Radius of Gyration

How much effort have you put in trying to find the answer?

Have you tried Wikipedia?

Have you tried to goggle it?

Is this a homework type question?

Yes I tried all the methods.

Iam getting theoretical answers.

But i want to know it practically so that i can apply.

praywin

This must be a homework day.

I have to assume that you're either taking a course in Statics or Dynamics -- hopefully it's not dynamics. To understand "radius of gyration," you must understand "moment of inertia" as well. To understand moment of inertia, you must also understand "centroid" and "center of gravity." Go back a little and re-read about the terms I just mentioned.

Yes I had been through those terms i.e moment of inertia, Centroid and centre of gravity

please proceed

I'm not sure what you're after. You say, "But i want to know it practically so that i can apply." I can understand your frustration, but I can't make you understand something which you don't know well enough yet to understand.

Its use is to get a handle on a number that indicates tendency of a beam or column to buckle for structural stuff, and I can't put it into words any more clearly than whoever wrote the article on Radius of Gyration for Wikipedia, for example.

It states for: "Applications in Structural Engineering:

In structural engineering, the two-dimensional radius of gyration is used to describe the distribution of cross sectional area in a beam around its centroidal axis. The radius of gyration is given by the following formula;

or

where I is the second moment of area and A is the total cross-sectional area. The gyration radius is useful in estimating the stiffness of a beam. However, if the principal moments of the two-dimensional gyration tensor are not equal, the beam will tend to buckle around the axis with the smaller principal moment. For example, a beam with an elliptical cross-section will tend to buckle around the axis with the smaller semiaxis.

It also can be referred to as the radial distance from a given axis at which the mass of a body could be concentrated without altering the rotational inertia of the body about that axis.

In engineering, where people deal with continuous bodies of matter, the radius of gyration is more usually calculated as an integral."

It states for: "Applications in Mechanics:

The radius of gyration about a given axis can be computed in terms of the moment of inertia I around that axis, and the total mass M;

or

It should be noted that I is a scalar, and is not the moment of inertia tensor."

After reading and understanding all the links referring to other terms used in mechanical and structural engineering, uses for R_g should be easier to understand.