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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].
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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 polar second moment of area can be insufficient for use to analyze beams and shafts with non-circular cross-sections, due their tendency to warp when twisted, causing out-of-plane deformations. In such cases, a torsion constant should be substituted, where an appropriate deformation constant is included to compensate for the warping effect.
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]
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.
Torsional vibration is the angular vibration of an object - commonly a shaft - along its axis of rotation. Torsional vibration is often a concern in power transmission systems using rotating shafts or couplings, where it can cause failures if not controlled. A second effect of torsional vibrations applies to passenger cars.
• Torsion, flat plates, and columns • Shells of revolution, pressure vessels, and pipes • Bodies under direct pressure and shear stress • Elastic stability • Dynamic and temperature stresses • Stress concentration • Fatigue and fracture • Stresses in fasteners and joints • Composite materials and solid biomechanics