钢筋混凝土梁临界斜裂缝倾角计算的概率模型

综合考虑剪跨比、混凝土强度、配筋率和配箍率等重要因素的影响，研究建立了RC梁临界斜裂缝倾角计算的概率模型。首先，基于修正压力场理论，建立了RC梁临界斜裂缝倾角的确定性计算模型；然后，引入剪跨比修正系数，并综合考虑主观不确定性和客观不确定性因素的影响，结合贝叶斯理论和马尔科夫链蒙特卡洛法（MCMC），建立了RC梁临界斜裂缝倾角计算的概率模型；最后，通过与试验数据和传统确定性计算模型的对比分析，验证了该模型的有效性和适用性。分析结果表明，随着剪跨比的增大，RC梁的临界斜裂缝倾角逐渐减小；临界斜裂缝倾角的试验测试值的范围为23°～41°，具有显著的离散性；本文概率模型不仅可以合理描述临界斜裂缝倾角的概率分布特性，而且可以校准传统确定性计算模型的计算精度和置信水平，以及根据预定的置信水平确定临界斜裂缝倾角的概率特征值，具有良好的计算精度和适用性。

Probabilistic model for critical crack angle of reinforced concrete beams

A probabilistic model for critical crack angle of RC beam was established by taking into account the influences of various important parameters such as shear span ratio,concrete strength,reinforcement ratio and stirrup ratio.The deterministic model for critical crack angle of RC beam was proposed based on the modified compression field theory (MCFT) first.Then,a probabilistic model of critical crack angle for RC beam which takes into account the influences of shear span ratio as well as both aleatory and epistemic uncertainties was developed by combining the Bayesian theorem and the Markov Chain Monte Carlo (MCMC) method.Finally,the applicability and efficiency of the proposed probabilistic model were validated by comparing with the experimental data and traditional deterministic models.Analysis results show that the critical crack angle of RC beam exhibits significant variation and decreases with the shear span ratio,which varies from 23° to 41°;the proposed probabilistic model can not only describe the probabilistic distribution characteristics of critical crack angle,but also provide a benchmark to calibrate the confidence level of traditional deterministic models and provide an efficient way to determine the characteristic values of critical crack angle with different confidence levels.