基于贝叶斯理论的钢筋混凝土柱受剪承载力计算
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摘要
现行混凝土结构设计规范中钢筋混凝土柱的受剪承载力公式为半经验半理论计算公式,由于试验数据的有限性和钢筋混凝土材料离散性较大的本质特性,规范建议公式缺乏明确的理论模型。该文以贝叶斯动态信息更新思路,根据主观经验信息选定现行规范中钢筋混凝土柱受剪承载力计算公式作为贝叶斯先验模型,通过已完成试验研究的柱受剪承载力数据,应用贝叶斯方法综合这两类信息进行推断,建立钢筋混凝土柱在反复荷载作用下受剪承载力的概率模型,对未知参数进行估计,修正先验模型并建立后验模型,以达到对先验模型的更新。通过先验模型计算值、后验模型计算值及试验值相互间的对比分析可知:贝叶斯方法继承了先验信息的完备性和大量试验数据的准确性,能够更准确地预测钢筋混凝土柱的受剪承载力。
The concrete code for the column shear-capacity design of a structure is gained through simi-empirical and semi theoretical.However,due to the limited test data and its own characteristics of a concrete structure,standardize formula cannot cover all the columns of shear calculations.Thusly,the thought of dynamic information updates based on Bayesian approach was introduced.A Bayesian prior model is proposed based on the epistemic information from the empirical formula.Two types of the information,the epistemic information and the experimental information,are synthesized by the Bayesian approach and inferred to update the prior model.And the probabilistic models for shear capacities of reinforced concrete column are constructed and unknown model parameters are estimated.Then modify the models and construct the new ones.Though the values of the prior model,posterior model and experiments are calculated and compared,the advantages of updating Bayesian dynamic information can be seen.The approach inherits the completeness of the prior model and the accuracy of number of experimental data information.Thus it can more accurately predict and verify the shear strength of concrete columns.
The concrete code for the column shear-capacity design of a structure is gained through simi-empirical and semi theoretical.However,due to the limited test data and its own characteristics of a concrete structure,standardize formula cannot cover all the columns of shear calculations.Thusly,the thought of dynamic information updates based on Bayesian approach was introduced.A Bayesian prior model is proposed based on the epistemic information from the empirical formula.Two types of the information,the epistemic information and the experimental information,are synthesized by the Bayesian approach and inferred to update the prior model.And the probabilistic models for shear capacities of reinforced concrete column are constructed and unknown model parameters are estimated.Then modify the models and construct the new ones.Though the values of the prior model,posterior model and experiments are calculated and compared,the advantages of updating Bayesian dynamic information can be seen.The approach inherits the completeness of the prior model and the accuracy of number of experimental data information.Thus it can more accurately predict and verify the shear strength of concrete columns.
引文
[1]GB 50010-2010,混凝土结构设计规范[S].北京:中国建筑工业出版社,2010.GB 50010-2010,Code for design of concrete structures[S].Beijing:China Architectural&Building Press,2010.(in Chinese)
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[3]ACI Committee 318,Building code Requirements for Structural Concrete(ACI 318-08)and commentary[S].American Concrete Institute,Farmington Hills,MI,2008.
[4]朱慧明,韩玉启.贝叶斯多元统计推断理论[M].北京:科学出版社,2006:1―11.Zhu Huiming,Han Yuqi.Bayesian multivariate statistical inference theory[M].Beijing:Science Press,2006:1―11.(in Chinese)
[5]张尧庭.贝叶斯统计推断[M].北京:科学出版社,1991:1―13.Zhang Yaoting.Bayesian statistical inference[M].Beijing:Science Press,1991:1―13.(in Chinese)
[6]Paolo Gardon,Armen Der Kiureghian.Probabilistic capacity models and fragility estimates for reinforced concrete columns based on experimental observations[J].Journal of Engineering Mechanics,2002,128(10):1024―1038.
[7]Junho Song,Won-Hee Kang.Probabilistic shear strength models for reinforced concrete beams without shear reinforcement[J].Journal of Engineering Mechanics,2010,34(1):15―38.
[8]广泽雅也,远藤利更穗,中天慎介,等.架柱抗震性能的试验研究[M].北京:地震出版社,1979:6―10.Hirosawa Masaya,Endo Riho,Nakayama Shinsuck,et al.Experimental study on seismic performance of reinforced concrete[M].Beijing:Seismological Press,1979:6―10.(in Chinese)
[9]路湛沁,陈家夔.钢筋混凝土框架柱在低周反复荷载作用下的抗弯强度及延性[J].西南交通大学学报,1987(1):1―10.Lu Zhanqin,Chen Jiakui.The bending strength and ductility in reinforced concrete columns under low reversed cyclic loading[J].Journal of Southwest Jiaotong University,1987(1):1―10.(in Chinese)
[10]张先进,胡幸生.钢筋混凝土框架柱抗剪强度分析[J].武汉城市建设学院学报,1995,12(4):32―38.Zhang Xianjin,Hu Xingsheng.Shear strength analysis of reinforced concrete frame column[J].Journal of Wuhan City College,1995,12(4):32―38.(in Chinese)
[2]GB 50011-2010,建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.GB 50011-2010,Code for seismic design of buildings[S].Beijing:China Architectural&Building Press,2010.(in Chinese)
[3]ACI Committee 318,Building code Requirements for Structural Concrete(ACI 318-08)and commentary[S].American Concrete Institute,Farmington Hills,MI,2008.
[4]朱慧明,韩玉启.贝叶斯多元统计推断理论[M].北京:科学出版社,2006:1―11.Zhu Huiming,Han Yuqi.Bayesian multivariate statistical inference theory[M].Beijing:Science Press,2006:1―11.(in Chinese)
[5]张尧庭.贝叶斯统计推断[M].北京:科学出版社,1991:1―13.Zhang Yaoting.Bayesian statistical inference[M].Beijing:Science Press,1991:1―13.(in Chinese)
[6]Paolo Gardon,Armen Der Kiureghian.Probabilistic capacity models and fragility estimates for reinforced concrete columns based on experimental observations[J].Journal of Engineering Mechanics,2002,128(10):1024―1038.
[7]Junho Song,Won-Hee Kang.Probabilistic shear strength models for reinforced concrete beams without shear reinforcement[J].Journal of Engineering Mechanics,2010,34(1):15―38.
[8]广泽雅也,远藤利更穗,中天慎介,等.架柱抗震性能的试验研究[M].北京:地震出版社,1979:6―10.Hirosawa Masaya,Endo Riho,Nakayama Shinsuck,et al.Experimental study on seismic performance of reinforced concrete[M].Beijing:Seismological Press,1979:6―10.(in Chinese)
[9]路湛沁,陈家夔.钢筋混凝土框架柱在低周反复荷载作用下的抗弯强度及延性[J].西南交通大学学报,1987(1):1―10.Lu Zhanqin,Chen Jiakui.The bending strength and ductility in reinforced concrete columns under low reversed cyclic loading[J].Journal of Southwest Jiaotong University,1987(1):1―10.(in Chinese)
[10]张先进,胡幸生.钢筋混凝土框架柱抗剪强度分析[J].武汉城市建设学院学报,1995,12(4):32―38.Zhang Xianjin,Hu Xingsheng.Shear strength analysis of reinforced concrete frame column[J].Journal of Wuhan City College,1995,12(4):32―38.(in Chinese)
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