Interaction of Internal Forces Acting on Reinforced Concrete Cross-Sections

Abstract

The dissertation begins by providing a concise overview of linear analysis for beams while accounting for the nonuniformity due to torsion and flexure. The objective is to develop a numerical method based on the finite element method (FEM) to address the Saint-Venant problem with arbitrary cross-sections, building upon Gruttmann's numerical method. In the first part, the author's proposed numerical model considers the shear lag effect caused by torsion and flexure using FEM. Furthermore, it investigates the phenomenon of bending-induced shear lag in arbitrary cross-sections of homogeneous materials. The non-uniform torsion problem and the shear deformation effect in thin-walled beams with arbitrary cross-sections made of homogeneous isotropic elastic material are also examined. Finally, the first part of the dissertation proposes an advanced beam theory that enhances the work of Sapountzakis and Dikaros through minor modifications. The second part of this dissertation is devoted to investigating the nonlinear analysis of reinforced concrete structures. The primary focus of this study is to examine the primary shear warping function profile of reinforced concrete sections under the effect of shear warping, which is still an unexplored topic in structural engineering. To simplify the computational process, the study uses the uniaxial stress-strain relationship and neglects the tensile strength of the concrete for nonlinear analysis. In the nonlinear analysis of beams, the displacement-based approach usually requires a two-step iteration process at both the section and element levels. To simplify this process, the author presents an alternative approach where the ultimate load is determined by detecting whether the concrete strain in the cross-section reaches or exceeds its ultimate strain and whether the Euclidean norm of the unbalanced force exceeds 1. This approach simplifies the previously complex iterative method used for force equilibrium at the element level. The proposed method employs the Newton-Raphson method to capture the plastic mechanism. The author validates the proposed approach through local and global analysis in this study. The dissertation presents significant findings regarding the validity of clauses 6.2.3 (7) and 9.2.1.3 (2) of EN 1992-1-1 (2004) concerning the interaction of shear and flexure. The numerical approach proposed in this research aligns with other reinforced concrete section analysis models and appropriately accounts for moment redistribution in the structural response. The outcomes of the global analysis demonstrate that the proposed method meets the safety and economic criteria. Moreover, the study highlights the underestimation of shear strength in EN 1992-1-1 (2004) compared to ACI 318-19, CSA A23:3:19, and Fib MC 2010 with Level of Approximation (LoA) III. Furthermore, numerical analysis demonstrates that the prescribed limits on moment redistribution outlined in EN 1992-1-1 (2004), ACI 318-19, and CSA A23.3:19 need not be reduced during moment distribution. The study on nonlinear analysis aims to solely present and validate the interaction between shear and flexure in simple cross-sections. However, it should be emphasized that this study simplified the investigation by focusing only on the interaction between shear and flexure. Future research will address the impact of transverse reinforcement and explore the interaction between shear, flexure, and torsion in complex cross-sections.