A prestressed simply supported I$-$beam has a span of $50ft$ and is $36in.$ deep. Assume center

of support is at the beam end. Its cross section is shown in the accompanying figure.

Check all ACI $318$ allowable concrete stresses immediately after prestress transfer and

at the stage when all service loads are applied. Provide additional No$.5$ mild steel rebars if the

concrete stresses exceed the allowable stresses $($your design needs to be justified$).$ If the location

of the neutral axis is below the top $6$ inches, conservatively assume that the width of the beam

section is constant along the height $(12$ inches$).$

Dead load $=384$ plf

Superimposed dead load $=200$ plf

Live load $=2,000$ plf

$f_{ci}^{\text{'}}=4,000$

$f_c^{\text{'}}=8,000$

Twelve $(12)0\mathrm{.}5$ in$.$ diameter $270$ksi low$-$relaxation strands

$e=13\mathrm{.}12$ in$.($all strands straight$)$

stress after transfer