We were discussing the concept of section modulus of beams, derivation of mass moment of inertia and also the derivation of area moment of inertia in our previous posts.

Now we are going further to start a new topic i.e. Polar modulus with the help of this post. We will also see here the polar modulus for various sections in this post.

### So, what is polar modulus?

Before going ahead, we must have to understand here first the basics of polar moment of inertia and after that it will be easy to understand the concept of Polar modulus.

Polar moment of inertia of a plane area is basically defined as the area moment of inertia about an axis perpendicular to the plane of figure and passing through the center of gravity of the area.
Polar moment of inertia will be displayed by J.

### Polar modulus

Polar modulus is basically defined as the ratio of the polar moment of inertia (J) to the radius of the shaft. Polar modulus will be displayed by ZP.

Polar modulus is also known as torsional section modulus. We can write here the expression for polar modulus as displayed here.
Polar Modulus = Polar moment of inertia/Radius of the shaft
ZP = J/R

### Polar modulus for various sections

Following figure, displayed here, indicates the polar modulus for various sections

Do you have suggestions? Please write in comment box.

We will now derive the torsional equation and in the category of strength of material, in our next post.

### Reference:

Strength of material, By R. K. Bansal