Problem # $1$

The simply supported prestressed beam shown in figure below is subjected to a liveload of $0\mathrm{.}9\frac{k}{f}t$ over a span length of $24ft.$

L$-$section of the Prestressed beam

X$-$section of the Prestressed beam

Considernormal weight concrete with $f_c^{\text{'}}=4500$ psi and an allowable $f_c^{\text{'}}=2050$ psi

$29$

Problem # $1$

Determine the maximum stresses at midspan section due to selfweight and following cases of prestressing:

$($a$)$ A uniform live load of $0\mathrm{.}9$kip$\frac{s}{f}t$

$($b$)$ A uniform live load of $0\mathrm{.}9$kip$\frac{s}{f}t$ and an axial centroidal longitudinal prestressing force of $P_e=259\mathrm{.}2$ kips

$($c$)$ A uniform live load of $2\mathrm{.}1$kip$\frac{s}{f}t$ and an eccentric longitudinal prestressing force of $P_e=259\mathrm{.}2$ kips acting at an eccentricity of $e=4$ in$.$

$30$