Section II.1-2

### Section II.1-2 Parallel Axis Theorem

The parallel axis theorem is used for finding the rectangular moment of inertia about an axis different from the centroidal axis of the section. For the figure below the centroidal rectangular moments of inertia are determined using

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

EXAMPLE PROBLEMS

• Example 1 Rectangular moments and product of inertia of a symmetric section
• Example 2 Rectangular moments and product of inertia of a symmetric skin-stringer section
• Example 3 Rectangular moments and product of inertia of an unsymmetric skin-stringer section
• Example 4 Rectangular moments and product of inertia of retangular box beam with 4 different size stiffeners

To Section II.1-1