Torsion Of Circular Shafts.

Torsion of Shaft and Combined Stresses

Torsion means twisting a structural Member when it is loaded by couplethat Produces rotation aboutlongitudinal axis.

If be the intensity of shear stress, on any layer at a distance r from the centre of shaft, then

Sign Convention

Sign convention of torque can be explained by right hand thumb rule.A positive torque is that in which there is tightening effect of nut on the bolt. From either side of the cross-section. If torque is applied in the direction of right hand fingers than right hand thumbs direction represents movement of the nut.

TMD = Torsion moment diagram

T = Torque

Rate of twist :

Total angle of twist :

Where, T = Torque,

J = Polar moment of inertia

G = Modulus of rigidity,

θ = Angle of twist

L = Length of shaft,

GJ = Torsional rigidity

Torsional stiffness;

Torsional flexibility

Axial stiffness;

Axial flexibility

Moment of Inertia About polar Axis:

For solid circular shaft,:For hollow circular shaft:

Power Transmitted in the Shaft

Power transmitted by shaft:

Where, N = Rotation per minute.

Compound Shaft

An improved type of compound coupling for connecting in series and parallel are given below

Series connection: Series connection of compound shaft as shown in figure. Due to series connection the torque on shaft 1 will be equal to shaft 2 and the total angular deformation will be equal to the sum of deformation of 1^st shaft and 2^nd shaft.

Therefore,

Where,

θ₁ = Angular deformation of 1^st shaft

θ₂ = Angular deformation of 2^nd shaft

Parallel connection: Parallel connection of compound shaft as shown in figure. Due to parallel connection of compound shaft the total torque will be equal to the sum of torque of shaft 1 and torque of shaft 2 and the deflection will be same in both the shafts.