Final answer:
To determine the deepest beam for a specified load and material strengths, one must perform flexural design calculations, following the guidelines from the ACI Code while considering the moment of inertia and flexural strength. The depth and reinforcement design are influenced by moment capacity, shear resistance, deflection limits, and ACI minimum and maximum reinforcement criteria.
Step-by-step explanation:
To calculate the deepest beam that can be achieved for a 12in wide beam supporting a uniformly distributed live load of 2K/FT and a service dead load of 3.5K/FT, we need to consider the flexural design according to the ACI (American Concrete Institute) Code. The concrete strength (F'c) is given as 3 Ksi and the yield strength of steel (Fy) is 60 Ksi.
As the question asks for the deepest beam possible, we consider the section's moment capacity and its compatibility with the material strengths provided. The moment caused by the loads must be resisted by the moment capacity of the section. The beam's depth will influence moment of inertia and thus the flexural strength. Proper design includes calculating the required area of steel reinforcement, ensuring the beam does not fail in shear, meeting deflection criteria, and satisfying maximum and minimum reinforcement requirements set by the ACI Code.
However, without specific formulas and calculations, it's impossible to determine the precise depth. Typically, a structural engineer would use the moment and shear calculations along with ACI Code requirements to design the beam's dimensions and required reinforcement, which includes the number, size, type, and placement of the reinforcement bars as well as possible stirrups for shear reinforcement.
A sketch must detail all required reinforcement, including the main longitudinal rebars placed at the tension side (bottom) of the beam and the stirrups, which are usually U-shaped rebars or closed loops to provide shear resistance.