Problem #$2$

a$)$ Using only statics and resultant forces to represent flexural stresses, what load P results in a maximum flexural stress of $500$ psi in the beam shown below? The beam cross section dimensions are $b=12in.$ and $h=24in.$ At this level of stress, the material is effectively elastic. Include the self$-$weight of the beam in your calculation. Assume a density of $150l\frac{b}{f}{t}^3$ for reinforced concrete.

b$)$ Check your answer using $f_c=\frac{My}{\text{I}}$