Ductility and ductility reduction factor for MDOF systems

  • Published : 2002.04.25


Ductility capacity is comprehensively studied for steel moment-resisting frames. Local, story and global ductility are being considered. An appropriate measure of global ductility is suggested. A time domain nonlinear seismic response algorithm is used to evaluate several definitions of ductility. It is observed that for one-story structures, resembling a single degree of freedom (SDOF) system, all definitions of global ductility seem to give reasonable values. However, for complex structures it may give unreasonable values. It indicates that using SDOF systems to estimate the ductility capacity may be a very crude approximation. For multi degree of freedom (MDOF) systems some definitions may not be appropriate, even though they are used in the profession. Results also indicate that the structural global ductility of 4, commonly used for moment-resisting steel frames, cannot be justified based on this study. The ductility of MDOF structural systems and the corresponding equivalent SDOF systems is studied. The global ductility values are very different for the two representations. The ductility reduction factor $F_{\mu}$ is also estimated. For a given frame, the values of the $F_{\mu}$ parameter significantly vary from one earthquake to another, even though the maximum deformation in terms of the interstory displacement is roughly the same for all earthquakes. This is because the $F_{\mu}$ values depend on the amount of dissipated energy, which in turn depends on the plastic mechanism, formed in the frames as well as on the loading, unloading and reloading process at plastic hinges. Based on the results of this study, the Newmark and Hall procedure to relate the ductility reduction factor and the ductility parameter cannot be justified. The reason for this is that SDOF systems were used to model real frames in these studies. Higher mode effects were neglected and energy dissipation was not explicitly considered. In addition, it is not possible to observe the formation of a collapse mechanism in the equivalent SDOF systems. Therefore, the ductility parameter and the force reduction factor should be estimated by using the MDOF representation.


  1. Chopra, A.K. (1995), Dynamics of Structures, Prentice Hall, New Jersey.
  2. Gao, L. and Haldar, A. (1995), "Nonlinear seismic analysis of space structures with PR connections", Int. J.Microcomputers in Civil Engineering, 10, 27-37.
  3. Engelkirk, R. (1990), Steel Structures, Controlling Behavior through Design, Wiley, New York.
  4. Hadjian, A.H. (1989), "An evaluation of the ductility reduction factor Q in the 1976 regulations for the federaldistrict of mexico", Earthq. Eng. and Struct. Dyn., 18, 217-231.
  5. Haldar, A. and Mahadevan, S. (2000), Reliability Assessment Using Stochastic Finite Element Analysis, NY, JohnWiley & Sons.
  6. Haldar, A. and Nee, K.M. (1989), "Elasto-plastic large deformation analysis of PR steel frames for LRFD",Comput. Struct., 31(5), 811-823.
  7. Kondoh, K. and Atluri, S.N. (1987), "Large deformation, elasto-plastic analysis of frames under non-conservativeloading, using explicitly derived tangent stiffness based on assumed stress", Comput. Mech. J., 2 (1), 1-25.
  8. Leon, R.T. and Shin K.J. (1995), "Performance of semi-rigid frames", Proceedings of Structure Congress, 1020-1035.
  9. Nassar, A. and Krawinkler, H. (1991), "Seismic demands of SDOF and MDOF systems", John A. BlumeEarthquake Engineering Center, Report No. 95, Stanford University.
  10. Nader, M.N. and Astaneh, A. (1991), "Dynamic behavior of flexible, semirigid and rigid frames". J.Construction Steel Research, 18, 179-192.
  11. Newmark, N.M. and Hall, W.J. (1982), Earthquake Spectra and Design, Monograph Series. Berkeley, California,Earthquake Engineering Research Institute.
  12. Osteraas, J.D. and Krawinkler, H. (1990), "Strength and ductility considerations in seismic design", BlumeEarthquake Engineering Center, Report No. 90, Stanford University.
  13. Osman, A., Ghobarah, A. and Korol, R.M. (1995), "Implications of design philosophies of seismic response ofsteel moments frames", Earthq. Eng. and Struct. Dyn., 24, 127-143.
  14. Roeder, C.W, Scheiner, S.P. and Carpenter, J.E. (1993a), "Seismic behavior of moment-resisting steel frames:analytical study", J. Struct. Eng., ASCE, 119(6), 1866-1884.
  15. Roeder, C.W, Scheiner, S.P. and Carpenter J.E. (1993b), "Seismic behavior of moment-resisting steel frames:experimental study", J. Struct. Eng., ASCE, 119(6), 1885-1902.
  16. Reyes-Salazar, A. (1997), "Inelastic seismic response and ductility evaluation of steel frames with fully, partiallyrestrained and composite connections", Ph.D. Thesis, Department of Civil Engineering and EngineeringMechanics, University of Arizona, Tucson, AZ.
  17. Reyes-Salazar, A. and Haldar, A. (2000), "Dissipation of energy in steel frames with PR connections", Struct.Eng. and Mech., An Int. J., 9(3), 241-256.
  18. SAC. (1995), Structural Engineers Associated of California, Applied Technology Council and CaliforniaUniversity for Research in Earthquake Engineering, Steel Moment Frame Connections, Advisory No. 3, D-146.
  19. Shi, G. and Atluri, S.N. (1988), "Elasto-plastic large deformation analysis of space-frames", Int. J. Num. Meth.Eng., 26, 589-615.
  20. Santa-Ana, P. and Miranda, E. (2000), "Strength reduction factors of multi-degree-of-freedom systems", 12thWorld Conference on Earthquake Engineering, paper 1446, Auckland, New Zealand, January.
  21. Uang, C.M. (1991a), "Establishing R (or Rw) and Cd factors for building seismic provisions," J. Struct. Eng.,117(1), 19-28.
  22. Uang, C.M. (1991b), "Structural overstrength and limit state philosophy in seismic design provisions", TechnicalReport No CE-91-03, Department of Civil Engineering, Northeastern University.
  23. Uniform Building Code (1988), Int. Conf. of Building Officials (ICBO), Whittier, California.
  24. Zahrah, T.F. and Hall, W.J. (1984), "Earthquake energy absorption in SDOF structures," J. Struct. Eng., 110(8),1757-1772.

