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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.
The Frenet–Serret formulas are: =, = +, =, where is the derivative with respect to arclength, κ is the curvature, and τ is the torsion of the space curve. (Intuitively, curvature measures the failure of a curve to be a straight line, while torsion measures the failure of a curve to be planar.)
Geometric relevance: The torsion τ(s) measures the turnaround of the binormal vector. The larger the torsion is, the faster the binormal vector rotates around the axis given by the tangent vector (see graphical illustrations). In the animated figure the rotation of the binormal vector is clearly visible at the peaks of the torsion function.
The torsion tensor thus is related to, although distinct from, the torsion of a curve, as it appears in the Frenet–Serret formulas: the torsion of a connection measures a dislocation of a developed curve out of its plane, while the torsion of a curve is also a dislocation out of its osculating plane.
To find the torsion coefficient of the wire, Cavendish measured the natural resonant oscillation period T of the torsion balance: = Assuming the mass of the torsion beam itself is negligible, the moment of inertia of the balance is just due to the small balls. Treating them as point masses, each at L/2 from the axis, gives:
Roark's Formulas for Stress and Strain is a mechanical engineering design book written by Richard G. Budynas and Ali M. Sadegh. It was first published in 1938 and the most current ninth edition was published in March 2020.
The torsion submodule of a module is the submodule formed by the torsion elements (in cases when this is indeed a submodule, such as when the ring is commutative). A torsion module is a module consisting entirely of torsion elements. A module is torsion-free if its only torsion element is the zero element.