Homework $8$: SFD&BMD and beam design

$1)$For the beam as shown, draw SFD and BMD of the beam. Also, determine $|V_{\text{m}\text{a}\text{x}}|$ and $|M_{\text{m}\text{a}\text{x}}|$

and their locations.

$2)$For the beam and loading as shown, design an economical wide$-$flange shape if the beam

is made of a material with ${}_{av}$ and ${}_{\text{a}\text{f}\text{f}}180$MPa and $100$MPa, respectively.