A rectangular pretensioned concrete beam is to be designed to carry superimposed dead and live load of $4\mathrm{.}38k\frac{N}{m}$ and $14\mathrm{.}59k\frac{N}{m}$ respectively on a $12m$ simple s$?$an$.$ Straight tendons will be used. Time$-$dependent losses will be approximately $16\%$ of the initial stress in the steel. Use ACI and NSCP provisions for allowable stresses. Concrete sirength used will be $fc=34\mathrm{.}5$MPa,$0\mathrm{.}82ff=1,153\mathrm{.}54$MPa,fci$=27\mathrm{.}6$MPa and $Ao=31\mathrm{.}67m{m}^2$

a$.$ Determine the required seclion moduli at the top and bottom fibers of the beam.

b$.$ Deterinine the concrete dimensions $($use $h=2\mathrm{.}5b,$ symmetrical rectangular section$)$ based on the max section modulus.

c$.$ Calculate the required initial prestress force.

d$.$ What is the required constant eccentricity?

e$.$ Calculate the number of tendons using a $6\mathrm{.}35mm$ diameter wire.

f$.$ Check the stresses at top & bottom for $+$ Self$-$wt$.$

g$.$ Check the stresses at top & bottom for Pefi $+$ Full Service Load.

The $1-$Beam shown is to carry a superimposeci cead toac of $5\mathrm{.}03k\frac{N}{m}$ and service live load of $17\mathrm{.}8k\frac{N}{m}$ in addition to its own weight of $3\mathrm{.}72k\frac{N}{m}.$ It is to be built of concrete with $f{c}^{\text{'}}=35$MPa and is prestrossed using tendons with $f_{PU}=1,860$MPa to an effective force $Pe=1,231kN.$ Find the required spacing of vertical $U_{-}$stirrups at a point $3\mathrm{.}0mts$ from the left support, if fy for the stirrup steel is $275\mathrm{.}6$MPa. Take $I_0=10\mathrm{.}1{10}^{9}m{m}^4.A_c=158{10}^{3}m{m}^2$ and $r^2=64{10}^{3}m{m}^2)$