Requirements for intermediate ring stiffeners placed below the ideal location on discretely supported shells

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. 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. Previous work done by the authors has identified the ideal location and the stiffness and strength requirements for the intermediate ring stiffener placed at this location. In cases where a shell with a large radius rests on a few supports, the ideal location can be quite high and the option of placing the intermediate ring stiffener below the ideal location may provide a viable solution. This paper explores strength and stiffness requirements for intermediate ring stiffeners placed 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