For solid or hollow shafts of uniform circular cross-section and constant wall thickness, the torsion relations are:
The shear stress at a point within a shaft is:
Note that the highest shear stress is at the point where the radius is maximum, the surface of the shaft. 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 its service life.
The angle of twist can be found by using:
where r is the radius of the object.
The polar moment of inertia for a pipe is:
where the o and i subscripts stand for the outer and inner radius of the pipe.
For a thin cylinder
US Patent Issued to UT-Battelle on May 15 for "Apparatuses for Prestressing Rod-Type Specimens in Torsion for In-Situ Passive Fracture Toughness Testing in an Extremely High-Pressure Environment of Hydrogen" (Tennessee Inventors)
May 23, 2012; ALEXANDRIA, Va., May 21 -- United States Patent no. 8,176,795, issued on May 15, was assigned to UT-Battelle LLC (Oak Ridge, Tenn...
Contribution of the perichondrial ring to capital femoral epiphysis in torsion.(Section on Orthopaedic and Trauma Surgery)(Brief Article)
Oct 01, 2004; The purpose of this study was to determine the torsional strength of the capital femoral epiphysis and the role of the...