Solved: For a bolted assembly, the stiffness of each bolt

Chapter 8, Problem 8-32

(choose chapter or problem)

For a bolted assembly, the stiffness of each bolt is \(k_b=4 \mathrm{Mlbf} / \mathrm{in}\) and the stiffness of the members is \(k_m=12 \mathrm{Mlbf}\) /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 \(P_{\max }=80 \mathrm{kips}\) and \(P_{\min }=20 \mathrm{kips}\). Assume the load is equally distributed to all the bolts. It has been determined to use \(\frac{1}{2}\) 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.