Problem $2$: The beam shown has No$.3$ stirrups at $12$ in$.$ and is reinforced for flexure with $4-$No$.9$ longitudinal bars. The geometry of the beam cross$-$section is shown below. The loads given are in addition to the beam weight. Use $f_c^{\text{'}}=5000,f_y=60,000,w_D=1\mathrm{.}5\frac{k}{f}t,$ and $w_L=2\mathrm{.}0\frac{k}{f}t.$ Check both flexure and shear strengths. Determine

a$)$ The design flexural strength of the beam

b$)$ The design shear strength of the beam

c$)$ The maximum concentrated service live load that can be applied at the tip of the beam.