Ideal Location of Intermediate Ring Stiffeners on Discretely Supported Cylindrical Shells
Publication: Journal of Engineering Mechanics
Volume 140, Issue 4
Abstract
Silos in the form of a cylindrical metal shell are commonly elevated to provide access to the space beneath, permitting the contained materials to be directly discharged. A few discrete column supports at evenly spaced intervals are commonly used. However, the structural design of discretely supported cylindrical shells presents a variety of challenges. The presence of discrete supports results in circumferential nonuniformity in the axial compressive stress as well as a progressive vertical decay above the support. Several approaches can be adopted in design depending on the severity of the nonuniformity of the stresses. Relevant research to date has focused mostly on the behavior of cylinders supported on brackets, local forces at the base, or stiff ring beams. The use of intermediate ring stiffeners to provide circumferential uniformity in the axial membrane stresses has long been recognized, but few studies have given a clear view of the practical requirements for such rings. In this paper, a combination of base and intermediate ring stiffeners is explored to develop a practical and cost-effective solution that leads to more uniformity in the axial membrane stresses above the intermediate ring stiffener. For the purposes of obtaining a simple analytical solution, the cylindrical shell is subjected to the fundamental harmonic of the column support and analyzed using membrane theory. It is shown that an ideal location exists for an intermediate ring stiffener such that the axial membrane stress above this ring is circumferentially completely uniform. The ideal location of this ring is determined analytically and is expressed in terms of the basic geometric variables. This ideal ring location is then independently verified using many linear finite-element analyses. A further study explores the effect of placing the intermediate ring stiffener below the ideal location. The results are presented in a manner that makes them suitable for direct adoption into traditional design specifications.
Get full access to this article
View all available purchase options and get full access to this article.
References
Ansys. (2010). Version 12.1 on-line user’s manual, Canonsburg, PA.
Calladine, C. R. (1983). Theory of shell structures, Cambridge University Press, Cambridge, U.K.
European Committee for Standardization. (2007). “Eurocode 3: Design of steel structures, part 4.1: Silos.” EN 1993-4-1, Brussels, Belgium.
Flügge, W. (1973). Stresses in shells, Springer, Berlin.
Gaylord, E. H., and Gaylord, C. N. (1984). Design of steel bins for storage of bulk solids, Prentice Hall, Englewood Cliffs, NJ.
Gould, P. L., Ravichandran, R. V., and Sridharan, S. (1998). “A local-global FE model for nonlinear analysis of column-supported shells of revolution.” Thin-walled Struct., 31(1–3), 25–37.
Gould, P. L., and Sen, S. K. (1974). “Column moments in eccentrically supported tanks.” J. Struct. Div., 100(3), 2165–2169.
Gould, P. L., Sen, S. K., Wang, R. S. C., Suryoutomo, H., and Lowrey, R. D. (1976). “Column supported cylindrical-conical tanks.” J. Struct. Div., 102(2), 429–447.
Greiner, R. (1983). “Zur Ingenieurmässigen Berechnung und Konstruktion zylindrischer behälter aus Stahl unter allgemeiner Bellastung.” Wissenschaft und Praxis StahlbauSeminar, Vol. 31, Akademie der Hochschule Biberach an der Riss, Biberach, Germany (in German).
Greiner, R., and Guggenberger, W. (1998). “Buckling behaviour of axially loaded steel cylinders on local supports—with and without internal pressure.” Thin-walled Struct., 31(1–3), 159–167.
Guggenberger, W., Greiner, R., and Rotter, J. M. (2000). “The behaviour of locally-supported cylindrical shells: Unstiffened shells.” J. Constr. Steel Res., 56(2), 175–197.
Guggenberger, W., Greiner, R., and Rotter, J. M. (2004). “Cylindrical shells above local supports.” Buckling of thin metal shells, J. G. Teng and J. M. Rotter, eds., Spon, London, 88–128.
Kildegaard, A. (1969). “Bending of a cylindrical shell subject to axial loading.” Proc., 2nd Symp. Theory of Thin Shells, Springer, Berlin, 301–315.
