Skip to main content

Nonlinear cyclic Truss Model for analysis of reinforced concrete coupled structural walls


This paper discusses the Truss Model proposed by Panagiotou et al. (ACI Struct J 109(2):205–214, 2012) for modeling reinforced concrete coupled structural walls. The model is validated with the landmark seismic testing of two 1:4 scale seven-story test specimens reported in Santhakumar (The ductility of coupled shear walls. Dissertation, University of Canterbury 1974) and in Paulay and Santhakumar (J Struct Div 102(1):93–108, 1976). The first specimen, Wall A, incorporated conventionally reinforced coupling beams whereas the second specimen, Wall B, incorporated diagonally reinforced coupling beams. These two specimens attained roof drift ratios of at least 1.7% before initiation of lateral strength degradation. Coupling beams in specimen Wall A exhibited significant strength degradation due to sliding shear, whereas coupling beams in specimen Wall B maintained the capacity throughout. We compare key overall and local responses reported for the two specimens with those computed with the Truss Models, as well as responses that could be only computed. In the latter, we show that when the beams effectively coupled the walls, the shear force at the wall base was mainly resisted by the wall being compressed. Moreover, the analysis shows that the first level coupling beams develop greater shear forces than the other beams despite all beams were identically reinforced. This is caused by the restraint provided by the fixed-base walls and by the kinematics of the strongly coupled walls. The Truss Model captures these responses because it explicitly considers the axial-flexure-shear interaction of RC walls and beams.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6: a
Fig. 7: a
Fig. 8: a
Fig. 9
Fig. 10: a
Fig. 11
Fig. 12


  • ACI (2014) Building code requirements for structural concrete (ACI 318-14) and commentary (ACI 318R-14). American Concrete Institute, Farmington Hills

    Google Scholar 

  • ASCE 41–17 (2017) Seismic evaluation and retrofit of existing buildings (41-17). American Society of Civil Engineers, Reston

    Google Scholar 

  • Carreño R (2018) Characterization of large diameter reinforcing bars under large strain cyclic reversals. Dissertation, University of California San Diego

  • CCA (2018) Demountable Mechanical Strain Gauge (DEMEC). British Cement and Concrete Association. Accessed May 2018

  • Coleman J, Spacone E (2001) Localization issues in nonlinear frame elements. J Struct Eng 127(11):1257–1265.

    Article  Google Scholar 

  • Collins MP, Mitchell D (1997) Prestressed concrete structures. Response Publications, Toronto

    Google Scholar 

  • Dashti F, Dhakal RP, Pampanin S (2017) Numerical modeling of rectangular reinforced concrete structural walls. J Struct Eng.

    Article  Google Scholar 

  • Dhakal R, Maekawa K (2002) Modeling for postyield buckled of reinforcement. J Struct Eng 128(9):1139–1147

    Article  Google Scholar 

  • Dodd LL, Restrepo-Posada JI (1995) Model for predicting cyclic behavior of reinforcing steel. J Struct Eng 121(3):433–445

    Article  Google Scholar 

  • Fischinger M, Rejec K, Isakovic T (2012). Modeling inelastic shear response of RC walls. In: Proceedings of 15th world conference on earthquake engineering, Lisbon, Portugal

  • Fischinger MA, Vidic TO, Fajfar P (1992) Nonlinear seismic analysis of structural walls using the multiple- vertical-line-element model. In: Krawinkler H, Fajfar P (eds) Nonlinear seismic analysis of RC buildings. Elsevier, London, pp 191–202

    Google Scholar 

  • Fleischman RB, Restrepo JI, Pampanin S, Maffei JR, Seeber K, Zahn FA (2014) Damage evaluations of precast concrete structures in the 2010–2011 Canterbury earthquake sequence. Earthq Spectra 30(1):277–306

    Article  Google Scholar 

  • Gomes A, Appleton J (1997) Nonlinear cyclic stress-strain relationship of reinforcing bars including buckling. Eng Struct 19(10):822–826

    Article  Google Scholar 

  • Kolozvari K, Wallace JW (2016) Practical nonlinear modeling of reinforced concrete structural walls. J Struct Eng.

    Article  Google Scholar 

  • LATBSDC (2017) An alternative procedure for seismic analysis and design of tall buildings located in the Los Angeles region. Los Angeles Tall Buildings Structural Design Council, Los Angeles

    Google Scholar 

  • Lu Y (2014) Three-dimensional seismic analysis of reinforced concrete wall buildings at near-fault sites. Dissertation, University of California Berkeley

  • Lu Y, Panagiotou M (2013) Three-dimensional cyclic beam–truss model for nonplanar reinforced concrete walls. J Struct Eng.

    Article  Google Scholar 

  • 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. Report 2014/18: PEER

  • Lu Y, Panagiotou M, Koutromanos I (2016) Three-dimensional beam–truss model for reinforced concrete walls and slabs—part 1: modeling approach, validation, and parametric study for individual reinforced concrete walls. Earthq Eng Struct Dyn.

    Article  Google Scholar 

  • Lu Y, Panagiotou M (2016) Three-dimensional beam–truss model for reinforced concrete walls and s labs—part 2: modeling approach and validation for slabs and coupled walls. Earthq Eng Struct Dyn.

