The shaft shown below is made from $1035$ CD steel that has a yield strength of $67$ ksi $.$

a$.$ Compute the support reactions.

b$.$ Draw the shear and bending moment diagrams in the $x-y$ and $x-z$ planes.

c$.$ Find the torque and maximum bending moment on the shaft.

d$.$ Find the bending stress and torsional sjear stress.

e$.$ Use a safety factor of $2$ and the maximum shear stress failure theory to calculate the required shaft diameter.

f$.$ Use a safety factor of $2$ and the distortion energy failure theory to calculate the required shaft diameter. $($please only use the answers to check your solution$)$