Design of Flexural Steel Members - Design of Modern Steel Railway Bridges - page 284

combinations (Table 4.5); F call is the allowable compressive stress, based on stability
considerations since the girder compression flange is susceptible to lateral-torsional
instability prior to yielding.
In addition to lateral-torsional buckling effects on the allowable compres-
sive stress, vertical and torsional buckling effects must be considered to ensure
compression flange stability.

7.2.6.1.2.1.1 Lateral-Torsional Buckling Compression flange lateral-
torsional instability is controlled by limiting allowable stresses to those given by
Equations 7.20 or 7.24. It should be noted that Equation 7.20 was developed assum-
ing an I section with equal flanges. Therefore, the smallest flange area, A f = bt f ,

should be used in Equation 7.20 when establishing critical buckling stress. It should
also be noted that Equation 7.24 precludes inelastic buckling by ensuring that the
girder compression area L/r y does not exceed the value of Equation 7.22, which is
presented again as Equation 7.40. Therefore, the length, L , should be taken as the
largest distance between compression flange lateral supports, L p , and r c y is deter-
mined as the minimum radius of gyration of the compression flange and that portion
of the web in compression (from the neutral axis to the edge of the web plate).
The larger of either Equations 7.20 or 7.24, presented again as Equations 7.41 and
7.42, respectively, is adopted to determine the allowable compressive bending stress,
F call , for design of the compression flange. Therefore the compression flange design
requirements are

5.55 E
F y

L p
r c y ≤

(7.40)

and the larger of

0.13 π E

F call =

L p d( √ 1

(7.41)

+ υ )/A f

or

L p
r c y

2

0.55 F y
6.3

F call = 0.55 F y − , (7.42)

2 E

π

where L p is the largest distance between compression flange lateral supports, A f = b t f

is the area of the smallest flange in the girder (even if tension flange), and r c y is the
minimum radius of gyration of the compression flange and that portion of the web in
compression. However, as illustrated by Figure 7.3, F call cannot exceed 0.55 F y .

7.2.6.1.2.1.2 VerticalFlexuralBuckling Ifthewebplatebuckledduetobend-
ing in the compression zone, it would be unable to provide support for the attached
compression flange and the compression flange could then buckle vertically as shown
in Figure 7.9. To avoid compression flange vertical buckling, flexural buckling of the
web plate is precluded by limiting the ratio of web height, h , to thickness, t w ,orby
including a longitudinal stiffener.