Compression members - The Behaviour and Design of Steel Structures to EC3 - page 55

/ N

Straight line of best fit
(see equation 3.10)

1

Slope =

N

cr

0

0

Central deflection

Figure 3.5 Southwell plot.

stresses) is given by

N L
N y =

1

Φ 2 − λ 2 ,

(3.11)

Φ +

in which
Φ = 1 + η + λ 2
2

, (3.12)

η = δ 0 b

2 i 2 ,

(3.13)

and b isthewidthofthemember.Thevariationofthedimensionlesslimitingaxial
load N L / N y withthegeneralisedslendernessratio λ isshowninFigure3.4forthe
case when

N y
N cr .

η = 1
4

(3.14)

For stocky members, the limiting load N L approaches the squash load N y , while
for slender members the limiting load approaches the elastic buckling load N cr .
Equations 3.11 and 3.12 are the basis for the member buckling resistance in EC3.

3.3 Inelastic compression members

3.3.1 Tangent modulus theory of buckling

The analysis of a perfectly straight elastic compression member given in
Section 3.2.1 applies only to a material whose stress-strain relationship remains