钢筋混凝土梁抗剪承载力计算的概率模型
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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。
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.
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.
引文
[1]曾庆响.混凝土双向受弯构件斜截面承载力设计简便方法[J].建筑结构,2005,35(1):72―75.Zeng Qingxiang.Convenient design method for oblique section strength of reinforced concrete beam subjected to biaxial bending[J].Building Structures,2005,35(1):72―75.(in Chinese)
[2]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 Architecture&Building Press,2010.(in Chinese)
[3]SL191―2008,水工混凝土结构设计规范[S].北京:中国水利水电出版社,2008.SL191―2008,Design code for hydraulic concrete structures[S].Beijing:China Water&Power Press,2008.(in Chinese)
[4]JTG D62―2012,公路钢筋混凝土及预应力混凝土桥涵设计规范[S].北京:人民交通出版社,2012.JTG D62―2012,Code for highway reinforced concrete and prestressed concrete bridges and culverts[S].Beijing:China Communication Press,2012.(in Chinese)
[5]ACI 318-11,Building code requirements of structural concrete[S].Farmington Hills:American Concrete Institute,2011.
[6]曾庆响,蔡健.双向受弯钢筋混凝土梁受剪承载力计算[J].土木工程学报,2009,42(4):27―32.Zeng Qingxiang,Cai Jian.Calculation of the shear capacity of reinforced concrete beams under biaxial bending[J].China Civil Engineering Journal,2009,42(4):27―32.(in Chinese)
[7]Ritter W.Die bauweise hennebique(Hennebiques construction method)[J].Schweizerische Bauzeitung,1899,33(7):59―61.
[8]Vecchio F.Disturbed stress field model for reinforced concrete:formulation[J].Journal of Structural Engineering,2000,126(9):1070―1077.
[9]Mitchell D,Collins M P.Diagonal compression field theory-a rational model for structural concrete in pure torsion[J].ACI Structural Journal,1974,71(8):396―408.
[10]Vecchio F J,Collins M P.Predicting the response of reinforced concrete beams subjected to shear using modified compression field theory[J].ACI Structural Journal,1988,85(3):258―268.
[11]Collins M P,Mitchell D.Prestressed concrete structures[M].Englewood Cliffs,NJ:Prentice Hall,1991.
[12]CSA A23.3-04,Design of concrete structures[S].Mississauga,Ontario:Canadian Standard Association,2004.
[13]AASHTO L,Bridge design specifications:SI Units[S].USA:American Association of State Highway and Transportation Officials,2007.
[14]魏巍巍,贡金鑫.钢筋混凝土构件基于修正压力场理论的受剪承载力计算[J].工程力学,2011,28(2):111―117.Wei Wewei,Gong Jinxin.Shear strength of reinforced concrete members based on modified compression field theory[J].Engineering Mechanics,2011,28(2):111―117.(in Chinese)
[15]Pan Z,Li B.Evaluation of shear strength design methodologies for slender shear-critical RC beams[J].Journal of Structural Engineering,2012,139(4):619―622.
[16]余波,陈冰,唐睿楷,等.钢筋混凝土梁临界斜裂缝倾角计算的概率模型[J].计算力学学报,2018(1):98―104.Yu Bo,Chen Bing,Tang Ruikai,et al.Probabilistic model for critical crack angle of reinforced concrete beams[J].Chinese Journal of Computational Mechanics,2018(1):98―104.(in Chinese)
[17]Bentz E C,Collins M P.Development of the 2004Canadian Standards Association(CSA)A23.3 shear provisions for reinforced concrete[J].Canadian Journal of Civil Engineering,2006,33(5):521―534.
[18]Bentz E C,Vecchio F J,Collins M P.Simplified modified compression field theory for calculating shear strength of reinforced concrete elements[J].ACI Structural Journal,2006,103(4):614―624.
[19]De Silva S,Mutsuyoshi H,Witchukreangkrai E.Evaluation of shear crack width in I-shaped prestressed reinforced concrete beams[J].Journal of Advanced Concrete Technology,2008,6(3):443―458.
