Answer:
52Mpa
76Mpa
Step-by-step explanation:
a. We need to perform a two step process to obtain the maximum shear stress on the shaft. For the solid shaft,
P=2×pi×N×T/60 or T=60×p/2×pi×N
Where P=power transmitted by the shaft=50×10³W
N=rotation speed of the shaft in rpm=730rpm
Pi=3.142
T is the twisting moment
By substituting the values for pi, N and P, we get
T=654Nm or 654×10³Nmm
Also, T=pi×rho×d³/16 or rho=16×T/pi×d³
Where rho=maximum shear stress
T = twisting moment=654×10³Nmm
d= diameter of shaft= 40mm
By substituting T, pi and d
Rho=52Mpa
b. For a hollow shaft, the value for rho is unknown
T=pi×rho(do⁴-di⁴/do)/16
Rho=T×16×do/pi×(do⁴-di⁴)
Where
T= twisting moment=654×10³Nmm gotten above
do=outside shaft diawter=40mm
di= inside shaft diameter =30mm
Pi=3.142
Substituting values for pi, do, di and T.
Rho=76Mpa