Frames - The Behaviour and Design of Steel Structures to EC3 - page 353

N N

Hh /2

H

h

H /2

H /2

Bending moments

-

N Hh/L N+Hh/L

L

Frame

(a) First-order analysis

Hh+R R

N N

R

H M max

R R

H R

First-order
analysis

H L

R L R R

Frame Bending moments

(b) Second-order behaviour

Figure 8.2 First-order analysis and second-order behaviour.

a preliminary design), and then compute the first-order member moments and
forces, and the joint deflections for each specified set of loads. Because these are
proportional to the loads, the results of individual analyses may be combined by
linear superposition.The results of computer first-order elastic analyses [18] of a
braced and an unbraced frame are given in Figures 8.3 and 8.4.

8.3.5.3 Elastic buckling of braced frames

Theresultsofanelasticbucklinganalysismaybeusedtoapproximateanysecond-
ordereffects(Figure8.2).Theelasticbucklinganalysisofarigid-jointedframeis
carried out by replacing the initial set of frame loads by a set which produces the
samesetofmemberaxialforceswithoutanybending,asindicatedinFigure8.5b.
The set of member forces N cr which causes buckling depends on the distribution
oftheaxialforcesintheframe,andisoftenexpressedintermsofaloadfactor α cr
bywhichtheinitialsetofaxialforces N i mustbemultipliedtoobtainthemember
forces N cr at frame buckling, so that

N cr = α cr N i (8.1)