F y S x
For symmetrical box sections loaded in the plane of symmetry and bent about
the major axis, M should be determined from Eq. (9.20) and L from Eq. (9.22)
r r
For compact beams with L > L , bent about the major axis,
b r
M n M cr C b M r (9.24)
where M critical elastic moment, kip in (MPa mm).
cr