(Solution) - For a bolted assembly the stiffness of each bolt is -(2025 Original AI-Free Solution)

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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 1/2 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.