Editing Radius of gyration (section)

==Applications in structural engineering==
In [[structural engineering]], the two-dimensional radius of gyration is used to describe the distribution of [[cross section (geometry)|cross sectional]] area in a column around its [[centroid]]al axis with the mass of the body. The radius of gyration is given by the following formula:

:<math>R_{\mathrm{g}} = \sqrt{ \frac {I} {A} }</math>

Where <math>I</math> is the [[second moment of area]] and <math>A</math> is the total cross-sectional area.

The gyration radius is useful in estimating the stiffness of a column. If the principal moments of the two-dimensional [[gyration tensor]] are not equal, the column will tend to [[buckling|buckle]] around the axis with the smaller principal moment. For example, a column with an [[ellipse|elliptical]] cross-section will tend to buckle in the direction of the smaller semiaxis.

In [[engineering]], where continuous bodies of matter are generally the objects of study, the radius of gyration is usually calculated as an integral.