Introduction to Elasticity/Torsion of thin walled closed sections

Torsion of thin-walled closed sections

The Prandtl stress function $\phi\,$ can be approximated as a linear function between $\phi_1\,$ and $0\,$ on the two adjacent boundaries.

The local shear stress is, therefore,

$\sigma_{3s} = \frac{\phi_1}{t}$

where $s\,$ is the parameterizing coordinate of the boundary curve of the cross-section and $t\,$ is the local wall thickness.

The value of $\phi_1\,$ can determined using

$\phi_1 = \frac{2\mu\alpha A}{\oint_S \frac{dS}{t}}$

where $A\,$ is the area enclosed by the mean line between the inner and outer boundary.

The torque is approximately

$T = 2A\phi_1 \,$