A post-tensioned concrete beam with a cable of 24 parallel wires (total area = 800 mm2 ) is tensioned with two wires at

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A post-tensioned concrete beam with a cable of 24 parallel wires (total area = 800 mm2 ) is tensioned with two wires at a time. The cable with zero eccentricity at the ends and 150 mm at the centre is on a circular curve. The span of the beam is 10 m. The cross-section is 200 mm wide and 450 mm deep. The wires are to be stressed from one end to a value of f1 to overcome frictional loss and then released to a value of f2 so that immediately after anchoring, an initial prestress of 840 N/mm2 would be obtained. Compute f1 and f2 and the final design stress in steel after all losses, given the following data: Coefficient of friction for curvature effect = 0.6 Friction coefficient for ‘wave’ effect = 0.003/m Deformation and slip of anchorage = 1.25 mm Es = 210 kN/mm2 Ec = 28 kN/mm2 Shrinkage of concrete = 0.0002 Relaxation of steel stress = 3 per cent of the initial stress
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