Please use tables or equations from Shigley's Mechanical Engineering Design book

For a bolted assembly with eight bolts, the stiffness of each bolt is $k_b=1\mathrm{.}0M\frac{N}{m}m$ and the

stiffness of the members is $k_m=2\mathrm{.}6M\frac{N}{m}m$ per bolt. The bolts are preloaded to $75$ percent of

proof strength. Assume the external load is equally distributed to all the bolts. The bolts are

M$61$ class $5\mathrm{.}8$ with rolled threads. A fluctuating external load is applied to the entire joint

with $P_{\text{m}\text{a}\text{x}}=60kN$ and $P_{\text{m}\text{i}\text{n}}=20kN.$

$($a$)$ Determine the yielding factor of safety.

$($b$)$ Determine the overload factor of safety.

$($c$)$ Determine the factor of safety based on joint separation.

$($d$)$ Determine the fatigue factor of safety using the Goodman criterion.

$($e$)$ Is the assembly design satisfactory? If not, what do you suggest?