Question $1$

$($a$)$ The cold$-$drawn AISI $1040$ steel bar shown in the Figure Q$1$ is subjected to a completely reversed axial load fluctuating between $28$ kN in compression to $28$ kN in tension. Estimate the fatigue factor of safety based on achieving infinite life and the yielding factor of safety. If infinite life is not predicted, estimate the number of cycles to failure:

$[40$ marks$]$

$($b$)$ If the above steel bar shown in Figure Q$1$ is subjected to load that fluctuates from $12$ kN to $28$ kN $,$ find the factor of safety using the Goodman, Gerber, and Morrow criteria and compare their predictions. Also, check for yielding factor of safety.