Optimum Seismic Design of Short to Mid-Rise Steel Moment Resisting Frames Based on Uniform Deformation Theory

Document Type : Structural Earthquake Engineering


Sharif University of Technology


In current work, an effective method is introduced for the optimal cross-section distribution in steel moment resisting frames under severe earthquakes by means of uniform deformation theory and adaptive method. The main goal is to distribute the construction material (weight) along the height of the structure in such a way that the lowest damage due to earthquakes is obtained. In adaptive method, materials gradually transfer from strong parts to weak parts by an iteration procedure during nonlinear time history analysis. In order to demonstrate the effectiveness of the proposed method, the optimal distribution of the cross-sections is obtained for 5 and 10 story steel moment resisting frames. In order to reduce the sensitivity of the optimal response to discrete cross-sections, continuous cross-sections fitted between DIN-Standard cross-sections have been used in order to achieve its optimal state. The steel moment resisting frames are optimized under five natural earthquakes. Results indicate that the optimal frames designed by this method show not only a more uniform deformation under earthquakes, but also less weight in comparison to the original structure designed according to the ASCE07-10 code. The reduction in structural weight reaches 40% in some cases leading to significant reduction in frame construction costs.


  1. Moghaddam, H. and Hajirasouliha, I. (2008) Optimum strength distribution for seismic design of tall buildings. The Structural Design of Tall and Special Buildings, 17(2), 331-349.
  2. Gong, Y., Grierson, D.E., and Xu, L. (2003) Optimal design of steel building frameworks under seismic loading. Response of Structures to Extreme Loading (XL2003), Canada, Toronto.
  3. Wen, Y.K., Collins, K.R., Han, S.W., and Elwood, K.J. (1996) Dual-level designs of buildings under seismic loads. Structural Safety, 18(2), 195-224.
  4. Manickarajah, D., Xie, Y.M., and Steven, G.P. (2000) Optimum design of frames with multiple constraints using an evolutionary method. Computers & Structures, 74(6), 731-741.
  5. Li, G., Zhou, R.G., Duan, L., and Chen, W.F. (1999) Multiobjective and multilevel optimization for steel frames. Engineering Structures, 21(6), 519-529.
  6. Sarma, K.C. and Adeli, H. (2001) Bilevel parallel genetic algorithms for optimization of large steel structures. Computer‐Aided Civil and Infrastructure Engineering, 16(5), 295-304.
  7. Liu, M. (2005) Seismic design of steel moment-resisting frame structures using multiobjective optimization. Earthquake Spectra, 21(2), 389-414.
  8. Antoniou, S. and Pinho, R. (2004) Advantages and limitations of adaptive and non-adaptive force-based pushover procedures. Journal of Earthquake Engineering, 8(04), 497-522.
  9. Mohammadi, R.K., El Naggar, M.H., and Moghaddam, H. (2004) Optimum strength distribution for seismic resistant shear buildings. International Journal of Solids and Structures, 41(22), 6597-6612.
  10. Hajirasouliha, I. and Moghaddam, H. (2009) New lateral force distribution for seismic design of structures. Journal of Structural Engineering, 135(8), 906-915.
  11. Moghaddam, H. and Mohammadi, R.K. (2006) More efficient seismic loading for multidegrees of freedom structures. Journal of Structural Engineering, 132(10), 1673-1677.
  12. American Society of Civil Engineers (ASCE) (2007) Seismic Rehabilitation of Existing Buildings. ASCE Standard ASCE/SEI 41-06.
  13. American Society of Civil Engineers (ASCE) (2010) Minimum Design Loads for Buildings and Other Structures. ASCE Standard ASCE/SEI 7-10.
  14. Moghaddam, H., Hosseini Gelekolai, S.M., Hajirasouliha, I., and Tajalli, F. (2012) Evaluation of various proposed lateral load patterns for seismic design of steel moment resisting frames. 15th World Conference on Earthquake Engineering, Lisbon, Portugal.
  15. American Institute of Steel Construction (AISC) (2010) Specification for Structural Steel Buildings. An American National Standard. ANSI/AISC 360-10.
  16. Pacific Earthquake Engineering Research Center (PEER) (2014) Open System for Earthquake Engineering Simulation (OpenSees). Version 2.4.3. http://opensees.berkeley.edu, University of California, Berkeley.