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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

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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 - Rectangular Section 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 - Rectangular Section 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 - Rectangular Section 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 - Rectangular Section with tilted axis

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 - 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 - 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 - Equilateral Triangle

Radius of Gyration for a equilateral triangle can be calculated as

r = h / (18)1/2                                (7)

Triangle

Radius of Gyration - Triangle

Radius of Gyration for a equilateral triangle can be calculated as

r = h / (6)1/2                                (8)

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  • en: radius gyration structural engineering cross sectional area axis
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