The Effect of Axial Force Variations on Nonlinear Modeling and Seismic Response of Reinforced Concrete Structures

Document Type : Research Papers


1 Faculty of Civil Engineering, Babol Noshirvani University of Technology

2 Department of Civil Engineering, Babolsar University of Mazandaran


In order to increase the accuracy of evaluating seismic response of structures, it is critical to conduct dynamic analyses based upon precise nonlinear models being as consistent as possible with the real conditions of corresponding structures. The concentrated plasticity model including one elastic element and two nonlinear spring elements at both ends has been considered within the research community for simulating beams and columns, counting the effect of strength and stiffness degradation. In this type of simulation, the axial force ratio generated in each structural component, which is a major factor in introducing nonlinear springs, has always been considered constant in the literature. The main objective of the present research is, therefore, to modify the fundamental weakness in this type of modeling approach; indeed, any variation of element’s axial effort, owing to redistribution of axial forces during an earthquake, is applied in the calculation of parameters of the concentrated plasticity model as a decisive step toward the development of nonlinear dynamic analysis. Moreover, an algorithm is presented for implementing this approach in the OpenSees software. Verification is established and the efficiency of the proposed method is illustrated through a reinforced concrete moment frame subjected to a specific record, as a case study building. Regarding the results, it is confirmed that the proposed algorithm is an appropriate tool for achieving quite a realistic nonlinear model and estimating reasonably accurate responses of structural systems with cyclic degrading behavior under earthquake loading.


