Design a simply supported rectangular concrete beam $($door lintel$)$ with a span

of $5$ feet. The beam has no steel reinforcement and should resist its own weight

and the weight of a brick wall above it without cracking. The brick wall has a

height of $3$ feet and a width of $6$ inches. Consider the following properties:

Unit weight of concrete: $150I\frac{b}{f}{t}^3$

Compressive strength of concrete $(f_0^{\text{'}})$: $4200$ psi

Unit weight of bricks: $115I\frac{b}{f}{t}^3$