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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].
There is a unique connection which absorbs the torsion, generalizing the Levi-Civita connection to other, possibly non-metric situations (such as Finsler geometry). The difference between a connection with torsion, and a corresponding connection without torsion is a tensor, called the contorsion tensor .
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.
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.
In general, there are an infinite number of metric connections for a given metric tensor; however, there is a unique connection that is free of torsion, the Levi-Civita connection. It is common in physics and general relativity to work almost exclusively with the Levi-Civita connection, by working in coordinate frames (called holonomic ...
is also a Riemannian metric on . We say that ~ is (pointwise) conformal to . Evidently, conformality of metrics is an equivalence relation. Here are some formulas for conformal changes in tensors associated with the metric.
In physics and mechanics, torque is the rotational analogue of linear force. [1] It is also referred to as the moment of force (also abbreviated to moment).The symbol for torque is typically , the lowercase Greek letter tau.
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. For the special case of unconstrained uniaxial tension or compression, Young's modulus can be thought of as a measure of the stiffness of a structure.