Compression members - The Behaviour and Design of Steel Structures to EC3 - page 72

1.0 1.0

0.8 0.8

0.6 0.6

k k 2

2

0.4 0.4

0.2 0.2

0 0

0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0

k 1 k 1

(a) Bracedmembers
(equations 3.42, 3.44)

(b) Unbraced members
(equations 3.46, 3.48)

Figure 3.21 Effective length ratios L cr / L for members in rigid-jointed frames.

inwhichthesummation

1 α isforalltheothermembersatend1, γ 2 issimilarly
defined, and 0 ≤ γ ≤∞ .The relative stiffnesses may also be expressed as

( 2 EI / L ) 12
0.5
1

2 γ 1
1 + 2 γ 1

k 1 =

α + ( 2 EI / L ) 12 =

(3.44)

and a similar definition of k 2 ( 0 ≤ k ≤ 1 ) . Values of the effective length
ratio L cr / L which satisfy equations 3.42-3.44 are presented in chart form in
Figure 3.21a.
In using the chart of Figure 3.21a, the stiffness factors k may be calculated
fromequation3.44byusingthestiffnessapproximationsofFigure3.19.Thusfor
braced restraining members of the type shown in Figure 3.18a, the factor k 1 can
be approximated by

( I / L ) 12

k 1 =

0.5
1

(3.45)

( I / L )( 1 − N / N cr , L ) + ( I / L ) 12

inwhich N isthecompressionforceintherestrainingmemberand N cr , L itselastic
buckling load.

3.6.5Buckling of unbraced members with end restraints

The buckling of an end-restrained compression member 1-2 is analysed in
Section3.10.5,whereitisshownthatifthememberisunbracedagainstsidesway,