For the given steel shaft is shown in Fig. the maximum shear stress due to torsion is found to be 45 MPa. What is the ratio of rate of twist of A to the rate of twist at B:

Concept:

Torsion formula, 

Angle of twist, 

Rate of twist is given by, 

Where, J = Polar moment of inertia

G = Modulus of rigidity

θ = Angle of twist in radian 

L = Length of the shaft

R = Radius of shaft

Series combination of shaft: 

Series combination of the shaft is done to transmit torque from one shaft to another shaft. For series, connection couplings are used. Torque in all shaft connections in series will be equal.

T1 = T2 = T

Total angle of twist from A to C

θAC = θAB + θBC

Calculation:

This is the case of series combination means if we have to apply torque M_t at B then torque developed at point A is also M_t.

ΣMt = 0, 

M_tA = M_tB

So in the given shaft, Twist (Mt), Modulus of rigidity, and Polar moment of inertia are constant.

So the ratio of the rate of twist (θ/L) at points A to B is 1.