In order to support a roof for a proposed reinforced concrete building, a beam design is needed that can withstand the design requirements. Further, the architect on the project is eccentric and is undecided on the final layout. You have been tasked to develop a singularly reinforced concrete beam, a doubly reinforced concrete beam and a T-beam section that will support the design requirements. The beams only need to be designed for bending (i.e. bending strength of the singularly reinforced beam, doubly reinforced beam, and the T-beam section) and have a maximum total height of 20 inches. The proposed roof section is 45 ft x 30 ft. The roof is designed to carry a 45 psf dead load and a 25 psf live load. Beams can run in either direction. Once your design is complete, the architect would like an estimate of the proposed material cost for the total design. For this cost analysis, concrete is to be taken as $110/yd3 and the steel as $1000/ton. Items to turn in include a 1-page summary (submitted as a memo) to be provided which has the total cost of the project and your recommendation for which beam design is the best. Provide justification for why you chose that beam. Further, a summary of your calculations is to be provided for each beam as well as detailed drawings showing cross sections of each design. The drawings and calculations should be professional such that they could be presented to a client (they can be hand-drawn or done in CAD). Drawings are to be scaled and provide details such as overall beam dimensions, rebar size, and rebar spacing within the beam. Since the beams support a roof inside the building, assume cover depth requirements for interior locations.