# How To Calculate Moment Of Inertia A Cantilever Beam

## Introduction

Moment of inertia is a measurement of an object’s resistance to angular acceleration. It is an important factor in engineering when calculating the strength of a beam or other objects. In this article, we will discuss how to calculate the moment of inertia of a cantilever beam. We will explain the necessary steps and equations that need to be used in order to get accurate results.

## Cantilever Beam Definition

A cantilever beam is a type of structural element that is supported only at one end. It is typically used in bridges, buildings, and other structures. It has a unique mechanical properties because of its shape. The cantilever beam is subject to bending, tension, and compression forces. The moment of inertia of a cantilever beam is important to calculate because it determines the strength of the beam.

## Equations to Calculate Moment of Inertia of a Cantilever Beam

The equations used to calculate the moment of inertia of a cantilever beam are as follows:

• Moment of inertia = mass x radius of gyration²
• Radius of gyration = area moment of inertia/ mass
• Area moment of inertia = b x h x (h² + b²)/12

Where b is the width of the beam, h is the height of the beam, and mass is the total mass of the cantilever beam.

## Steps to Calculate Moment of Inertia of a Cantilever Beam

The following are the steps in calculating the moment of inertia of a cantilever beam:

1. Determine the width (b) and height (h) of the cantilever beam.
2. Calculate the area moment of inertia of the cantilever beam using the equation, b x h x (h² + b²)/12.
3. Calculate the mass of the cantilever beam.
4. Calculate the radius of gyration using the equation, area moment of inertia/ mass.
5. Calculate the moment of inertia using the equation, mass x radius of gyration².

## Conclusion

In conclusion, calculating the moment of inertia of a cantilever beam is a relatively simple process. By following the steps and utilizing the equations discussed in this article, you can accurately calculate the moment of inertia of a cantilever beam. This is an important calculation to make in order to ensure the strength of the beam.