Example $($This is a big one....$)$

The figure illustrates the non$-$permanent connection of a steel cylinder head to a grade $30$ cast$-$iron pressure vessel using $N$ bolts. A confined gasket seal has an effective sealing diameter $D.$ The cylinder stores gas at a maximum pressure $pg.$ For the specifications given in the table, select a suitable bolt length assuming bolts are available in increments of $5$ mm $($or refer to Table A$\mathrm{.}17),$ then determine the yielding factor of safety $n_p,$ the load factor $n_L,$ the joint separation factor $n_0,$ and the fatigue factor of safety $n_f.$

$\backslash$table$[[A,20$ mm$],[B,20$ mm$],[C,100$ mm$],[D,150$ mm$],[E,200$ mm$],[F,300$ mm$],[N,10],[p_g,6$ MPa$],[$Bolt grade,$1509\mathrm{.}8],[$Bolt spec.,$M121\mathrm{.}75$