This term, like moment of inertia, is the expression of a certain value of any section, and is one of the factors in the principal column formulas for determining the strength of cast-iron and steel columns.

### Rule

The radius of gyration (R) of any section is equal to the square root of the quotient obtained by dividing the moment of inertia † of the section (I) by the area of the section (A).

The rule may be thus expressed by formula:

R = ; or R2 = I / A

For convenient formulas to obtain the radius of gyration of usual sections, see Table XII, page 83. For the radius of gyration of rolled shapes, see tables on pages 84 to 93.

### Example

What is the least radius of gyration of the structural steel-column section shown in Fig. 9?

### Solution

The value of I, or moment of inertia (found by one of the methods given on pages 78 to 80), on the axis XX, is equal to 1,129, while on the axis Y Y it is equal to 366.1. The sectional area is 41.44 sq. in. Using the least value of I, there results,

R= Square root of (366.1/41.44') = 2.97

Fig. 9.

* To find area of irregular figures, see page 36. In obtaining dimensions necessary for determining the area, the same scale should be adopted as used in laying out the section at (a), Fig. 8. † See pages 77 to 81.

* See page 77. † See page 76.