Given:
the cross-section to the right.
Determine: The Moments of Inertia, Ixx and Iyy of this section.
Solution:
The moment of inertia of a rectangular shape such as this one is easily calculated by using the equation I = 1/12 bh3. However, it is crucial that b and h are assigned correct values.
Ixx= 1/12(6in)(9in)3 = 364.5 in4
Iyy= 1/12(9in)(6in)3 = 162 in4
In this case, observation will confirm the choices for b and h. It is logical that Ixx is greater than Iyy because a larger amount of the rectangular area lies further from the x-x axis than the y-y axis. This causes the shape to have a greater resistance to rotation around the x-x axis and therefore a larger moment of inertia around that axis.