Elasticity/Torsion of thin walled open sections

Torsion of thin-walled open sections

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Examples are I-beams, channel sections and turbine blades.

We assume that the length   is much larger than the thickness  , and that   does not vary rapidly with change along the length axis  .

Using the membrane analogy, we can neglect the curvature of the membrane in the   direction, and the Poisson equation reduces to

 

which has the solution

 

where   is the coordinate along the thickness direction.

The stress field is

 

Thus, the maximum shear stress is