Skip to main content
SpringerLink
Log in

A nonlinear quadrilateral thin flat layered shell element for the modeling of reinforced concrete wall structures

  • S.I. : Nonlinear Modelling of Reinforced Concrete Structural Walls
  • Published:
Bulletin of Earthquake Engineering Aims and scope Submit manuscript

Abstract

In this article, a simple and accurate quadrilateral thin flat layered shell element formulation for the nonlinear analysis of reinforced concrete (RC) wall systems under static and cycling loads is presented. The 4 node shell element, with 6 degree of freedom (DOF) per node (3 displacements and 3 rotations) is created by superposing the quadrilateral layered membrane element with drilling degrees of freedom (12 DOF, 2 displacement and 1 rotation per node) developed by Rojas et al. (Eng Struct 124:521–538, 2016), and the Discrete Kirchhoff Quadrilateral Element (12 DOF, 1 displacement and 2 rotations) formulated by Batoz and Tahar (Int J Numer Methods Eng 18(11):1655–1677, 1982), to model the in-plane and the out of plane bending behavior of the shell element, respectively. In addition, to model the complex behavior and coupling of the axial, flexural and shear behavior, observed in complex RC wall structures, the transversal section of the shell element consists of a layered system of fully bonded, smeared steel reinforcement and smeared orthotropic concrete material with the rotating angle formulation. The formulation used a tangent stiffness matrix approach, which include the coupling of membrane and bending effects. For verification, the shell element formulation is used to model a set of experimental results for T-shaped RC walls that are available in the literature. The proposed element is robust, simple to implement, and it can predict the global results (load vs. displacement and maximum capacity) and also the local behavior (vertical strain at the base level along the web and the flange) observed in RC wall structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • ACI 318 (2014) Building code requirements for structural concrete and commentary (ACI 318-14). ACI, Farmington Hill

    Google Scholar 

  • Ayoub A, Filippou FC (1998) Nonlinear finite-element analysis of RC shear panels and walls. J Struct Eng 124(3):298–308

    Article  Google Scholar 

  • Batoz JL, Dhatt G (1979) Incremental displacement algorithms for nonlinear problems. Int J Numer Methods Eng 14(8):1262–1267

    Article  Google Scholar 

  • Batoz JL, Tahar M (1982) Evaluation of a new quadrilateral thin plate bending element. Int J Numer Methods Eng 18(11):1655–1677

    Article  Google Scholar 

  • Belarbi A, Hsu TTC (1994) Constitutive laws of concrete in tension and reinforcing bars stiffened by concrete. ACI Struct J 91(4):465–474

    Google Scholar 

  • Bertero VV (1980) Seismic behaviors of RC wall structural system. In: 7th World conference on earthquake engineering, vol 6, Instanbul, Turkey, September 1980, pp 323–330

  • Cervera M, Hinton E, Hassan O (1987) Nonlinear analysis of reinforced concrete plate and shell structures using 20-noded isoparametric brick elements. Comput Struct 25(6):845–869

    Article  Google Scholar 

  • Collins MP, Porasz A (1989) Bulletin D’Information no. 193: design aspects of high strength concrete. In: Shear strength for high strength concrete, Paris, France, pp 75–83

  • Cook RD (1994) Four-node flat shell element: drilling degrees of freedom, membrane-bending coupling, warped geomtry, and behavior. Comput Struct 50(4):549–555

    Article  Google Scholar 

  • Kabeyesawa TH, Shiohara S, Otani S, Aoyama H (1982) Analysis of the full-scale 7-story R.C. test structure. In: 3rd Joint Technical Coordinating Committee, U.S. Japan Cooperative Earthquake Research Program. Building Research Institute, Tsukuba

  • Kim D-K (2016) Seismic response analysis of reinforced concrete wall structure using macro model. Int J Concr Struct Mater 10(1):99–112

    Article  Google Scholar 

  • Kim T, Choi J, Kim W (2005) Nonlinear analysis of reinforced and prestressed concrete shells using layered elements with drilling DOF. J Korea Concr Inst 17(4):645–654

    Article  Google Scholar 

  • Kolozvari K, Orakcal K, Wallace JW (2015) Modeling of cyclic shear–flexure interaction in reinforced concrete structural walls. I: theory. J Struct Eng 141(5):04014135

    Article  Google Scholar 

  • Loo YC, Guan H (1997) Cracking and punching shear failure analysis of RC flat plates. J Struct Eng 123(10):1321–1330

    Article  Google Scholar 

  • Macneal RH (1978) A simple quadrilateral shell element. Comput Struct 8:175–183

    Article  Google Scholar 

  • Massone LM, Moroder D (2009) Buckling modeling of reinforcing bars with imperfections. Eng Struct 31(3):758–767

    Article  Google Scholar 

  • Massone LM, Orakcal K, Wallace JW (2006) Shear–flexure interaction for structural walls. ACI Spec Publ SP–236(2):127–150

    Google Scholar 

  • Massone LM, Muñoz G, Rojas F (2019) Experimental and numerical cyclic response of RC walls with openings. Eng Struct 178:318–330

    Article  Google Scholar 

  • Menegotto M, Pinto PE (1973) Method of analysis of cyclically loaded reinforced concrete plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending. In: IABSE symposium on the resistance and ultimate deformability of structures acted on by well-defined repeated loads, Lisbon

