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This and the next 3 images are from:
Cornelia Doerich (2007) “Strength and Stability of locally supported cylinders.” PhD thesis, Institute of Infrastructure and Environment, University of Edinburgh, Edinburgh (Supervisors J. Michael Rotter and Jin Ooi)
ABSTRACT: Large quantities of particulate solids and fluids are stored in cylindrical metal shell silos and tanks with a vertical axis. Such metal silos and tanks are often required to be elevated above ground level to permit trains, trucks or conveying systems to be placed beneath a hopper from which the solid or fluid is withdrawn. Elevated silos must be supported, and access requirements often mean that the supports must be local (either on columns or supported from an elevated floor system). The connection of a local support to an elevated cylindrical metal silo shell is a long-standing difficult problem in shell analysis, and most designs are based on simple ideas using past experiences of successes and failures. Smaller silo structures are often supported on local brackets attached to the side of the shell, but very few investigations of the behaviour or strength of such an arrangement have ever been made. This thesis presents a comprehensive investigation into the behaviour of a cylindrical steel shell that is discretely supported on several brackets, each rigidly connected to a stiff column or floor. The study has been conducted within the framework of the European Standard for Shell Structures (EN1993-1-6, 2006), which requires that the two reference strengths of the small displacement theory plastic collapse resistance and the linear bifurcation critical elastic resistance should both be evaluated to establish the context in which more sophisticated analyses are judged, and to provide a rapid means of producing reliable but simple design information. Therefore this thesis begins with a thorough investigation of the predictions of these two reference strengths for these structures, discovering the challenges inherent in this methodology and finally developing equations that can be used in hand calculations intended for the simple evaluation of the reference strengths for a wide variety of geometries. The influence of geometric nonlinearity is next explored, both with and without geometric imperfections. The results pose some interesting questions concerning the relative importance of geometric nonlinearity and geometric imperfections in shell buckling problems where the stress field is far from uniform. In the final part of the investigation, analyses are conducted that include both material and geometric nonlinearity with and without geometric imperfections. The results of these analyses are presented and analysed in the context of interaction capacity curves.
Following this extensive parametric investigation using linear and nonlinear analyses of all kinds, design recommendations are formulated so that bracket supports of this type can be used on thin cylindrical shells of any thickness and with any bracket dimensions necessary to transmit the loads. Finally, proposals are made for key future research investigations.
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