For a bolted assembly, the stiffness of each bolt is kb = 4 Mlbf/in and the stiffness of the members is km = 12 Mlbf/in per bolt. The joint is subject to occasional disassembly for maintenance and should be preloaded accordingly. A fluctuating external load is applied to the entire joint with Pmax = 80 kips and Pmin = 20 kips. Assume the load is equally distributed to all the bolts. It has been determined to use / in-13 UNC grade 8 bolts with rolled threads. (a) Determine the minimum number of bolts necessary to avoid yielding of the bolts. (b) Determine the minimum number of bolts necessary to avoid joint separation. (c) Find the Goodman and Gerber safety factor.