Seismic assessment of steel structures through a cumulative damage

  • Perera, R. (Department of Structural Mechanics, Technical University of Madrid (UPM)) ;
  • Gomez, S. (Department of Structural Mechanics, Technical University of Madrid (UPM)) ;
  • Alarcon, E. (Department of Structural Mechanics, Technical University of Madrid (UPM))
  • Published : 2001.09.25


In the present work a constitutive model is developed which permits the assessment of the structural performance through a criterion based on cumulative damage. For it, a damage index is defined and is evaluated through the application of the Miner's rule in low-cycle fatigue. However, the damage index is not considered as a posteriori variable since is incorporated explicitly as an internal variable in the constitutive equations which produces a direct coupling between the damage and the structural mechanical behaviour allowing the possibility of considering as a whole different coupled phenomena. For the elaboration of this damage model, the concepts of the mechanics of continuum medium are applied on lumped dissipative models in order to obtain a coupled simplified model. As a result an elastoplastic model coupled with damage and fatigue damage is obtained.


continuum damage mechanics;low cycle fatigue;steel structures;seismic design;simplified model


  1. Lemaitre, J. and Chaboche, J. (1985), Mecanique des materiaux solides.,Dunod, Paris
  2. Lemaitre, J. (1996), A Course on Damage Mechanics., Springer-Verlag, Berlin
  3. Manson, S.S. (1953), "Behavior of materials under conditions of thermal stress", Heat Transfer Symposium, University of Michigan Engineering research Institute, Ann Harbor, Michigan, 9-75.
  4. Miner, M.A. (1945), "Cumulative damage in fatigue", J. Appl. Mech. 12, A-159.
  5. Ortiz, M. (1985), "A constitutive theory for the inelastic behavior of concrete", Mech. Mater., 4, 67-93.
  6. Palmgren, A. (1924), "Die lebensdauer von kugellagern", Verfahrentechinik, Berlin, 68, 339-341.
  7. Perera, R., Carnicero, A., Alarcon, E. and Gomez, S. (1998), "A damage model for seismic retrofitting of structures", Advances in Civil and Structural Engineering, CIVIL-COMP Press, 309-315.
  8. Rabotnov, Yu N. (1968), "A model of an elastic-plastic medium with delayed yielding", Zh. Prikl. Mekh. y Tekhn. Fiz., 3, 45-51.
  9. Ballio, G. & Castiglioni, C. (1994), "An approach to the seismic design of steel structures based on cumulative damage criteria", Earthq. Eng. And Struct. Dyn., 23, 969-986.
  10. Carnicero, A., Perera, R., Alarcon, E. (1998), "A simplified model for evaluation of fatigue damage in frames", Proc. Eleventh European Conf. on Earthquake Eng., Paris.
  11. Chaboche, J. (1985), "Continuum damage mechanics and its application to structural lifetime prediction", Rech. Aerosp., 4, 37-53.
  12. Cipollina, A., Lopez-Hinojosa, A., Florez-Lopez, J. (1995), "A simplified damage mechanics approach to nonlinear analysis of frames", Comput. & Struct., 54, 1113-26.
  13. Cohn, M.Z., Franchi, A. (1979), "Structural plasticity computer system STRUPL", J. Struct. Div., 105, 789-804.
  14. Florez-Lopez, J. (1995), "Simplified model of unilateral damage for RC frames", J. Struc. Eng., 121(12), 1765-1772.
  15. Ju, J.W. (1989), "On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects", Int. J. Solids Structures., 25(7), 803-833.
  16. Koh, S.K. and Stephen, R.I. (1991), "Mean stress effects on low cycle fatigue for high strength steel", Fatigue Fract. Engng. Mater., 14, 413-428.
  17. Krawinkler, H. and Zohrei, H. (1983), "Cumulative damage in steel structures subjected to earthquake ground motions", Computers & Structures, 16, 531-541.
  18. Kunnath, S.K., El-Bahy, A., Taylor, A. and Stone, W. (1997), "Cumulative seismic damage of reinforced concrete bridge piers", Technical Report NCEER-97-0006. National Center for Earthquake Engineeing Research. State University of New York at Buffalo.