Torsion members - The Behaviour and Design of Steel Structures to EC3 - page 436

10.2 Uniform torsion

10.2.1 Elastic deformations and stresses

10.2.1.1 General

In elastic uniform torsion, the twist rotation per unit length is constant along the
length of the member. This occurs when the torque is constant and the ends of
the member are free to warp, as shown in Figure 10.1a.When a member twists in
this way,

(a) lines which were originally parallel to the axis of twist become helices,
(b) cross-sections rotate φ as rigid bodies about the axis of twist, and
(c) cross-sections warp out of their planes, the warping deflections ( u ) being
constant along the length of the member (see Figure 10.4).

The uniform torque T t acting at any section induces shear stresses τ xy , τ xz which
act in the plane of the cross-section. The distribution of these shear stresses can
be visualised by using Prandtl's membrane analogy, as indicated in Figure 10.5
for a rectangular cross-section. Imagine a thin uniformly stretched membrane
whichisfixedtothecross-sectionboundaryanddisplacedbyauniformtransverse
pressure. The contours of the displaced membrane coincide with the shear stress

T t

Helix

Element δ x × δ s × t

Warping
displacements u

T t

x

y

z

Figure 10.4 Warping displacements u due to twisting.