Steiner's Theorem

In this article you will learn what Steiner's Theorem (Parallel axis theorem) is and how to apply it in practice.

1. Steiner's theorem - definition

2. Steiner's theorem - application example

Steiner's theorem - definition

Steiner's theorem makes it possible to calculate the moment of inertia of a plane figure about an axis that is parallel to a given central axis, i.e. passing through the center of gravity of the figure.

Fig.1 Steiner's theorem

As shown in the figure above, Steiner's Theorem allows us to calculate the moment of inertia about any parallel axis away from the central axis of our figure. Knowing the value of the moment about the central axis, if we add the area of figure "A" multiplied by the distance of the axis squared.

The product of inertia according to Steiner's Theorem is calculated by adding the product of the area and the distance of the axes "a" and "b" to the value of the moment of deviation of the figure relative to the central axes.

Steiner's theorem - application example

You can find more examples of using and calculating moments of inertia using Steiner's Theorem in my Moment of Inertia calculator. Feel free to use it!!

As an example of the application of Steiner's Theorem, let's analyze the rectangle with sides b1 and h1 shown in the figure below. Formulas for the moments of inertia of simple figures such as a rectangle can be found in this entry.

Fig.2 Calculation of the moment of inertia using Steiner's Theorem for the x and y axes.