AREA MOMENT OF INERTIA OF HOLLOW RECTANGULAR SECTION

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.

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

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 = BD³/12

Area moment of inertia of the rectangular section EFGH about XX axis = bd³/12

Moment of inertia of hollow rectangular section about XX axis = [BD³/12]-[bd³/12]

I_XX = (BD³-bd³)/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 = DB³/12

Area moment of inertia of the rectangular section EFGH about YY axis = db³/12

Moment of inertia of hollow rectangular section about YY axis = [DB³/12]-[db³/12]

I_YY = (DB³-db³)/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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