Kraus, H. (1967). Thin elastic shells, Wiley, New York.
Novozhilov, V. V. (1959). The theory of thin shells, Noordhoff, Groningen, Netherlands.
Öry, H., and Reimerdes, H. G. (1987). “Stresses in and stability of thin walled shells under non-ideal load distribution.” Proc., Int. Colloquium on Stability of Plate and Shell Structures, European Convention for Constructional Steelwork, Brussels, Belgium, 555–561.
Öry, H., Reimerdes, H. G., and Tritsch, W. (1984). “Beitrag zur bemessung der schalen von metallsilos.” Stahlbau, 53(8), 243–248.
Rotter, J. M. (1985). “Analysis and design of ringbeams.” Design of steel bins for storage of bulk solids, J. M. Rotter, ed., Univ. of Sydney, Sydney, Australia, 164–183.
Rotter, J. M. (1986). “The analysis of steel bins subject to eccentric discharge.” Proc., 2nd Int. Conf. on Bulk Materials Storage Handling and Transportation, Institution of Engineers, Canberra, Australia, 264–271.
Rotter, J. M. (1987a). “Bending theory of shells for bins and silos.” Trans. Mech. Eng., Inst. Eng., Aust., 12(3), 147–159.
Rotter, J. M. (1987b). “Membrane theory of shells for bins and silos.” Trans. Mech. Eng., Inst. Eng., Aust., 12(3), 135–147.
Rotter, J. M. (1990). “Structural design of light gauge silo hoppers.” J. Struct. Eng., 1907–1922.
Rotter, J. M. (2001). Guide for the economic design of circular metal silos, Spon, London.
Rotter, J. M. (2004). “Buckling of cylindrical shells under axial compression.” Buckling of thin metal shells, J. G. Teng and J. M. Rotter, eds., Spon, London, 42–87.
Rotter, J. M., Cai, M., and Holst, J. M. F. G. (2011). “Buckling of thin cylindrical shells under locally elevated axial compression stresses.” J. Pressure Vessel Technol., 133(1), 011204.
Rotter, J. M., and Schmidt, H., eds. (2008) Stability of steel shells: European design recommendations, 5th Ed., European Convention for Constructional Steelwork, Brussels, Belgium.
Safarian, S. S., and Harris, E. C. (1985). Design and construction of silos and bunkers, Van Nostrand Reinhold, New York.
Seide, P. (1975). Small elastic deformations of thin elastic shells, Noordhoff, Leiden, Netherlands.
Teng, J. G., and Rotter, J. M. (1992). “Linear bifurcation of perfect column-supported cylinders: Support modeling and boundary conditions.” Thin-walled Struct., 14(3), 241–263.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability, 2nd Ed., McGraw Hill, New York.
Timoshenko, S. P., and Woinowsky-Krieger, S. (1959). Theory of plates and shells, McGraw Hill, New York.
Topkaya, C., and Rotter, J. M. (2011). “Ring beam stiffness criterion for column supported metal silos.” J. Eng. Mech., 846–853.
Trahair, N. S., Abel, A., Ansourian, P., Irvine, H. M., and Rotter, J. M. (1983). Structural design of steel bins for bulk solids, Australian Institute of Steel Construction, Sydney, Australia.
Ventsel, E., and Krauthammer, T. (2001). Thin plates and shells: Theory, analysis, and applications, Marcel Dekker, New York.
Vlasov, V. Z. (1964). General theory of shells and its applications in engineering, National Aeronautics and Space Administration (NASA), Washington, DC.
Wozniak, R. S. (1979). “Steel tanks.” Section 23, Structural engineering handbook, 2nd Ed., E. H. Gaylord and C. N. Gaylord, eds., McGraw Hill, New York.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 140 • Issue 4 • April 2014
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Apr 13, 2012
Accepted: Jul 1, 2013
Published online: Jul 4, 2013
Published in print: Apr 1, 2014
Discussion open until: May 24, 2014
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.