Hybrid approach for simulating shear–flexure interaction in RC walls with nonlinear truss and fiber models

  • Carlos A. ArtetaEmail author
  • Gustavo A. Araújo
  • Andrés M. Torregroza
  • Andrés F. Martínez
  • Yuan Lu
S.I. : Nonlinear Modelling of Reinforced Concrete Structural Walls


An alternative approach to the nonlinear truss model (NLT) is proposed to simulate the seismic behavior of reinforced concrete (RC) walls with various aspect ratios (ratio between the height and the length of the wall, hw/lw). The alternative consists of a hybrid model comprising an NLT panel connected in series with a forced-based fiber-beam–column model through a rigid elastic beam element (HyNLT-F model). The HyNLT-F approach saves computational time as compared to the default NLT model while keeping the capabilities of modeling inelastic shear response and shear–flexure interaction under static cyclic or dynamic loading. These capabilities are first validated for the default NLT model using the experimental test data of two RC-wall panels subjected to reversed cyclic loading, one whose response is flexure-dominated and another with a shear–predominant behavior. The numerically computed lateral force–displacement relationships, lateral displacement contributions, shear–flexure interaction, and vertical strain distribution at different levels of drift demand show a good agreement with the experimentally recorded responses. The hybrid alternative is then validated using three RC-wall panel experiments with high (hw/lw = 3.1), moderate (hw/lw = 2.3) and low aspect ratio (hw/lw = 1.5). The capabilities of the hybridization are evaluated at the global and local level of  response, as well as in terms of computational time needed to run the model in comparison with the default NLT model. As an application, a HyNLT-F model is implemented in a multistory non-ductile RC frame-wall structure, to evaluate the impact of the nonlinear shear response at the critical section in the global structural behavior under static and dynamic loading. The results show that the HyNLT-F can model features of the wall response such as inelastic shear and shear–flexure interaction at the critical section, which of interest for certain structural typologies.


Hybrid Nonlinear truss model Fiber model Shear–flexure interaction Inelastic shear Reinforced concrete wall Numerical simulation 



Funding for the Universidad del Norte team was provided by CEER—Colombian Earthquake Engineering Research Network through Universidad del Norte, Universidad Militar Nueva Granada, Universidad EIA, Universidad de Medellín through research project INV-ING-2743.


