# Radius of Gyration in Structural Engineering

In structural engineering the Radius of Gyration is used to describe the distribution of cross sectional area in a column around its centroidal axis.

The structural engineering radius of gyration can be expressed as

*r = (I / A) ^{1/2} (1)*

*where*

*r = radius of gyration (m, mm, ft, in...)*

*I = Area Moment Of Inertia (m ^{4}, mm^{4}, ft^{4}, in^{4} ..)*

*A = cross sectional area (m ^{2}, mm^{2}, ft^{2}, in^{2}...)*

### Some typical Sections and their Radius of Gyration

#### Rectangle - with axis in center

Radius of Gyration for a rectangle with axis in center can be calculated as

*r _{max} = 0.289 h (1)*

*where*

*r _{max} = max radius of gyration (strong axis moment of inertia) *

#### Rectangle - with excentric axis

Radius of Gyration for a rectangle with excentric axis can be calculated as

*r = 0.577 h (2)*

#### Rectangle - with tilted axis

Radius of Gyration for a rectangle with tilted axis can be calculated as

*r = b h / (6 (b ^{2} + h^{2}))^{1/2} (3)*

#### Rectangle - with tilted axis II

Radius of Gyration for a rectangle with tilted axis can be calculated as

*r = (((h ^{2} + cos^{2}a) + (b^{2} sin^{2}a)) / 12)^{1/2} (4)*

#### Hollow Square

Radius of Gyration for a hollow square can be calculated as

*r = ((H ^{2} + h^{2}) / 12)^{1/2} (5)*

#### Hollow Square - with tilted axis

Radius of Gyration for a hollow square with tilted axis can be calculated as

*r = ((H ^{2} + h^{2}) / 12)^{1/2} (6)*

#### Equilateral Triangle with excentric axis

Radius of Gyration for a equilateral triangle can be calculated as

*r = h / (18) ^{1/2} (7)*

#### Triangle

Radius of Gyration for a equilateral triangle can be calculated as

*r = h / (6) ^{1/2} (8)*

## Related Topics

### • Beams and Columns

Deflection and stress in beams and columns, moment of inertia, section modulus and technical information.

### • Mechanics

The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

## Related Documents

### Area Moment of Inertia - Typical Cross Sections I

Typical cross sections and their Area Moment of Inertia.

### Area Moment of Inertia Converter

Convert between Area Moment of Inertia units.

### Euler's Column Formula

Calculate buckling of columns.

### Mass Moment of Inertia

The Mass Moment of Inertia vs. mass of object, it's shape and relative point of rotation - the Radius of Gyration.

### Pipe and Tubing Formulas

Pipe and Tube Equations - moment of inertia, section modulus, traverse metal area, external pipe surface and traverse internal area - imperial units

### Square Hollow Structural Sections - HSS

Weight, cross sectional area, moments of inertia - Imperial units

### Structural Lumber - Section Sizes

Basic size, area, moments of inertia and section modulus for timber - metric units.