A cold worked, $52$ mm diameter, AISI $1045$ steel $($ultimate tensile strength of $720$ MPa and a yield strength of $550$ MPa$)$ rod is subjected to constant amplitude cyclic bending. The surface factor & size factor are assumed to be $0\mathrm{.}5$ and $0\mathrm{.}81$ respectively. Determine the following using Soderberg criterion:

a$)$ The fully reversed fatigue strength at $106$

cycles

b$)$ Sa and Sm for $105$

cycles if R $=0$