Question

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

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

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

c) Estimate the approximate total short-term and long-term deflection under the load combination G + 0.7Q. Assume Pi = 1750 kN and 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 two iterations of dn are required.

Answer 1