A $40$ mm$-$diameter bar has been machined from an AISI $1050$ cold$-$drawn bar. This part is

to withstand a fluctuating tensile load varying from $0$ to $70$ kN$.$ Because of the ends, and

the fillet radius, a fatigue stress$-$concentration factor Kf is $1\mathrm{.}85$ for $106$ or larger life. Find

Sa and Sm and the factor of safety guarding against fatigue and first$-$cycle yielding, using

$($a$)$ the Gerber fatigue line; $($b$)$ the ASME$-$elliptic fatigue line; $($c$)$ Modified Goodman; $($c$)$

Soderberg. Also show the load line and critical line for the first three criteria in separate

graphs.