Problem $2(30\%)$

Calculate the factored moment capacity for the three beams shown in the figure below using the equivalent

rectangular stress block. The concrete compressive strength is $f_c^{\text{'}}=5,000$ and the yield strength of the

reinforcement $f_y=60$ksi. The area of each #$9$ reinforcing bar is $1\mathrm{.}0i{n}^2.$ From your results, comment on the

effect of adding compression reinforcement to the moment capacity and the ductility, and whether adding

compression reinforcement can be a cost$-$effective way of increasing the flexural strength of a beam.

$($b$)$

$($c$)$