Problem $2.$

Construct the shear$-$force and bending$-$moment diagrams for the beam shown. You can use the graphical $($integration$)$ method to solve for internal $\backslash ($ V$($x$)\backslash )$ and $\backslash ($ M$(\backslash$mathrm$\{$x$\})\backslash )($Hibbeler Ch $6\mathrm{.}2).$ Label all significant points on each diagram and identify the maximum moments along with their respective locations. The shape and dimensions of the beam cross$-$section are shown. Additionally:

$($a$)$ Determine $\backslash ($ V $\backslash )$ and $\backslash ($ M $\backslash )$ in the beam at a point located $\backslash (\backslash$mathbf$\{1.50\}\backslash$mathbf$\{$m$\}\backslash )$ to the right of $\backslash (\backslash$boldsymbol$\{$B$\}\backslash ).$

$($b$)$ Determine $\backslash ($ V $\backslash )$ and $\backslash ($ M $\backslash )$ in the beam at a point located $\backslash (\backslash$mathbf$\{1.25\}\backslash$mathbf$\{$m$\}\backslash )$ to the left of $\backslash (\backslash$boldsymbol$\{$D$\}\backslash ).$

$($c$)$ What is the magnitude and sign $($tension or compression$)$ of the maximum bending stress $\backslash (\backslash$left$(\backslash$sigma$\_\{\backslash$mathrm$\{$x$\}\}\backslash$right$)\backslash ),$ and is this maximum stress located on the top or bottom of the beam?