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# 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       (m4, mm4, ft4, in4 ..)

A = cross sectional area (m2, mm2, ft2, in2...)

### 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

rmax = 0.289 h                                (1)

where

rmax = 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 (b2 + h2))1/2                                (3)

#### Rectangle - with tilted axis II

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

r = (((h2 + cos2a) + (b2 sin2a)) / 12)1/2                                (4)

#### Hollow Square

Radius of Gyration for a hollow square can be calculated as

r = ((H2 + h2) / 12)1/2                                (5)

#### Hollow Square - with tilted axis

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

r = ((H2 + h2) / 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, moment of inertia, section modulus and technical information of beams and columns.

### • Mechanics

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 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.

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