We were discussing “The perpendicular axis theorem and its
proof”, “The theorem of parallel axis about moment
of inertia”, “Method to determine the area moment of inertia for the
rectangular section” and “Area moment of inertia” in our
previous posts.

Today we will see here the method to determine the
area moment of inertia for the rectangular section about a line passing through
the base of the rectangular section with the help of this post.

Let us consider one rectangular section ABCD as
displayed in following figure. Let us assume that one line is passing through
the base of the rectangular section and let us consider this line as line CD
and we will determine the area moment of inertia for the rectangular section
about this line CD.

B = Width of the rectangular section ABCD

D = Depth of the rectangular section ABCD

I

_{CD}= Moment of inertia of the rectangular section about the CD line###
*Now
we will determine the value or expression for the moment of inertia of the
rectangular section about the line CD*

*Now we will determine the value or expression for the moment of inertia of the rectangular section about the line CD*

Let us consider one rectangular elementary strip
with thickness dY and at a distance Y from the line CD as displayed in above
figure.

*Let us determine first the area and moment of inertia of the rectangular elementary strip about the line CD*

Area of rectangular elementary strip, dA = dY.B

Moment of inertia of the rectangular elementary
strip about the line CD = dA.Y

^{2}
Moment of inertia of the rectangular elementary
strip about the line CD = B Y

^{2}dY
Now
we will determine the moment of inertia of entire area of rectangular section
about the line CD and it could be easily done by integrating the above equation
between limit 0 to D.

Therefore, moment of inertia of entire area of
rectangular section about the line CD will be as displayed here in following
figure

Therefore, moment of inertia of the rectangular
section about the line CD

**I**

_{CD}=BD^{3}/3
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 hollow rectangular section in the
category of strength of material.