Torsion members - The Behaviour and Design of Steel Structures to EC3 - page 448

First yield Fully plastic First yield Fully plastic

Sections
and
member
contours

Chisel wedge

Parabola Cone

Parabola

Membranes
and
sand heaps

(a) Circular cross-section (b) Rectangular cross-section

Figure 10.18 First yield and fully plastic uniform torsion shear stress distributions.

The corresponding first yield uniform torque may be obtained from
equations 10.9 and 10.11 as
T ty = π R 3 / 2 τ y (10.26)

and so the uniform torsion plastic shape factor is T tp / T ty = 4 / 3.
The sand heap for a fully plastic rectangular section b × t is chisel-shaped
as shown in Figure 10.18b. In this case, the fully plastic uniform torque is
given by

T tp = bt 2
2

1 − t
3 b

τ y , (10.27)

and for a narrow rectangular section this becomes T tp ≈ ( bt 2 / 2 )τ y . The
corresponding first yield uniform torque is
T ty ≈ bt 2 / 3 τ y (10.28)

and so the uniform torsion plastic shape factor is T tp / T ty = 3 / 2.
Forthin-walledopensections, thefullyplasticuniformtorqueisapproximated

by

T tp ≈ bt 2 / 2 τ y

(10.29)

and the first yield torque is obtained from equation 10.18 as

T ty = τ y I t
t max

(10.30)