Comparative Review of the Performance Based Design of Building Structures Using Static Non-Linear Analysis, Part B: R/C Frames


1 Associate Professor, Faculty of Engineering, University of Porto (FEUP), Porto, Portugal

2 Ph.D. Student, Faculty of Engineering, University of Porto (FEUP), Porto, Portugal

3 Assistant Professor, Faculty of Civil Engineering, Semnan University, Semnan, Iran

4 Ph.D. Student, Faculty of Civil Engineering, Semnan University, Semnan, Iran


The objective of this review to be submitted in two independent parts, for steel frames and for RC frames, is to compare their structural performance with respect to the proposed N2-method, and so also of the consequent convenience of using pushover methodology for the seismic analysis of these structures. A preliminary investigation is presented on a pushover analysis used for the seismic performance of metallic braced frames equipped with diagonal X-bracing and K-bracing systems. Three steel frames are analysed corresponding to 3, 6 and 10 floor regular buildings that were modelled in the MIDAS/Civil finite element software. To obtain the pushover curve a non-linear static methodology is used. For the RC frames three commercial programs (SAP 2000, SeismoStruck and MIDAS/Civil) are used in order to perform a parametric study based on pushover analyses. The equivalent strut method is applied to simulate the influence of the masonry infill panels; to evaluate the influence of these on the capacity curves, several strut width values are considered. The parametric study also addresses the influence of other parameters on the structural behaviour and non-linear capacity curves of the RC frame, namely: length and position of the plastic hinges and different loading patterns (uniform, modal and triangular distributions).


