A solid round bar, $30$ mm in diameter, has a groove $\backslash (3-\backslash$mathrm$\{$mm$\}\backslash )$ deep with a $\backslash (5-\backslash$mathrm$\{$mm$\}\backslash )$ radius machined into it$.$ The bar is made of AISI $1018$ CD steel and is subjected to constant combined loading $-500$ N $($in tension$),\backslash (100\backslash$mathrm$\{$~N$\}-\backslash$mathrm$\{$m$\}\backslash )($in bending$),$ and $\backslash (150\backslash$mathrm$\{$~N$\}-\backslash$mathrm$\{$m$\}\backslash )($in torsion$).$

a$)$ Determine the theoretical stress$-$concentration factors for different kinds of loading using appropriate charts. Explain how you have determined these factors, showing all the calculations.

b$)$ Calculate nominal stresses for different loading.

c$)$ Calculate maximum stresses due to stress concentration factor.

d$)$ What will be the change in the maximum stress due to tension if the groove parameters are changed to $\backslash (2-\backslash$mathrm$\{$mm$\}\backslash )$ deep with $\backslash (2-\backslash$mathrm$\{$mm$\}\backslash )$ radius? Compare the result with the previous case and comment.