Q$5(20$ points$)$ The cylindrical bar shown in the figure has AB and BD sections. It's simply supported. The $B$ connection region has a fillet.

Yield strength: $700$ MPa ; Ultimate tensile strength: $900$ MPa $.$

The cyclic force, $F$:$3kN6kN.$

At B location, $K_t=1\mathrm{.}5$; notch sensitivity $q=1\mathrm{.}8$

$K_a=0\mathrm{.}8$;$K_k=0\mathrm{.}85$;$K_c=1$;$K_e=0\mathrm{.}897$

$(3$ points$)$ Find the reaction forces at A and D when the cyclic force reaches $6$ kN $.$

$(3$ points$)$ Find the shear force and bending moment at $B$ when the cyclic force reaches $6$ kN $.$

$(2$ points$)$ Find fatigue stress$-$concentration factor, $K_f$ at B location.

$(4$ points$)$ Find the alternating stress ${}_a$ and mean$/$average stress ${}_m$ at $B$ location.

$(8$ points$)$ Establish the Goodman diagram for $1$ million cycle fatigue and calculate the factor of safoter for $R$ Incation