# Moment of Inertia of a Circular Section

Moment of inertia of a circular section can be calculated by using either radius or diameter of a circular section around centroidal x-axis or y-axis.

# Example

Find the moment of inertia of a circular section whose radius is 8” and diameter of 16”.

## Solution

Moment of inertia of a circular section is same around both centriodal axis. This is because of symmetry of a section around both axis.

Therefore, moment of inertia about centroidal x-axis.

$$I_{x_{0}}= \frac{\Pi R^{4}}{4}= \frac{\Pi D^{4}}{64}$$

….

$$I_{x_{0}}= \frac{\Pi R^{4}}{4}= \frac{\Pi \times 8^{4}}{4}$$

….

$$I_{x_{0}}= 6.28\space in^{4}$$

…..

$$I_{y_{0}}= I_{x_{0}}= 6.28\space in^{4}$$