PROBLEM $1$

$i_{5^k}^k$

$f^{\text{'}}c=5,000$

$f_y=60,000$

$b=18in.(width)$

$h=24in.(total$ depth$)$

$d=21\mathrm{.}5in.(effective$ depth$)$

$A_s=(6)$#$10$ bars $in$ a single layer

For the beam shown, answer the following:

$($a$)$ Using the appropriate load combinations provided in ACI$318-19,$ draw the factored shear $(V_u)$ and bending moment diagram $(M_u)$ for the DL and LL shown. Ignore beam selfweight.

$($b$)$ Provide a sketch of the beam cross section at support reaction $"B"$ showing the reinforcing and the corresponding distance from the extreme compression fiber to the centroid of the reinforcement $($note that this sketch does not have to be drawn to scale$).$

$($c$)$ If $=0\mathrm{.}9,$ calculate the design flexural strength. Is the beam adequate for the loading shown?