A $90-$ft long simply supported post$-$tensioned concrete beam which has a constant I$-$shaped x$-$

section. See below for more details on the beam.

$$ The post$-$tensioning of the beam has a parabolic profile in the longitudinal direction to mirror

the dead load moment demand of the beam.

$$ The post$-$tensioning starts at the CG at each end of the beam and has a maximum eccentricity

at midspan, emidspan $=18.$

Question $1.(2$ points$)$

Calculate the gross x$-$sectional area, Ag and the gross moment of inertia, Ig for the beam x$-$

section above.

Question $2.(2$ points$)$

Calculate the self$-$weight of the concrete beam $($in KLF$)$ using the unit weight of concrete,

wconc $=0\mathrm{.}150$ KCF$.$ Calculate the moment demand due to self$-$weight only at midspan, Msw$.$