Question $3(10$ points$)$

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A reinforced concrete beam must resist a dead load moment of $80ft.-$kips and a live load moment of $115ft.$ kips, with the following

$f_c^{\text{'}}=3,000,f_y=60,000,b={12}^{\text{'}\text{'}},d={32}^{\text{'}\text{'}}$

$M_{DL}=80ft-$ kips $M_{LL}=115ft-$kips

Select the reinforcing steel assuming a total of $4$ lengths of rebar is used at the bottom of the beam $(4$ bars at the bottom$-$ Hint$-$ Divide total area of steel by $4$ to get the are of each bar and then pick the bar from the chart$)$

$\backslash$table$[[$ASTM STANDARD REINFORCING BARS$],[$Bar size,$\backslash$table$[[$Nominal$],[$diameter$.],[$in$.]],\backslash$table$[[$Nominal$],[$area$,],[$sq in$.]],\backslash$table$[[$Nominal$],[$weight$],[$ib per ft$]]],[\backslash$table$[[33],[4],[5],[6],[7],[8],[9],[10],[11],[14],[18]],\backslash$table$[[0\mathrm{.}375],[0\mathrm{.}500],[0\mathrm{.}625],[0\mathrm{.}750],[0\mathrm{.}875],[1\mathrm{.}000],[1\mathrm{.}128],[1\mathrm{.}270],[1\mathrm{.}410],[1\mathrm{.}693],[2\mathrm{.}257]],\backslash$table$[[0\mathrm{.}11],[0\mathrm{.}20],[0\mathrm{.}31],[0\mathrm{.}44],[0\mathrm{.}60],[0\mathrm{.}79],[1\mathrm{.}00],[1\mathrm{.}27],[1\mathrm{.}56],[2\mathrm{.}25],[4\mathrm{.}00]],\backslash$table$[[0\mathrm{.}376],[0\mathrm{.}668],[1\mathrm{.}043],[1\mathrm{.}502],[2\mathrm{.}044],[2\mathrm{.}670],[3\mathrm{.}400],[4\mathrm{.}303],[5\mathrm{.}313],[7\mathrm{.}650],[13\mathrm{.}600]]]]$

$4x$#$8$

$4x$#$12$

$4x$#$14$

$4x$#$10$