Last Updated on February 24, 2024 by Maged kamel

## Mohr’s Circle of Inertia part-2.

### Point of minimum value of inertia.

The point of the minimum value of inertia is point Zâ€™ where the Ixy value equals zero. What about the direction of the V axis? The direction is obtained from Mohrâ€™s circle of inertia by an enclosed angle of (180-2Î¸p) in the anti-clockwise or (2Î¸p )from the Y-axis in the clockwise direction.

While in the Normal view, it has an angle of (90-Î¸p) from the x-axis in the anti-clockwise direction.

### The expression of tan 2Î¸p.

In Mohr’s Circle of Inertia part-2, the value 2Î¸p can be estimated from the third equation by setting Ixâ€™yâ€™ to be equal to zero, this will give tan 2Î¸p value as equal to (-Ixy/(Ix-Iy/2). The negative sign will include that the angle is in the clockwise direction.

### The expression of Imax using Mohr’s circle.

The value of Imax or Iu can be estimated as equal to the shift which is (Ix+Iy)/2 plus the radius value. Checking the tan 2Î¸p expression we can draw an angle and get the radius value in terms of Ixy, Ix, and Iy.

### The expression of Imin using Mohr’s circle.

From the next slide in Mohr’s Circle of Inertia part-2, the value of I minimum or Imin or Iv can be estimated as equal to shift which is (Ix+Iy)/2 minus the radius value. Checking the tan 2Î¸p expression we can draw an angle and get the radius value in terms of Ixy, Ix, and Iy and deduct the value of (Ix+Iy)/2.

### The expression of pole point.

The pole point in Mohrâ€™s circle of inertia is the point from which you can get direction, and the center of the circle is the pole point. When we join to point x will give the X-axis.

While joining with point y you can get the Y direction similarly a line from the center of the circle to point Z will give the principal maximum direction or the U direction.

**The pole point in Mohr’s circle for the normal view.**

From the last slide, we can get the pole of the normal view as point Zâ€™ joining to the mirror point of x, which will give the U direction in the normal view, and joining to the mirror of point y will give the V direction.

Thanks a lot and peace be upon you all.

This is the next post, which is titled: Easy Approach to Mohr’s Circle of inertia-First Case.

This is a link to a useful external resource. Calculator for Cross Section, Mass, Axial and Polar Area Moment of Inertia, and Section Modulus.