| 基于共轭先验分布的深受弯构件受剪承载力概率模型分析 |
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| 引用本文： | 刘伯权,刘喜,吴涛.基于共轭先验分布的深受弯构件受剪承载力概率模型分析[J].工程力学,2015,32(4):169-177. |
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| 作者姓名： | 刘伯权 刘喜 吴涛 |
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| 作者单位： | 长安大学建筑工程学院,西安,山西 710061 |
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| 基金项目： | 国家自然科学基金项目(51108032); 陕西省自然科学基金项目(2012JM7011); 长安大学创新团队资助项目(2013G3282015); 中央高校; 基本业务费助研项目(2013G5280005) |
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| 摘 要： | 钢筋混凝土深受弯构件由于影响因素多、受力复杂,其计算模型和设计方法未形成统一定论。贝叶斯理论已被应用于钢筋混凝土部分构件承载力的预测和设计中,且合理性、准确性及优越性已得到证明,然其先验分布的选取不同,对计算结果的精度影响不同。采用共轭分布法推导了贝叶斯参数先验分布,利用贝叶斯多元统计理论,建立了基于共轭分布的钢筋混凝土深受弯构件受剪承载力贝叶斯概率模型,通过贝叶斯后验参数剔除法简化概率模型,并结合国内外学者已完成115组钢筋混凝土深受弯构件受剪性能试验结果验证模型。研究表明:基于贝叶斯简化模型得到的深受弯构件受剪承载力与试验结果吻合良好,较各国规范建议设计方法的计算结果更接近试验值。简化模型能较为合理地进行深受弯构件受剪承载力预测及设计。
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| 关 键 词： | 贝叶斯参数估计 钢筋混凝土深受弯构件 误差分析 概率模型 抗剪强度 |
| 收稿时间： | 2014-03-07 |
PROBABILISTIC SHEAR STRENGTH MODEL FOR DEEP FLEXURAL MEMBERS BASED ON CONJUGATE PRIOR DISTRIBUTION |
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| Affiliation: | School of Civil Engineering, Chang’an University, Xi’an, Shaanxi 710061, China |
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| Abstract: | Some models have been presented by domestic and foreign scholars for shear capacity of deep reinforced concrete flexural members, but there is still no generally accepted shear theory model. Bayesian theory has been applied to predict and design the bearing capacity for some reinforced concrete members, the reasonability, accuracy and superiority of which have been demonstrated, too. However, the calculation results and accuracy are different for different prior distributions. This paper develops probabilistic shear strength models for reinforced concrete deep flexural members by using of Bayesian multivariate statistical theory based on conjugate prior distribution. These probabilistic models are simplified through the Bayesian parameters removal process. Their performance is confirmed by comparison with 115 collected test results. This shows that the deep flexural members' shear strengths, as obtained by the simplified model based on Bayesian theory, are in good agreement with test results, and they are closer to the experimental values than the results given by models used in many nations’ codes. The simplified models can be used in shear strength prediction and design for deep flexural members. |
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