Civil Engineering Reference
In-Depth Information
6.10.2 Design rules
EC3 has no specific rules for designing monosymmetric beams against lateral
buckling, because it regards them as being the same as doubly symmetric beams.
Thus it requires the value of the elastic buckling moment resistance
M
cr
of the
monosymmetric beam to be used in the simple general design method described
in Section 6.5.3. However, the logic of this approach has been questioned [49],
and in some cases may lead to less safe results.
A worked example of checking a monosymmetric T-beam is given in
Section 6.15.6.
6.11 Non-uniform beams
6.11.1 Elastic buckling resistance
Non-uniform beams are often more efficient than beams of constant section, and
are frequently used in situations where the major axis bending moment varies
along the length of the beam. Non-uniform beams of narrow rectangular section
are usually tapered in their depth. Non-uniform I-beams may be tapered in their
depth,orlesscommonlyintheirflangewidth,andrarelyintheirflangethickness,
while steps in flange width or thickness are common.
Depth reductions in narrow rectangular beams produce significant reductions
in their minor axis flexural rigidities
EI
z
and torsional rigidities
GI
t
. Because of
this, there are also significant reductions in their resistances to lateral buckling.
Closed form solutions for the elastic buckling loads of many tapered beams and
cantilevers are given in the papers cited in [13, 16, 51, 52].
Depth reductions in I-beams have no effect on the minor axis flexural rigidity
EI
z
,andlittleeffectonthetorsionalrigidity
GI
t
,althoughtheyproducesignificant
reductionsinthewarpingrigidity
EI
w
.Itfollowsthattheresistancetobucklingof
a beam which does not depend primarily on its warping rigidity is comparatively
insensitive to depth tapering. On the other hand, reductions in the flange width
cause significant reductions in
GI
t
and even greater reductions in
EI
z
and
EI
w
,
while reductions in flange thickness cause corresponding reductions in
EI
z
and
EI
w
and in
GI
t
. Thus the resistance to buckling varies significantly with changes
in the flange geometry.
General numerical methods of calculating the elastic buckling loads of tapered
I-beams have been developed in [51-53], while the elastic and inelastic buckling
oftaperedmonosymmetricI-beamsarediscussedin[53-55].Solutionsforbeams
withconstantflangesandlinearlytapereddepthsunderunequalendmomentsare
given in [56, 57], and more general solutions are given in [58]. The buckling of
I-beams with stepped flanges has also been investigated, and many solutions are
tabulated in [59].
Approximations for the elastic buckling moment
M
cr
of a simply supported
non-uniformbeamcanbeobtainedbyreducingthevaluecalculatedforauniform
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