$002(50$ points$)$:

Determine the total immediate DL $+$ LL deflection and the long$-$term deflection $($DL $+$ sustained

LL$)$ for the non$-$prestressed reinforced concrete beam having a cross section shown in Figure

below and subjected to maximum moments of $Mpt=20ft-$ kips and ML$.=15ft.-$kips. Assume a

$50\%$ sustained live load and a sustained load time period of more than $5$ years. Assume normal$-$

weight concrete. Use $fc=3000$ psi and fy $-60,000$ psi. The beam is on a simple span of $30$ ft $.$