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

$T=2A\phi _{1}\,$

Elasticity