Torsion of Circular Shafts
The product of this turning force and the distance between the point of application of the force and the axis of the shaft is known as torque, turning moment or twisting moment. And the shaft is said to be subjected to torsion. Due to this torque, every cross-section of the shaft is subjected to some shear stress.
Assumptions for Shear Stress in a Circular Shaft Subjected to Torsion
1. The material of the shaft is uniform throughout.
2. The twist along the shaft is uniform.
3. Normal cross-sections of the shaft, which were plane and circular before the twist, remain plane and circular even after the twist.
4. All diameters of the normal cross-section, which were straight before the twist, remain straight with their magnitude unchanged, after the twist.
Torsional Stresses and Strain
Consider a circular shaft fixed at one end and subjected to a torque at the other end as shown in
T = Torque in N-mm,
l = Length of the shaft in mm and
R = Radius of the circular shaft in mm.
As a result of this torque, every cross-section of the shaft will be subjected to shear stresses. Let the
line CA on the surface of the shaft be deformed to CA′ and OA to OA′ as shown in Fig.1
∠ACA′ = φ in degrees
∠AOA′ = θ in radians
τ = Shear stress induced at the surface and
C = Modulus of rigidity, also known as torsional rigidity of the shaft
We know that shear strain = Deformation per unit length
Strength of a Solid Shaft