[1] Fajfar, P., Fischinger, M. “N2 – A Method for Non-Linear Seismic Analysis of Regular Buildings”. Proceedings of the 9th World Conference in Earthquake Engineering, 1988, Vol.5, 111-116, Tokyo-Kyoto, Japan.
[2]     EC 8, Eurocode 8: Design of structures for earthquake resistance; Part 1: General Rules, Seismic Actions and Rules for Buildings; CEN, Brussels, 2003.
[3] Cesar, M.B., Barros, R.C., “Estudo Preliminar sobre o Desempenho Sísmico de Pórticos Metálicos Contraventados a partir de Análises Estáticas Não-Lineares (Pushover)”; Proceedings of ‘Métodos Numéricos e Computacionais em Engenharia CMNE 2007 e XXVIII CILAMCE’, Congresso Ibero Latino-Americano sobre Métodos Computacionais em Engenharia, FEUP, Porto, 13-15 Junho 2007; CMNE/CILAMCE 2007, Paper 1184 – pp. 1-18; Edts: A. Rodriguez-Ferran, Javier Olivier, Paulo R.M. Lyra, José L.D. Alves; APMTAC / SEMNI, 2007.
[4] Cesar, M.B., Barros, R.C., “Seismic Performance of Metallic Braced Frames by Pusho-ver Analyses”, Computational Methods in Structural Dynamics and Earthquake Engi-neering (COMPDYN 2009), M. Papadrakakis, N.D. Lagaros, M. Fragiadakis (eds.), Rhodes, Greece, 22–24 June 2009.
[5] Pereira, V.G., Barros, R.C. and Cesar, M.B., “A Parametric Study of a R/C Frame Based on Pushover Analysis”, 3rd International Conference on Integrity, Reliability & Failure (IRF 2009), J.F. Silva Gomes and S.A. Meguid (eds.), Porto, Portugal, 20-24 July 2009.
[6] Pereira, V.G., Barros, R.C. and Cesar, M.B., “Pushover Analyses of a R/C Frame by distinct Software”, 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science (EPMESC XII), Hong-Kong and Macao, 30 Nov–3 Dec 2009.
[7] Elghazouli, A.Y. (editor), “Seismic Design of Buildings to Eurocode 8”, Spon Press, Abingdon, Oxon, UK, 2009.
[8] FEMA - Federal Emergency Management Agency, “NEHRP guidelines for the seismic rehabilitation of buildings”, FEMA-273; “NEHRP commentary on the guidelines for the seismic rehabilitation of buildings”, FEMA-274; Washington, D.C., 1997.
[9] R.F. Almeida, R.C. Barros, “A new multimode load pattern for pushover analysis: the effect of higher modes of vibration”, Earthquake Resistant Engineering Structures IV, Eds.: G. Latini and C.A. Brebbia, WIT Press, (2003), U.K., pp. 3-13.
[10] R. C. Barros, R. Almeida, “Pushover analysis of asymmetric three-dimensional buildings frames”, Journal Civil Engineering & Management, Vol. XI, Number 1, pp. 3-12, Vilnius, Lithuania, 2005.
[11] Chopra, A.K., Goel, R.K., “A modal pushover analysis procedure to estimate seismic demands for unsymmetric-plan buildings”, Earthquake Engng Struct. Dyn. 33: 903–927, John Wiley & Sons Ltd, 2004.
[12] H.N. Li, G. Li, Simplified method for pushover curves of asymmetric structure with dis-placement dependent passive energy dissipation devices, Advances in Structural Engi-neering, Vol. 10, Issue 5, (2007), 537-649.
[13] G. Li, H.N. Li, Direct displacement-based design for buildings with passive energy dis-sipation devices, Gongcheng Lixue/Engineering Mechanics, Vol. 25, Issue 3, (2008), 49-57.
[14] ATC, Seismic evaluation and retrofit of concrete buildings, Report ATC-40, Applied Technology Council, Redwood City CA (1996).
[15] FEMA-356, Prestandard and commentary for the seismic rehabilitation of buildings, Report FEMA 356, Federal Emergency Management Agency, Washington, (2000).
[16] P. Fajfar, A nonlinear analysis method for performance-based seismic design, Earth-quake Spectra, Vol. 16, EERI, (2000), pp. 573-592.
[17] R. Bento, S. Falcão, F. Rodrigues, Avaliação sísmica de estruturas de edifícios com base em análises estáticas não lineares, SISMICA 2004 – 6º Congresso Nacional de Sismologia e Engenharia Sísmica, Guimarães, Portugal, 2004.
[18] MIDASIT, “MIDAS/Civil – General purpose analysis and optimal design system for civil structures”, MIDAS Information Technology Co, Ltd., Korea, 2005.
[19] M.S. Williams, F. Albermani, Evaluation of displacement-based analysis and design methods for steel frames with passive energy dissipators, Civil Engineering Research Bulletin No. 24, University of Queensland, Australia, 2003.
[20] Braz-Cesar, M., Oliveira, D.V. and R. Carneiro-Barros, “Numerical Validation of the Experimental Cyclic Response of RC Frames”, Chapter 12 in the book Trends in Com-putational Structures Technology, Edited by: B.H.V. Topping, Saxe-Coburg Publications, ISBN 978-1-874672-39-5, pp. 267-291, Stirlingshire, Scotland, 2008.
[21] H. Krawinkler, G.D.P.K. Seneviratna, Pros and cons of a pushover analysis of seismic performance evaluation, Engineering Structures, Vol. 20, (1998), pp. 452-464.
[22] Park, R. and T. Paulay, Reinforced Concrete Structures. John Wiley & Sons Inc., New York, 1975.
[23] Park, R., Priestley, M.J.N., and W.D. Gill; “Ductility of square-confined concrete col-umns”, Journal of the Structural Division, ASCE, Vol. 108, No. ST 4, pp. 929-950, 1982.
[24] Priestley, M.J.N., Seible, F. and G.M.S. Calvi, Seismic design and retrofit of bridges. John Wiley & Sons Inc., New York, 1996.
[25] Polyakov, S. V., Masonry in framed building: an investigation into the strength and stiffness of masonry infilling, Moscow, 1957.
[26] Stafford Smith, B. and C. Carter, “A method of analysis for infilled frames”, Proceed-ings of the Institution of Civil Engineers, Vol. 44, 1969.
[27] Riddington, J. R. and B. Stafford Smith, “Analysis of infilled frames subject to racking with design recommendations”, The Structural Engineer, Vol. 55, Nº 6, 1977.
[28] Paulay, T. and M. Priestley, Seismic Design of Reinforced Concrete and Masonry Buildings, John Wiley & Sons, 1992.
[29] Crisafulli F.J., Seismic Behaviour of Reinforced Concrete Structures with Masonry Infills, PhD Thesis, University of Canterbury, New Zealand, 1997.
[30] Fardis, M.N. and T.B. Panagiotakos, “Seismic design and response of bare and masonry-infilled reinforced concrete buildings – Part II: Infilled structures”, Journal of Earth-quake Engineering, Vol. I, No 3, 475-503, 1997.
[31] Eurocódigo 2: Projecto de estruturas de betão; Parte 1-1: Regras gerais e regras para edifícios. Comité Europeu de Normalização, Brussels, 2004.
[32] Fagus, Fagus-5: Version 1.22.0 Build 275, Cubus AG, Zurïch, 2000-2006.
[33] Computers & Structures Inc.; “SAP 2000 v10.0.1 – Structural Analysis Program”. Berkeley, California, U.S.A., 2005.
[34] SeismoSoft SeismoStruck, “A Computer Program for Static and Dynamic Nonlinear Analysis of Framed Structures”. Available online at:; 2006.
[35] Blandon, C.A., “Implementation of an Infill Masonry Model for Seismic Assessment of Existing Buildings”, Individual Study, European School for Advanced Studies in Reduc-tion of Seismic Risk (ROSE School), Pavia, Italy, 2005.