PSC IInd Assignment (LAST DATE - 07/04/2014)

1. A post-tensioned bridge girder with unbounded is of box section of overall dimensions 1200 mm wide by 1800 mm deep, with wall thickness of 150 mm. The high tensile steel has an area of 4000 mm² and is located at an effective depth of 1600 mm. The effective prestress in steel after all losses is 1000 N/mm² and the effective span of the girder is 24 m. If f_ck = 40 N/mm² and f_p = 1600 N/mm², estimate the ultimate flexural strength of the section.                                                                                                                                                                                                                                                   
2. A prestressing force of 250kN is transmitted through a distribution plate 120 mm wide and 120 mm deep, the centre of which is located at 100 mm from the bottom of an end block having a section 120 mm wide and 300 mm deep. Evaluate the position and magnitude of the maximum tensile stress on horizontal section passing through the centre of the distribution plate using the methods of (a) Magnel (b) Guyon. Find the area of the steel necessary to resist the largest tensile force resulting from any of these methods.  Take Yield Stress in steel = 260 N/mm²                                                                                            
3. A concrete beam with a rectangular section, 100 mm wide and 300 mm deep, is stressed by 3 cables, each carrying an effective force of 240kN. The span of the beam is 10 m. The first cable is parabolic with an eccentricity of 50 mm below the centroidal axis at the centre of span and 50 mm above the centroidal axis at the supports.  The second cable is parabolic with zero eccentricity at the supports and an eccentricity of 50 mm at the centre of span. The third cable is straight with an uniform eccentricity of 50 mm below the centroidal axis.                                                                                If the beam supports a uniformly distributed live load of 5 kN/m and E_c = 38 kN/mm², estimate the instantaneous deflection at the following stages:                                                                              (a)    Prestress + Self weight of beam and                                                                                        (b)   Prestress + Self weight + Live load                                                                                              
4. Explain the design of composite sections.