The maximum shear stress in a solid round bar of diameter, $d,$ due to an applied torque, $T,$ is given by

${}_{\text{m}\text{a}\text{x}}=\frac{16T}{(d^3)}$

A round, cold$-$drawn $1018$ steel rod is subjected to a mean torsional load of $\frac{?}{\text{b}\text{a}\text{r}}(T)=1\mathrm{.}4kN*m$ with a standard deviation of $260N*m.$ The rod material has a mean shear yield strength of $\frac{?}{\text{b}\text{a}\text{r}}(S{)}_{sy}=312$MPa with a standard deviation is $40$MPa. Assuming the strength and load have normal distributions, what value of the design factor $\frac{?}{\text{b}\text{a}\text{r}}(n{)}_d$ corresponds to a reliability of $0\mathrm{.}99$ against yielding? Determine the corresponding diameter of the rod.

The design factor is

The diameter of the rod is mm$.$