A shaft is said to be under pure torsion when it is subjected to two equal & opposite couples in a plane perpendicular to the longitudinal axis of the shaft (i.e. twisting couples) in such a way that the magnitude of twisting moment remains constant throughout the length of the shaft.
It’s magnitude is given as the product of the force and the distance between the force.
Torque, T = p x d
Magnitude and representation of Torque
Figure shows a bar or shaft of circular section, subjected to torque T. Such a case is a case of pure torsion,
Shaft is under pure torsion
J/R is known as torsional section modulus.,& GJ is known as torsional rigidity of the bar or the shaft.
The above relation states that the intensity of shear stress at any point in the cross-section of a shaft subjected to pure torsion is proportional to its distance from the center and the variation of shear stress with respect to radial distance is linear.
Variation of Torsional Shear StressPolar moment of inertia
(a) For a solid shaft of circular section,
Torsional section modulus
(b) For a hollow circular shaft,
It is zero at the center and increases in the radially outward direction and become maximum at the outer periphery And for hollow circular shaft, it is minimum at inner radius and maximum at the outer periphery.
Design of Shaft
While designing a shaft, we calculate the maximum torque that can be transmitted from the shaft.
The resisting couple should be equal to the applied torque. Hence
for two shafts in series T1 = T2 = T
θAC = θAB + θBC
For parallel connection of shaft
Torque is cumulative, T = T1 + T2 and θ1 = θ2
T1L1 / G1J1 = T2L2 / G2J2
Consider a solid shaft of length L, under the action of torque T.
The torsional strain energy of shaft is equal to the work done in twisting.
Torsional Stiffness (K)
Torsional stiffness is defined as the amount of torque or twisting couple required to produce a twist of unit radian. And it represented by ‘K’
θ = TL / GJ, K = GJ / L