Mohr's circle

The Mohr's circle of inertia is a graphical method to determine the area moments of inertia that are related to the principal axes of the associated surface at any angle. The method has been estimated in previous years because of its uncomplicated handling and due to the lack of powerful computing machines. Graphical methods are now in the statics as obsolete. However, they have still with their clarity of some importance in the training of engineers. The Mohr's circle of inertia for example, shows that the Relevant centrifugal moment is equal to zero at the principal moments of inertia I1 and I2. At an angle of 45 degrees, the two moments of inertia Ix and Iy are the same size and the corresponding centrifugal Ixy is simultaneously maximized.

The circle in the center vector notation R with

And the radius r

The area moments of inertia obtained serves among other things to determine the bending and buckling loads in the strength of materials.

The Mohr's circle of inertia has a great similarity between the Mohr stress circle, although tensions and moments of inertia initially have nothing in common with each other. However, both the physical values ​​can be described by the tensor, which provides the mathematical basis for the two circles. Both the Mohr inertia and the Mohr stress circle were first described by Christian Otto Mohr.

• Engineering Mechanics