Robust Design of Reinforced Concrete Moment-Resisting Frames

Document Type : Original Article


Urmia university


Reinforced concrete moment resisting frame (RCMRF) is one of the most popular structural systems. Conventionally, buildings with RCMRF systems are designed to satisfy the relative displacement, resistance, and flexibility requirements defined by the design codes. Structural design codes have given different ranges of design parameters that the designers and engineers must consider in the design process of structures and the values selected for these parameters affect the seismic behaviour of the structures. However, performance assessment of the RCMRF under the earthquake loading to limit the probable levels of damage has a complicated and difficult procedure that is time-consuming for designing of ordinary buildings. In this study, to prevent this time-consuming process, tighter ranges for design parameters have been attempted to improve the seismic performance of the RCMRFs. In this regard, databases of RCMFs were created for different ranges of design parameters. The Particle Swarm Optimization (PSO) algorithm is used to create these databases and RCMRFs are optimally designed according to ACI 318-14 code. Then, nonlinear time history analysis according to ASCE/SEI 7-16 code was performed on the RCMRFs in each one of the databases and the statistical analysis of local and global results acquired from the nonlinear time history analysis is carried out. Finally, tighter ranges of design parameters have been determined to achieve more robust structures without involvement in time-consuming processes.


[1]      American Concrete Institute (ACI). Building code requirements for structural concrete. ACI 318-14, 2014.
[2]      Kennedy, J. and R.C. Eberhart, Particle swarm optimization. Proceedings of the IEEE International Conference on Neural Networks, 1999. 4: p. 1942-1948, DOI: 10.1109/ICNN.1995.488968
[3]      Kuntz, G.L. and Browning, J., 2003. Reduction of column yielding during earthquakes for reinforced concrete frames. American Concrete Institute.
[4]      Maffei, J., Bonelli, P., Kelly, D., Lehman, D.E., Lowes, L., Moehle, J., Telleen, K., Wallace, J. and Willford, M., 2014. Recommendations for seismic design of reinforced concrete wall buildings based on studies of the 2010 Maule, Chile earthquake.
[5]      American Society of Civil Engineers (ASCE) – Structural Engineering Institute. Minimum Design Loads and Associated Criteria for Buildings and Other Structures. ASCE/SEI 7-16, 2016.
[6]      Lee, C. and J. Ahn, Flexural Design of Reinforced Concrete Frames by Genetic Algorithm. Journal of Structural Engineering, 2003. 129(6): p. 762-774. DOI: 10.1061/(ASCE)0733-9445(2003)129:6(762)
[7]      GN, V., Numerical Optimization Techniques for Engineering Design: With Application. 1984, NewYork: McGraw-Hill.
[8]      Eberhart RC., Kennedy J. “A new optimizer using particles swarm theory”, Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 1995, 39–43.
[9]      Kennedy J., Eberhart RC. “Particle Swarm Optimization”, Proceedings of the IEEE International Conference on Neural Networks, Vol. IV, Piscataway, NJ, 1995, 1942–1948.
[10]   Perez RE., Behdinan K. “Particle swarm approach for structural design optimization”, Computers & Structures, 2007(85), 1579-1588.
[11]   Shi Y., Eberhart R. “A modified particle swarm optimizer”, IEEE International Conference on Evolutionary Computation, IEEE Press, Piscataway, NJ, 1998, 69–73.
[12]   Li LJ., Huang ZB., Liu F., Wu QH. “A heuristic particle swarm optimizer for optimization of pin connected structures”, Computers & Structures, 85, 340-349,2007. DOI: 10.1016/j.compstruc.2006.11.020
[13]   Fourie P., Groenwold A. “The Particle Swarm Optimization algorithm in size and shape optimization”, Structural and Multidisciplinary Optimization, 23, 259-267, 2002.
[14]   Ch. Gheyratmand, S. Gholizadeh and B. Vahabzadeh. Optimization of RC. Frames by an improved artificial bee colony algorithm. International Journal of Optimization in Civil Engineering, 2015. 5(2):189-203.
[15]   Fadaee MJ, Grierson DE. Design optimization of 3D reinforced concrete structures. Structural Optimization, Vol. 12, No. 2 (1996): 127-134.
[16]   Park G, Lee T, Lee K, Hwang K. Robust design: an overview. AIAA Journal, Vol. 44, No. 1 (2006):181–191. DOI: 10.2514/1.13639
[17]   Michalis Fragiadakis, Nikos D. Lagaros, An overview to structural seismic design optimization frameworks, Computers and Structures 89 (2011) 1155–1165. DOI: 10.1016/j.compstruc.2010.10.021
[18]    Cochran, W.G. 1963. Sampling Techniques, 2nd Ed., New York: John Wiley and Sons, Inc.
[19]   National Institute of Standards and Technology (NIST). Seismic Design of Reinforced Concrete Special Moment Frames: A Guide for Practicing Engineers. NEHRP Seismic Design Technical Brief No. 1, NIST GCR 8-917-1.
[20]   American Society of Civil Engineers (ASCE) – Structural Engineering Institute. Seismic Evaluation and Retrofit of Existing Buildings. ASCE/SEI 41-13, 2013.
[21]   Y. Menasri, M. S. Nouaouria, M. Brahimi. Probabilistic Approach to the Seismic Vulnerability of RC Frame Structures by the Development of Analytical Fragility Curves. International Journal of Engineering, Transactions A: Basics, 2017. 30(7):945-954. doi: 10.5829/ije.2017.30.07a.03
[22]   Federal Emergency Management Agency (FEMA) - National Earthquake Hazards Reduction Program (NEHRP). Quantification of Building Seismic Performance Factor. FEMA P695/ June 2009.
[23]   Federal Emergency Management Agency (FEMA). Quantification Instructional Material Complementing FEMA 451, Design Examples, Seismic Load Analysis.
[24]   J. B. Mander, M. J. N. Priestley and R. Park. Observed Stress-Strain Behavior of Confined Concrete. Journal of Structural Engineering, 1988, 114(8): 1827-1849.
[25]   J. B. Mander, M. J. N. Priestley and R. Park. Theoretical Stress-Strain Model For Confined Concrete. Journal of Structural Engineering, 1988, 114(8): 1804-1826.
[26]   M Heidari, F Behnamfar, H Zibasokhan, A Macro-model for Nonlinear Analysis of 3D Reinforced Concrete Shear Walls. International Journal of Engineering, Transactions B: Applications, 2018. 31(2):220-227. doi: 10.5829/ije.2018.31.02b.05