Using the parallel axis theorem, the moments of inertia about axes XX and YY parallel to the centroidal axes x and y can be determined as
The parallel axis theorem is useful for finding the centroidal moments of inertia of a cross section composed of several simpler geometric parts as shown below.
The cross section is broken up into several simple shapes, the individual moments of inertia are found, then the moments of inertia about the centroidal axes of the entire section are found using parallel axis theorem.
Usually the broken pieces are made up of rectangles. From mechanics of materials, the x and y moments of inertia of a rectangle are
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