A beam with the following geometry and cross$-$section is constructed with concrete of

compressive strength of $3000$psi, $3$ No$.6$ bars at the bottom face, and $3$ No$.6$ bars at the top face

of the beam. The beam supports a total dead load $($including self$-$weight$)$ of $725$ plf$,{}_{L1}$ of $600$ plf$,$

and ${}_{L2}$ of $1040$ plf$.$ Note that ${}_{L1}$ and ${}_{L2}$ are live loads which may or may not be active at any

given time. Consider all possible loading scenarios and

a$.$ determine the unfactored shear force and bending moment envelope diagrams.

b$.$ determine the maximum tensile and compressive stresses in the steel and concrete at the points

of maximum and minimum negative moments.

c$.$ determine if the beam will crack. If the beam cracks, sketch where in the beam the crack$($s$)$ will

form.