Design a socket and spigot cotter joint to connect two steel rods of equal diameter shown in Fig$\mathrm{.}1.$ Each rod is subjected to an axial tensile force of $40$ kN $.$ Select the material as plain carbon steel of grade $30$C$8$ for all the parts of cotter joint having yield strength in tension as $400\frac{N}{m}{m}^2.$ Assume that the yield strength in compression is twice the yield strength in tension. The factor of safety for rods, spigot end and socket end is assumed as $6$ and for cotter factor of safety is taken as $4.$ Design all the parts and draw a neat sketch of an assembly drawing.

Fig$\mathrm{.}1.$ Socket and Spigot Cotter Joint