21.8 PRODUCT OF INERTIA

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À  p

When we want to find the maximum moment of inertia of an area we can start by finding the product of inertia.

This value can be either positive or negative.

The value will be zero if either x or y is an axis of symmetry. This will allow us to find the product of inertia if we know the area and location of the centroid.

If we want to find the maximum and minimum moment of inertia we can use the derived relationship below. We can also find the axis of these maxima and minima,

We can also shift the moment of inertia values to other arbitrary axes using the following relationships,

Consider the example below

If we plot out the values as we rotate the axis, we generate a plot called Mohr's force circle.