$3\mathrm{.}7$ The I$-$beam shown in Fig. P$3\mathrm{.}7$ is to be used in a roof support system spanning $45$ ff

between simple supports. It will carry a superimposed dead load of $400l\frac{b}{f}t$ and

service live load of $425l\frac{b}{f}t$ in addition to its own weight. The member will be

post$-$tensioned with a force $P_i=190$kips. At midspan the eccentricity is $11\mathrm{.}5in.$

Time$-$dependent losses of $20$ percent will be assumed. Normal weight concrete is

specified with $f_c^{\text{'}}=5,000,$ and at time of stressing, $f_{ci}^{\text{'}}=3,750.($a$)$ Find

concrete flexural stresses at midspan at the time of initial tensioning and compare

with ACI limits$.($b$)$ Find concrete stresses at full service load and compare with ACI

FIGURE P$3.7$