Design Exercise #$1$ Specification

In the system shown below in Figure $1,$ a shaft carries $3$ gears $($at locations B$,$ C$,$ and D$)$ with bearings to support on the ends $($at locations A and E$).$ Each of the gears weighs $6\mathrm{.}0$ kN $.$ The shaft is going to be machined out of ASTM$-$A$242.$

The gear at location C is driven with a power of $3{10}^{6}N\frac{m}{s}$ at a speed of $500$ rpm $.$ Gears at locations B and D transmit power of $1\mathrm{.}5{10}^{6}N\frac{m}{s}.$

Calculate a minimum shaft diameter that will support the load using a factor of safety of $3.$ Once the diameter is found, calculate the following parameters.

Torque

Torsional shear stress

Maximum bending moment

Tensile bending stress

Principal stresses

von Mises stress or Distortion Energy