# Radius of Gyration in Structural Engineering

## Radius of gyration is used to describe the distribution of cross sectional area in a column around its centroidal axis

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 ^{3}, 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 = 0.289 h (1)*

#### 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)*