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Saint-Venant [2] conjectured in 1856 that of all domains D of equal area A the circular one has the greatest torsional rigidity, that is . A rigorous proof of this inequality was not given until 1948 by Pólya. [3]
Torsion of a square section bar Example of torsion mechanics. In the field of solid mechanics, torsion is the twisting of an object due to an applied torque [1] [2].Torsion could be defined as strain [3] [4] or angular deformation [5], and is measured by the angle a chosen section is rotated from its equilibrium position [6].
The torsion constant or torsion coefficient is a geometrical property of a bar's cross-section. It is involved in the relationship between angle of twist and applied torque along the axis of the bar, for a homogeneous linear elastic bar. The torsion constant, together with material properties and length, describes a bar's torsional stiffness.
Similarly, the torsional stiffness of a straight section is = where is the rigidity modulus of the material, is the torsion constant for the section. Note that the torsional stiffness has dimensions [force] * [length] / [angle], so that its SI units are N*m/rad.
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
Simply put, the polar moment of area is a shaft or beam's resistance to being distorted by torsion, as a function of its shape. The rigidity comes from the object's cross-sectional area only, and does not depend on its material composition or shear modulus. The greater the magnitude of the second polar moment of area, the greater the torsional ...
The determination of the stress and strain throughout a solid object is given by the field of strength of materials and for a structure by structural analysis. In the above figure, it can be seen that the compressive loading (indicated by the arrow) has caused deformation in the cylinder so that the original shape (dashed lines) has changed ...
Rigidity is the property of a structure that it does not bend or flex under an applied force. The opposite of rigidity is flexibility.In structural rigidity theory, structures are formed by collections of objects that are themselves rigid bodies, often assumed to take simple geometric forms such as straight rods (line segments), with pairs of objects connected by flexible hinges.