A bolt is subjected to a direct axial tensile load of $20$kN and a shear load of $15$kN$.$ Material of the bolt is ductile and has a yield strength of $300$ MPa and Poisson$$s of $0\mathrm{.}25.$ Compute the root diameter of the bolt according to all the theories of failure and suggest a suitable size of the bolt. Take the factor of safety as $3.$