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

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

$(1)(40\%)$ 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

$$ cif $=4,000$ psi

$$ cf $=8,000$ psi

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

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

$$ f pi $($stress after transfer$)=189$ ksi

$$ f pe $($stress after allowance for all prestress losses$)=170$ ksi; l tr $=($f pe $/3)$db

Section Properties

$$ Ac $=369$ in$\mathrm{.}2$

$$ I g $=50,979$ in$\mathrm{.}4$

$$ y b $=15\mathrm{.}83$ in$.$

$$ y t $=20\mathrm{.}17$ in$.$

$$ Sb $=3,220$ in$\mathrm{.}3$

$$ St $=2,527$ in$\mathrm{.}3$

$$ Class T member

$(2)(10\%)$ Give five other solutions if the concrete stresses exceed the allowable stresses $($no

calculation is needed