MOMENT OF INERTIA OF A HOLLOW CIRCULAR SECTION

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.

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

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 = ПD⁴/64

Moment of inertia of the cut-out circular section about XX axis = Пd⁴/64

Moment of inertia of hollow circular section about XX axis = [ПD⁴/64]-[Пd⁴/64]

I_XX = П (D⁴-d⁴)/64

Similarly, Moment of inertia of hollow circular section about YY axis, I_YY = П (D⁴-d⁴)/64

Therefore, we have concluded

I_XX = П (D⁴-d⁴)/64

I_YY = П (D⁴-d⁴)/64

Do you have any suggestions? Please write in comment box