$(35\%)$ The architect wants to add a plaster ceiling to the roof of a building just completed. A section through the roof framing indicating a typical beam section is shown in Figure below. Design Loads: Assume the total proposed service dead loads $($including beam weight and plaster ceiling$)$ is equivalent to $800$ plf and the service live load is $170$ plf for each beam. Materials: Normal weight concrete $f^{\text{'}}c=3,000$ psi and steel fy $=60$ksi. Beams are simply supported with $50-$ft span. All dead loads are sustained loads for the expected $40-$year life of the building. Required: What would be your recommendations to the architect regarding the existing concrete beams in terms of their structural capacities and serviceability. Provide complete computations to support

Span Length $={50}^{\text{'}}$

$I_o=16,500in.$

$d=27in.$