Structural Investigation of Negative Gaussian Curvature Shells as Liquid-Storage Vessels - Mahlelebe, Hlasoa (Department of Civil Engineering, 2024)
Shells of negative Gaussian curvature, such as hyperboloid of revolution, can be seen in most parts of the world in application in the energy industry as cooling towers supported on the large surface area on the ground (Zingoni, 2018). Hyperboloid of revolution shell has been found to resist self-weight stresses better when used as a cooling tower, and it is constructed to heights up to 200m or even more (Zingoni, 1999). Concrete can be moulded into almost any shape, provided the formwork is well constructed to give the desired shape. This makes it possible to be built into a large-capacity supersized tank (Zingoni, Mokhothu & Enoma, 2015). Some research has emerged on the analysis and design aspects of some elevated liquid containment vessels such as cylindrical, spherical, conical, and an Inze tank (a tank of compound geometry comprising of spherical top closure, vertical cylindrical sides, a conical transition in a lower part and a spherical bottom closure). The current study explores the structural investigation of hyperboloidal shells of revolution when used on a different application as a form of elevated liquid-containing vessel, making the current study novel in liquid containment application. In the current study, closed-form analytical solutions for membrane stress resultants due to hydrostatic loading have been developed and were used to conduct the structural investigation. The solutions developed were based on the membrane theory for shells of revolution for the concrete vessel and can be used to assess the membrane stress state at any point on the hyperboloidal vessel subjected to hydrostatic loading. It was found that increasing the geometric ratio of b/a decreased the maximum membrane meridional stress resultant from vessel to vessel. However, the same increase of b/a increased the maximum hoop stress resultants. The hoop stress resultants were 2.3 times the meridional stress resultant for the geometric ratio b/a =2.1 and 4.4 times for b/a = 2.8. Therefore, the hoop stresses were taken as governing the structural design. The Finite Element Method (FEM) using ABAQUS software was also used to check the accuracy of the derived closed-form solutions. These were in good agreement with an error of less than 5% for both hoop and meridional stresses, hence the developed equations are reliable in predicting stresses in the vessel due to hydrostatic loading. Furthermore, the FEM method using ABAQUS software was used to conduct a linear eigenvalue buckling analysis for zones that experience significant compressive stresses in the hyperboloidal vessel. The meridional stresses were entirely in compression throughout the vessel for all eight tested vessels from a b/a ratio of 2.1 to a b/a ratio of 2.8. It was found that increasing the geometric ratio of b/a increases the linear buckling capacity of the vessel when subjected to hydrostatic loading. The eigenvalues occurred in pairs, which resembles a feature of symmetry of symmetrical structural systems.