Question $4$ Serviceability $(20$ points$)$

The cantilever reinforced concrete beam shown below is subjected to a uniform dead load $($including beam weight$)$ and a concentrated live load at the free end of the beam. $n=8.f_c^{\text{'}}=5000$ psi, and $f_y=60,000$ psi.

$($a$)$ Determine the $I_g$ and $M_{cr}.(5$ pts$)$

$($b$)$ Calculate the $I_{cr}$ and $M_a.(5$ pts$)$

$($c$)$ Compute the $I_e.(5$ pts$)$

$($d$)$ Calculate the instantaneous deflection due to dead and live load. $(5$ pt$.)$

Normal Weight Concrete

$f_c=5000$