Torsion (mechanics)
In solid mechanics,
torsion is the twisting of an object due to an applied torque. It is expressed in newton metres or foot-pound force. 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: where: ▪
T is the applied torque or moment of torsion in Nm. ▪ is the maximum shear stress at the outer surface ▪
JT is the torsion constant for the section. It is identical to the second moment of area
Jzz for concentric circular tubes or round solid shafts only. For other shapes,
J must be determined by other means. For solid shafts, the membrane analogy is useful, and for thin-walled tubes of arbitrary shape, the shear flow approximation is fairly good, if the section is not re-entrant. For thick-walled tubes of arbitrary shape, there is no simple solution, and finite element analysis may be the best method. ▪
r is the distance between the rotational axis and the farthest point in the section. ▪
ℓ is the length of the object the torque is being applied to or over.