Analysis of silo supporting ring beams and intermediate ring stiffeners

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2018
Zeybek, Özer
Silos in the form of a cylindrical metal shell are commonly supported by a few discrete columns to permit the contained materials to be directly discharged. The discrete supports produce a circumferential non-uniformity in the axial membrane stresses in the silo shell. One way of reducing the non-uniformity of these stresses is to use a very stiff ring beam which partially or fully redistributes the stresses from the local support into uniform stresses in the shell. Another alternative is to use a combination of a flexible ring beam and an intermediate ring stiffener. A three part analytical and numerical study has been undertaken to address the issues related with silo supporting ring beams and ring stiffeners. A stiff ring beam is utilized in larger silos to transfer and evenly distribute the discrete forces from the supports into the cylindrical shell wall. A stiffness criterion was developed by Rotter to assess the degree of non-uniformity in axial compressive stresses around the circumference. The stiffness criterion is based on the relative stiffnesses of the ring beam and the cylindrical shell and was verified for loading conditions that produce circumferentially uniform axial stresses around the circumference. The first part of the study has been undertaken to investigate the applicability of the stiffness criterion to cylindrical shells under global shear and bending. Pursuant to this goal extensive finite element analyses were conducted where different ring beam and cylindrical shell combinations are subjected global shearing and bending actions. The results revealed that the stiffness criterion can be extended to shells under this loading condition. The degree of non-uniformity in axial stresses is quantified and presented as simple formulas that can be readily adopted by design standards. The ring beam plays an important role in redistributing the majority of the discrete forces from the column supports into a more uniform stress state in the cylindrical wall. The Eurocode EN 1993-4-1 only provides design equations for stress resultants (internal forces) produced in the isolated ring beam under uniform transverse loading. The behavior of a ring beam which interacts with the silo shell is much more complex than that of an isolated ring beam. In traditional design treatments, it is assumed that the discrete support forces are redistributed entirely by the ring beam to provide circumferentially uniform axial membrane stresses in the silo shell. But this assumption is only approximately valid if the ring beam is much stiffer than the silo shell. Since the cylindrical shell is very stiff in its own plane, the ring beam must be remarkably stiff to be stiffer than the shell. The second part of the study has been undertaken to explore the ring beam stress resultants when closed section ring beams of lower stiffness and practical dimensions are used. A finite element parametric study is undertaken to explore the stress resultants and displacements in more flexible ring beams connected to a silo shell. A combination of a ring beam and an intermediate ring stiffener can be used for large silos to redistribute the stresses from the local support into uniform stresses in the shell. Topkaya and Rotter (2014) has identified the ideal location for the intermediate ring stiffener. The third part of the study explored strength and stiffness requirements for intermediate ring stiffeners placed at or below the ideal location. Pursuant to this goal, the cylindrical shell below the intermediate ring stiffener is analyzed using the membrane theory of shells. The reactions produced by the stiffener on the shell are identified. Furthermore, the displacements imposed by the shell on the intermediate ring stiffener are obtained. These force and displacement boundary conditions are then applied to the intermediate ring stiffener to derive closed form expressions for the variation of the stress resultants around the circumference to obtain a strength design criterion for the stiffener. A stiffness criterion in the form of a simple algebraic expression is then developed by considering the ratio of the circumferential stiffness of the cylindrical shell to that of the intermediate ring stiffener. These analytical studies are then compared with complementary finite element analyses that are used to identify a suitable value for the stiffness ratio for ring stiffeners placed at different locations.

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Citation Formats
Ö. Zeybek, “Analysis of silo supporting ring beams and intermediate ring stiffeners,” Ph.D. - Doctoral Program, Middle East Technical University, 2018.