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.

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

(I

_{m})_{XX}= Mass moment of inertia of hollow rectangular section about XX axis
(I

_{m})_{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*

*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 = MD

^{2}/12
Mass moment of inertia of the rectangular section
EFGH about XX axis = md

^{2}/12
Mass moment of inertia of hollow rectangular section
about XX axis = [MD

^{2}/12]-[md^{2}/12]###
**(I**_{m})
_{XX} = (MD^{2}- md^{2})/12

_{m})

_{XX}= (MD

^{2}- md

^{2})/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 = MB

^{2}/12
Mass moment of inertia of the rectangular section
EFGH about YY axis = mb

^{2}/12
Mass moment of inertia of hollow rectangular section
about YY axis = [MB

^{2}/12]-[mb^{2}/12]###
**(I**_{m})
_{YY} = (MB^{2}- mb^{2})/12

_{m})

_{YY}= (MB

^{2}- mb

^{2})/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 mass moment of inertia of circular section in the category
of strength of material.

## No comments:

## Post a Comment