A $25m$ long concrete $($concrete unit weight: $25k\frac{N}{m^3})$ bridge girder with the cross section shown below is prestressed with twenty four $0\mathrm{.}6$ inch diameter $(d$:$15mm,$ area: $140m{m}^2)$ sevenwire straight tendons. The beam is used in a bridge construction project at the age of $30$ days $($Self weight is the only load acting on the beam for $30$ days$).$ Starting from $30$ days, additional superimposed sustained load of $10k\frac{N}{m}$ acts on the girder in addition to the self weight for $5$ years. When the bridge is in service, the traffic loading on the girder can be assumed to be $15k\frac{N}{m}($Note that this is not a sustained load$).$

Calculate all the prestress losses at the midspan at

a$)$ Initial transfer

b$)30$ days

c$)5$ years

Using TS$3233$ provisions for losses. Assume high relative humidity for shrinkage calculations. Assume the following material properties:

$f_{pk}=1860$MPa $($ultimate tensile strength of $7-$wire strands$)$

$f_{pj}=0\mathrm{.}75f_{pk}($The tendons are initially stressed to $0\mathrm{.}75f_{pk})$

$f_{ck}=50$MPa

$f_{cjk}=40$MPa