We were discussing “The perpendicular axis theorem and its
proof”, “The theorem of parallel axis about moment
of inertia”, “Area moment of inertia for the rectangular section about a line passing through the base” in our previous posts.

Today we will see here the method to determine the
area 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.

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

I

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

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

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

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

Area moment of inertia of the rectangular section ABCD
about XX axis = BD

^{3}/12
Area moment of inertia of the rectangular section EFGH
about XX axis = bd

^{3}/12
Moment of inertia of hollow rectangular section
about XX axis = [BD

^{3}/12]-[bd^{3}/12]###
**I**_{XX}
= (BD^{3}-bd^{3})/12

_{XX}= (BD

^{3}-bd

^{3})/12

Similarly, and hence area 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.

Area moment of inertia of the rectangular section ABCD
about YY axis = DB

^{3}/12
Area moment of inertia of the rectangular section EFGH
about YY axis = db

^{3}/12
Moment of inertia of hollow rectangular section
about YY axis = [DB

^{3}/12]-[db^{3}/12]###
**I**_{YY}
= (DB^{3}-db^{3})/12

_{YY}= (DB

^{3}-db

^{3})/12

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.
Determination of the moment of inertia of a circular section in the category of
strength of material.

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