Torsion members - The Behaviour and Design of Steel Structures to EC3 - page 439

the boundary and is equal to

τ t , max = T t R

I t .

(10.11)

For other solid cross-sections, equation 10.10 gives a reasonably accurate
approximation for the torsion section constant, but the maximum shear stress
depends on the precise shape of the section. When sections have re-entrant cor-
ners, the local shear stresses may be very large (as indicated in Figure 10.7),
althoughtheymaybereducedbyincreasingtheradiusofthefilletatthere-entrant
corner.

10.2.1.3 Rectangular cross-sections

Thestressfunction θ foraverynarrowrectangularsectionofwidth b andthickness
t is approximated by

t 2

4 − z 2

θ ≈ G d φ
d x

. (10.12)

The shear stresses can be obtained by substituting equation 10.12 into
equations 10.2, whence

τ xy =− 2 zG d φ

d x ,

(10.13)

which varies linearly with z as shown in Figure 10.8c. The torque effect of the
τ xy shear stresses can be obtained by integrating their moments about the x axis,

3.0

t

2.5

Equal angle section [3]
with large b / t ratio

r

Note crowding of
contours at re-entrant
corner, corresponding
to stress concentration

2.0

Approximation [2]

1.5

t

1.0

0 0.5 1.0 1.5 2.0

Ratio r/t

(a) Membrane contours at re-entrant corner (b) Increased shear stresses

Figure 10.7 Stress concentrations at re-entrant corners.