CIVIL ENGINEERING FORMULAS

BUILDING AND STRUCTURES FORMULAS 213

where Fywspecified minimum yield stress of web, ksi(MPa)
Frcompressive residual stress in flange
10 ksi (68.9 MPa) for rolled shapes, 16.5 ksi(113.6 MPa), for
welded sections
FLsmaller of FyfFrorFyw
Fyfspecified minimum yield stress of flange, ksi (MPa)
X 1 
X 2 (4Cw/Iy) (Sx/GJ)^2
Eelastic modulus of the steel
Gshear modulus of elasticity
Sxsection modulus about major axis, in^3 (mm^3 ) (with respect to the
compression flange if that flange is larger than the tension flange)
Cwwarping constant, in^6 (mm^6 ) (see AISC manual on LRFD)
Iymoment of inertia about minor axis, in^4 (mm^4 )

For the previously mentioned shapes, the limiting buckling moment Mr, ksi (MPa),
may be computed from

(9.20)

For compact beams with LbLr, bent about the major axis,

(9.21)

whereCb1.751.05(M 1 /M 2 )0.3(M 1 /M 2 )2.3, where M 1 is the smaller
andM 2 the larger end moment in the unbraced segment of the beam; M 1 /M 2 is
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 Criteriafor Metal Structures, 4th ed., John Wiley & Sons, New
York,for use of larger values of Cb.)
For solid rectangular bars bent about the major axis,

(9.22)

and the limiting buckling moment is given by:

(9.23)

For symmetrical box sections loaded in the plane of symmetry and bent about
the major axis, Mrshould be determined from Eq. (9.20) and Lrfrom Eq. (9.22)
For compact beams with Lb>Lr, bent about the major axis,

(9.24)

whereMcrcritical elastic moment, kipin (MPamm).

MnMcrCbMr

MrFySx

Lr57,000

ry

Mr

JA

MnCbMp(MpMr)

LbLp

LrLp

Mp

MrFLSx

( /Sx) 2 EGJA/2