    Article  Google Scholar 

  • Mander JB, Priestley JN, Park R (1988) Theoretical stress-strain model for confined concrete. J Struct Eng 114(8):1804–1826

    Article  Google Scholar 

  • McKenna F (2018) OpenseesWiki. Accessed May 2018

  • Mihaylov BI, Franssen R (2017) Shear-flexure interaction in the critical sections of short coupling beams. Eng Struct 152:370–380

    Article  Google Scholar 

  • Moharrami M, Koutromanos I, Panagiotou M, Girgin SC (2015) Analysis of shear-dominated RC columns using the nonlinear truss analogy. Earthq Eng Struct Dyn 44:677–694

    Article  Google Scholar 

  • Mohr D, Lehman D, Lowes L (2007) Performance based design and nonlinear modeling of coupled shear walls and coupling beams. ASCE structure congress 2007: new horizons and better practices.

  • Naish D, Fry A, Klemencic R, Wallace J (2013) Reinforced concrete coupling beams—part II: modeling. ACI Struct J 110-S87:1067–1076

    Google Scholar 

  • NZSS 1900 (1965) New Zealand standard model building by-law, Basic design loads. New Zealand Standards Institute, Wellington

    Google Scholar 

  • Panagiotou M, Restrepo J, Schoettler M, Kim G (2012) Nonlinear cyclic truss model for reinforced concrete walls. ACI Struct J 109(2):205–214

    Google Scholar 

  • Paulay T (1969) The coupling of shear walls. Dissertation, University of Canterbury

  • Paulay T, Priestley MJN (1992) Seismic design of reinforced concrete and masonry buildings. Wiley, New York

    Book  Google Scholar 

  • Paulay T, Santhakumar AR (1976) Ductile behavior of coupled shear walls. J Struct Div 102(1):93–108

    Google Scholar 

  • Petracca M, Candeloro F, Camata G (2017a) STKO user manual. ASDEA Software Technology, Pescara

    Google Scholar 

  • Petracca M, Candeloro F, Camata G (2017) STKO: a revolutionary visualization toolkit for OpenSees, keynote lecture, OPENSEES DAYS Europe, First European conference on OPENSEES, June 19–20, 2017, Porto, Portugal

  • Presland R (1999) Seismic performance of retrofitted reinforced concrete bridge piers. Dissertation, University of Canterbury

  • Rajapakse C, Wijesundara K, Nascimbene R, Bandara C, Dissanayake R (2019) Accounting axial–moment–shear interaction for force-based fiber modeling of RC frames. Eng Struct 184(2019):15–36

    Article  Google Scholar 

  • Rashid JY, Dameron R, Dowell R (2000) Recent advances in concrete material modeling and application to the seismic evaluation and retrofit of California bridges. 12WCEE

  • Restrepo-Posada JI (1993) Seismic behavior of connections between precast concrete elements. Dissertation, University of Canterbury

  • Restrepo JI, Rahman A (2007) Seismic performance of self-centering structural walls incorporating energy dissipators. J Struct Eng 133(11):1560–1570

    Article  Google Scholar 

  • Rokugo K, Iwasa M, Susuki T, Koyanagi W (1989) Testing method to determine tensile softening curve and fracture energy of concrete. In: Fracture toughness and fracture energy, Balkema, pp 153–163

  • Santhakumar AR (1974) The ductility of coupled shear walls. Dissertation, University of Canterbury

  • Stevens N, Uzumeri S, Collins M, Will T (1991) Constitutive model for reinforced concrete finite element analysis. ACI Struct J 88(1):49–59

    Google Scholar 

  • Vulcano A (1992) Use of wall macroscopic models in the nonlinear analysis of RC frame-wall structures. In: Proceedings of the tenth world conference on earthquake engineering, Balkema, Rotterdam, pp 4309–4312

  • Toprak AE, Bal IE, Gulay FG (2015) Review on the macro-modeling alternatives and a proposal for modeling coupling beams in tall buildings. Bull Earthq Eng 13:2309–2326

    Article  Google Scholar 

  • Vecchio F, Collins M (1986) The modified compression-field theory for reinforced concrete elements subjected to shear. J Am Concr Inst 83(2):219–231

    Google Scholar 

  • Zhang P, Restrepo JI, Conte JP, Ou J (2017) Nonlinear finite element modeling and response analysis of the collapsed Alto Rio building in the 2010 Chile Maule earthquake. Struct Design Tall Spec Build 45:45.

    Article  Google Scholar 

  • Zhao J, Sritharan S (2007) Modeling of strain penetration effects in fiber-based analysis of reinforced concrete structures. ACI Struct J, V 104(2):133

    Google Scholar 

Download references


We acknowledge to the CONACYT, UCMEXUS and COMEXUS for providing financial support.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Rodolfo Alvarez.

Additional information

The authors would like to pay tribute to the memory of Professor Tom Paulay from the University of Canterbury, New Zealand. Tom was an outstanding design engineer and educator. The second and last authors were students of Tom. He was also a pioneer in experimental methods in earthquake engineering and the experimental work described in this paper was the most complex in the field in many years. Last but not least, Tom was an extraordinary human being and mentor.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alvarez, R., Restrepo, J.I., Panagiotou, M. et al. Nonlinear cyclic Truss Model for analysis of reinforced concrete coupled structural walls. Bull Earthquake Eng 17, 6419–6436 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: