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Tuesday, 28 February 2017

MOMENT OF INERTIA OF A HOLLOW CIRCULAR SECTION


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
IXX = Moment of inertia of hollow circular section about XX axis
IYY = 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]
IXX = П (D4-d4)/64

Similarly, Moment of inertia of hollow circular section about YY axis, IYY = П (D4-d4)/64
Therefore, we have concluded
IXX = П (D4-d4)/64
IYY = П (D4-d4)/64
Do you have any suggestions? Please write in comment box

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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