Problem $2$ Serviceability: Deflection using ACI method $(40$ Points$)$

$10ft$ cantilever beam shown in the figure $2.$ has external dead load including its own weight of $0\mathrm{.}5\frac{k}{f}t$ and live load of $0\mathrm{.}4\frac{k}{f}t.$

$F_c^{\text{'}}=4000,f_y=60,000,E_s=29000$ksi. Rectangular cross section has total width of $10",$ full depth of $18".$ Concrete cover is given as $2".3$#$9$ are used as a tension Rebars. if $35\%$ of L$.$L is continuously applied for $3$ years Determine:

Instantaneous or Short$-$term deflection due to Dead Load Only. $(15$ Points$)$

Short term defection due to Dead load $+$ Live Load Only. $(5$ Points$)$

Short term deflection due to L$.$L only. $(2$ Points$)$

Instantaneous deflection due to D$.$L$+$ Sustained Live Load. $(8$ Points$)$

Deflection for Sustained Live Load only. $(2$ Points$)$

Calculate the Long$-$term deflection $({}_{LT})(8$ Points$)$

Hint: Make sure you use cantilever beam deflection formula for short term deflection.

Figure $2.$ Cantilever beam