7.8 Torsion of Thin-Walled Sections
243
U =
M
2
t dl
8A 2 G
dS
t
Hence, the twist or the rotation per unit length (dl = 1) is
θ =
∂U
∂ M t
=
M t
4 A 2 G
dS
t
or
θ =
2q A
4 A 2 G
dS
t
or
θ =
q
2 AG
dS
t
(7.24)
7.9 Torsion of Thin-Walled Multiple-Cell Closed Sections
Consider a two-cell section shown in Fig. 7.9. Let A 1 and A 2 be the areas of the cells 1
and 2, respectively. Consider the equilibrium of an element at the junction as shown
in Fig. 7.9b. In the direction of the axis of the tube, we can write
Fig. 7.9 Torsion of thin-walled multiple-cell closed section
243
U =
M
2
t dl
8A 2 G
dS
t
Hence, the twist or the rotation per unit length (dl = 1) is
θ =
∂U
∂ M t
=
M t
4 A 2 G
dS
t
or
θ =
2q A
4 A 2 G
dS
t
or
θ =
q
2 AG
dS
t
(7.24)
7.9 Torsion of Thin-Walled Multiple-Cell Closed Sections
Consider a two-cell section shown in Fig. 7.9. Let A 1 and A 2 be the areas of the cells 1
and 2, respectively. Consider the equilibrium of an element at the junction as shown
in Fig. 7.9b. In the direction of the axis of the tube, we can write
Fig. 7.9 Torsion of thin-walled multiple-cell closed section