We were discussing “Mass moment of inertia” and “Area moment of inertia” in our previous posts. We have also seen mass moment of inertia for the rectangular section about a line passing through the center of gravity of rectangular section and mass moment of inertia for the rectangular section about its base line too.

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

Let us consider one hollow rectangular section, where we can see that ABCD is as main section and EFGH as the cut-out section as displayed in following figure.
B = Width of the rectangular section ABCD
b = Width of the rectangular section EFGH
D = Depth of the rectangular section ABCD
d = Depth of the rectangular section EFGH
M = Mass of the rectangular section ABCD
m= Mass of the rectangular section EFGH

(Im)XX = Mass moment of inertia of hollow rectangular section about XX axis
(Im)YY = Mass moment of inertia of hollow rectangular section about YY axis

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

As we have already seen the mass moment of inertia for the rectangular section and hence mass moment of inertia of the rectangular section ABCD about XX axis and mass moment of inertia of the rectangular section EFGH about XX axis will be determined as mentioned here.

Mass moment of inertia of the rectangular section ABCD about XX axis = MD2/12
Mass moment of inertia of the rectangular section EFGH about XX axis = md2/12
Mass moment of inertia of hollow rectangular section about XX axis = [MD2/12]-[md2/12]

### (Im) XX = (MD2- md2)/12

Similarly, and hence mass moment of inertia of the rectangular section ABCD about YY axis and area moment of inertia of the rectangular section EFGH about YY axis will be determined as mentioned here.

Mass moment of inertia of the rectangular section ABCD about YY axis = MB2/12
Mass moment of inertia of the rectangular section EFGH about YY axis = mb2/12
Mass moment of inertia of hollow rectangular section about YY axis = [MB2/12]-[mb2/12]

### (Im) YY = (MB2- mb2)/12

Do you have any suggestions? Please write in comment box

### Reference:

Strength of material, By R. K. Bansal