A 1200 mm deep by 750 mm wide post-tensioned simply supportedbeam is shown below. The beam spans 12.0 m and is subject to asuperimposed dead load of 50 kN/m and a live load of 35 kN/m. Boththe superimposed dead load and live load are applied after transfer(after stressing has taken place). The tendon is located at themid-height of the beam at each end, and its centreline sits 50 mmfrom the base at midspan. The concrete strength at transfer is 22MPa, and at maturity is 40 MPa. Assume Ec = 32800 MPa, γc = 24kN/m3 and ignore any prestress losses. You are to assess thefollowing:

a) If Pi = 2700 kN, assess the adequacy of the beam at transfer.In addition, assuming Pi cannot be changed, briefly describe threemethods that could be used to ensure the transfer stresses arewithin code limits.

b) If Pi = 1750 kN and all the load has been applied, determinethe percentage of the total dead load balanced.

c) Estimate the approximate total short-term and long-termdeflection under the load combination G + 0.7Q. Assume Pi = 1750 kNand Фcc = 2.8.

d) If the beam has the reinforcement arrangement shown below,assess the ultimate moment capacity under the load combination 1.2G+ 1.5Q. Assume fpy = 1780 MPa, fpb = 1920 MPa and fsy = 500 MPa.Note: Ast = 2464 mm2, Asc = 1808 mm2 and Ap = 1790 mm2. Only twoiterations of dn are required.