Abad, J., Réveillère, A., Ulrich, T., Gehl, P. and Bernard, R. (2013). “Fragility of pre-damaged elements: Realisation of fragility functions of elements pre-damaged by other past events and demonstration on a scenario”, Deliverable 4.2- .MATRIX - New methodologies for multi-hazard and multi-risk assessment methods for Europe.
Abdollahzadeh, G., Sazjini, M. and Asghari, A. (2015). “Seismic fragility Aassessment of Special Truss Moment Frames (STMF) using the capacity spectrum method”, Civil Engineering Infrastructures Journal, 48(1), 1-8.
ACI 318-63. (1963). Building code requirements for reinforced concrete, American Concrete Institute, Detroit, MI.
Asgarian, B., Khazaee, H. and Mirtaheri, M. (2012). “Performance evaluation of different types of steel moment resisting frames subjected to strong ground motion through incremental dynamic analysis”, International Journal of Steel Structures, 12(3), 363-379.
Baker, J.W. (2015). “Efficient analytical fragility function fitting using dynamic structural analysis”, Earthquake Spectra, 31(1), 579-599.
Ebrahimi, E., Abdollahzadeh, G. and Jahani, E. (2019). “Assessment of axial load effect on nonlinear modeling and seismic response of reinforced concrete‐structures based on fuzzy set theory  using genetic algorithm”, Structural Concrete, 20(2), 614-627.
Elwood, K.J., Matamoros, A., Wallace, J.W., Lehman, D., Heintz, J., Mitchell, A., Moore, M., Valley, M., Lowes, L.N., Comartin, C. and Moehle, J.P. (2007). “Update to ASCE/SEI 41 concrete provisions”, Earthquake Spectra, 23(3), 493-523.
Gaetani d’Aragona, M. (2015). “Post-earthquake assessment of damaged non-ductile buildings: detailed evaluation for rational reparability decisions”, Ph.D. Thesis, University of Naples Federico II.
Haselton, C., Deierleien, G., Bono, S., Ghannoum, W., Hachem, M., Malley, J., Hooper, J., Lignos, D., Mazzoni, S., Pujol, S., Uang, C.M., Hortascu, A. and Cedillos, V. (2016). “Guidelines on nonlinear dynamic analysis for performance-based seismic design of steel and concrete moment frames”, In 2016 SEAOC Convention (No. CONF).
Haselton, C.B., Liel, A.B., Taylor Lange, S. and Deierlein, G.G. (2008). Beam-column element model calibrated for predicting flexural response leading to global collapse of RC frame buildings, Berkeley, California: Pacific Earthquake Engineering Research Center, Report No. 2007/03.
Ibarra, L.F., Medina, R.A. and Krawinkler, H. (2005). “Hysteretic models that incorporate strength and stiffness deterioration”, Earthquake Engineering and Structural Dynamics, 34(12), 1489-1511.
Kabeyasawa, T., Shen, F.H., Kuramoto, H. and Rubiano, N.R. (1991). “Experimental study on behavior of ultra-high-strength reinforced concrete columns under tri-axial forces”, Transactions of the Japan Concrete Institute, 13, 279-286.
Kazantzi, A.K., Vamvatsikos, D. and Lignos, D.G. (2014). “Seismic performance of a steel moment-resisting frame subject to strength and ductility uncertainty”, Engineering Structures, 78, 69-77.
Mohammadizadeh, M.R., Vahidi, K. and Ronagh, H.R. (2018). “Seismic reliability analysis of offshore fixed platforms using incremental dynamic analysis”, Civil Engineering Infrastructures Journal, 51(2), 229-251.
NGA-West2. (2013). Peer ground motion database, Available at:
OpenSees (2017). Open system for earthquake engineering simulation, Pacific Earthquake Engineering Research Center, Available at:
Panagiotakos, T.B. and Fardis, M.N. (2001). “Deformations of reinforced concrete at yielding and ultimate”, ACI Structural Journal, 98(2), 135-147.
Park, R. and Paulay, T. (1975). Reinforced concrete structures, John Wiley and Sons, New York.
Razvi, S.R. and Saatcioglu, M. (1994). “Strength and deformability of confined high-strength concrete columns”, ACI Structural Journal, 91(6), 678-687.
Rissman, A. (1965). Drawings of Holiday Inn building, Rissman and Risman Associated Ltd.
Rodrigues, H., Arede, A., Varum, H. and Costa, A.G. (2013). “Experimental evaluation of rectangular concrete column behaviour under biaxial cyclic loading”, Journal of Earthquake Engineering and Structural Dynamics, 42(2), 239-259.
Rodrigues, H., Furtado, A. and Arêde, A. (2015). “Behaviour of rectangular reinforced-concrete columns under biaxial cyclic loading and variable axial loads”, Journal of Structural Engineering, 142(1), 04015085.
Rodrigues, H., Furtado, A., Arêde, A. and Varum, H. (2018a). “Influence of seismic loading on axial load variation in reinforced concrete columns”, E-GFOS, 9(16), 37-49.
Rodrigues, H., Furtado, A., Arêde, A., Vila-Pouca, N. and Varum, H. (2018b). “Experimental study of repaired RC columns subjected to uniaxial and biaxial horizontal loading and variable axial load with longitudinal reinforcement welded steel bars solutions”, Engineering Structures, 155, 371-386.
Saadeghvaziri, M.A. and Foutch, D.A. (1991). “Dynamic behavior of R/C highway bridges under the combined effect of vertical and horizontal earthquake motions”, Journal of Earthquake Engineering and Structural Dynamics, 20(6), 535-549.
Saadeghvaziri, M.A. (1997). “Nonlinear response and modelling of RC columns subjected to varying axial load”, Engineering Structures, 19(6), 417-424.
Saatcioglu, M. and Ozcebe, G. (1989). “Response of reinforced concrete columns to simulated seismic loading”, ACI Structural Journal, 86(1), 3-12.
Shome, N. and Cornell, C.A. (1999). Probabilistic seismic demand analysis of nonlinear structures, Stanford, California: Stanford University, Report No. RMS-35.
Vamvatsikos, D. and Cornell, C.A. (2002). “Incremental dynamic analysis”, Earthquake Engineering and Structural Dynamics, 31(3), 491-514.
Vamvatsikos, D., Jalayer, F. and Cornell, C.A. (2003). “Application of incremental dynamic analysis to RC-structures”, The FIB Symposium on Concrete Structures in Seismic Regions, Athens, 1-12.
Xu, G., Wu, B., Jia, D., Xu, X. and Yang, G. (2018). “Quasi-static tests of RC columns under variable axial forces and rotations”, Engineering Structures, 162, 60-71.
Zareian, F.and Krawinkler, H. (2007). “Assessment of probability of collapse and design for collapse safety”, Earthquake Engineering and Structural Dynamics, 36, 1901-1914.
Volume 52, Issue 2
December 2019
Pages 379-395
  • Receive Date: 05 March 2019
  • Revise Date: 28 September 2019
  • Accept Date: 13 October 2019
  • First Publish Date: 01 December 2019