Torsion members - The Behaviour and Design of Steel Structures to EC3 - page 434

Constant torque
ends free to warp

Varying torque End warping prevented

(a) Uniform torsion (b) Non-uniform torsion (c) Non-uniform torsion

Figure 10.1 Uniform and non-uniform torsion of an I-section member.

1.0

Closed
sections
Angles

Very thin-walled

Hot-rolled
I-sections

channel sections

0.8

Warping
torsion Uniform

Non-uniform

torsion torsion

0.6

0.4

L

0.2

0

0.1 1 10

2 2

= (

EI

w / GI t L )

Torsion parameter K

Figure 10.2 Effect of cross-section on torsional behaviour.

Figure 10.2, which are appropriate for most hot-rolled I- or channel-section
members.
Whetheramemberisinastateofuniformornon-uniformtorsionalsodepends
ontheloadingarrangementandthewarpingrestraints.Ifthetorqueresistediscon-
stant along the member and warping is unrestrained (as in Figure 10.la), then the
member will be in uniform torsion, even if the torsional rigidity is very small. If,
however,thetorqueresistedvariesalongthelengthofthemember(Figure10.1b),
or if the warping displacements are restrained in any way (Figure 10.1c), then
the rate of change of the angle of twist rotation will vary, and the member will
be in non-uniform torsion. In general, these variations must be accounted for,
but in some cases they can be ignored, and the member analysed as if it were
in uniform torsion. This is the case for members of very low warping rigidity