$0/1$ point

A simply supported beam with an overhang on each side is loaded as shown below. The center span of the beam has a length of $L=6m$ and each overhang has length that is $a=50\%$ of the center span length. The beam is made of wood for which the allowable normal stress is ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=8$MPa. Knowing that $w=7k\frac{N}{m}$ and that the beam has width of $b=100mm,$ determine required height of the beam, $h.$ Enter the required height of the beam below. Express your answer in mm to the next highest whole mm $.$

In addition to the required height, your written solution must include calculation of the beam reactions and the shear and moment diagrams for the beam.