Shear Lag
Simple beam theory assumes that plane cross
sections remain plane, and that therefore the bending
stress is directly proportional to the distance
from the neutral axis. Thus in any flange-and-web
type of beam, the stress should be constant across
the flanges. However, in most cases the bending
is not caused by the applica tion of a pure couple
to the ends of the beam; rather, it is caused by
vertical loads, and these loads are ab sorbed by the
webs of the beam and not by the flanges. That is,
even for a hull girder, in which the vertical loads
may initially act on the flanges (e.g., pressure on
the bottom), they are immediately transferred to
the webs by transverse beams and frames; the
plating of the flanges can only take longi tudinal
in-plane loads (we are discussing principal loads,
not small local loads). Therefore, the vertical
loads act on the webs and cause them to deflect to
some radius of curvature, thus inducing maximum
strain in the flanges. Since they carry maximum
strain, and hence maximum stress, the flanges
make the largest contribution to the bending
stiffness. But, it is important to note that this
maximum strain comes ini tially from the webs
and only reaches the flanges by shear. This is
illustrated, which shows a portion
of a box girder cantilever loaded by a vertical
force F. The force is reacted by, or carried by, the
webs, which deflect to some radius of curvature
such that the upper and lower edges of the web
are elon gated and shortened. For simplicity, the
curvature is not shown; only the change in length.
At the upper edge the elongated web pulls the
flange plating with it, through shear forces, and
this sets up shear stresses in the flange; these
were discussed fully in the previous section. The
bending and shear stresses cause stretch ing and
in-plane distortion of the flange. On the left and
right sides of the figure, an element is shown
before and after this stretching and distortion.
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