Parallel Axis Theorem | Principal Axes and Principal Moments of Inertia

**Radius of Gyration:** The radius of
gyration is a parameter that relates the moment of inertia to the
area of a section. The radii of gyration corresponding to
I_{x}, I_{y}, and J are expressed as

(9) |

We can think of the radii of gyration r_{x} and r_{y} as the x and y coordinates of
an imaginary point at which the entire area is lumped. As such, a
radius of gyration does not have any physical significance. It is
simply a way of relating the moment of inertia about a particular
axis to the area.

**Application:** In buckling analysis of
columns a quantity of importance is the so-called slenderness ratio denoted by L/r. This quantity relates the length (L) of
the column to its cross-sectional radius of gyration (r).

Parallel Axis Theorem | Principal Axes and Principal Moments of Inertia