A timber beam of nominal width $4$ in$.($actual width $=5\mathrm{.}25in.)$ is to support the three concentrated loads shown. Knowing that for the grade of timber used, ${}_{\text{a}\text{l}\text{l}}=2250$ and $,$ determine the minimum required depth $d$ of the beam.

Solution Strategy:

Develop shear and bending moment diagrams. Identify the maximums.

Determine the beam depth based on allowable normal $($bending$)$ stress.

Determine the beam depth based on allowable shear stress.

Required beam depth is equal to the larger of the two depths found.

Modelling:

Develop shear and bending moment diagrams. Identify:

$V_{\text{m}\text{a}\text{x}}$ and $M_{\text{m}\text{a}\text{x}}$