A rectangular concrete beam with dimensions b $=12$ inches and d $=27$ inches and h $=30$

inches is reinforced with three No$.9$ bars. Material strengths are fy $=60000$ psi and

f$$c $=5000$ psi. $(20$ points$)$

a$)$ Find the moment that will produce the first cracking at the bottom surface of the beam,

using the gross moment of inertia of the concrete.

b$)$ Find the nominal flexural strength, Mn$,$ of the beam