Problem:

$12$

$($of $14)$

Do not round intermediate answers. Give your final answer$($s$)$ to three decimal places. Check your units.

Note: This problem is optional and not graded. It is not part of the homework set and does not carry any points.

Draw the shear and bending$-$moment diagrams for the beam and loading shown, and determine the maximum value $($including the sign$)$:

$($a$)$ of the shear, and

$($b$)$ of the bending moment.

$\backslash [$

$\backslash$begin$\{$aligned$\}$

$\backslash$mathbf$\{$V$\}(\backslash$max $)=$ & $\backslash$mathrm$\{$kN$\}\backslash \backslash$

$\backslash$mathbf$\{$M$\}(\backslash$max $)=$ & $\backslash$mathrm$\{$kN$\}-\backslash$mathrm$\{$m$\}$

$\backslash$end$\{$aligned$\}$

$\backslash ]$