  • Moehle J, Wallace JW, Maffei J, Sempere C, Celestino A, Besa JJ, Dragovich J, Westenenk B, Millan A, Frings C, Herranz JP (2010) Chile earthquake reconnaissance team investigation: reinforced concrete buildings. Reconnaissance report, EERI, 27 Feb 2010

  • Naeim F, Lew M, Carpenter LD, Youssef NF, Rojas F, Saragoni GR, Schachter M (2011) Performance of tall buildings in Santiago, Chile during the 27 February 2010 offshore Maule, Chile earthquake. Struct Des Tall Spec Build 20(1):1–16

    Article  Google Scholar 

  • Oñate E (1992) CISM course and lectures no. 328. International Centre for Mechanical Sciences: nonlinear analysis of shells by finite elements. In: Nonlinear finite element analysis of concrete. Springer, Wien, pp 195–256

  • Orakcal K, Massone LM, Wallace JW (2006) Analytical modeling of reinforced concrete walls for predicting flexural and coupled-shear-flexural responses. PEER report 2006/07, Pacific Earthquake Engineering Research Center. University of California, Los Angeles

  • Palermo D (2002) Behavior and analysis of reinforced concrete walls subjected to reversed cycling loading. PhD thesis, Department of Civil Engineering, University of Toronto, Toronto, Canada

  • Palermo D, Vecchio FJ (2003) Compression field modeling of reinforced concrete subjected to reversed loading: formulation. ACI Struct J 100(5):616–625

    Google Scholar 

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

    Google Scholar 

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

    Book  Google Scholar 

  • Polak MA, Vecchio FJ (1993) Nonlinear analysis of reinforced-concrete shells. J Struct Eng 119(12):3439–3462

    Article  Google Scholar 

  • Rojas F, Naeim F, Lew M, Carpenter LD, Youssef NF, Saragoni GR, Schachter M (2011) Performance of tall buildings in concepción during the 27 February 2010 moment magnitude 8.8 offshore Maule, Chile earthquake. Struct Des Tall Spec Build 20(1):37–64

    Article  Google Scholar 

  • Rojas F, Anderson JC, Massone LM (2016) A nonlinear quadrilateral layered membrane element with drilling degrees of freedom for the modeling of reinforced concrete walls. Eng Struct 124:521–538

    Article  Google Scholar 

  • Smyrou E, Sullivan T, Priestley N, Calvi M (2013) Sectional response of t-shaped RC walls. Bull Earthq Eng 11(4):999–1019

    Article  Google Scholar 

  • Song H-W, Shim S-H, Byun K-J, Maekawa K (2002) Failure analysis of reinforced concrete shell structures using layered shell element with pressure node. J Struct Eng 128(5):655–664

    Article  Google Scholar 

  • Thomsen JH, Wallace JW (1995) Displacement-based design of reinforced concrete structural walls: an experimental investigation of walls with rectangular and t-shaped cross sections. Report no. CU/CE-95-06, Clarkson University

  • Thomsen JH, Wallace JW (2004) Displacement-based design of slender reinforced concrete structural walls: experimental verification. J Struct Eng 130(4):618–630

    Article  Google Scholar 

  • Thorenfeldt E, Tomaszewicz A, Jensen JJ (1987) Mechanical properties of high-strength concrete and application in design. In: Symposium utilization of high-strength concrete, Stavanger, Norway

  • Uniform Building Code (1994) International conference of building officials, Whittier, California, 1994

  • Vecchio FJ (1992) Finite element modeling of concrete expansion and confinement. J Struct Eng 118(9):2390–2406

    Article  Google Scholar 

  • Vulcano A, Bertero VV (1987) Analytical models for predicting the lateral response of RC shear walls: evaluation of their reliability. UCB/EERC 87/19, Earthquake Engineering Research Center. University of California, Berkeley

  • Wallace JW (2012) Behavior, design, and modeling of structural walls and coupling beams: lessons from recent laboratory tests and earthquakes. Int J Concr Struct Mater 6(1):3–18

    Article  Google Scholar 

  • Zhang YX, Bradford MA, Gilbert RI (2007a) A layered shear–flexural plate/shell element using Timoshenko beam functions for nonlinear analysis of reinforced concrete plates. Finite Elem Anal Des 43(11–12):888–900

    Article  Google Scholar 

  • Zhang YX, Bradford MA, Gilbert RI (2007b) A layered cylindrical quadrilateral shell element for nonlinear analysis of RC plate structures. Adv Eng Softw 38(7):488–500

    Article  Google Scholar 

  • Zhong J (2005) Model-based simulation of reinforced concrete plane stress structures. PhD dissertation, Department of Civil and Environmental Engineering, University of Houston, Houston, USA

Download references

Acknowledgements

This study was financially supported by Chile’s National Commission on Scientific and Technological Research (CONICYT) for the Fondecyt Initiation into Research 2014—Project No. 11140429. Also, the help with some figures by Mr. Fernando Muñoz is thanked.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, University of Chile, Av. Blanco Encalada 2002, Santiago, Chile

    F. Rojas & L. M. Massone

  2. Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, USA

    J. C. Anderson

Authors
  1. F. Rojas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. C. Anderson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. M. Massone
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Rojas.

Additional information

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

Rojas, F., Anderson, J.C. & Massone, L.M. A nonlinear quadrilateral thin flat layered shell element for the modeling of reinforced concrete wall structures. Bull Earthquake Eng 17, 6491–6513 (2019). https://doi.org/10.1007/s10518-019-00566-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10518-019-00566-8

Keywords

Search

Navigation