Given a reinforced concrete beam made with 3000psi concrete and grade 40 steel. The effective width is 12 inches, the beam depth is 24 inches and the reinforcement is 4#7 bars centered 2-1/2 inches from the bottom of the beam. The beam carries its own weight and a single live concentrated load of 28k at the center of a 20 foot simply supported span.
a) Determine the steel ratio.
b) Prove the beam is over or under reinforced based on the
limiting ? for a tension controlled beam.
c) Determine the location of the neutral axis at failure
(yielding).
d) Find the ultimate moment capacity according to ACI 318.
e) Determine the design moment (the factored moment caused by the beam loading).
f) Based on your solution to (d) and (e) prove whether or not this beam expected to fail?