# Torsion of rectangular cross section rotated at an angle?

I want to use a rectangular cross section to act as a torsion spring that can be adjusted. The idea is that the adjustment would be made via rotating the rectangular cross section about it's center at an angle theta. I've used parallel axis theorem before, but I don't think that is applicable here since it is just one shape. How can I calculate the polar moment of inertia so that I can then use other stress equations? If you're curious for what it's for, it's intended to be a blade type anti-roll bar.

Thanks for the help!

The torsion of non-circular cross sections is way more complicated than for circular cross sections. That's why torsion springs and anti-roll bars are usually circular in cross-section.

The torsion constant J is no longer equal to the polar moment of inertia for non-circular sections, and the calculation of stress is also no longer a simple procedure.

http://en.wikipedia.org/wiki/Torsion_constant

The parallel-axis theorem can be used with one shape if you break that shape down to smaller, more elementary shapes. For example, an I-beam can be broken down into 3 rectangles and determining the moment of inertia of the flanges from the simple formula bh^3/12 will require the parallel-axis theorem since the rotation axis isn't at the center of mass of the object (which the formula assumes).