Introduction - The Behaviour and Design of Steel Structures to EC3 - page 15

Load

4 Buckling

1 Linear

3 Geometric non-linearity

Material
non-linearity

2

6 Fully plastic

Material and geometric
non-linearity

5

7 Local buckling

8

Brittle fracture

Deformation

Figure 1.12 Member behaviour.

that the member response remains linear until more general yielding occurs. The
member behaviour then becomes non-linear (curve 2) and approaches the condi-
tion associated with full plasticity (curve 6). This condition depends on the yield
stress f y .
The member may also exhibit geometric non-linearity, in that the bending
momentsandtorquesactingatanysectionmaybeinfluencedbythedeformations
as well as by the applied forces. This non-linearity, which depends on the elastic
moduli E and G ,maycausethedeformationstobecomeverylarge(curve3)asthe
condition of elastic buckling is approached (curve 4).This behaviour is modified
whenthematerialbecomesnon-linearafterfirstyield,andtheloadmayapproach
a maximum value and then decrease (curve 5).
The member may also behave in a brittle fashion because of local buckling
in a thin plate element of the member (curve 7), or because of material fracture
(curve 8).
Theactualbehaviourofanindividualmemberwilldependontheforcesacting
on it. Thus tension members, laterally supported beams, and torsion members
remain linear until their material non-linearity becomes important, and then they
approachthefullyplasticcondition.However,compressionmembersandlaterally
unsupportedbeamsshowgeometricnon-linearityastheyapproachtheirbuckling
loads.Beam-columnsarememberswhichtransmitbothtransverseandaxialloads,
and so they display both material and geometric non-linearities.

1.4.2 Structure behaviour

The behaviour of a structure depends on the load-transferring action of its mem-
bers and joints. This may be almost entirely by axial tension or compression,
as in the triangulated structures with joint loading as shown in Figure 1.13a.