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Civil Engineering thin cylindrical shells such as silos and tanks are normally subjected to axial compression that arises from a stored solid, wind, earthquake, self-weight or roof loads. The walls of these shells are very thin, generally of the order of 6 to 25 mm, and massively less than the radius, which is typically 5 to 30 m. They are thus very thin shell structures, like those of rockets, spacecraft, motor vehicles and aircraft. The commonest failure mode is elastic buckling under axial compression. It has long been known that the buckling strength of a thin cylindrical shell under axial compression is very sensitive to tiny deviations of geometry, reducing the buckling strength to perhaps 10 or 20% of the value for the perfect structure. A normal internal pressure usually accompanies the axial compression, caused by stored granular solids or fluids. At relatively low pressures, the elastic buckling strength under axial compression rises, but an elastic-plastic buckling phenomenon intervenes at higher pressures, causing a dramatic decrease in buckling resistance associated with an elephant’s foot collapse mode. To construct such large shells, the fabrication technique is generally the assembly of many rolled plates or panels, joined by short longitudinal welds and continuous circumferential welds. The process of welding produces a distinctive geometric imperfection form at each weld joint, which in turn is extremely detrimental to the shell axial buckling carrying capacity. The strength may be further reduced by slight misalignments between adjacent panels, or in bolted construction, by vertical and horizontal lap splices. Due to the pattern of loading, both the axial compression and internal pressure increase progressively down the wall. Accordingly, practical construction usually uses a stepped wall, formed from panels of uniform thickness, but with larger thicknesses at lower levels. Since the loading varies smoothly, but each panel has constant thickness, the critical location for buckling lies at the base of a panel. But the greater thickness of the lower panel can usefully enhance the buckling strength of the critical panel above it. This thesis presents an extensive computational study that examines all the above influences, divided into chapters that are outlined here. A full exploration of the effect of the cylinder length on the perfect and imperfect elastic buckling strength is presented in Chapter 3. In Chapter 4, the elastic-plastic buckling resistance of imperfect cylinders is described, including strain hardening. These lead to many capacity curves, for which the key parameters are extracted. The effect of internal pressure on the buckling resistance of imperfect elastic cylinders is explored in Chapter 5. Chapter 6 studies the effect of high pressures that produce elastic-plastic elephant’s foot buckling at circumferential welds in imperfect shells. Next, a step change in plate thickness is studied in Chapter 7 for imperfect butt jointed cylinders with and without the internal pressure. Chapter 8 presents an exploration of the effect of plate misalignments at a circumferential joint, as well as the full misalignment of a circumferential lap joint in bolted construction. These are investigated in both the elastic and elastic-plastic domains. The entire thesis is conceived in the context of EN 1993-1-6 (2007) and the ECCS Recommendations on Shell Buckling (2008). This research has shown significant weaknesses in both the concepts and the detailed rules of these standards. Many conditions are found where either the standard is unnecessarily conservative, or its safety margin may be too low. Thus, some new provisions are proposed for each of the above practical problems. These are expected to provide useful knowledge for the design of such structures against buckling in the future.

It is widely accepted that, for many buckling problems of plates and shells in the plastic range, the flow theory of plasticity either fails to predict buckling or significantly overestimates buckling stresses and strains, while the deformation theory, which fails to capture important aspects of the underlying physics of plastic deformation, provides results that are more in line with experimental findings and is therefore generally recommended for use in practical applications. This thesis aims to contribute further understanding of the reasons behind the seeming differences between the predictions provided by these two theories, and therefore provide some explanation of this so-called ‘plastic buckling paradox’. The study focuses on circular cylindrical shells subjected to either axial compression or non-proportional loading, the latter consisting of combined axial tensile stress and increasing external pressure. In these two cases, geometrically nonlinear finite-element (FE) analyses for perfect and imperfect cylinders are conducted using both the flow and the deformation theories of plasticity, and the numerical results are compared with data from widely cited physical tests and with analytical results. The plastic buckling pressures for cylinders subjected to non-proportional loading, with various combinations of boundary conditions, tensile stresses, material properties and cylinder’s geometries, are also obtained with the help of the differential quadrature method (DQM). These results are compared with those obtained using the code BOSOR5 and with nonlinear FE results obtained using both the flow and deformation theories of plasticity. It is found that, contrary to common belief, by using a geometrically nonlinear FE formulation with carefully determined and validated constitutive laws, very good agreement between numerical and test results can be obtained in the case of the physically more sound flow theory of plasticity. The reason for the ‘plastic buckling paradox’ appears to be the over-constrained kinematics assumed in many analytical and numerical treatments, such as BOSOR5 and NAPAS, whereby a harmonic buckling shape in the circumferential direction is prescribed.

Abstract Storage tanks are above or below ground vessels for storing chemicals, petroleum and other liquid products. Above ground vertical cylindrical shells are typically thin walled structures prone to buckling and lose their stability especially when they are empty or have lower fluid level due to external loads.According to the Swedish National board of Housing, Building and Planning (Boverket), the Eurocodes and the Swedish national annex and building code for structural design, EKS (BFS 2011:10) should be used for verification of mechanical resistance of storage tanks. However the industry has been using a European design standard EN14015, for design of large site built steel tanks. The research question is if this design fulfils the requirements in the Swedish building code EKS and the Eurocodes. In order to investigate this, a parametric study of the buckling resistance of an empty tank has been performed, by comparing the design according to EN14015 With the requirements according to the Swedish building code and the Eurocodes. The finite element analysis was done with the finite element tool ABAQUS, The parametric study was carried out for three terrain categories0, I and II, for thesix snow load zones and for six basic wind velocities according to the Swedish snow and wind maps in EKS. The buckling resistance also further investigated for three reliability classes, reliability class 1, 2 and 3 according to the Swedish national annex and for two fabrication classes, fabrication class A and B usingEN1991-1-6The finite element analysis result of linear elastic and nonlinear buckling analysis with imperfections showed that, design according to EN14015 can meet the requirements of Eurocodes and EKS at lower basic wind velocities, terrain category (I and II) for smaller imperfections . But it does not meet the requirements at terrain category-0, for all reliability classes and all imperfection classes.The tank shell showed in some cases an increase in the load proportionality factorin nonlinear analysis for the load combinations considered in this study. It is thus necessary to study further on the finite element modelling of thin walled large tanks on relations of local buckling effect due to highly stiffened regions and the effect of magnitudes and applications of imperfections for large tanks using EN1993-1-6