Problem $1$:

A $300$mmx $500$ mm reinforced concrete cross$-$section is used on a cantilever beam. It is subjected to factored uniform load $w_u$ along its entire length. It is reinforced at the top with two layers of steel $(3$ No$.25$ per layer$).$ Determine the maximum value of $w_u$ that can be safely placed on the beam according to the ACI $318$ code based on flexure. The material properties are: $f_c^{\text{'}}=42$MPa $($normal weight$)$ and $f_y=460$MPa.