Problem $1$

A bolted joint using $7$ bolts $($side view shown below$)$ has been operating successfully under a load of $36$ kip for several months. However, there was a water spill that resulted in the bolt to begin rusting. You need to replace

the bolts and nuts with new identical ones. Both the bolt and adjoining members have the same elastic modulus, and you know that the bolt stiffness is $k_b=5\mathrm{.}21Ml\frac{b}{i}n,$ while the nut width is $\frac{15}{16}$ in and its height$($thickness$)\frac{35}{64}in.$ The preload for reusable fasteners is typically $75\%$ of the proof load, but for this given applied load find theminimum preload that will prevent joint separation.

$A_t=0\mathrm{.}226i{n}^2,$ the bold major diameter is $\frac{5}{8}$ in$.$

If you have difficulties please start working out the problem and you will be able to solve for whatever constants you may be missing.

$\frac{5}{8}$ in$-11$ UNC $2\frac{1}{4}$ in grade $5$