Compression members - The Behaviour and Design of Steel Structures to EC3 - page 77

x

L

f

z

y

Figure 3.24 Torsional buckling of a cruciform section.

Acompression member of doubly symmetric cross-section may buckle elasti-
cally by twisting at a torsional buckling load (see Section 3.11) given by

GI t + π 2 EI w
L cr , T

N cr , T = 1
i 0

(3.54)

in which GI t and EI w are the torsional and warping rigidities (see Chapter 10),
L cr , T is the distance between inflexion points of the twisted shape, and
i 0 = i p + y 0 + z 0 (3.55)

in which y 0 , z 0 are the shear centre coordinates (which are zero for doubly
symmetric sections, see Section 5.4.3), and
i p = √ { ( I y + I z )/ A } (3.56)

is the polar radius of gyration. For most rolled steel sections, the minor axis
buckling load N cr , z is less than N cr , T , and the possibility of torsional buckling
can be ignored. However, short members which have low torsional and warping
rigidities (such as thin-walled cruciforms) should be checked. Such members can
bedesignedbyusingFigure3.23withthevalueof N cr , T substitutedfortheelastic
buckling load N cr .
Monosymmetric and asymmetric section members (such as thin-walled tees
and angles) may buckle in a combined mode by twisting and deflecting. This
action takes place because the axis of twist through the shear centre does not