A nonlinear quadrilateral layered membrane element with drilling degrees of freedom for the modeling of reinforced concrete walls F. Rojas a,⇑ , J.C. Anderson b , L.M. Massone a a Department of Civil Engineering, University of Chile, Av. Blanco Encalada 2002, Santiago, Chile b Department of Civil and Environmental Engineering, University of Southern California, 3620 S. Vermont Av., Los Angeles, CA 90089, USA article info Article history: Received 26 February 2016 Revised 20 May 2016 Accepted 17 June 2016 Available online 6 July 2016 Keywords: Reinforced concrete walls Smeared orthotropic concrete material Smeared steel reinforcement Membrane element with drilling degrees of freedom abstract In this article, the formulation and verification of a nonlinear quadrilateral layered membrane element with drilling degrees of freedom for the nonlinear analysis of reinforced concrete (RC) walls under static and cycling loads are presented. The formulation is based on a quadrilateral element with twelve degrees of freedom (DOF), two displacements and one drilling DOF per node, which is defined by a blended field interpolation for the displacements over the element, and a layered system for the element section con- sisting of fully bonded, smeared steel reinforcement and smeared orthotropic concrete material with a rotating angle formulation, and a stiffness tangent approach. The drilling DOF refers to the incorporation of the in-plane rotation as a DOF at each element node. The blended field interpolation has the advantage of producing a smoother strain distribution inside each element, which facilitates element convergence, and the layered section formulation allows for the properties of the concrete and steel over the thickness of the wall to be modified to properly represent the different wall components, such as the concrete cover, steel rebar and confined concrete. Additionally, the formulation introduces a rotational DOF at each node, which allows the membranes to connect directly to beam and column elements. Moreover, this formulation incorporates the coupling of axial, flexural and shear behavior observed on the different configurations of RC wall structures. To verify this formulation, the results of a set of available experimen- tal data reported in the literature for RC wall elements, with different configurations (slender walls, squat walls, wall with irregular disposition of openings) and levels of confinement, under monotonic and reversed loads are compared with the results obtained from the corresponding analytical model. The formulation is notably consistent with the experimental data and can predict the maximum capacity, the global (force vs deformation) and local responses (strain along the wall) and incorporate the coupling of axial, flexural and shear behavior observed in the different configurations of RC wall structures. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction Although the design of RC walls is a relatively simple procedure when using current codes, the behavior of RC walls is actually highly complex because they behave differently depending on their configuration (wall size, height/length ratio, steel reinforce- ment, etc.) and loading conditions. This scenario implies that the behavior of RC walls depends on the interrelation and coupling of a combination of flexural, shear, and axial deformation over their cross-sections at different levels, along with other complex mechanisms such as rigid body rotation for the bond slippage of the longitudinal reinforcement at the base of the wall, effects of confinement, dowel action in reinforcement, cracking, aggregate interlock, creep, and tension stiffening, which have been demonstrated by various researchers [1–4]. For example, the walls used in mid- to high-rise buildings exhi- bit mainly flexural behavior, with the deformation concentrated at the larger moment, typically near the ground level. Failure in this type of wall is characterized by horizontal cracks at the edges of the wall. In low-rise buildings, however, the walls behave primarily in shear, and diagonal cracks are produced. These main behaviors typically occur in isolated walls. Once these walls are combined with other elements or walls in the building, the behav- ior can change, producing combinations of flexural, compression and shear failure. Such behavior has been described in the reports of the Reconnaissance team of the Los Angeles Tall Building Structural Design Council [5–8] and of the ERRI Reconnaissance team [9] after the recent Chilean earthquake. Because of this http://dx.doi.org/10.1016/j.engstruct.2016.06.024 0141-0296/Ó 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: frojas@ing.uchile.cl (F. Rojas), jamesa@usc.edu (J.C. Anderson), lmassone@ing.uchile.cl (L.M. Massone). Engineering Structures 124 (2016) 521–538 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct