The Effect of Semi-active Control on Nonlinear Response of Structures through Incremental Dynamic Analysis

Document Type : Research Article


Civil Engineering Group, Faculty of Engineering, University of Guilan, Rasht, Iran


It this paper, incremental dynamic analysis (IDA) of the controlled structures is presented. Nonlinear dynamic analyses for controlled structures are performed through Force Analogy Method (FAM) and State-space. IDA curves are demonstrated for un-controlled structures, under optimal control and under semi-active control. Therefore, the influence of control system for structures and changes in its behavior could be observed. Introductions for IDA, structural control, Semi-active Hydraulic Damper (SHD) and Force Analogy Method (FAM) are explained in the article. Full Static Condensation Model (FSCM) is introduced as a recent method that could consider non-linear behavior (through FAM and State-Space), static condensation and full Rayleigh damping matrix. In this article, FSCM is extended for the structures which are protected by optimal or semi-active control system. Therefore nonlinear behavior of controlled structures was considered. Numerical examples for a 5-story frame under scaled earthquakes were presented. The structure, for both controlled and un-controlled conditions, was modeled by the way that it could consider non-linear behavior. Control algorithms that have been used in the program were optimal control and SHD semi-active control. MATLAB codes were developed and IDA curves for no-control, optimal control and SHD control (with different arrangements of SHD control tools) are calculated and illustrated. At the end of the numerical section, some results and interpretations were extracted from IDA curves of controlled and un-controlled frames. They are explained in details and could give better understanding for dynamic behavior of the structures.


Main Subjects

[01]King, A. 1998. Earthquake Loads & Earthquake Resistant Design of Buildings. Porirua, N.Z.: Building Research Association of New Zealand (BRANZ).
[02]Vamvatsikos, D. and Cornell, C.A. 2002. Incremental Dynamic Analysis. Earthquake Engineering & Structural Dynamics, 3)31), 514-491.
[03]Vamvatsikos, D. and Fragiadakis, M. 2009. Incremental Dynamic Analysis for Estimating Seismic Performance Sensitivity and Uncertainty. Earthquake Engineering & Structural Dynamics, 2)39), 163-141.
[04]Mahdavi, N., Ahmadi, H. R. and Mahdavi, H. 2012. A comparative study on conventional push-over analysis method and IDA approach.Scientific research and essays, 7)7), February 2012.
[05]Vamvatsikos, D. and Cornell, C.A. 2004. Applied Incremental Dynamic Analysis. Earthquake Spectra, 2)20), 553-523.
[06]Lu, D.G. Song, P.Y. Cui, S.S. and Chen, Z.H. 2010. Vertical IDA for Assessing Progressive Collapse Resistance and Failure Modes of Structures. In: 4th International Workshop on Reliable Engineering Computing (REC 2010), Professional Activities Center, National University of Singapore: Research Publishing Services, 172-159.
[07]Mehanny, S. S. F., and Cordova, P.P. 2004. Development of a Two-Parameter Seismic Intensity Measure and Probabilistic Design Procedure. Journal of Engineering and Applied Science, 2)51), 252-233.
[08]Kurata, N. Kobori, T. Takahashi, M. Niwa, N. 1999. Actual Seismic Response Controlled Building with Semi-Active Damper System. Earthquake Engineering and Structural Dynamics. 28, 1447-1427.
[09]Nagarajaiah, S. and Narasimhan, S. 2006. Smart baseisolated benchmark building Part II: phase I sample controllers for linear isolation systems. Structural Control & Health Monitoring, 3‐2 (13) 589-604.
[10]Erkus, B. Johnson, E.A. 2006. Smart base-isolated benchmark building Part III: a sample controller for bilinear isolation. Structural Control & Health Monitoring, 3-2 (13)625-605 .
[11]Narasimhan, S. Nagarajaiah, S. Gavin, H.P. and Johnson, E.A. 2002. Benchmark Problem for Control of Base Isolated Buildings. In: 15th ASCE ngineering Mechanics Conference. Columbia University, New York, NY.
[12]Narasimhan, S. Nagarajaiah, S., Johnson, E.A. and Gavin, H.P. 2006. Smart base-isolated benchmark building Part I: problem definition. Structural Control & Health Monitoring, 3‐2)13). 588-573.
[13]Ohtori, R. Christenson, R.E. Spencer, B.F. Dyke, S.J. 2004. Benchmark control problems for seismically excited nonlinear Buildings. Journal of Engineering Mechanics. 130 (4). 385-366.
[14]Spencer, B.F. Christenson, R.E. and Dyke, S.J. 1999. Next Generation Benchmark Control Problem for Seismically Excited Buildings. Available at: https://pdfs. 58667ee0bc.pdf [Accessed 20.04.2018].
[15]Johnson, E.A and Christenson, R.E. 2017. Structural Control: Benchmark Comparisons. Available at: http:// [last updated: 17/5/7] [Accessed 20.04.2018].
[16]Lynch, J.P. Law, K.H. 2000. A Market-Based Control Solution for Semi-Active Structural Control. In: Computing in Civil and Building Engineering: Proceedings of the Eighth International Conference. Stanford, CA: Reston, Va: American Society of Civil Engineers.
[17]Zhang, J. Xi, W. Dyke, S. Ozdagli, A.I. and Wu B. 2012. Seismic Protection Design of Nonlinear Structures Using Hybrid Simulation. In: 15th World Conference on Earthquake Engineering (15 WCEE). Lisbon, Portugal.
[18]Wong, K.K.F. Wang, Y. 2002. Seismic Energy Dissipation in Structures Using Active Control. In: Structural Stability and Dynamics - The Second International Conference. Singapore, 16 – 18 December 2002. Pages 855-850.
[19]Wong, K.K.F. 2005. Structural Control Energy Efficiency Based on Elastic Displacement. In: IUTAM Symposium on Vibration Control of Nonlinear Mechanisms and Structures. Dordrecht: Springer, 374-365.
[20]Wong, K.K.F. Yang, R. 2003. Predictive instantaneous optimal control of inelastic structures during earthquakes. Earthquake Engineering and Structural Dynamics, 32, .9712–5912
[21]Wong, K.K.F. Hart, G.C. 1997. Active Control of Inelastic Structural Response during Earthquake. The Structural Design of Tall Buildings, 2)6), 149–125.
[22]Wong, K.K.F. Johnson, J. 2009. Seismic Energy Dissipation of Inelastic Structures with Multiple Tuned Mass Dampers. Journal of Engineering Mechanics,135, 275-265.
[23]Wong, K.K.F. Harris, J.L. 2013. Seismic Fragility and Cost Analyses of Actively Controlled Structures. The Structural Design of Tall and Special Buildings, 7)22), 583-569.
[24]Bahar, H. Bahar, A. 2018. A force analogy method (FAM) assessment on different static condensation procedures for frames with full Rayleigh damping. The structural Design of Tall and Special Buildings, [online] 9)27), 14, Available at: [Accessed 19.05.2018].
[25]Vejdani-Noghreiyan, H.R. Shooshtari, A. 2008. Comparison of Exact IDA and Approximate MPA-Based IDA for Reinforced Concrete Frames. In: The 14th World Conference on Earthquake Engineering. Beijing, China. 
[26]Yao, J.T.P. 1972. Concept of Structural Control. Journal of the Structural Division, 7)98), 1574-1567.
[27]Soong, T.T. Spencer, B.F.Jr., 2000. Active, SemiActive and Hybrid Control of Structures. In: 12th World Conference on Earthquake Engineering. Auckland: Upper Hutt, N.Z.: New Zealand Society for Earthquake Engineering.
[28]Hart, G.C. and Wong, K.K.F. 2000. Structural Dynamics for Structural Engineers, New York: John Wiley & Sons, Inc.
[29]Li, G. and Wong, K.K.F. 2014. Theory of Nonlinear Structural Analysis - The Force Analogy Method for Earthquake Engineering. Singapore: John Wiley & Sons, Pte. Ltd.
[30]Li, G. Qifeng, L. Hongnan, L. 2011. Inelastic Structural Control Based on MBC and FAM. Mathematical Problems in Engineering. Volume 2011, Article ID 460731, Hindawi Publishing Corporation, 18 pages.
[31]Casciati, F. Magonette, G. Marazzi, F. 2006. Technology of Semiactive Devices and Applications in Vibration Mitigation. Chichester, West Sussex: John Wiley & Sons, Ltd.
[32]Chopra, A.K. 2012. Dynamics of Structures, Theory and Application to Earthquake Engineering (4th Edition). Prentice Hall.
[33]Wong, K.K.F. and Yang, R. 1999. Inelastic Dynamic Response of Structures using Force Analogy Method. Journal of Engineering Mechanics, 125, 1199-1190.
[34]S. Mazzoni, F. McKenna, M. H. Scott, G. L. Fenves. (2007) OpenSees Command Language Manual, open system for earthquake engineering simulation (OpenSEES). Available at: manuals/usermanual. [Accessed 20.04.2018]
[35]MATLAB, MathWorks Inc., Natick, Ma, USA
[36]Vamvatsikos, D. and Cornell, C.A., 2004. Investigating the Influence of Elastic Spectral Shape on the Limit-State Capacities of a 9-Story Building through IDA. In: 13th World Conference on Earthquake Engineering. Vancouver, B.C., Canada, Paper No. 1463.
[37]Vamvatsikos, D. Jalayer, F. and Cornell, C.A. 2003. Application of IDA to an RC-Structure. Available at: publication/228578842_Application_of_Incremental_ D y n am i c _ A n a ly s i s _ to _ an _ RC - _ St r u c tu re / links/541046ac0cf2d8daaad33395.pdf [Accessed 20.04.2018.]