$6\mathrm{.}5.$ A reinforced concrete beam is continuous over two equal $22ft$ spans, simply supported at the two exterior supports, and fully continuous at the interior support. Concrete cross$-$sectional dimensions are $b=10in.,h=22in.,$ and $d=19\mathrm{.}5$ in$.$ for both positive and negative bending regions. Positive reinforcement in each span consists of two No$.9($No$.29)$ bars, and negative reinforcement at the interior support is made up of three No$.10($No$.32)$ bars. No compression steel is used. Material strengths are $f_y=60,000$ psi and $f_c^{\text{'}}=5000.$ The beam will carry a service live load, applied early in the life of the member, of $1800l\frac{b}{f}t$ distributed uniformly over both spans; $20$ percent of this load will be sustained more or less permanently, while the rest is intermittent. The total service dead load is $1000l\frac{b}{f}t$ including selfweight.

$($a$)$ Find the immediate deflection when shores are removed and the full dead load is applied.

$($b$)$ Find the long$-$term deflection under sustained load.

$($c$)$ Find the increment of deflection when the short$-$term part of the live load is applied.

Compare with ACI Code deflection limits; piping and brittle conduits are carried that would be damaged by large deflections. Note that midspan deflection may be used as a close approximation of maximum deflection.