Problem $2$

The timber beam $AB$ of span $10ft$ and width $3\mathrm{.}5in.$ is to support the three concentrated loads shown. For the grade of timber used, ${}_{\text{a}\text{l}\text{l}}=1800$ and ${}_{\text{a}\text{l}\text{l}}=120$ psi. Determine the minimum required depth $d$ of the beam.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{M}_4=0$