Advertisement

An Alternative Approach to the Buckling Resistance Assessment of Steel, Pressurised Spherical Shells

  • Paweł Błażejewski
  • Jakub MarcinowskiEmail author
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 110)

Abstract

Provisions leading to the assessment of the buckling resistance of pressurised spherical shells are available since 2008 when they were published first time as the European Design Recommendations (EDR) (cf. Rotter and Schmidt in Buckling of Steel Shells: European Design Recommendations. ECCS, 2008 [13], Rotter and Schmidt in Buckling of Steel Shells: European Design Recommendations. ECCS, 2013 [14]). This collection of recommendations comprises rules which refer to the buckling resistance of steel shells of different shapes. In the first step of the general procedure, the calculation of two reference quantities: the elastic critical buckling reference pRcr and the plastic reference resistance pRpl is required. These quantities should be determined in the linear buckling analysis (LBA) and in the materially nonlinear analysis (MNA) respectively. Only in the case of spherical shells the existing procedure has exceptional character. It is based on the geometrically nonlinear analysis (GNA) and on the geometrically and materially nonlinear analysis (GMNA), respectively. From this reason, in this particular case there was a need to change the existing provisions. The first version of a new procedure was presented in the work of Błażejewski and Marcinowski (Buckling capacity curves for pressurized spherical shells. Taylor & Francis Group, London, pp. 401–406, 2016 [4]). All steps of the procedure leading to the assessment of buckling resistance of pressurized steel, spherical shells were presented in that work. The elaborated procedure is consistent with provisions of Eurocode EN1993-1-6 (cf. Błażejewski and Marcinowski in The worst geometrical imperfections of steel spherical shells, pp. 219–226, 2014 [3]) and with general recommendations inserted in Europeans Design Recommendations. In the present work the proposed capacity curves were compared with the existing provisions of ECCS for three different fabrication quality classes predicted. Comparisons of the author’s proposal with some experimental results obtained by other authors are presented as well. They have confirmed that the proposed procedure is less conservative than the existing one but it is still safe.

Keywords

Steel spherical shell Buckling resistance Buckling curve External pressure Clamped edge Numerical simulations Design recommendations 

References

  1. 1.
    Błachut, J.: Buckling of shallow spherical caps subjected to external pressure. J. Appl. Mech. Trans. ASME 72, 803–806 (2005)CrossRefGoogle Scholar
  2. 2.
    Błażejewski, P., Marcinowski, J.: A new approach to the buckling resistance assessment of pressurized spherical shells, SSTA. In: Proceedings of the 10th Conference, Gdańsk, Polska, pp. 179–182. Taylor & Francis Group, London (2013)Google Scholar
  3. 3.
    Błażejewski, P., Marcinowski, J.: Najbardziej niekorzystne imperfekcje geometryczne stalowych powłok sferycznych. The worst geometrical imperfections of steel spherical shells. Budownictwo i Architektura 13(3), 219–226 (2014). (in Polish)Google Scholar
  4. 4.
    Błażejewski, P., Marcinowski, J.: Buckling capacity curves for pressurized spherical shells. In: Recent Progress in Steel and Composite Structures: Proceedings of the XIII International Conference on Metal Structures—ICMS 2016, Zielona Góra, Poland, pp. 401–406. Taylor & Francis Group, London (2016)Google Scholar
  5. 5.
    Błażejewski, P., Marcinowski, J., Rotter, M.: Buckling of externally pressurised spherical shells. Experimental results compared with recent design recommendations. Presented in EUROSTEEL 2017, September 13–15, 2017, Copenhagen, Denmark (2017)Google Scholar
  6. 6.
    COSMOS/M: Finite element analysis system, version 2.5, Structural Research and Analysis Corporation, Los Angeles, California (1999)Google Scholar
  7. 7.
    Doerich, C., Rotter, J.M.: Generalised capacity curves for stability and plasticity: application and limitations. Thin Walled Struct. 49(9), 1132–1140 (2011)CrossRefGoogle Scholar
  8. 8.
    EN1993-1-1: Eurocode 3: design of steel structures, part 1.1: general rules and rules for buildings, CEN (2005)Google Scholar
  9. 9.
    EN1993-1-6: Eurocode 3: design of steel structures, part 1.6: strength and stability of shell structures, CEN (2006)Google Scholar
  10. 10.
    Kaplan, A., Fung, Y.C.: A nonlinear theory of bending and buckling of thin elastic shallow spherical shells. U.S.N.A.C.A. Technical Note 3112 (1954)Google Scholar
  11. 11.
    Leibenson, L.S.: About an adoption of harmonic functions of Thompson to stability problems of spherical and cylindrical shells (in Russian). Reports of Jurovskovo University, No. 5, pp. 1–47 (1917)Google Scholar
  12. 12.
    Rotter, J.M.: Shell buckling and collapse analysis for structural design: the new framework of the European standard. In: Drew, H.R., Pellegrino, S. (eds.) New Approaches to Structural Mechanics, Shells and Biological Structures, pp. 355–378. Kluwer Academic Publishers, London (2002)CrossRefGoogle Scholar
  13. 13.
    Rotter, J.M., Schmidt, H. (eds.): Buckling of Steel Shells: European Design Recommendations, 5th edn. Published by ECCS (2008)Google Scholar
  14. 14.
    Rotter, J.M., Schmidt, H. (eds.): Buckling of Steel Shells: European Design Recommendations, 5th edn. Revised Second Impression, Published by ECCS (2013)Google Scholar
  15. 15.
    Schmidt, H.: The German code DIN 18800 Part 4: stability of shell-type steel structures, design philosophy and practical applications, International Colloquium on Buckling of Shell Structures on Land, in the Sea and in the Air, Villeurbanne, Lyon, France, 17–19 Sept., pp. 265–269 (1991)Google Scholar
  16. 16.
    Schmidt, H.: Stability of shells, CEN TC250 SC3 PT 3 (Masts, Chimneys, Pipelines) Report, August, 12 (1994)Google Scholar
  17. 17.
    Seaman, L.: The nature of buckling in thin spherical shells. Watertown Arsenal Laboratories, Monograph Series No 46 (1962)Google Scholar
  18. 18.
    Zoelly, R.: Über ein Knickungsproblem an der Kugelschale (“About a buckling problem of spherical shell”—in German). Thesis, Zürich (1915)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Civil Engineering, University of Zielona GóraZielona GóraPoland

Personalised recommendations