Fire Technology

, 46:91 | Cite as

Numerical Modelling of Thin-Walled Stainless Steel Structural Elements in Case of Fire

  • Nuno Lopes
  • Paulo Vila Real
  • Luís Simões da Silva
  • Jean-Marc Franssen


In this paper, the structural response of stainless steel thin-walled elements submitted to fire is analysed numerically by means of the geometrically and materially non-linear Finite Element program SAFIR, including imperfections. In order to make these simulations, two main changes in the program were made: (i) the code was changed in order to deal with the stainless steel 2D material constitutive law to be used with shell elements and (ii) the possibility of the program to take into account residual stresses with shell finite elements was introduced. The stainless steel stress–strain relationship at high temperatures was based on the one presented in part 1.2 of Eurocode 3. To model the strain hardening exhibited by the stainless steels, using the shell element formulation, an approximation to the Eurocode 3 constitutive law was needed. Local and global geometrical imperfections were considered in the simulations. The paper shows the influence of the residual stresses on the ultimate load-carrying capacity of thin-walled stainless steel structural elements in case of fire.


stainless steel fire thin-walled numerical modelling local buckling 


a, b, c, d

Parameters to calculate the stainless steel stress–strain relationship: and also parameters to calculate the approximation proposed in this paper to the stainless steel hardening rule


Parameter to calculate the stainless steel stress–strain relationship


Tensile strength


The proof strength at 0.2% plastic strain


Plastic strain


Slope of the linear elastic range


Slope of the linear elastic range


Slope at proof strength


Total strain at proof strength


Ultimate strain

σ1, σ2

Principal stresses


Comparison stress of the residual stresses


Stress from the hardening rule


Matrix of residual stresses in the axis i (x, y and xy)


Matrix of residual strains in the axis i (x, y and xy)


  1. 1.
    Estrada I (2005) Shear design of stainless plate girders. PhD Thesis, Universitat Politècnica de Catalunya, Barcelona, SpainGoogle Scholar
  2. 2.
    Gardner L (2005) The use of stainless steel in structures. Prog Struct Eng Mater 7(2):45–55. doi:10.1002/pse.190 CrossRefGoogle Scholar
  3. 3.
    Euro Inox and Steel Construction Institute (2006) Design manual for structural stainless steel, 3rd edn. Euro Inox and Steel Construction Institute, LondonGoogle Scholar
  4. 4.
    European Committee for Standardisation (2006) EN 1993-1-4 Eurocode 3: design of steel structures—Part 1.4.: general rules—supplementary rules for stainless steels. Brussels, BelgiumGoogle Scholar
  5. 5.
    European Committee for Standardisation (2005) EN 1993-1-2 Eurocode 3: design of steel structures—Part 1.2: general rules—structural fire design. Brussels, BelgiumGoogle Scholar
  6. 6.
    Franssen J-M 2005 “SAFIR. A Thermal/Structural Program Modelling Structures under Fire”, Engineering Journal, A.I.S.C., Vol. 42, No. 3, pp. 143–158Google Scholar
  7. 7.
    Franssen J.-M. (1993) Residual stresses in steel profiles submitted to the fire: an analogy. In: 3rd CIB/W14 workshop “modelling”, TNO building and construction research. Rijswijk, The NetherlandsGoogle Scholar
  8. 8.
    Doneux C, Franssen J-M (2003) 2D constitutive models for the shell elements of the finite element software SAFIR. M&S report, translation of “Rapport interne—SPEC/97_01” by C. Doneux. University of Liege, Liege, BelgiumGoogle Scholar
  9. 9.
    Jandera M, Gardner L, Machaceka J (2008) Residual stresses in cold-rolled stainless steel hollow sections. J Constructional Steel Res 64:1255–1263. doi:10.1016/j.jcsr.2008.07.022 CrossRefGoogle Scholar
  10. 10.
    Ala-Outinen T, Oksanen T (1997) Stainless steel compression members exposed to fire, VTT research notes 1864. Espoo, FinlandGoogle Scholar
  11. 11.
    Cheung YK 1976 Finite strip method in structural analysis. New York: Pergamon PressMATHGoogle Scholar
  12. 12.
    Ashraf M, Gardner L, Nethercot DA 2005 “Strength enhancement of the corner regions of stainless steel cross sections”, in Journal of Constructional Steel Research 61(1): 37-52.CrossRefGoogle Scholar
  13. 13.
    ECCS (1984) Ultimate limit state calculation of sway frames with rigid joints, 1st ednGoogle Scholar
  14. 14.
    Gardner L, Nethercot DA (2004) Numerical modeling of stainless steel structures components—a consistent approach. J Struct Eng (October):1586–1601. doi:10.1061/(ASCE)0733-9445(2004)130:10(1586)
  15. 15.
    Chen WF, Lui EM 1991 “Stability design of steel frames”. CRC Press, LondonGoogle Scholar
  16. 16.
    European Committee for Standardisation (2006) EN 1993-1-5 Eurocode 3: design of steel structures—Part 1.5: plated structural elements. Brussels, BelgiumGoogle Scholar
  17. 17.
    European Committee for Standardisation (2005) EN 1090-2. Execution of steel and aluminium structures—Part 2: technical requirements for the execution of steel structures. Brussels, BelgiumGoogle Scholar
  18. 18.
    Uppfeldt B, Outinen T, Veljkovic M 2008 A design model for stainless steel box columns in fire. Journal of Constructional Steel Research 64(11): 1294–1301CrossRefGoogle Scholar
  19. 19.
    Schafer BW (1997) Cold-formed steel behaviour and design: analytical and numerical modeling of elements and members with longitudinal stiffeners. PhD Dissertation, Cornell University, IthacaGoogle Scholar
  20. 20.
    Sarawit AT, Kim Y, Bakker MCM, Peko T (2003) The finite element method for thin-walled members-applications. Thin-Walled Struct Elsevier 41:191–206. doi:10.1016/S0263-8231(02)00087-3 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Nuno Lopes
    • 1
  • Paulo Vila Real
    • 1
  • Luís Simões da Silva
    • 2
  • Jean-Marc Franssen
    • 3
  1. 1.Department of Civil EngineeringLABEST - University of AveiroAveiroPortugal
  2. 2.Department of Civil EngineeringISISE - University of CoimbraCoimbraPortugal
  3. 3.Structural EngineeringUniversity of LiegeLiegeBelgium

Personalised recommendations