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

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 Z

_{P}.
Polar modulus is also known as torsional section
modulus.Â We can write here the expression for polar modulus
as displayed here.

Polar Modulus = Polar moment of inertia/Radius of
the shaft

Z

_{P}= 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 equationÂ andÂ number of bolts required for a flange couplingÂ in the
category of strength of material, in our next post.

###
**Reference:**

Strength of material, By R. K. Bansal

Image Courtesy: Google

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