  1. Arteta CA (2015). Seismic response assessment of thin boundary elements of special concrete shear walls. (10188056 Ph.D.), University of California, Berkeley, Ann Arbor. Retrieved from. ProQuest Dissertations & Theses A&I database
  2. Arteta CA, Abrahamson NA (2019) Conditional scenario spectra (CSS) for hazard-consistent analysis of engineering systems. Earthq Spectra 35(2):737–757. CrossRefGoogle Scholar
  3. Beyer K, Dazio A, Priestley MJN (2011) Shear deformations of slender reinforced concrete walls under seismic loading. ACI Struct J 108(2):167–177Google Scholar
  4. Coleman J, Spacone E (2001) Localization issues in force-based frame elements. J Struct Eng 127(11):1257–1265. CrossRefGoogle Scholar
  5. Dazio A, Beyer K, Bachmann H (2009) Quasi-static cyclic tests and plastic hinge analysis of RC structural walls. Eng Struct 31(7):1556–1571. CrossRefGoogle Scholar
  6. Filippou FC, Popov EP, Bertero VV (1983) Effects of bond deterioration on hysteretic behavior of reinforced concrete joints. Report UCB/EERC-83/19. Retrieved from BerkeleyGoogle Scholar
  7. Fischinger M, Rejec K, Isakovic T (2012) Modeling inelastic shear response of RC walls. Paper presented at the 15th world conference on earthquake engineering, Lisbon, PortugalGoogle Scholar
  8. Fischinger M, Rejec K, Isaković T (2014) Inelastic shear response of rc walls: a challenge in performance based design and assessment. In: Fischinger M (ed) Performance-based seismic engineering: vision for an earthquake resilient society, vol 32. Springer, DordrechtGoogle Scholar
  9. Galanis PH, Moehle JP (2015) Development of collapse indicators for risk assessment of older-type reinforced concrete buildings. Earthq Spectra 31(4):1991–2006CrossRefGoogle Scholar
  10. Hiraishi H (1984). Evaluation of shear and flexural deformations of flexural type shear walls. Paper presented at the 8th world conference on earthquake engineering, San Francisco, USGoogle Scholar
  11. Holmes WT, Liel AB, Mehrain M, Moehle JP, Somers P (2017) Seismic evaluation of older concrete frame, frame-wall, and bearing wall buildings for collapse potential, ATC-78-6. Preliminary report. Retrieved from Redwood CityGoogle Scholar
  12. Hoshikuma J, Kawashima K, Nagaya K, Taylor AW (1997) Stress-strain model for confined reinforced concrete in bridge piers. J Struct Eng 123(5):624–633. CrossRefGoogle Scholar
  13. Jansen DC, Shah SP (1997) Effect of length on compressive strain softening of concrete. J Eng Mech 123(1):25–35CrossRefGoogle Scholar
  14. Jiang H, Kurama YC (2010) Analytical modeling of medium-rise reinforced concrete shear walls. ACI Struct J. Google Scholar
  15. Kent DC, Park R (1971) Flexural members with confined concrete. J Struct Div 97(7):1969–1990Google Scholar
  16. Kolozvari K, Orakcal K, Wallace JW (2014) Modeling of cyclic shear–flexure interaction in reinforced concrete structural walls. I: theory. J Struct Eng 141(5):04014135. CrossRefGoogle Scholar
  17. Kolozvari K, Arteta C, Fischinger M, Gavridou S, Hube M, Isakovic T, Wallace J (2018) Comparative study of state-of-the-art macroscopic models for planar reinforced concrete walls. ACI Struct J 115(6):20. Google Scholar
  18. Lu Y, Panagiotou M (2014) Three-dimensional cyclic beam-truss model for nonplanar reinforced concrete walls. J Struct Eng 140(3):04013071. CrossRefGoogle Scholar
  19. Lu Y, Panagiotou M, Koutromanos I (2014) Three-dimensional beam-truss model for reinforced-concrete walls and slabs subjected to cyclic static or dynamic loading, PEER Report 2014/18, Pacific Earthquake Engineering Research Center. University of California, BerkeleyGoogle Scholar
  20. Lu Y, Henry RS, Gultom R, Ma MT (2017) Cyclic testing of reinforced concrete walls with distributed minimum vertical reinforcement. J Struct Eng 143(5):04016225. CrossRefGoogle Scholar
  21. Massone LM, Wallace JW (2004) Load-deformation responses of slender reinforced concrete walls. ACI Struct J 101(1):103–113Google Scholar
  22. Massone LM, Orakcal K, Wallace JW (2006) Shear–flexure interaction for structural walls. Special Publication, New York. Google Scholar
  23. Mazzoni S, McKenna F, Fenves GL (2007) Steel02 & hysteretic—material behavior. OpenSees comparison of modelling tools. Retrieved from
  24. McKenna F, Fenves GL, Scott MH, Jeremic B (2000) Open system for earthquake engineering simulation (OpenSees) (version 2.4.3.). Pacific Earthquake Engineering Research Center, University of California, BerkeleyGoogle Scholar
  25. Mohd Yassin MH (1994) Nonlinear analysis of prestressed concrete structures under monotonic and cyclic loads. Retrieved fromGoogle Scholar
  26. Morsch E (1922) Der Eisenbetonbau-Seine Theorie und Anwendung (Reinforced concrete construction-Theory and application) (5th ed. vol. 1). Stuttgart, GermanyGoogle Scholar
  27. Panagiotou M, Restrepo JI, Schoettler M, Kim G (2012) Nonlinear cyclic truss model for reinforced concrete walls. ACI Struct J 109:205Google Scholar
  28. Park H, Eom T (2007) Truss model for nonlinear analysis of rc members subject to cyclic loading. J Struct Eng 133(10):1351–1363. CrossRefGoogle Scholar
  29. Parra PF, Arteta CA, Moehle JP (2019) Modeling criteria of older non-ductile concrete frame-wall buildings. Bull Earthq Eng (in press) Google Scholar
  30. Ritter W (1899) Die Bauweise Hennebique. Schweizerishe Bauzeitung 33(7):59–61Google Scholar
  31. Schlaich J, Schäfer K (1991) Design and detailing of structural concrete using strut-and-tie models. Struct Eng 69(6):113–125Google Scholar
  32. Schlaich J, Weischede D (1982) Detailing of concrete structures: first draft of a design manual (in German), bulletin d’Information 150. Comité Euro-International du Beton, ParisGoogle Scholar
  33. Scott MH, Fenves GL (2006) Plastic hinge integration methods for force-based beam–column elements. J Struct Eng 132(2):244–252. CrossRefGoogle Scholar
  34. Scott M, Filippou FC (2016) Hysteretic material. Retrieved from.
  35. Scott BD, Park R, Priestley MJN (1982) Stress–strain behavior of concrete confined by overlapping hoops at low and high strain rates. ACI J Proc 79(1):13–27. Google Scholar
  36. Spacone E, Filippou FC, Taucer FF (1996) Fibre beam–column model for non-linear analysis of R/C frame: part I formulation. Earthq Eng Struct Dyn 25:711–725CrossRefGoogle Scholar
  37. Stevens NJ, Uzumeri SM, Collins MP, Will TG (1991) Constitutive model for reinforced concrete finite element analysis. ACI Struct J 88:49Google Scholar
  38. Thomsen JH, Wallace JW (2004) Displacement-based design of slender reinforced concrete structural walls-experimental verification. J Struct Eng Asce 130(4):618–630. CrossRefGoogle Scholar
  39. Tran TA, Wallace JW (2015) Cyclic testing of moderate-aspect-ratio reinforced concrete structural walls. ACI Struct J 112(6):653–665CrossRefGoogle Scholar
  40. Vecchio FJ, Collins MP (1986) The modified compression-field theory for reinforced concrete elements subjected to shear. ACI J 83(2):219–231Google Scholar
  41. Vecchio FJ, Collins MP (1993) Compression response of cracked reinforced concrete. J Struct Eng 119(12):3590–3610CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversidad del NorteBarranquillaColombia
  2. 2.Computers and Structures IncWalnut CreekUSA

Personalised recommendations