simply supported concrete beam with a span of 23m is provided with the following two posttensioned...

 

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simply supported concrete beam with a span of 23m is provided with the following two posttensioned cables: (i) the first prestressed cable that has a parabolic profile with zero eccentricity at its ends increasing to an eccentricity of 618 mm at the mid-span, as shown in Figure-1. The tendon is stressed with an effective prestressing force of Pej = 2277 kN (Oer = 1100 MPa) and at the mid-span of the beam, the tendon is at a depth dpi = 1300 mm; Ap1 = 2070 mm? (fp=1700MPa; fab=1900MPa at a rupture strain of 0.035) and (ii) the second prestressed cable that has a straight profile with a constant eccentricity of 518 mm throughout the span, as shown in Figure-1. The tendon is stressed with an effective prestressing force of Pez = 2350 kN (Ooe2 = 1135 MPa) and at the mid-span of the beam, the cable is at an effective depth d2 = 1200 mm; Ag2 = 2070 mm? (fyp=1700MPA; fot=1900MPa at a rupture strain of 0.035). The beam is also provided with a layer of non-prestressed conventional reinforcement layer in tension region (Ast = 1200 mm2; f,-400 MPa) at an effective depth of det = 1450 mm. Other data: unit weight of reinforced concrete = 25 kN/m3; fc= 45 MPa; f'af= 0.6(f. )12 =4.0 MPa; E.= 35,000 MPa;; Eş= E, = 200,000 MPa; n = no = E/E, = 5.7; e's=550x10-8. (a) For a given neutral axis depth of 650mm estimate the moment at mid-span and the corresponding curvature. For this carry out detailed linear elastic cracked analysis to satisfy the strain compatibility and force equilibrium conditions. 1200 200 300 d- 1200 -682 900 D-1500 CG Y=818 Aa- 2070mn Siratght cable 100 400 Ap=2070 Parabolicdy 1300mum I150 Au-1200mam d-1450mum .. + 600 Figure-1: Cross-section at mid-span (all dimensions are in mm) simply supported concrete beam with a span of 23m is provided with the following two posttensioned cables: (i) the first prestressed cable that has a parabolic profile with zero eccentricity at its ends increasing to an eccentricity of 618 mm at the mid-span, as shown in Figure-1. The tendon is stressed with an effective prestressing force of Pej = 2277 kN (Oer = 1100 MPa) and at the mid-span of the beam, the tendon is at a depth dpi = 1300 mm; Ap1 = 2070 mm? (fp=1700MPa; fab=1900MPa at a rupture strain of 0.035) and (ii) the second prestressed cable that has a straight profile with a constant eccentricity of 518 mm throughout the span, as shown in Figure-1. The tendon is stressed with an effective prestressing force of Pez = 2350 kN (Ooe2 = 1135 MPa) and at the mid-span of the beam, the cable is at an effective depth d2 = 1200 mm; Ag2 = 2070 mm? (fyp=1700MPA; fot=1900MPa at a rupture strain of 0.035). The beam is also provided with a layer of non-prestressed conventional reinforcement layer in tension region (Ast = 1200 mm2; f,-400 MPa) at an effective depth of det = 1450 mm. Other data: unit weight of reinforced concrete = 25 kN/m3; fc= 45 MPa; f'af= 0.6(f. )12 =4.0 MPa; E.= 35,000 MPa;; Eş= E, = 200,000 MPa; n = no = E/E, = 5.7; e's=550x10-8. (a) For a given neutral axis depth of 650mm estimate the moment at mid-span and the corresponding curvature. For this carry out detailed linear elastic cracked analysis to satisfy the strain compatibility and force equilibrium conditions. 1200 200 300 d- 1200 -682 900 D-1500 CG Y=818 Aa- 2070mn Siratght cable 100 400 Ap=2070 Parabolicdy 1300mum I150 Au-1200mam d-1450mum .. + 600 Figure-1: Cross-section at mid-span (all dimensions are in mm)