QUESTION $3$

$[12]$

$3\mathrm{.}1.$ An architect on a reinforced concrete building project requires a beam with a maximum depth of $450mm$ for aesthetic reasons. The span between the two supporting columns supporting the beam is $12m.$ The project's consulting engineer advises that the beam's shear and bending stresses must not exceed $1\mathrm{.}264$MPa and $33\mathrm{.}98$MPa, respectively. Utilizing the full $450mm$ depth is recommended.

The beam will be subjected to a uniformly distributed load of $12k\frac{N}{m}$ across its entire span and a point load of $20kN$ located $4m$ from one of the columns. As the junior engineer, you are tasked to size a beam that meets these requirements.