Problem $3$: The AISI $1095$ HR grooved round bar is subjected cyclic forces $Fx(t)$ and $Fy(t)$ and a cyclic moment $My(t)$ as shown. Knowing that $D=167mm,d=159mm,r=4mm,h_1=150mm,h_2=25mm,$ and that $Fx,Fy$ and $My$ vary with time as shown in the table below:

$\backslash$table$[[$Time $($s$),$Fx $($kN$),$Fy $($kN$),$My $($kN$.$m$)],[0\mathrm{.}00,0\mathrm{.}00,0\mathrm{.}00,-8\mathrm{.}00],[0\mathrm{.}25,8\mathrm{.}75,70\mathrm{.}00,4\mathrm{.}00],[0\mathrm{.}50,17\mathrm{.}50,140\mathrm{.}00,16\mathrm{.}00],[0\mathrm{.}75,8\mathrm{.}75,70\mathrm{.}00,4\mathrm{.}00],[1\mathrm{.}00,0\mathrm{.}00,0\mathrm{.}00,-8\mathrm{.}00],[1\mathrm{.}25,-8\mathrm{.}75,70\mathrm{.}00,4\mathrm{.}00],[1\mathrm{.}50,-17\mathrm{.}50,140\mathrm{.}00,16\mathrm{.}00],[1\mathrm{.}75,-8\mathrm{.}75,70\mathrm{.}00,4\mathrm{.}00],[2\mathrm{.}00,0\mathrm{.}00,0\mathrm{.}00,-8\mathrm{.}00]]$

Draw the cycles for all loading.

Determine the factor of safety guarding against first cycle yielding.

Determine the factor of safety against fatigue using modified Goodman.

Use Microsoft Excel to draw the designer's fatigue diagram for $($c$).$