Compression members - The Behaviour and Design of Steel Structures to EC3 - page 67

2 2

4 EI / L

N cr

Braced first mode
(equations 3.65 and 3.66)

/2

8

L /2

6

< L ≥

L

Second mode
(equation 3.30)

4

v

L /2

2

L = 16 2 EI / L 3 (equation 3.31)

x

/2

0

0 10 20 30 40

Stiffness /(16 EI / L 3 )

(a) Braced first
mode

(b) Second
mode

(c) Buckling load

Figure 3.16 Compression member with an elastic intermediate restraint.

3.6.2 Intermediate restraints

In Section 3.6.1 it was shown that the elastic buckling load of a simply supported
member is increased by a factor of 4 to N cr = 4 π 2 EI / L 2 when an additional
lateral restraint is provided which prevents it from deflecting at its centre, as
shown in Figure 3.15b. This restraint need not be completely rigid, but may be
elastic(Figure3.16),provideditsstiffnessexceedsacertainminimumvalue.Ifthe
stiffness α of the restraint is defined by the force αδ acting on the restraint which
causes its length to change by δ , then the minimum stiffness α L is determined in
Section 3.10.1 as

α L = 16 π 2 EI / L 3 .

(3.31)

The limiting stiffness α L can be expressed in terms of the buckling load N cr =
4 π 2 EI / L 2 as

α L = 4 N cr / L . (3.32)

Compression member restraints are generally required to be able to transmit 1%
(Clause 5.3.3(3)) of EC3) of the force in the member restrained. This is a little
less than the value of 1.5% suggested [2] as leading to the braces which are
sufficiently stiff.

3.6.3 Elastic end restraints

When the ends of a compression member are rigidly connected to its adjacent
elasticmembers,asshowninFigure3.17a,thenatbucklingtheadjacentmembers