The Design of Modern Steel Bridges - TEDI

cross-section in which the secant stiffness factor times the nominal flange area
is taken as effective.
The maximum bending moment M occurring at the mid-span of the length L
of the strut can be shown to be very close to
where
Stiffened Compression Flanges of Box and Plate Girders 163
M ¼ Pðe1 þ e2Þ PE
PE P
P E ¼ Euler column buckling load ¼ (p 2 EI e)/L 2
e 1 ¼ end eccentricity of applied loading
e 2 ¼ maximum amplitude of a sinusoidal initial imperfection pattern
L ¼ length of the strut between its pinned ends.
The end eccentricity of applied loading on the flange stiffener arises from the
non-uniformity of the stress distribution on the cross-section of a box or plate
girder. It is theoretically reasonable to assume that the linear elastic theory of
bending predicts satisfactorily the stress distribution on the girder crosssections
at the locations of stiff crossgirders or crossframes. Thus the magnitude
and the pattern of the loading at the ends of the longitudinal flange
stiffeners can be obtained by applying the simple beam theory to the girder
cross-section. This loading pattern is shown in Fig. 6.4; the shaded block can
be represented by an axial load P ¼ s aA e acting at an eccentricity e 1 ¼ r 2 /h
with respect to the centroid of the stiffener cross-section, where r is the radius
of gyration of the stiffener cross-section and h is the distance between the
stiffener centroid and the neutral axis (i.e. level of zero stress) of the girder.
Figure 6.4 Stress pattern on the ends of flange stiffeners.