A nonlinear quadrilateral layered membrane element with drilling degrees of freedom for the modeling of reinforced concrete walls

• A quad membrane element with drilling DOF for the modeling of RC Wall is presented.
• The new element is easy to implement.
• The new formulation can be used for rectangular or distorted mesh elements.
• The new formulation is tested against some examples available in the literature.
• The new formulation is able to represent the global and local response of RC Walls.

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 consisting 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 experimental 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.