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.
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Typical cross sections and their Area Moment of Inertia.
Area Moment of Inertia Converter
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Euler's Column Formula
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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.
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