Solution:

A shaft is a rotating part of machine which transmits power from one point to other. When a force acts tangentially at a point on the surface of the shaft it rotates or twist. The twisting is due to the moment of a tangential force at the axis of rotation. The shaft is said to be in torsion.

The study of behavior of the shaft in torsion without taking into account bending moment due to self-weight or other longitudinal forces known as pure torsion.

Due to torsion shearing stress are induced in the material of the shaft. Every point in the material of the shaft is subjected to pure shear.

Torsional Equation is

$\frac{G \theta}{L}=\frac{T}{I_{p}}=\frac{\tau}{R}$

Where,

T = Torque or Turning moment (N-mm)

IP = Ixx + Iyy Polar momet of inertia of the shaft section (mm4 )

G = Modulus of rigidity of the shaft material (N/mm2 )

θ = Angle through which the shaft is twisted due to torque i.e. angle of twist (radians)

L= Lenght of the shaft (mm)

$\tau$ = Maximum shear stress induced at the outermost layer of the shaft (N/mm )

R= Radius of the shaft (mm)