Problem $2$

$(15$ marks$)$

The figure shows the free$-$body diagram of a connecting$-$link portion having stress concentration at two sections i$.$e$.$ at fillet and at groove. The dimensions are $r_f=2\mathrm{.}25mm,d_f=30mm,r_g=2mm,d_g=39mm,$ and $D=45mm.$ The force $F$ fluctuates between a tension of $18$ kN and a compression of $72$ kN $.$

$($a$)$ Neglect column action and find the factor of safety guarding against fatigue at the groove if the material is cold$-$drawn AISI $1018$ steel.

$($b$)$ Estimate the fatigue safety factor at the groove if the operating temperature is $450C.$