Example

For a bolted assembly with six bolts, $$e stiffess of each bolt is $k_b=0\mathrm{.}52M\frac{N}{m}m$ and the stiffness of the members is $k_m=2\mathrm{.}10M\frac{N}{m}m$ per bolt. An external load of $356$ kN is applied to the entire joint. Assume the load is equally distributed to all the bolts. It has been determined to wse $12\mathrm{.}7$ mand $13$ UNC grade $ bolis with rolled threads. Assume the bolts are preloaded to $75$ percent of the proof load.

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

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

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