In-plane bending of beams - The Behaviour and Design of Steel Structures to EC3 - page 180

(a ) Can til e v e rs and over- hanging beams
(b) S i ngle-span beams
(c ) Multi-span beams
Figure 5.29 Beam plastic collapse mechanisms.
generally collapse as single-bar mechanisms with a plastic hinge at the support.
When there is a reduction in section capacity, then the plastic hinge may form in
the weaker section.
Single-span beams generally collapse as two-bar mechanisms, with a hinge
(plastic or frictionless) at each support and a plastic hinge within the span.
Sometimes general plasticity may occur along a uniform moment region.
Multi-spanbeamsgenerallycollapseinonespanonly,asalocaltwo-barmech-
anism, with a hinge (plastic or frictionless) at each support, and a plastic hinge
within the span. Sometimes two adjacent spans may combine to form a three-bar
mechanism,withthecommonsupportactingasafrictionlesspivot,andoneplastic
hinge forming within each span. Similar mechanisms may form in over-hanging
beams.
Potential locations for plastic hinges include supports, points of concentrated
load,andpointsofcross-sectionchange.Thelocationofaplastichingeinabeam
with distributed load is often not well defined.
5.5.5 Methods of plastic analysis
Thepurposeofthemethodsofplasticanalysisistodeterminetheultimateloadat
whichacollapsemechanismfirstforms.Thus,itisonlythisfinalmechanismcon-
ditionwhichmustbefound,andanyintermediateloadconditionscanbeignored.
A further important simplification arises from the fact that in its collapse condi-
tion, the beam is a mechanism, and can be analysed by statics, without any of the
difficultiesassociatedwiththeelasticanalysisofastaticallyindeterminatebeam.
The basic method of plastic analysis is to assume the locations of a series of
plastichingesandtoinvestigatewhetherthethreeconditionsofequilibrium,mech-
anism and plasticity are satisfied. The equilibrium condition is that the bending