Structural Analysis II Section I.6
**
Section
I.6 Torsion of
Thin -
Wall
Closed
Sections
**

So far, we have considered the torsion of solid and hollow circular sections,
thin-walled open sections, and solid noncircular sections. Now we would like to
consider the torsion of thin-walled closed sections of various geometry, typical of aircraft wing
and fuselage. As before we are interested in calculating the shear stress
distribution and overall angle of twist due to applied torque(s). Such analysis
can be used to determine, based on a specified material and loading condition,
(a) the
margin of safety for an existing structure, or (b) the structural sizing such as
wall thickness necessary to safely carry the applied loads.
Here are some examples of typical shear stress distributions in
thin-walled, single- and multi-cell closed sections under pure torsion.

Derivation

Angle of Twist

By applying strain energy equation due to shear and Castigliano's
Theorem the angle of twist for a thin-walled closed section can
be shown to be

If the wall thickness is constant along each segment of the cross section,
the integral
can be replaced by a simple summation

Here is an example.

Important Observations:

In thin-walled structures failure is governed by buckling
instability; therefore, the limiting stress is not necessarily
the elastic limit stress.

EXAMPLE
PROBLEMS

- Example 1 Maximum shear stress and
angle of twist in a single-cell section

To Index Page of
Pure Torsion
To Section
I.5
To Section
I.7