Compression members - The Behaviour and Design of Steel Structures to EC3 - page 61

which was developed as a compromise between major and minor axis buckling
of hot-rolled I-section members. It can be seen that this simple compromise is
very similar to the relationship given by equation 3.19 for the rectangular section
member.

3.4 Real compression members
The conditions under which real members act differ in many ways from the
idealised conditions assumed in Section 3.2.1 for the analysis of the elastic buck-
ling of a perfect member. Real members are not perfectly straight, and their
loads are applied eccentrically, while accidental transverse loads may act. The
effects of small imperfections of these types are qualitatively the same as those
of initial curvature, which were described in Section 3.2.2. These imperfections
can therefore be represented by an increased equivalent initial curvature which
has a similar effect on the behaviour of the member as the combined effect
of all of these imperfections. The resulting behaviour is shown by curve A in
Figure 3.12.
A real member also has residual stresses, and its elastic modulus E and yield
stress f y may vary throughout the member. The effects of these material vari-
ations are qualitatively the same as those of the residual stresses, which were
described in Section 3.3.4, and so they can be represented by an equivalent set of
theresidualstresses.TheresultingbehaviourofthememberisshownbycurveBin
Figure 3.12.
Since real members have both kinds of imperfections, their behaviour is as
shownbycurveCinFigure3.12,whichisacombinationofcurvesAandB.Thus
the real member behaves as a member with equivalent initial curvature (curveA)
until the elastic limit is reached. It then follows a path which is similar to and
approaches that of a member with equivalent residual stresses (curve B).

Load

Elastic buckling

N cr

Elastic bending

N L
N cr,t

Curve A - equivalent
initial curvature

N max

Curve B - equivalent
residual stresses
Curve C - real members

Elastic limit

Lateral deflection

Figure 3.12 Behaviour of real compression members.