A 15m single span post-tensioned rectangular concrete beam is 400mm wide by 1000mm deep, with two...

 

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A 15m single span post-tensioned rectangular concrete beam is 400mm wide by 1000mm deep, with two cables running side by side, shown in Figure Q3. Each cable is formed by 5 strands, the cable properties are given in Table Q3. These strands are initially stressed to 75% of the breaking load and assume a 20% prestress loss in long-term service. The beam is to support a slab which is 770mm wide and 200mm thick. The slab forms part of the bridge deck and is to be cast prior to post-tensioning. The concrete class is C40/50, and take the permissible concrete stresses as: In service: fmax = 0.6fck, fmin = 0N/mm² At transfer: f'max = 0.6fcks fmin = -1N/mm² (a) If the cable eccentricity is 300mm from the neutral axis, check: i. If the beam is able to take the prestressing load during transfer. ii. If the beam is able to carry a Serviceability Limit State (SLS) Moment MEd,sls 700kNm. Cable 1000 300 400 Figure Q3 [14 marks] Nominal Strand Type tensile Norminal Norminal strength fpk (N/mm²) dia (mm) area (mm²) Norminal mass (kg/m) Min breaking strength (kN) 0.1% Proof Load (kN) 15.2 Drawn 1820 15.2 165 1.295 300 255 Table Q3 Prestressing Cable Properties Question 3 continues on the following page Question 3 continued (b) Assuming that the maximum SLS Moment MEd, sls = 700kNm occurs at the centre of the span, and it is calculated from the selfweight of the beam, the slab and a traffic load which is uniformly distributed, find the cable zone limits and sketch the permissible cable zone for the beam. [11 marks] A 15m single span post-tensioned rectangular concrete beam is 400mm wide by 1000mm deep, with two cables running side by side, shown in Figure Q3. Each cable is formed by 5 strands, the cable properties are given in Table Q3. These strands are initially stressed to 75% of the breaking load and assume a 20% prestress loss in long-term service. The beam is to support a slab which is 770mm wide and 200mm thick. The slab forms part of the bridge deck and is to be cast prior to post-tensioning. The concrete class is C40/50, and take the permissible concrete stresses as: In service: fmax = 0.6fck, fmin = 0N/mm² At transfer: f'max = 0.6fcks fmin = -1N/mm² (a) If the cable eccentricity is 300mm from the neutral axis, check: i. If the beam is able to take the prestressing load during transfer. ii. If the beam is able to carry a Serviceability Limit State (SLS) Moment MEd,sls 700kNm. Cable 1000 300 400 Figure Q3 [14 marks] Nominal Strand Type tensile Norminal Norminal strength fpk (N/mm²) dia (mm) area (mm²) Norminal mass (kg/m) Min breaking strength (kN) 0.1% Proof Load (kN) 15.2 Drawn 1820 15.2 165 1.295 300 255 Table Q3 Prestressing Cable Properties Question 3 continues on the following page Question 3 continued (b) Assuming that the maximum SLS Moment MEd, sls = 700kNm occurs at the centre of the span, and it is calculated from the selfweight of the beam, the slab and a traffic load which is uniformly distributed, find the cable zone limits and sketch the permissible cable zone for the beam. [11 marks]