This is a property of a section. It is also a function of the second moment of area. The radius of gyration gives the stiffness of a section. It is based on the shape of the cross-section. Normally, we use this for compression members such as a column.
As shown in the diagram, the member bends in the thinnest plane.
Using the radius of gyration, we can compare the behavior of various structural shapes under compression along an axis. It can be used to predict buckling in a compression member such as a column.
The Formula for the Radius of Gyration – r
Where I = the second moment of area
A = cross-sectional area of the member
The unit of measurement is mm.
The smallest value of the radius of gyration is considered for the calculations of the structural stiffness of the member. That is the plane in which the member is most likely to fail or buckle.
Square or circular shapes have the same radius of gyration about any plane. There is no smallest value. Therefore, these sections are ideal selections for columns.
Calculating the radius of gyration
The plan view of a column is shown below.
First, we have to calculate the I value about x-x and y-y axes.
Ixx = 33.3 x 106 mm4
Iyy = 2.08 x 106 mm4
A = cross sectional area = 50 mm x 200 mm = 10,000 mm2
Substituting the value of Ixx and cross-sectional area A in the above formula we can get rxx.
This is the value of the r about the x-x axis.
This is the value of the r about the y-y axis.
Since ryy is smaller, probable failure occurs about the y-y plane.