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

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

a downward transverse load of $3$ KN on the shaft.

Determine the following $($use at least three decimal places$)$:

The reaction at A $($in N $)$

The maximum bending moment $($in $N-m)$

The transmitted torque $($in $N-m)$

The diameter of the shaft $($of circular solid section $-$ in mm $)$ if the maximum

principal stress is not exceed $500$ MPa

The bending stress $($in MPa$)$

The torsional stress $($in MPa$)$

The diameter of the shaft $($of circular solid section $-$ in mm $)$ if the permissible

stress is not exceed $500$MPa $($use Von Mises equivalent stress$)$

If the diameter of section $AC$ is $d_{AC}=70mm$ and the diameter of section $CB$ is

$d_{CB}=75mm,$ find the following: $(E=200$GPa$-$ angles are positive ccw $)$

The slope in $A($in milliradians$)$

The slope in B $($in milliradians$)$

The deflection at C $($in mm $)$