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The radius of gyration is given by the following formula: = Where is the second moment of area and is the total cross-sectional area. The gyration radius is useful in estimating the stiffness of a column.
In structural engineering, Johnson's parabolic formula is an empirically based equation for calculating the critical buckling stress of a column. The formula is based on experimental results by J. B. Johnson from around 1900 as an alternative to Euler's critical load formula under low slenderness ratio (the ratio of radius of gyration to ...
The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field.
This formula was derived in 1744 by the Swiss mathematician Leonhard Euler. [2] ... is the radius of gyration, is the second moment of area (area moment of inertia ...
In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members.Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness.
Since the gyration tensor is a symmetric 3x3 matrix, ... The squared radius of gyration is the sum of the principal moments: = ...
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A quantity frequently used in polymer physics is the radius of gyration: = It is worth noting that the above average end-to-end distance, which in the case of this simple model is also the typical amplitude of the system's fluctuations, becomes negligible compared to the total unfolded length of the polymer N l {\displaystyle N\,l} at the ...