Problem $1$: A round shaft with diameter $D=6cm$ has a shoulder with a smooth fillet to decrease

the diameter. The shaft experiences a fully reversible bending moment of $M=200$

$N*m$ and a constant applied torque of $T=300N*m.$ If the fillet radius is $r=5mm,$

what is the minimum size the shaft diameter can be reduced to $($d$)$ while maintaining

a factor of safety of $2?$ The shaft is constructed from AISI $1030$ cold drawn steel with

a cumulative endurance limit modifier of $K=0\mathrm{.}65.($Hint: To start this problem, you'll

need to make initial guesses at what the fatigue stress concentration factors should be

and iterate your design.$)$