Problem $2.$ Assume $f_c^{\text{'}}=4,000$ psis $f_y=60,000$ psi. A uniform factored lond of $w_{id}=5\frac{k}{f}t$ is applied. The cross section is $1424,$ with a side, lop and bottom covers of $2\mathrm{.}5$ in $.$ All reinforcement bers are uncoated. Stirrups are $13.$

$($a$)$ Using the long equation, determine the development length of the $49$ bars used for positive moment resistance. Assume $s=10in,A_{\text{r}\text{e}\text{q}}=2\mathrm{.}23i{n}^2.$

$($b$)$ Determine the theoretical cutoff points of the $2$ #$9$ bars, measured from the left support and the actual cutoff points as allowed by ACI. Show a sketch of the #$9$ bottom steel bars, with dimensions end$-$toend measured from the supports.

$($c$)$ Draw the envelope of available positive moment and the required moment, using the maximum cutoff.