Problem $2(20$ Marks$)$

The steel rotating$-$beam test specimen below has an ultimate strength of $S_{ut}=230k$ and a yield strength of $S_{yt}=135k.$

a$)$ Estimate the fatigue strength corresponding to a life of $150$k cycles of stress reversal.

b$)$ If it is desired to test low$-$cycle fatigue at approximately $500$ cycles. Check if this is possible without yielding by determining the necessary reversed stress amplitude.