A pretensioned beam with an I$-$section has a span of $12\mathrm{.}20$ m as shown below. The initial prestressing force exerted on the beam $($Pi$)$ is $766$ kN$.$ The beam is subjected to a dead load and live load intensity summing up to $8,180$ N$/$m except the self$-$weight. Find the concrete stresses at the top and bottom fibers at the mid$-$span for each loading stage, i$.$e$.,(1)$ at initial prestressing, $(2)$ at transfer $($addition of self$-$weight$),$ and $(3)$ at final service stage. Assume that the time$-$dependent losses of prestress due to creep, shrinkage, and relaxation are $15\%($Pe $=0\mathrm{.}85$ Pi$).$ PLEASE SHOW ALL YOUR WORK TO OBTAIN FULL CREDIT. start by finding IC$($total$).$ A pretensioned beam with an I$-$section has a span of $12\mathrm{.}20$ m as shown below. The initial prestressing force exerted on the beam $\backslash (\backslash$left$($P$\_\{$i$\}\backslash$right$)\backslash )$ is $766$ kN $.$ The beam is subjected to a dead load and live load intensity summing up to $\backslash (8,180\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash )$ except the self$-$weight.

Find the concrete stresses at the top and bottom fibers at the mid$-$span for each loading stage, i$.$e$.,(1)$ at initial prestressing, $(2)$ at transfer $($addition of self$-$weight$),$ and $(3)$ at final service stage. Assume that the time$-$dependent losses of prestress due to creep, shrinkage, and relaxation are $\backslash (15\backslash \%\backslash$left$($P$\_\{$e$\}=0\mathrm{.}85$ P$\_\{$i$\}\backslash$right$)\backslash ).$

PLEASE SHOW ALL YOUR WORK TO OBTAIN FULL CREDIT.