Problem $1.$ A post tensioned concrete T beam has a flange width of $508$ mm and is $76$ mm thick. The web is $127$ mm wide and $533$ mm deep below the flange. The prestressing cable $968$ sq mm is $101$ mm above bottom of web. Initial prestress is $1034$ MPa. The beam is $9\mathrm{.}1$ m long on a simple span and is to carry a load of $11\mathrm{.}67$ KN$/$m$.$ If prestressing losses amount to $15\%,$ check the stresses at transfer and at working. Draw stress diagrams.

Problem $2.$ If losses are neglected in the beam in Problem $1,$ what will be the resulting stresses at transfer and at working? Draw the stress diagrams.