[20]刘虎堂.既有钢筋混凝土构件抗力的推断和验证[D].西安:西安建筑科技大学,2010.Liu Hutang.Resistance predicting and verifing of existing reinforce concrete member[D].Xi’an:Xi’an University of Architecture and Technology,2010.(in Chinese)
[21]吕大刚,宋鹏彦,王光远.考虑模型不确定性的结构可靠度分析方法[J].哈尔滨工业大学学报,2011,43(8):11―15.LüDagang,Song Pengyan,Wang Guangyuan.Reliability analysis methods of structures considering statistical uncertainty[J].Journal of Harbin Institute of Technology,2011,43(8):11―15.(in Chinese)
[22]Gilks W R,Richardson S,Spiegelhalter D J.Markov Chain Monte Carlo in practica[J].Computing Science&Statistics,1996,91(8):497―537.
[23]Cladera A,Mari A.Experimental study on high-strength concrete beams failing in shear[J].Engineering Structures,2005,27(10):1519―1527.
[24]易伟建,吕艳梅.高强箍筋高强混凝土梁受剪试验研究[J].建筑结构学报,2009,30(4):94―101.Yi Weijian,LüYanmei.Experimental study on shear behavior of high-strength concrete beams with high-strength stirrups[J].Journal of Building Structures,2009,30(4):94―101.(in Chinese)
[25]Ahmad S,Xie Y,Yu T.Shear ductility of reinforced lightweight concrete beams of normal strength and high strength concrete[J].Cement and Concrete Composites,1995,17(2):147―159.
[26]金琰,苏幼坡,康谷贻.集中荷载作用高强箍筋混凝土梁斜裂缝的出现与发展[J].建筑结构,2003,33(1):15―16.Jin Yan,Su Youpo,Kang Guyi.Appearance and development of diagonal crack of RC beams using high-strength stirrup under concentrated load[J].Building Structures,2003,33(1):15―16.(in Chinese)
[27]Li B,Tran C T N.Reinforced concrete beam analysis supplementing concrete contribution in truss models[J].Engineering Structures,2008,30(11):3285―3294.
[28]Bresler B,Scordelis A C.Shear strength of reinforced concrete beams[J].ACI Structural Journal,1969,111(4):809―818.
[29]Clark A P.Diagonal tension in reinforced concrete beams[J].ACI Structural Journal,1951,48(10):145―156.
[30]Krefeld W J,Thurston C W.Studies of the shear and diagonal tension strength of simply supported reinforced concrete beams[J].ACI Structural Journal,1966,63(4):451―476.
[31]Kong P Y L.Shear strength of high performance concrete beams[J].ACI Structural Journal,1998,95(6):677―688.
[2]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 Architecture&Building Press,2010.(in Chinese)
[3]SL191―2008,水工混凝土结构设计规范[S].北京:中国水利水电出版社,2008.SL191―2008,Design code for hydraulic concrete structures[S].Beijing:China Water&Power Press,2008.(in Chinese)
[4]JTG D62―2012,公路钢筋混凝土及预应力混凝土桥涵设计规范[S].北京:人民交通出版社,2012.JTG D62―2012,Code for highway reinforced concrete and prestressed concrete bridges and culverts[S].Beijing:China Communication Press,2012.(in Chinese)
[5]ACI 318-11,Building code requirements of structural concrete[S].Farmington Hills:American Concrete Institute,2011.
[6]曾庆响,蔡健.双向受弯钢筋混凝土梁受剪承载力计算[J].土木工程学报,2009,42(4):27―32.Zeng Qingxiang,Cai Jian.Calculation of the shear capacity of reinforced concrete beams under biaxial bending[J].China Civil Engineering Journal,2009,42(4):27―32.(in Chinese)
[7]Ritter W.Die bauweise hennebique(Hennebiques construction method)[J].Schweizerische Bauzeitung,1899,33(7):59―61.
[8]Vecchio F.Disturbed stress field model for reinforced concrete:formulation[J].Journal of Structural Engineering,2000,126(9):1070―1077.
[9]Mitchell D,Collins M P.Diagonal compression field theory-a rational model for structural concrete in pure torsion[J].ACI Structural Journal,1974,71(8):396―408.
[10]Vecchio F J,Collins M P.Predicting the response of reinforced concrete beams subjected to shear using modified compression field theory[J].ACI Structural Journal,1988,85(3):258―268.
[11]Collins M P,Mitchell D.Prestressed concrete structures[M].Englewood Cliffs,NJ:Prentice Hall,1991.
[12]CSA A23.3-04,Design of concrete structures[S].Mississauga,Ontario:Canadian Standard Association,2004.
