compound shafts

COMPOUND SHAFTS

A compound shaft is made up of two or more different materials joined together in such a way that the shaft is elongated or compressed as a single shaft.

The total torque transmitted by a compound shaft is the sum of the torques transmitted by each individual shaft and the angle of twist in each shaft will be equal.

SOLVED PROBLEMS

Example 3.38 

A composite shaft length of 4.5m consists of a steel rod 75 mm diameter surrounded by a closely fitting tube of brass. A torque of 1200 N-m is applied to the composite shaft and it will be shared equally by the two materials. If modulus of rigidity of steel is 0.9 × 10⁵ N/mm2 and modulus of rigidity of brass is 0.5 × 105 N/mm², find

(i) Outside diameter of the brass tube

(ii) Maximum shear stress in each material

(iii) Angle of twist

Given data:

To find:

1. Outside diameter of brass tube, d0

2. Maximum shear stress in each material, τ_s, τb

3. Angle of twist, θ

Solution: 

We know that.

=

For composite shaft, angle twist in each shaft will be equal.

Result:

Example 3.39

A composite concrete shaft is made up of a solid steel shaft of 25 mm radius encased in a hollow steel tube of 40 mm inner radius and 60 mm outer radius. If both the shafts are of length 1 m. Find

(i) Shear stress induced in both shafts

(ii) Angle of twist

Take C = 1× 105 Mpa, Torque, T = 1 kN-m

Given data:

To find: 

1. Shear stress induced in both shafts

2. Angle of twist

Solution: 

Let τ₁ = Shear stress induced in the hollow shaft.

τ₂ = Shear stress induced in the solid shaft.

We know that,

Result:

1. Shear stress induced in hollow shaft, τ₁ = 3.528 N/mm2

Shear stress induced in solid shaft, τ₂ = 1.47 N/mm2

2. Angle of twist, θ = 0°. 2'

Example 3.40 

A composite shaft consists of copper rod of 25 mm diameter enclosed in a steel tube of external diameter 45 mm and 5 mm thick. The shaft is required to transmit a torque of 1100 N-m and both the shafts have equal lengths, welded to a plate at each end, so that their twists are equal. If the modulus of rigidity for steel as twice that of copper, find

1. Shear stress developed in copper

2. Shear stress developed in steel

Given data:

To find:

1. Shear stress developed in copper, τ_c

2. Shear stress developed in steel tube, τ_s

Solution: 

For composite shaft, angle of twist are same

Result:

1. Shear stress developed in copper, τ_c = 25 N/mm2

. Shear stress developed in steel tube, τ_s = 90.17 N/mm2