II$.[$total: $25\backslash \%]$ A steel step$-$shaft subjected to a concentrated load of $10$ kN is shown in Figure $1.$ Assume Young's modulus of steel is $200$ GPa $.$

$($a$)$ Determine the reaction force $\backslash ($ R$\_\{$A$\}\backslash )$ and $\backslash ($ R$\_\{$D$\}\backslash )$ acting at $\backslash ($ A $\backslash )$ and $\backslash ($ D $\backslash ).[2\backslash \%]$

$($b$)$ Plot the shear$-$force $\backslash ($ V$($x$)\backslash )$ and bending$-$moment $\backslash ($ M$($x$)\backslash )$ diagrams along the $\backslash ($ x $\backslash )-$axis. Please label the diagram properly and provide values at all key points. $[8\backslash \%]$

$($c$)$ Find the maximum shaft deflection. $[11\backslash \%]$

$($d$)$ Find the shaft deflection at B$.[2\backslash \%]$

$($e$)$ Find the angle $\backslash (\backslash$theta$\_\{$D$\}\backslash )$ at end $\backslash ($ D $\backslash ).[2\backslash \%]$

Hint: You can use the integration method, or the singularity functions in Reference $2.$