A torsion bar $($Structural ASTM A $36)$ with yield strenghth of $250$ MPa is loaded as shown. The stress concentration factors are $1\mathrm{.}6$ for bending and $1\mathrm{.}25$ for torsion. Determine the diameter d to resist loads P $=20$ kN and T $=1\mathrm{.}0$ kN$/$m$.$

Using a safety factor n $=2\mathrm{.}5.$ Apply

a$)$ maximum principal stress theory

b$)$ the coloumb$-$Mohr theory