machine construction exercise

[PDS]

Good morning;
I am a mechanical engineering student and exercising myself for the construction examination of machines I came across this exercise. Whereas it is a finite fatigue dimensioning, on the wohler diagram I considered the correct fatigue limit from the various coefficients for the geometry in question, in particular I hypothesized b2 of 0.85 (since I could not calculate an equivalent diameter).
on wohler I hypothesized the knee of the curve to (10^6; sigmalf').
I then built the haigh diagram and from the ratio between the vertical segments I drew the report for the safety coefficient (considering a condition in which the average sigma does not vary) according to the unknown a.
I wanted to ask if that reasoning was correct, because I should still assume a safety coefficient.
Thank you in advance.

 

[meccanicamg]

diagram construction is indicated in my post qui.
on a practical level I would not attempt to make the reverse formula even if graphically it is as you say. I would turn the excel as long as it suits me.
you will have as tension of von mises without cutting the composition of bending and cutting at the distance of 40mm.... and already here remains in function of "a".
then determine the alternating voltage and use it on the wöhler diagram.
varying "a" read the cycles you do.

 

[PDS]

Good evening, I have tried this approach since my professor is not so much in agreement to use iterative processes .
I thank you anyway for the comment and for the notes attached.