A stationary torsion$-$bar, spring loaded statically by the forces F$=15$N and by a

torque T$,$ which varies from $0$ to $1$N$-$m$,$ is shown in Figure $2.$ The bar is to be made

of AM $350$ stainless steel. It is expected that the bar will be lathe$-$turned with the

shoulder fillets fine ground. The ratio of fillet radius, r to the diameter, d can vary

from $0\mathrm{.}05$ to $0\mathrm{.}2.$ The diameter, D can be approximately $1\mathrm{.}5$ to $2$ times of d$.$ If a

reliability of $99\%$ is desired and a safety factor of $1\mathrm{.}8$ specified, find a suitable diameter

d by making necessary assumptions and design choices. Please show your calculations

for each design iteration. Round up the diameter to the nearest mm and explicitly

justify your answer and its limitations $($if any$).(40$ pts$.)$

Figure $2$: Torsion bar. Dimensions in mm$.$

You need to show multiple iterations for q $.$ At least $3.($Dont just put the right q immediately, show how you got there with at least three trials$).$