Problem $1.[35$ pts$.]$ The $10$ ft $.$ long cantilevered singly reinforced concrete beam with the shown cross$-$section carries the shown service loads $($i$.$e$.,$ un$-$factored superimposed dead load of $1ki\frac{p}{f}t$ in and un$-$factored concentrated live load of $12$ kips $,$ as shown$).$ Using normal$-$weight concrete with unit weight of $150pcf,f^{\text{'}}=4,000$ and Grade $60$ reinforcing steel:

$($a$)$ Compute the design moment capacity $(M_n)$ of the beam assuming that $6$ No$.8$ bars located at the top of the beam are in tension $($at the top of the section are in tension $($also must check the given reinforcing steel for ductile behavior$)$

$($b$)$ Determine the combined factored beam moment at its support $(M_u=1\mathrm{.}2MD+1\mathrm{.}6ML)$ and show

$6$ No$.8$ bars

cross$-$section