Radius of Gyration: Definition, Applications & Examples

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The radius of gyration is defined as the distance from an axis at which the mass of an object can be thought to be concentrated for the purposes of calculating its moment of inertia. It is expressed mathematically as I = mr_{g}^{2}, where I is the moment of inertia, m is mass, and r_{g} is the radius of gyration. This concept is practically applied in various fields, particularly in structural engineering, where it plays a crucial role in determining the buckling strength of columns through Euler's buckling theory. Experimental determination of the radius of gyration can be achieved by measuring applied torque and angular acceleration. Understanding the radius of gyration is essential for ensuring structural integrity and stability in engineering applications.
chandran
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what is radius of gyration? How this is practically applied ? Any application example website?
 
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Given an object of mass m and arbitrary shape, its radius of gyration with respect to a fixed axis is the number r_{g} so that the moment of inertia "I" of that object with respect to that axis can be written:
I=mr_{g}^{2}
Assuming you've got a way to measure applied torque and angular acceleration, the object's radius of gyration can be determined experimentally.
 
any application in practical?
 
Columns, it is the determining factor for Euler buckling.
 
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