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State the assumption made in theory of Torsion Or analysis of pure Torsion and define torsional rigidity. State the Torsional formula and explain the term involved in it.
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The assumptions made in the Theory of Pure Torsion or made in deriving the equation for pure torsion are as follows:

• The material is homogeneous and isotropic
• Hook's law is obeyed by the material.
• The shaft is circular in section.
• The cross-section of the shaft remains uniform throughout.
• The shaft is subjected to pure torque only.
• The shaft is not subjected to any initial torque.
• The transverse sections which were plane before application of torque remain plane even after application of torque.

Torsional Formula or Torque Twist Shear Stress or Equation of Pure Torsion:

Where is Shear Stress (MPa), is the length of the solid shaft (mm), r is the radius of the shaft (mm), T is the torque or twisting moment (Nmm), G is the Modulus of rigidity (N/mm^2), θ = angle of twist (radians), is the polar moment of inertia.

Torsional Rigidity: It is defined as the torque that produces a twist of one radian in a shaft of unit length. It is represented by k or . Hence k=G=