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# Radius of Gyration in Structural Engineering

## Radius of gyration describes the distribution of cross sectional area in columns around their 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       (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 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.

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## Citation

• The Engineering ToolBox (2008). Radius of Gyration in Structural Engineering. [online] Available at: https://www.engineeringtoolbox.com/radius-gyration-structural-engineering-d_1331.html [Accessed Day Month Year].

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7.25.9

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