Explanation And Calculation Of Principal Moments Of Inertia

To understand this topic, please take a look at the article and calculator about the area moment of inertia. 

Principal axes are the axes that product moment of inertia of different beams is zero. So, the area moment of inertia about these principal axes is called the principal moment of inertia. 

Statics (Engineering Mechanics)

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Principal Moment Of Inertia Calculator

Principal Moments Of Inertia Calculator

The use of the calculator above is very simple. You just need to enter the required values into the brackets and click on the ‘Calculate!’ button. If you want to do another calculation, click on the ‘Reset’ button.

The unit of the whole inputs is the fourth power of length units such as millimeters and inches. Use the consistent units to obtain correct results.

How To Calculate Principal Moment Of Inertia?

There is a strict similarity between principal stresses with the principal moment of inertia. The numerical calculations of them are the same in principle. 

Here is the numeric equation that you can use for calculation of the principal moment of inertias;

Like principal stresses, one of the principal moment of inertia values is the minimum moment of inertia and the other one is the maximum principal moment of inertia.
In this equation;
I1 and I2 are the minimum and maximum principal moments of inertia values.
Ix and Iy are the area moment of inertia values of the given shape or plane.
Ixy is the product of inertia.

Here, θp is the angle of orientation of principal axes. The second principal axis is oriented with the first one in 90 degrees. 


So the logic of the principal moment of inertia is like this. 

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