Kindly solve the problem below and produce what the problem requires:

$1.$ Design a rectangular post tensioned concrete beam to carry a uniform live load of $14\mathrm{.}60$ KN$/$m in addition to its own weight. The beam is simply supported over a $15$ m span. It is required that depth should not exceed twice the width. Using the Approximate Design Method, determine the dimensions at midspan and amount of prestressing steel needed. Allowable stresses for concrete and steel are $17\mathrm{.}23$ MPa and $1035$ MPa respectively.

$2.$ Design the beam in #$1$ using Balanced Design Method. Use the ff stresses:

Fct $=$ Fcw $=14$ MPa

Ftt $=$ Ftw $=-1\mathrm{.}00$ MPa

Fs $=1035$ MPa $($steel$)$

Use usymmetrical I section with $15\%$ losses.

$3.$ Redo problem #$2$ using Balanced Design Method. Use the ff stresses:

Fct $=19\mathrm{.}30$ MPa Fcw $=22\mathrm{.}10$ MPa

Ftt $=-1\mathrm{.}00$ MPa Ftw $=-1\mathrm{.}40$ MPa

Fs $=1035$ MPa $($steel$)$

Use unsymmetrical I section with $15\%$ losses.