What is Radii of Gyration? Application

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Radii of Gyration is a measure of an object's stiffness and rigidity, indicating how far the material is distributed from its centroid. In the context of a 50x100 tube under wind pressure, a greater Radius of Gyration results in increased rigidity compared to a round rod with the same cross-sectional area. The tube's design allows more material to be positioned farther from the center, enhancing its resistance to bending. This principle illustrates that even with identical cross-sectional areas, different shapes can exhibit varying structural behaviors. Understanding this concept is crucial for applications in structural engineering and design.
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I am looking a definition and application of Radii of Gyration. I want to understand this concept by looking at a 50x100 Tube withstanding wind pressure as I have drawn using Autocad. So far I do know that the greater the Radii of Gyration, the greater the rigidity of the section i.e the greatest the distance away from the centroid the most rigid is the section.

Thanks in advance.
 

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Not really my field but wikipedea seems to cover it.

http://en.wikipedia.org/wiki/Radius_of_gyration

In short.. if you look at the cross section of a tube all the metal is a long way from the center of area (the middle). If you compare that with a round rod having the same same cross sectional area you see that all the metal is close to the center. So they have the same cross sectional area but different Radii of Gyration.

If you try and bend the rod and tube (using wind if you like) you find the tube is stiffer even though they have same cross sectional area of metal.
 

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