Use the following assumptions and material properties in all of your caleulations Ignore the effect of steel bars when you are caleulating gross cross sectional properties (i.e. I, and A4,) and location of centroidal axis for the gross cross section. Ignore the friction between the wall and the backfill. The elastie modulus of conventional steel bars and hot-rolled prestressing bars is E,- 200 GPa. The characteristic compressive strength of concrete is f - 50 MPa. Density of concrete is p=2500 kg/m'. The displacement d at the free end of a cantilever (with length L) subjected to different types of load; PxL wx L* Wx L 3x Ex! 8x Ex1 30x Ex/ Question-1: The cantilever tapered retaining wall shown in Figure-I is post-tensioned and it is constructed in an arid environment. The cross-section of the wall and the location and spacing of the post-tensioning bars are also shown in Figure-1. The prestressing bars are 32 mm diameter hot-rolled super grade according to AS/NZS4672.1 and the prestressing bars have greased-and-wrapped coating. The backfill is a mix of sand and gravel with a dry weight per unit volume of y- 20 kN/m', angle of internal friction of = 15 and no cohesion. For at rest earth pressure calculation take k,= 1.0 - Sin(). Thickness of the wall varies lincarly. Wall thickness is 360 mm at the base and 300 mm at the top. - Determine the initial prestressing induced in each (super grade) bar before removing the jacks in such a way that no flexural erack occurs in the wall under the self-weight and at rest lateral earth pressure (both with a load factor of 1.0). No surcharge to be considered. Assume that all the short- and long-term prestressing losses are negligible. Assume that the final shrinkage strain is e = 800x 10*. (30 marks) - Assuming that the initial prestress in the 632 bars is o= 620 MPa and assuming that all the short- and long-term prestressing losses are negligible; calculate the short-lerm lateral displacement on top of the retaining wall under short-term service load including self-weight of the wall, permanent surcharge of 1.5 kPa (on the backfill) and lateral carth pressure (All loads with a load factor of 1.0). (20 marks) 300 mm All covers given to the surcharge: s Lateral displacement 44 centroid of the bars. -N10@200 mm 40 mm Sand & gravel -150 mm mm 432@ 400 mm post-tensioned 032@400 mm post-lensioned N10@200 mm Section A-A A 360 mm Dead end Sand & gravel anchorage 1000 mm - 1000 mm Figure 1 Geometric outline of the cantilever tapered retaining wall. 1 w% 300-360 mm -150 mm wu 008 - 3600 mm