Question

What are the applications of the radius of gyration in structural engineering?

Answer 1

The radius of gyration:

1. The radius of gyration is a measure of the elastic stability of a cross-section against buckling.
2. The radius of gyration can be defined as the imaginary distance from the centroid at which the region of the cross-section is imagined to be concentrated at a point in order to achieve the same moment of inertia.
3. The radius of gyration of a body is always about an axis of rotation.
4. The radius of gyration is represented by the letter $\mathrm{k}$.
5. Mathematically, the radius of gyration $\left(\mathrm{k}\right)$ can be represented as:

$\mathrm{k}=\sqrt{\frac{\mathrm{I}}{\mathrm{m}}}$, where, $I$ is the moment of inertia, and, $\mathrm{m}$ is the mass of the body.

Applications of the radius of gyration:

1. It is being used to examine the performance of various structural geometries under compressing along an axis. It is employed in the prediction of buckling inside a compression member.
2. The two-dimensional ($2\mathrm{D}$) radius of gyration describes the arrangement of cross-sectional area inside columns around its centroidal axis with respect to the mass of the body.
3. The gyration radius can be used to estimate the toughness of a column. If somehow the fundamental moments of the $2\mathrm{D}$ gyration tensor are not equivalent or comparable, the column would bend around the axis with the lower principle moment.
4. The gyration radius is helpful in the assessment of the solidness of a segment.