余波, 陈冰, 唐睿楷. 钢筋混凝土梁抗剪承载力计算的概率模型[J]. 工程力学, 2018, 35(5): 170-179. DOI: 10.6052/j.issn.1000-4750.2017.01.0075
引用本文: 余波, 陈冰, 唐睿楷. 钢筋混凝土梁抗剪承载力计算的概率模型[J]. 工程力学, 2018, 35(5): 170-179. DOI: 10.6052/j.issn.1000-4750.2017.01.0075
YU Bo, CHEN Bing, TANG Rui-kai. A PROBABILISTIC MODEL FOR SHEAR STRENGTH OF REINFORCED CONCRETE BEAMS[J]. Engineering Mechanics, 2018, 35(5): 170-179. DOI: 10.6052/j.issn.1000-4750.2017.01.0075
Citation: YU Bo, CHEN Bing, TANG Rui-kai. A PROBABILISTIC MODEL FOR SHEAR STRENGTH OF REINFORCED CONCRETE BEAMS[J]. Engineering Mechanics, 2018, 35(5): 170-179. DOI: 10.6052/j.issn.1000-4750.2017.01.0075

钢筋混凝土梁抗剪承载力计算的概率模型

A PROBABILISTIC MODEL FOR SHEAR STRENGTH OF REINFORCED CONCRETE BEAMS

  • 摘要: 传统的钢筋混凝土(RC)梁抗剪承载力模型属于确定性模型,难以有效考虑几何尺寸、材料特性、边界约束条件等因素存在的客观(物理)不确定性和在模型推导过程中存在的主观(模型)不确定性的影响,导致计算结果的离散性较大,计算精度和适用性有限。鉴于此,该文首先结合修正压力场理论和考虑剪跨比影响的临界斜裂缝倾角模型,建立了RC梁的确定性抗剪承载力模型;然后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梁抗剪承载力计算的概率模型;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,所建立的概率模型不仅可以合理地描述RC梁抗剪承载力的概率分布特性,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,还可以根据预定的置信水平确定RC梁抗剪承载力的概率特征值,具有良好的计算精度和适用性。

     

    Abstract: Traditional models for shear strength of reinforced concrete (RC) beams are generally deterministic models and exhibit low computational accuracy and large numerical fluctuation, due to the fact that they do not take into account the aleatory (physical) uncertainties of various parameters such as geometry, material properties and boundary conditions as well as epistemic (model) uncertainties of the modelling. Based on the modified compression field theory (MCFT) and the critical crack angle model considering the influence of shear span ratio, a deterministic model for shear strength of RC beams was established first. Subsequently, a probabilistic model for shear strength of RC beam was developed by using the Bayesian theory and the Markov Chain Monte Carlo (MCMC) to take into account the influences of both epistemic and aleatory uncertainties. Finally, the applicability and efficiency of the proposed probabilistic model were validated by comparing with experimental data and traditional deterministic models. Analysis results show that the proposed probabilistic model is of good accuracy and adaptability. The model not only can describe the probabilistic distribution characteristics of shear strength of RC beams, 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 shear strength of RC beams with different confidence levels.

     

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