Analysis Of Flexural Behavior Of Reinforced Concrete Beams And Its Size Effect

Concrete is a quasi-brittle material, and its strength is size dependent.With the development of large span structure, the component size is even bigger and the high-strength concrete is widely used. Researchers began to realize the phenomenon of size effect and related research has been carried out. In the last decades, extensive studies, both experimentally and theoretically, on the flexural behavior of reinforced concrete (RC) beams have been conducted. However, for the flexural behavior of reinforced concrete beams, whether there is a size effect is still controversial. Moreover, studies on flexural behavior, especially on deformation capacity, of double-reinforced high strength beams, are still scarce. In this paper, based on the results of experimental studies conducted by team members, numerical investigation on moment capacity, deformation behavior and related size effect of reinforced concrete beams were carried out. The main contents are:(1) Based on the assumption of plane section, simplified methods for calculating the yield moment and ultimate moment of flexural members were established, and the limit state criterion of reinforced concrete beam was discussed. Flexural displacement was calculated with the ideal polyline moment-curvature relationship based on the determined yield and ultimate moments. In the determination of ultimate moment, the possible states controlled by spalling of concrete cover and that controlled by the failure of confined core concrete in compression zone of the section after the spalling of concrete cover were considered. Different models for confined concrete were adopted to calculate the ultimate moment of the members. Numerical studies show that the confined concrete models predict the yield moment, ultimate moment and the corresponding yield deformation well and that both the nominal yield moment and nominal ultimate moment of different sizes of specimens did not show a significant size effect, which is consistent with the observation in the experiment. However, the ultimate deformation and plastic rotation were significantly overestimated with all the models. Among the models used in this study, the model which adopts expressions by Biskinis considering the influence of the depth of compression zone on the ultimate strain in determination of properties of confined concrete, and considers the influence of curvature and the length of plastic hinges in calculation of deformation of specimens can predict the trend of decrease of plastic rotation capacities and displacement ductility factors with the increase of specimen depths as observed in the experiments.(2) A program for the analysis of moment capacity and deformation behavior of reinforced concrete members was developed in the Matlab environment. The moment-curvature curves were determined firstly using layered approach, and then based on the calculated moment-curvature curves, the numerical integration method was used to calculate the rotations and displacement at any location of the member by dividing the member into a number of segments. In the layered approach, different stress-strain relationships were adopted for cover concrete and confined core concrete. In order to investigate the influence of different models for confined concrete on the analysis results, four models, i.e. Mander model, Razvi model M.Akiyama model and overlapping crack model, were used. Among these models, M.Akiyama model and overlapping crack model are based on fracture mechanics, considered the size effect of concrete stress-strain relationship in compression (length effect). The program was used to analysis the test specimens. It is shown that all the models predicted the cracking moment, yield moment, ultimate moment, and yield displacement of the flexural members well and that the nominal cracking moment, nominal yield moment and nominal ultimate moment of different sizes of specimens did not show a significant size effect, which is consistent with the observation of the experiment. However, there is a comparatively large deviation between the calculated and the experimental ultimate deformation and plastic rotation. The plastic rotation and displacement ductility simulated by M.Akiyama model and overlapping crack model showed a significant size effect, while the results by Mander model and Razvi model did not show a size effect. Compared with the simplified approach, the layered approach obtained better predictions of plastic rotation and ultimate displacement.