[13]AASHTO L,Bridge design specifications:SI Units[S].USA:American Association of State Highway and Transportation Officials,2007.
[14]魏巍巍,贡金鑫.钢筋混凝土构件基于修正压力场理论的受剪承载力计算[J].工程力学,2011,28(2):111―117.Wei Wewei,Gong Jinxin.Shear strength of reinforced concrete members based on modified compression field theory[J].Engineering Mechanics,2011,28(2):111―117.(in Chinese)
[15]Pan Z,Li B.Evaluation of shear strength design methodologies for slender shear-critical RC beams[J].Journal of Structural Engineering,2012,139(4):619―622.
[16]余波,陈冰,唐睿楷,等.钢筋混凝土梁临界斜裂缝倾角计算的概率模型[J].计算力学学报,2018(1):98―104.Yu Bo,Chen Bing,Tang Ruikai,et al.Probabilistic model for critical crack angle of reinforced concrete beams[J].Chinese Journal of Computational Mechanics,2018(1):98―104.(in Chinese)
[17]Bentz E C,Collins M P.Development of the 2004Canadian Standards Association(CSA)A23.3 shear provisions for reinforced concrete[J].Canadian Journal of Civil Engineering,2006,33(5):521―534.
[18]Bentz E C,Vecchio F J,Collins M P.Simplified modified compression field theory for calculating shear strength of reinforced concrete elements[J].ACI Structural Journal,2006,103(4):614―624.
[19]De Silva S,Mutsuyoshi H,Witchukreangkrai E.Evaluation of shear crack width in I-shaped prestressed reinforced concrete beams[J].Journal of Advanced Concrete Technology,2008,6(3):443―458.
[20]刘虎堂.既有钢筋混凝土构件抗力的推断和验证[D].西安:西安建筑科技大学,2010.Liu Hutang.Resistance predicting and verifing of existing reinforce concrete member[D].Xi’an:Xi’an University of Architecture and Technology,2010.(in Chinese)
[21]吕大刚,宋鹏彦,王光远.考虑模型不确定性的结构可靠度分析方法[J].哈尔滨工业大学学报,2011,43(8):11―15.LüDagang,Song Pengyan,Wang Guangyuan.Reliability analysis methods of structures considering statistical uncertainty[J].Journal of Harbin Institute of Technology,2011,43(8):11―15.(in Chinese)
[22]Gilks W R,Richardson S,Spiegelhalter D J.Markov Chain Monte Carlo in practica[J].Computing Science&Statistics,1996,91(8):497―537.
[23]Cladera A,Mari A.Experimental study on high-strength concrete beams failing in shear[J].Engineering Structures,2005,27(10):1519―1527.
[24]易伟建,吕艳梅.高强箍筋高强混凝土梁受剪试验研究[J].建筑结构学报,2009,30(4):94―101.Yi Weijian,LüYanmei.Experimental study on shear behavior of high-strength concrete beams with high-strength stirrups[J].Journal of Building Structures,2009,30(4):94―101.(in Chinese)
[25]Ahmad S,Xie Y,Yu T.Shear ductility of reinforced lightweight concrete beams of normal strength and high strength concrete[J].Cement and Concrete Composites,1995,17(2):147―159.
[26]金琰,苏幼坡,康谷贻.集中荷载作用高强箍筋混凝土梁斜裂缝的出现与发展[J].建筑结构,2003,33(1):15―16.Jin Yan,Su Youpo,Kang Guyi.Appearance and development of diagonal crack of RC beams using high-strength stirrup under concentrated load[J].Building Structures,2003,33(1):15―16.(in Chinese)
[27]Li B,Tran C T N.Reinforced concrete beam analysis supplementing concrete contribution in truss models[J].Engineering Structures,2008,30(11):3285―3294.
[28]Bresler B,Scordelis A C.Shear strength of reinforced concrete beams[J].ACI Structural Journal,1969,111(4):809―818.
[29]Clark A P.Diagonal tension in reinforced concrete beams[J].ACI Structural Journal,1951,48(10):145―156.
[30]Krefeld W J,Thurston C W.Studies of the shear and diagonal tension strength of simply supported reinforced concrete beams[J].ACI Structural Journal,1966,63(4):451―476.
[31]Kong P Y L.Shear strength of high performance concrete beams[J].ACI Structural Journal,1998,95(6):677―688.