Problem #$2$: $($need to show all calculations in detail$).$

$(50\%)$

For the beam and loading shown:

Draw the shear and bending$-$moment diagrams $($need to show all calculations in detail$).$

Determine the maximum absolute value $($a$)$ of the shear and $($b$)$ of the bending moment.

Determine the minimum required width $b,$ knowing that cross section depth $h=150mm,$ and knowing that for the grade of timber used, ${}_{\text{a}\text{l}\text{l}}=11\mathrm{.}80$MPa and ${}_{\text{a}\text{l}\text{l}}=800$kPa.