The minimum diameter $\mathrm{d}$ can now be computed:

$$\begin{gathered} {\mathrm{d}}^3=\frac{16}{\mathrm{\pi }} \frac{\mathrm{T}}{\mathrm{\tau }} \\ =\frac{16}{\mathrm{\pi }} \frac{(424.413 \mathrm{N-m})(\mathrm{1,000} \mathrm{mm/m})}{75 \mathrm{N/mm}{}^2} \\ \therefore \mathrm{d}=30.660 \mathrm{mm}=\mathbf{30}\mathbf{.}\mathbf{7}\mathbf{ }\mathbf{mm} \end{gathered}$$

The diameter of the solid shaft must be at least $\mathrm{d}=30.7 \mathrm{mm}$. Typically, this value would be rounded up to the next larger standard size.