In-plane bending of beams - The Behaviour and Design of Steel Structures to EC3 - page 174

Approximate shear flow given
by conventional theory

C

x

y

(a) Shear flow due to a
vertical shear V z

z

(b) Warping displacements due to shear

Figure 5.23 Warping of an I-section beam.

there is a sudden change in the shear force, such as at the mid-point of the beam
of Figure 5.21a, leads to two different distributions of warping displacement, as
showninFigure5.21b.Theseareclearlyincompatible,andsochangesarerequired
inthebendingstressdistribution(andconsequentlyintheshearstressdistribution)
toremovetheincompatibility.Thesechanges,whichareillustratedinFigure5.22,
constitute the shear lag effect.
Shearlageffectsareusuallyverysmallexceptnearpointsofhighconcentrated
loadoratreactionpointsinshort-spanbeamswiththinwideflanges.Inparticular,
shear lag effects may be significant in light-gauge, cold-formed sections [14]
and in stiffened box girders [15-17]. Shear lag has no serious consequences in
a ductile structure in which any premature local yielding leads to a favourable
redistribution of stress. However, the increased stresses due to shear lag may be
of consequence in a tension flange which is liable to brittle fracture or fatigue
damage, or in a compression flange whose strength is controlled by its resistance
to local buckling.
An approximate method of dealing with shear lag is to use an effective width
concept, in which the actual width b of a flange is replaced by a reduced width
b eff given by

b eff
b

= nominal bending stress

maximum bending stress .

(5.32)

This is equivalent to replacing the actual flange bending stresses by constant
stresses which are equal to the actual maximum stress and distributed over the
effectiveflangearea b eff × t .Somevaluesofeffectivewidthsaregivenin[14-16].