A rectangular reinforced concrete beam has dimensions b = 12 in, d=12 in, and h=24, and is reinforce with three No. 10 bars Material strengths are fy=60,000 psi and fc=4000 psi. 

(a) Find the moment that will produce the first cracking at the bottom surface of the beam, basing your calculation on Ig, the moment of inertia of the gross concrete section. 

(b) Repeat the calculation using Iut, the moment of inertia of the uncracked transformed section.

 (c)Determine the maximum moment that can be carried without stressing the concrete beyond 0.45fc, or the steel beyond 0.40fy. 

(d) Find the nominal flexural strength and design strength of this beam.