Torsion members - The Behaviour and Design of Steel Structures to EC3 - page 433

Torsion members
10.1 Introduction
The resistance of a structural member to torsional loading may be considered to
be the sum of two components. When the rate of change of the angle of twist
rotationisconstantalongthemember(seeFigure10.1a),itisinastateofuniform
(or StVenant) torsion [1, 2], and the longitudinal warping deflections are also
constant along the member. In this case, the torque acting at any cross-section
is resisted by a single set of shear stresses distributed around the cross-section.
The ratio of the torque acting to the twist rotation per unit length is defined as the
torsional rigidity GI t of the member.
The second component of the resistance to torsional loading may act when
the rate of change of the angle of twist rotation varies along the member (see
Figures 10.1b and c), so that it is in a state of non-uniform torsion [1]. In this
casethewarpingdeflectionsvaryalongthemember,andanadditionalsetofshear
stresses may act in conjunction with those due to uniform torsion to resist the
torque acting. The stiffness of the member associated with these additional shear
stresses is proportional to the warping rigidity EI w .
When the first component of the resistance to torsional loading completely
dominates the second, the member is in a state of uniform torsion. This occurs
when the torsion parameter K = √ (π 2 EI w / GI t L 2 ) is very small, as indicated
in Figure 10.2, which is adapted from [1]. Thin-walled closed-section members
whose torsional rigidities are very large behave in this way, as do members with
narrow rectangular sections and angle and tee-sections, whose warping rigidi-
ties are negligible. If, on the other hand, the second component of the resistance
to torsional loading completely dominates the first, the member is in a limit-
ing state of non-uniform torsion referred to as warping torsion. This may occur
when the torsion parameter K is very large, as indicated in Figure 10.2, which
is the case for some very thin-walled open sections (such as light gauge cold-
formed sections) whose torsional rigidities are very small. Between these two
extremes, the torsional loading is resisted by a combination of the uniform and
warping torsion components, and the beam is in the general state of non-uniform
torsion. This occurs for intermediate values of the parameter K , as shown in