In-plane bending of beams - The Behaviour and Design of Steel Structures to EC3 - page 156

However, in an indeterminate beam, a substantial redistribution of bending
moment may occur after the first hinge forms, and failure does not occur until
sufficient plastic hinges have formed to cause the beam to become a mechanism.
The load which causes this mechanism to form provides the basis for the more
rational method of plastic design.
Whenshearpredominates,asinsomeheavilyloadeddeepbeamsofshortspan,
the ultimate strength is controlled by the shear force which causes complete plas-
tificationoftheweb.Inthemorecommonsections,thisisclosetotheshearforce
which causes the nominal first yield in shear, and so the shear design is carried
out for the shear forces determined from an elastic analysis. In this chapter, the
in-plane behaviour and design of beams are discussed. It is assumed that neither
localbuckling(whichistreatedinChapter4)norlateralbuckling(whichistreated
inChapter6)occurs.BeamswithaxialloadsarediscussedinChapter7,whilethe
torsion of beams is treated in Chapter 10.
5.2 Elastic analysis of beams
The design of a steel beam is often preceded by an elastic analysis of the bending
ofthebeam.Onepurposeofsuchananalysisistodeterminethebendingmoment
and shear force distributions throughout the beam, so that the maximum bend-
ing moments and shear forces can be found and compared with the moment and
shear capacities of the beam.An elastic analysis is also required to determine the
deflections of the beam so that these can be compared with the desirable limiting
values.
The data required for an elastic analysis include both the distribution and the
magnitudes of the applied loads and the geometry of the beam. In particular, the
variation along the beam of the effective second moment of area I of the cross-
section is needed to determine the deflections of the beam, and to determine the
moments and shears when the beam is statically indeterminate. For this purpose,
localvariationsinthecross-sectionsuchasthoseduetoboltholesmaybeignored,
but more general variations, including any general reductions arising from the
use of the effective width concept for excessively thin compression flanges (see
Section 4.2.2.2), should be allowed for.
The bending moments and shear forces in statically determinate beams can be
determined by making use of the principles of static equilibrium. These are fully
discussedinstandardtextbooksonstructuralanalysis[1,2],asarevariousmethods
of analysing the deflections of such beams. On the other hand, the conditions of
statics are not sufficient to determine the bending moments and shear forces in
statically indeterminate beams, and the conditions of compatibility between the
various elements of the beam or between the beam and its supports must also
be used. This is done by analysing the deflections of the statically indeterminate
beam. Many methods are available for this analysis, both manual and computer,
andthesearefullydescribedinstandardtextbooks[3-8].Thesemethodscanalso