Cited by

  1. Ductility reduction factors for steel buildings considering different structural representations vol.13, pp.6, 2015,
  2. Force reduction factors for steel buildings with welded and post-tensioned connections vol.14, pp.10, 2016,
  3. Strength or force reduction factors for steel buildings: MDOF vs SDOF systems vol.19, pp.4, 2017,
  4. Seismic Vulnerability Assessment of Modular Steel Buildings vol.13, pp.8, 2009,
  5. Modification of Ductility Reduction Factor for Strength Eccentric Structures Subjected to Pulse-Like Ground Motions vol.20, pp.1, 2016,
  6. Seismic response of 3D steel buildings with hybrid connections: PRC and FRC vol.22, pp.1, 2016,
  7. Performance-Based Seismic Design of Steel Buildings Using Rigidities of Connections vol.4, pp.1, 2018,
  8. The Modification of Strength Reduction Factors for MDOF Effect vol.9, pp.4, 2006,
  9. Seismic Ductility Reduction Factors for Multi-Degree-of-Freedom Systems vol.9, pp.5, 2006,
  10. Effect of Damping and Yielding on the Seismic Response of 3D Steel Buildings with PMRF vol.2014, 2014,
  11. Ductility Reduction Factors for Steel Buildings Modeled as 2D and 3D Structures vol.595, pp.1662-7482, 2014,
  12. Energy Dissipation and Local, Story, and Global Ductility Reduction Factors in Steel Frames under Vibrations Produced by Earthquakes vol.2018, pp.1875-9203, 2018,
  13. Seismic response and energy dissipation of 3D complex steel buildings considering the influence of interior semi-rigid connections: low- medium- and high-rise vol.16, pp.11, 2018,
  14. Local, Story, and Global Ductility Evaluation for Complex 2D Steel Buildings: Pushover and Dynamic Analysis vol.9, pp.1, 2019,