Analysis Of Deep Flexural Member Shear Bearing Capacity Based On Bayesian-MCMC Method

The Bayesian posterior inference method can inherit the objective laws of history a priori information,reflect a priori model of subjective understanding,which can accurately forecast and analysis of bearing capacity of concrete members,to establish a high precision shear bearing capacity calculation model.The Markov Chain Monte Carlo method(MCMC method)is able to apply stochastic simulation to the calculation of high-dimensional integrals,to further improve the calculation accuracy.The deep flexural member is a typical stress disorder zone,so far there is no unified calculation model and design method,The Bayesian-MCMC method is introduced into the prediction and analysis of the shear bearing capacity of deeply bent members,providing a method with high accuracy for predicting the shear bearing capacity of such members.The main research content includes:1.The accuracy of the shear capacity calculation method in the current code is identified by analyzing the collected database of 645 groups of deeply bent members,the difference between shear test value and different standard calculation value was compared and the significance of each influencing factor was analyzed,Based on Bayesian theory and random sampling theory,the Gibbs sampling method and Metropolis-Hastings sampling method in MCMC method are studied,and the calculation process of shear bearing capacity of deep flexural members by Bayesian-MCMC method is deduced.2.The R language is used to simulate the parameters of probability model of deep flexural member by MCMC,based on the prior model,the probability model of shear capacity of reinforced concrete deep flexural members is established,According to different confidence levels,the characteristic values of shear bearing capacity of deep flexural members are determined.The results show that: the probability model of shear capacity obtained based on the Bayesian-MCMC method is the result generated after 50,000 iterations of analysis,which can reasonably explain the uncertainty affecting parameters and has a high credibility.3.The calculation results of the shear probability model are compared with those of the four codes,the study shows that: the calculated results of the probability model of shear capacity based on the Bayesian-MCMC method are in good agreement with the test results,the mean of the ratio to the test value is closer to 1,and the standard deviation is smaller,the probabilistic model based on the four-country norm is closer to the experimental failure value than the four-country norm calculation model,with less dispersion and higher accuracy.4.The Bayesian-MCMC method is introduced into the reliability calculation,based on the Bayesian importance sampling method,the reliability of the probability model of shear bearing capacity of deep flexural members in the ultimate state is analyzed,and the reliability index is obtained.The results show that: the probability calculation model of shear bearing capacity based on Bayesian-MCMC method is reliable,The reliability index in the limit state of bearing capacity meeting the requirements of the current code.In this paper,the Bayesian-MCMC method is used to solve the shear capacity of deeply flexural members,and the Bayesian theory and MCMC method are further introduced into the prediction and analysis of the shear capacity of deeply flexural members,and combined with the theory of random sampling,the Bayesian-MCMC method is introduced into the solution of reliability,which has important theoretical significance and practical value in ensuring engineering safety.