Radius of gyration
Radius of gyration or gyradius refers to distribution of the components of an object around an axis. In terms of mass moment of inertia, it is the perpendicular distance from the axis of rotation to a point mass (of mass, m) that gives an equivalent inertia to the original object(s) (of mass, m). The nature of the object does not affect the concept, which applies equally to a surface, a bulk mass, or an ensemble of points.
Mathematically the radius of gyration is the root mean square distance of the object's parts from either its center of mass or a given axis, depending on the relevant application.
In structural engineering, the two-dimensional radius of gyration is used to describe the distribution of cross sectional area in a column around its centroidal axis. The radius of gyration is given by the following formula:
or
Where I is the second moment of area and A 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 buckle around the axis with the smaller principal moment. For example, a column with an elliptical cross-section will tend to buckle in the direction of the smaller semiaxis.
It also can be referred to as the radial distance from a given axis at which the mass of a body could be concentrated without altering the rotational inertia of the body about that axis.
In engineering, where continuous bodies of matter are generally the objects of study, the radius of gyration is usually calculated as an integral.
The radius of gyration about a given axis () can be computed in terms of the mass moment of inertia around that axis, and the total mass m;
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