We were discussing “Method to determine the area moment of
inertia for a hollow rectangular section”, “The
theorem of parallel axis about moment of inertia”, “Moment of inertia of a circular section” and “Area moment of inertia for rectangular section” in our
previous posts.

Today we will see here the method to determine the
moment of inertia of a hollow circular section with the help of this post.

Let us consider one hollow circular section, where we can see that D is the diameter of main section and d is the diameter of cut-out section as displayed in following figure. O is the centre of the circular section as displayed in following figure.

Let us consider one hollow circular section, where we can see that D is the diameter of main section and d is the diameter of cut-out section as displayed in following figure. O is the centre of the circular section as displayed in following figure.

D = Diameter of the circular section

d = diameter of cut-out circular section

O = Centre of the circular section

I

_{XX}= Moment of inertia of hollow circular section about XX axis
I

_{YY}= Moment of inertia of hollow circular section about YY axis###
*Now
we will determine the value or expression for the moment of inertia of hollow circular
section about XX axis and also about YY axis*

*Now we will determine the value or expression for the moment of inertia of hollow circular section about XX axis and also about YY axis*

As we have already seen the basic principle of moment of inertia for the circular section and hence moment of inertia of the main circular
section about XX axis and moment of inertia of the cut-out circular section about
XX axis will be determined as mentioned here.

Moment of inertia of the main circular section about
XX axis = ПD

^{4}/64Moment of inertia of the cut-out circular section about XX axis = Пd

^{4}/64

Moment of inertia of hollow circular section about
XX axis = [ПD

^{4}/64]-[Пd^{4}/64]
I

_{XX}= П (D^{4}-d^{4})/64
Similarly, Moment of inertia of hollow circular
section about YY axis, I

_{YY}= П (D^{4}-d^{4})/64
Therefore, we have concluded

*I*_{XX}= П (D^{4}-d^{4})/64

*I*_{YY}= П (D^{4}-d^{4})/64
Do you have any suggestions? Please write in comment
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**Reference:**

Strength of material, By R. K. Bansal

Image Courtesy: Google

We will see another important topic i.e. moment of inertia of triangular section in the category of strength of material.

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