Study On The Shear Performance Of Reinforced Concrete Deep Flexural Members Based On Bayesian Theory

The failure mode of reinforced concrete deep flexural members is always brittle shear failure. Some models have been presented by domestic and foreign scholars for shear capacity of reinforced concrete deep flexural members, but there is still no generally accepted shear theory model. The study of shear strength of concrete members is always a hot point in the field of civil engineering. Bayesian statistics has been one of the two statistic schools to keep pace with classic statistics. According to Bayesian theory, the prior information of unknown parameters can be updated by sample information to get the posterior information. As a result, the posterior information obtained will inherit the completeness of prior information and the accuracy of large experimental data. Comparing with traditional methods, more accurate results would be got by Bayesian theory. Based on existing research and the application of Bayesian multivariate linear parameter estimation method, probabilistic models for calculating the shear strength of reinforced concrete deep flexural members are established based on the Bayesian theory in this paper. Two types of information, the prior models that shear capacity calculation formulas in Chinese code, United States code, Canada code and Europe code, and the prior information that the collected 271 test results, are synthesized into Bayesian statistical inference and Bayesian posterior estimate for unknown parameters based on non-information prior distribution and conjugate prior distribution. In this paper the main work accomplished are listed as follows.(1) In this paper, the shear failure mechanisms of reinforced concrete members are introduced simply first, and then the main influent parameters that effect the shear capacity of reinforced concrete deep flexural members are analyzed. The shear design methods of reinforced concrete deep flexural members in codes of GB 50010-2010, ACI318-08, CSA and EC2 are introduced and studied.(2) The collected 271 test results of reinforced concrete deep flexural members under the action of symmetrical concentrated loads are organized to build the database of experimental results of deep flexural members on the base of native and international literature.(3) The Bayesian theory about non-information prior distribution is introduced. Based on this theory and the collected 271 test results, the probabilistic shear models for reinforced concrete deep flexural members are developed by using shear models in codes as prior models. These probabilistic models are simplified through the Bayesian parameters removal process. And the performance of the developed models is confirmed and can be used in calculating shear strength for deep flexural members.(4) The Bayesian theory about conjugated prior distribution is introduced. Based on this theory and the collected 271 test results, the conjugated probabilistic shear models for reinforced concrete deep flexural members are developed by using shear models in codes as prior models. These conjugated probabilistic models are simplified through the Bayesian parameters removal process. And the performance of the developed models is confirmed and can be used in calculating shear strength for deep flexural members.The deep flexural members’shear strengths obtained by the simplified models based on Bayesian are in good agreement with test results, and they are closer to the experimental values than the results designed by models in codes. The simplified models can be used in the shear strength prediction and design for deep flexural members.