Three-dimensional shear-flexure interaction model for analysis of non-planar reinforced concrete walls

This paper presents theoretical formulation and results of experimental validation studies of a novel threedimensional macroscopic nonlinear model that captures the interaction between axial-flexural and shear behavior in reinforced concrete (RC) walls. The original Shear-Flexure-Interaction Multiple-Vertical-LineElement-Model (SFI-MVLEM) developed previously by the authors, which is essentially a two-dimensional line element for rectangular walls subjected to in-plane loading, is extended in this study to a three-dimensional model formulation (SFI-MVLEM-3D) by applying geometric transformation of the element degrees of freedom that convert it into a four-node element, as well as by incorporating linear elastic out-of-plane behavior based on Kirchhoff plate theory. The proposed three-dimensional, four-node model element is implemented in the official version of open-source analysis software OpenSees and validated against experimental data obtained for four well-instrumented U-shaped wall specimens tested under complex multidirectional loading protocols. Comprehensive and detailed comparisons were conducted between various experimentally-measured and analyticallypredicted wall responses including the load-displacement behavior of the wall specimens in various loading directions, contributions of nonlinear flexural and shear deformations to wall displacements, vertical and horizontal profiles of flexural strains, and crack patterns. Results presented demonstrate that the proposed analytical model captures, with good accuracy, most of the experimentally-measured responses of non-rectangular walls subjected to multidirectional loading. Model predictions of the wall lateral load capacity and local responses (strains) are, although reasonable, relatively less accurate when the walls are subjected to diagonal loading conditions, due to the plane-sections-remain-plane assumption implemented in the proposed model formulation that disregards the experimentally-observed shear lag effect.