equation for polar moment of inertia circle

If you have a better denotation, please share it with me. I just want to reinforce that I have not seen this method formally taught, and I made up Sj. In many cases, it will speed the calculation process along, but in others it will only make it more cumbersome. It is similar to the section modulus for bending, but it is used with torsion. I have add a column for the “Torsional” Section Modulus, S j, which is a term that I have come up with. Here are the Polar Moment of Inertia on common shapes.

The table below has the polar moment of inertia for common shapes. If you don’t have 3D CAD, why not? I guess we will have to do this the old fashioned way. This means that it will always be the largest number there, which prevents confusion when your coordinates may be in a different orientation.Įvery major 3D CAD software has a method to look up the section properties. One thing to note is that the two are moment of inertia will add together to give you the polar moment of inertia. The ones that aren’t are the area and polar moment of inertia. In the section above that, you will get 9 numbers and 6 of them will be zero. The circled number is the polar moment of inertia at the centroid. Don’t get overwhelmed because we don’t need most of it. Knowing if the slot is substantial depends on the beam shape and length, slot length and torque applied. However, if the slot is substantial in length, you now need to consider this as an open section.

If a section has a few holes or a short slot in it, it is still considered closed. These are sections like round bars and tubes. The traditional formulas for the polar moment of inertia work only for closed or continuous sections. Traditional Polar Moment of Inertia Formulas The Polar Moment of Inertia can be used to calculate shear stress and torsional deflection. Resistance to torsion is based entirely on the shape of the section and not the material properties. The Polar Moment of Inertia is a member’s ability to resist twisting from torsional loads. It didn’t take but 2 minutes for Marvin to set us straight the traditional formulas for torsion just don’t work on open sections. Now, it was time to summon to “old guy” to come help us out.

We went back and calculated our torsional deflection again and found no issues. The torsional deflection was excessively high. Image is Public DomainĪ few weeks later, we starting running Finite Element Analysis on the design and the structure lit up like a Christmas tree! At first we thought it was an error in the loading, but we quickly realized the problem.

Equation for polar moment of inertia circle