Theory of Torsion:

For the purpose of nature of stress distribution and state of stress at any point in the shaft a portion of the shaft along its length will be selected and equal and opposite torques will be assumed to be acting at the two ends of the shaft. All considerations will be restricted to circular section (or cylindrical) shafts only. Following assumptions are built for developing theory of torsion, i.e. correlating the torque on cylindrical shafts with the stress and strain.

 (a) The material of the shaft is isotropic and homogeneous.

 (b) Normal cross-sections of the shaft, which were circular and plane before twist, remain plane and circular after twist, that means. no warping or distortion of parallel planes normal to the axis of the member takes place.

 (c) Homogeneous makes sure uniform properties throughout. An isotropic material will have same magnitude of elastic constants in all directions.

 (d) The cross-section rotates as if rigid which means that each diameter of the cross-section rotates through the same angle after loading. This angle is called angle of twist.

 (e) Material is elastic & follows Hooke's law that means that stress is proportional to strain, in the elastic limit.