For the RC beam section shown below, $f_c^{\text{'}}=3$ ksi, $f_y=60$ ksi. Use $29,000$ ksi as the modulus of elasticity for steel.

a$)$ Determine the cracking moment of the section.

b$)$ What is the nominal moment capacity of the beam?

c$)$ Calculate the maximum bending stresses of the top concrete fibers

and steel rebars at the nominal moment.

d$)$ Is the beam tension controlled? Explain.

e$)$ What is the ACI design moment capacity.

f$)$ Redesign the RC beam to hold a dead load bending moment of $25$

$ft-k$ and a live load bending moment of $15ft-k.$