$4$

$5$ points

Problem $2($Part $3-$ Factor of safety and life$)$

A circular shaft of diameter $D=1\frac{1}{8}$ in $(1\mathrm{.}125$ in$.)$ is made of AISI $1045$ CD$.$ It has a notch of radius $\frac{1}{16}$ in$.$ at the midway point. The shaft is subjected to a steady torque of

$1200$ lbf $-$in$.$ The forces on the shaft in the xy and xz planes are shown in the figure below. Design for a reliability of $99\%.$

$($i$)$ Find the factor of safety for single cycle failure

$($ii$)$ Find the factor of safety for infinite life

$($iii$)$ If infinite life factor of safety is less than $1,$ find the number of cycles to failure.

$($iv$)$ Indicate the following on an idealized S$-$N plot $(S_{ut},f{S}_{ut},{}_{ar}$ and $S_e)$

$($Scan and upload after completing part $3)($EXTRA CREDIT QUESTION AVAILABLE AFTER COMPLETING PART $3)$