818 Hollow square section | Moment of Inertia and Radius of Gyration

Problem 818
A hollow square cross section consists of an 8 in. by 8 in. square from which is subtracted a concentrically placed square 4 in. by 4 in. Find the polar moment of inertia and the polar radius of gyration with respect to a z axis passing through one of the outside corners.
 

Moment of Inertia and Radius of Gyration

Moment of Inertia
Moment of inertia, also called the second moment of area, is the product of area and the square of its moment arm about a reference axis.
 

Moment of inertia about the x-axis:

$\displaystyle I_x = \int y^2 \, dA$

 

000_moment_of_inertia.gif