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# 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       (m4, mm4, ft4, in4 ..)

A = cross sectional area (m3, 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

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 (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

• Mechanics - Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more
• Beams and Columns - Deflection and stress, moment of inertia, section modulus and technical information of beams and columns

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