Civil Engineering Reference
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Q
2
Q
2
Warping displacements
due to positive shear
Warping displacements
due to negative shear
Q
Q
2
(+)
Q
2
(-)
(b) Warping displacements calculated
from conventional theory
(a) Beam and shear
for diagram
Figure 5.21
Incompatible warping displacements at a shear discontinuity.
Real behaviour
Approximate
conventional
theory
Approximate
conventional
theory
Real behaviour
(a) Bending stress distribution
(b) Shear flow distribution
Figure 5.22
Shear lag effects in an I-section beam.
stresses calculated by the conventional theory are as shown in Figure 5.23a, and
theseinducethewarping(longitudinal)displacementsshowninFigure5.23b.The
warping displacements of the web are almost linear, and these are responsible for
thesheardeflections[13]whichareusuallyneglectedwhencalculatingthebeam's
deflections. The warping displacements of the flanges vary parabolically, and it
is these which are responsible for most of the shear lag effect. The application
of the conventional theory of bending at either side of a point in a beam where
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