Answer Happy

Question 5 (15%) Failure of Concrete in Multiaxial Stresses Background A concrete gravity platform is one that is placed on the seabed by its own weight, and is capable of withstanding the environmental forces (wind and waves) it may be exposed to during its lifetime. These gravity-type concrete platforms are used for oil-drilling purposes in the oil industry. They are used when the soil rock of the seabed is hard and relevant for supporting them since they rest directly on the ocean floor without pile foundation. Concrete platforms are larger and heavier than steel platforms. Although there are various designs of a concrete gravity platform, the base part is usually made of reinforced concrete and consisted of huge sub-sea concrete tanks. These tanks are used for the storage of crude oil, at the same time provide the stability of the overall structure. We would like to consider one of the concrete cylinders (see Figure 1) as part of the base of a gravity platform. The base structure is built to such a height that when the dock is flooded the base has sufficient freeboard to float on its buoyancy. The base is then towed out into the deep water site and the tanks are flooded, causing the base to sink to the seabed. ZA 02 07 o X 02 у Figure 1. Schematic Diagram of a Hollow Concrete Cylinder as part of a Concrete Gravity Structure
Uniaxial failure condition Consider the hollow concrete cylinder having the dimensions of 0.6 m wall thickness, 18 m inner diameter and 46 m height. Considering only the uniaxial stress, a, how deep could the open, flooded cylinder be placed before being crushed by the water pressure? Use constant gravity weight for seawater. Consider the tank as an open ended tube to simplify the problem and ignore the pressure acting on the ends of the cylinders. Also, ignore the effects of any reinforcement. Assume fe' to be 40 MPa, and gravity g can be taken as 10 m/s?
For Question 5, you need P = rgH < fc' for evaluating the uniaxial failure and the height (H) is 4,000m. For the biaxial failure, just follow the given equation for sketching the curve. However, it is reminded that the given equation is symmetrical in the first quadrant against the diagonal line in the x-y plot.