To calculate the shear stress, τ and angular deflection, θ caused by a torsional moment generated by the application of forces acting at some distance from the centroid, the polar moment of inertia for the respective section, Ϳ is required.
![](https://www.cisc-icca.ca/wp-content/uploads/2020/07/figure1-1.jpg)
Figure 1: Typical Tubular Sections
For a Hollow Circular Tube:
For a Hollow Square Tube: