A shaft is to be designed for transmitting $120kW$ power at $500$ rpm$.$ The shaft is supported by

bearings $3m$ apart and at $1m$ from one bearing $(A)$ a pulley exerting a downward transverse

load of $3KN$ on the shaft. Determine the following:

The reactions at the bearing

The transmitted torque

The maximum bending moment

The diameter of the shaft $($of circular solid section$)$ if the maximum principal stress is not to

exceed $500$MPa

The diameter of the shaft $($of circular solid section$)$ if the permissible stress is not to exceed

$600$ MPa

Consider a diameter for the section $AC$ of $d_{AC}=70mm$ and for the section $CB{d}_{CB}=75mm.$

Determine the slope at $A,$ the slope at $B$ and the deflection at $C.E=200$GPa