A simply$-$supported beam with a rectangular cross section as shown in Fig $1$ spans $10m$ and carries a live load of $30k\frac{N}{m}.$ The beam is post$-$tensioned with a single cable, which consists of ten $7-$wire ordinary strands. The tendon profile is parabolic, with no eccentricity at both ends and a maximum eccentricity $e$ of $300mm$ at the mid$-$span. All strands are stressed to $70\%$ of their characteristic breaking loads.

Determine the allowable initial prestress force to satisfy the adequacy of section at mid$-$span at transfer according to Cl$8\mathrm{.}1\mathrm{.}6\mathrm{.}2$ of AS$3600.$ Considering the assumed immediate losses, is the applied jacking force suitable for design at transfer?

What is the additional uniformly distributed load required to achieve decompression at the critical section under service loads?

If the beam is subjected to a live load of $30k\frac{N}{m},$ in addition to the self$-$weight, check whether the beam is fully prestressed under service loads.

Calculate the equivalent distributed load due to prestress.

Given the following material properties:

Concrete

Characteristic compressive strength $f_c^{\text{'}}=50$MPa

Strength at transfer $f_{cp}^{\text{'}}=30$MPa

Density of concrete $($with steel$)=25k\frac{N}{m^3}$

Strands

Characteristic breaking load of a $7-$wire ordinary strand $=184kN$

Nominal steel area of a $7-$wire ordinary strand $=100m{m}^2$

Loss of prestress

Assume immediate losses to be $15\%,$ and the deferred losses after initial prestress to be at $10\%,$ at mid$-$span.

$($See Fig $1$ on the next page$)$

Parabolic cable profile