$[2]$ As shown in the figure, there is a cylindrical pressure vessel with an inner diameter of $400$ mm in which a certain internal pressure of $980$ kPa acts. Twelve bolts are to be fastened at equal intervals on the circumference to fix the container cover.

Initial tightening force of bolt $20,525$ N$,$ stiffness of bolt is plate Determine the minimum diameter of the bolt as a safety factor of $2\mathrm{.}5$ when the tensile stress of the bolt is $47$ MPa $,$ which is twice the stiffness. $(25$ points$)$