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Torsion (mechanics) : ウィキペディア英語版
Torsion (mechanics)

In the field of solid mechanics, torsion is the twisting of an object due to an applied torque. It is expressed in newton metres (N·m) or foot-pound force (ft·lbf). In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius.
For shafts of uniform cross-section the torsion is:
: T = \frac \tau= \frac G \theta
where:
* ''T'' is the applied torque or moment of torsion in Nm.
* \tau is the maximum shear stress at the outer surface
* ''JT'' is the torsion constant for the section. It is almost equal to the second moment of area ''Jz = Iz'' for twisting about axis z. For more accuracy, finite element analysis (FEA) is the best method. Other calculation methods include membrane analogy and shear flow approximation. 〔Case and Chilver "Strength of Materials and Structures〕
* ''r'' is the distance between the rotational axis and the farthest point in the section (at the outer surface).
* ''ℓ'' is the length of the object the torque is being applied to or over.
* ''θ'' is the angle of twist in radians.
* ''G'' is the shear modulus, also called the modulus of rigidity, and is usually given in gigapascals (GPa), lbf/in2 (psi), or lbf/ft2.
* The product ''JT G'' is called the torsional rigidity ''wT''.
==Properties==
The shear stress at a point within a shaft is:
: \tau_
Note that the highest shear stress occurs on the surface of the shaft, where the radius is maximum. High stresses at the surface may be compounded by stress concentrations such as rough spots. Thus, shafts for use in high torsion are polished to a fine surface finish to reduce the maximum stress in the shaft and increase their service life.
The angle of twist can be found by using:
: \varphi_.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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