$1.$ Determine the loading on the shaft

$2.$ Determine the plane stresses magnitudes and directions

$3.$ Draw a Mohr's circle of the situation

$4.$ Explain and determine principal stresses and their directions

$5.$ Determine the suitable solid shaft diameter under the condition and given material grade

$6.$ Determine the outer diameter of a hollow shaft, given that the inner diameter is as calculated in sub$-$question$5,$ under the specified conditions and material grade. Additionally, calculate the resulting weight gain.

$7.$ Determine the factor of safety if you consider Tresca failure theory

$8.$ Determine the factor of safety if you consider Von Mises failure theory

$9.$ Determine the critical rotation speed in case of a solid shaft and, in case of the hollow shaft$\mathrm{.}10.$ Prepare a comprehensive report documenting the design process, calculations, drawings, and analysis results $(6$ pages maximum$).$All other necessary parameters assume generic values and for your shaft determined dimensions, select standard sizes.