Radius of Gyration

The radius of gyration of bar cross-section is defined by

$$r_x = \sqrt{\frac{I_x}{S}} \protect$$ (E.7)

where $S$ is the cross-section area, and $I_x$ is the moment of inertia of the cross-section about the line $x$ lying in the plane of the cross-section (usually passing through its centroid):

$$I_x = \int_S z^2 dS,$$

where $z$ denotes the distance of the differential area element $dS$ from the axis of gyration (line $x$).