ε-Optimum Reliability-Based Cost Design of Longitudinally Stiffened Welded Steel Plates

  • Luis M. C. Simões
  • Károly Jármai
  • Zoltán Virág
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The aim of this work is the reliability-based optimization of a stiffened plate subjected to in-plane or combined in-plane and transverse loading. The design variables are the thickness of the base plate, the number of stiffeners and their thickness. The constraints deal with the overall plate buckling, the stiffener failure and the distortion of the plate due to welding. The cost function includes the cost of material, assembly and welding. Randomness is considered both in loading and material properties. A level II reliability method (FORM) is employed. The overall structural reliability is obtained by using Ditlevsen method of conditional bounding. The branch and bound strategy is employed to enumerate ε-optimum costs, which are solutions within a specified tolerance of the optimum.


Stiffened plates Optimization Reliability 



The described article was carried out as part of the EFOP-3.6.1-16-2016-00011 “Younger and Renewing University – Innovative Knowledge City – institutional development of the University of Miskolc aiming at intelligent specialisation” project implemented in the framework of the Szechenyi 2020 program. The realization of this project is supported by the European Union, co-financed by the European Social Fund.


  1. 1.
    Farkas, J., Jármai, K.: Analysis and Optimum Design of Metal Structures. Balkema, Rotterdam-Brookfield (1997)Google Scholar
  2. 2.
    Farkas, J., Jármai, K.: Economic design of welded steel structures. J. Constr. Steel Res. 46(1-3), 35–36 (1998). Full paper on CD-ROM. Paper No. 142CrossRefGoogle Scholar
  3. 3.
    Virág, Z., Jármai, K.: Parametric studies of uniaxially compressed and laterally loaded stiffened plates for minimum cost. In: International Conference on Metal Structures (ICMS), pp. 237–242. Millpress, Rotterdam (2003)Google Scholar
  4. 4.
    Jarmai, K., Farkas, J., Simoes, L.M.C, Virag, Z.: Minimum cost design of longitudinally stiffened welded plates loaded by eccentric compression. In: Proceedings of the Third European Conference on Steel Structures, Coimbra (2002)Google Scholar
  5. 5.
    Farkas, J., Simoes, M.C., Jármai, K.: Minimum cost design of a welded stiffened square plate loaded by biaxial compression. Struct. Multi. Optim. 29(4), 298–303 (2005)CrossRefGoogle Scholar
  6. 6.
    Jármai, K., Farkas, J., Horikawa, K.: Economic design of steel bridge decks. Weld. World 41(1), 49–59 (1998)Google Scholar
  7. 7.
    Simões, L.M.C, Jarmai, K., Farkas, J.: Minimum cost design of uniaxially compressed plates with welded trapezoidal stiffners considering a reliability constraint. In: Jarmai, K., Farkas, J. (eds.) Metal Structures - Design, Fabrication, Economy, pp. 209–216. Millpress Rotterdam, Rotterdam (2003). ISBN 90-77017-75-5Google Scholar
  8. 8.
    Simões, L.M.C., Farkas, J., Jármai, K.: Reliability-based optimum design of a welded stringer-stiffened steel cylindrical shell subject to axial compression and bending. Struct. Multi. Optim. 31(2), 147–155 (2006)CrossRefGoogle Scholar
  9. 9.
    Simões, L.M.C., Farkas, J., Jármai, K.: Optimization of a cylindrical shell housing a belt-conveyor bridge. Comput. Struct. 147, 159–164 (2015)CrossRefGoogle Scholar
  10. 10.
    Simões, L.M.C., Farkas, J., Jarmai, K.: Optimization of orthogonally stiffened plate considering fatigue constraints. In:. Jarmai, K., Farkas, J. (eds.) Design, Fabrication and Economy of Welded Structures, pp. 27–34. Horwood Publishing, Reino Unido (2008). ISBN 978-1-904275-28-2CrossRefGoogle Scholar
  11. 11.
    Mikami, I., Niwa, K.: Ultimate compressive strength of orthogonally stiffened steel plates. J. Struct. Eng. ASCE 122(6), 674–682 (1993)CrossRefGoogle Scholar
  12. 12.
    COSTCOMP Programm zur Berechnung der Schweisskosten. Deutscher Verlag für Schweisstechnik, Düsseldorf (1990)Google Scholar
  13. 13.
    Farkas, J., Jármai, K.: Optimum design of a stiffened conical roof considering the residual welding distortions. Weld. World 43(5), 54–59 (1999)Google Scholar
  14. 14.
    Hasofer, A.M., Lind, N.C.: Exact and invariant second moment code format. J. Eng. Mech. Div. 100(1), 111–121 (1974)Google Scholar
  15. 15.
    Stahlbau Handbuch, Band 2. Köln, Stahlbau-Verlag (1985)Google Scholar
  16. 16.
    Eurocode 3. Design of steel structures. Part 1.1. General rules and rules for buildings. European Prestandard ENV 1993-1-1. CEN European Committee for Standardisation, Brussels (1992)Google Scholar
  17. 17.
    Paik, J.K., Thayamballi, A.K., Kim, B.J.: Large deflection orthotropic plate approach to develop ultimate strength formulations for stiffened panels under combined biaxial compression/tension and lateral pressure. Thin Walled Struct. 39, 215–246 (2001)CrossRefGoogle Scholar
  18. 18.
    Ditlevsen, O.: Narrow reliability bounds for structural systems. J. Struct. Mech. 7(4), 453–472 (1979)CrossRefGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of CoimbraCoimbraPortugal
  2. 2.University of MiskolcMiskolcHungary

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