Compression members - The Behaviour and Design of Steel Structures to EC3 - page 74

2

EI / L 2

Mode 1

N cr 2.0

L

≥

1.5

< L

Mode 2

1.0

L

0.5

L = 2 EI / L 3
(equation 3.50)

0

0 10 20 30 40

Stiffness

/( EI / L 3 )

(a) Mode 2 (b) Mode 1 (c) Buckling load

Figure 3.22 Compression member with an elastic sway brace.

3.7 Other compression members

3.7.1 General

ThedesignmethodoutlinedinSection3.5,togetherwiththeeffectivelengthcon-
cept developed in Section 3.6, are examples of a general approach to the analysis
and design of the compression members whose ultimate resistances are governed
by the interaction between yielding and buckling. This approach, often termed
design by buckling analysis, originates from the dependence of the design com-
pression resistance N b , Rd of a simply supported uniform compression member on
its squash load N y and its elastic buckling load N cr , as shown in Figure 3.23,
whichisadaptedfromFigure3.13.Thegeneralisationofthisrelationshiptoother
compressionmembersallowsthedesignbucklingresistance N b , Rd ofanymember
to be determined from its yield load N y and its elastic buckling load N cr by using
Figure 3.23.
In the following subsections, this design by buckling analysis method is
extended to the in-plane behaviour of rigid-jointed frames with joint loading,
and also to the design of compression members which either are non-uniform,
or have intermediate loads, or twist during buckling. This method has also
been used for compression members with oblique restraints [3]. Similar and
related methods may be used for the flexural-torsional buckling of beams
(Sections 6.6-6.9).

3.7.2 Rigid-jointed frames with joint loads only

The application of the method of design by buckling analysis to rigid-jointed
frames which only have joint loads is a simple extrapolation of the design