Compression members - The Behaviour and Design of Steel Structures to EC3 - page 60

Thus,forarectangularsectionmemberwhichhasthesimplifiedresidualstress
distribution shown in Figure 3.10, the effective flexural rigidity ( EI ) t about the z
axis is (see Section 3.9.2)

( EI ) t = EI [ 2 ( 1 − N / N y ) ] 1 / 2 ,

(3.18)

when the axial load N is greater than 0.5 N y at which first yield occurs, and the
axial load at buckling N cr , t is given by

N cr
N y

2

N cr , t
N y

{[ 1 + 2 ( N y / N cr ) 2 ] 1 / 2 − 1 } . = (3.19)

The variation of this dimensionless tangent modulus buckling load N cr , t / N y with

the generalised slenderness ratio λ = √ ( N y / N cr ) is shown in Figure 3.11.
For stocky members, the buckling load N cr , t approaches the squash load N y ,
while for intermediate length members it approaches the elastic buckling load
N cr as λ = √ ( N y / N cr ) approaches √ 2. For more slender members, prema-
ture yielding does not occur, and these members buckle at the elastic buckling
load N cr .
Also shown in Figure 3.11 is the dimensionless tangent modulus buckling load
N cr , t / N y given by

N cr , t
N y

= 1 − 1
4

N y
N cr ,

(3.20)

1.2

Complete
yield

1.0

Elastic buckling
N cr / N y

0.8

--- =1 - 1

N
N

--- N

y
cr

cr,t
y

---

N

0.6 (equation 3.20)

0.4

Inelastic buckling of
rectangular section
shown in Fig. 3.10
(equation 3.19)

0.2

√2

0

0 0.5 1.0 1.5 2.0 2.5

Generalised slenderness = N /

y N

cr

Figure 3.11 Inelastic buckling of compression members with residual stresses.