De cirkel van Mohr voor traagheidsmomenten: Probleemoplossing

Consider the cross-sectional area of a beam for which the moments and product of inertia about the Cartesian coordinate axes are known. To determine the principal moments of inertia and the orientation of the principal axes, Mohr's circle can be used.

The moments and product of inertia are plotted on the x-axis and y-axis of a rectangular coordinate system, respectively.

The average of the rectangular moments of inertia gives the circle's center from the origin.

The circle's radius is determined from the moments and products of inertia.

Now, Mohr's circle is constructed with the obtained values of the circle's center and radius. 

This circle intersects the moment of inertia axis at two points, corresponding to the minimum and maximum moments.

The values of these can be calculated using the circle's radius and the average moment of inertia.

The angle between a line joining the center to a reference point on the circumference and the horizontal axis is obtained using trigonometry.

Rotating the x-axis counterclockwise through half of this angle yields the major principal axis.