Flexural shear failure is a brittle failure mode that can occur in reinforced concrete (RC) beams without stirrups due to the combination of flexural and shear stresses. The failure mode begins with vertical flexural cracks at the bottom of the RC beam central span area due to flexural tensile stresses, followed by diagonal cracks. During stabilization, a diagonal crack enlarges, leading to flexural shear failure. The failure mode is brittle due to the significant bearing capacity reduction making it more difficult to predict.
Accurately predicting the capacity of concrete structures is important for ensuring their safety, especially in the case of brittle failures. Various design codes are available to design and assess such structures, but an advanced numerical method called the Non-Linear Finite Element Analysis (NLFEA) is an alternative to these codes. NLFEA allows for more detailed and accurate modeling of the structure behavior by considering material, geometry, and boundary conditions nonlinearity. By using NLFEA, engineers can optimize their design and gain a deeper understanding of the behavior of RC beams without stirrups. The NLFEA model requires several modeling decisions to accurately simulate the structures’ behavior.
Sensitivity analysis on different modeling aspects is crucial to obtain a numerical model that can accurately simulate the RC beam. To be considered accurate, the numerical model should simulate approximately the same damage progression, failure mode, and failure load compared to the experiments. The sensitivity analysis is performed to modeling aspects with uncertainties identified during the literature review. These uncertainties are in the constitutive model, finite element discretization, and analysis procedure modeling aspects. Sensitivity analysis on various modeling aspects is per-formed using four experimental beams with distinct geometrical sizes, while some material configura-tions differ. This research investigates whether, using sensitivity analysis, a numerical model can be obtained that accurately simulates flexural shear failure for RC beams without stirrups.
The total strain crack models’ crack orientation sensitivity analysis shows that the rotating crack orientation can suffer from over-rotation, which causes delamination of the concrete cover. Over-rotation also shows a strong correlation with many non-converged steps. In addition, the fixed crack orientation simulates a more realistic representation of the experimental failure mode. The compression-compression confinement sensitivity analysis shows that this modeling aspect does not influence simulations for cases with flexural shear failure much and can thus be excluded. A slightly lower failure load is simulated with the confined numerical model for one of the four cases. The sensitivity analysis on the FIB bond-slip relation and Shima bond-slip relation reveals that the former has a lower initial stiffness when using the same material configurations for their modeling assumptions. Due to the lower initial stiffness, there is a higher relative displacement between the concrete and reinforcement. In some cases, this results in either increased convergence problems, a higher possibility of dowel failure, a lower failure load, or a combination of them.
For the fourth sensitivity analysis modeling aspect, the full Newton-Raphson (NR) iteration scheme simulations are slightly more representative of the experiment than the Secant iteration scheme. This result is obtained despite the full NR scheme having more convergence problems during the initial crack. In addition, for a few cases, the Secant iteration scheme simulates symmetrical flexural shear failure due to failing to include material nonlinearity.
Sensitivity analysis of the reinforcement elements shows that simulations with truss elements are more accurate than beam elements. The beam elements models show compatibility issues when combined with plane stress elements. The interface elements fail to correctly tie the beam elements’ extra rotational degree of freedom to the transitional degree of freedom. This incompatibility results in convergence problems. Also, higher relative displacements and a higher stiffness after the initial crack is noticed in some cases compared to the experiment. The final sensitivity analysis reveals that the element size sensitivity increases with an increase in the geometrical beam size. Too-large element sizes decrease the accuracy of simulations. In contrast, too-small element sizes increase the computational cost but can also simulate irregular crack patterns not representative of the experiment. A formula is introduced from the sensitivity analysis for beams up to a depth of 1200 mm to predict an appropriate element size.
The sensitivity analysis reveals that the most accurate numerical model is a fixed crack orientation and the Shima bond-slip relation combined with truss elements using the full NR iteration scheme. The sensitivity analysis is followed by a quantitative analysis of 76 experimental cases to verify the accuracy of the obtained numerical model for a broad range of differently configured experimental cases. Analysis shows that dowel failure can get captured due to an excessive change in the dam-age-based shear retention factor using the obtained numerical model. However, decreasing sensitive load step sizes to very small ones results in flexural shear failure. Also, the quantitative simulations show that the numerical model simulations are largely accurate, with 62 simulated cases below a failure load percentage difference of 10 % compared to the experiment. The average percentage difference is 6 % between the simulations and the experiment.
Analysis shows that this research successfully obtains a numerical model that accurately simulates flexural shear failure for RC beams without stirrups. The information obtained from this research can be used to make modeling choices. In addition, some uncertainties for other modeling aspects are introduced for future research. These modeling aspects are the shear retention model, concrete elements compatibility with the reinforcements beam elements, and the global element size for beams deeper than 1200 mm.