既有钢筋混凝土结构性能的数值模拟
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摘要
随着服役时间的推移,城市既有钢筋混凝土建筑的性能不断退化,影响结构的安全使用,衰减结构的预定功能。研究既有钢筋混凝土结构的性能,不仅可以揭示潜在危险,而且研究成果还可以直接用于指导结构设计。
本文以我国存在大量城市既有建筑为背景,利用人工神经网络模型和非线性有限元分析软件OpenSEES为工具,从材料、构件和整体结构三个层次研究了城市既有混凝土结构的性能。
首先,总结分析国内外有关混凝土强度预测研究成果的基础上,运用MATLAB神经网络工具箱,建立了既有建筑混凝土强度退化的计算模型,研究了既有建筑材料性能退化的情况。本文所建立的模型主要考虑了混凝土强度随时间的退化规律,其成果可用于大面积普查既有建筑的抗震性能。
其次,在收集国外大量抗剪试验数据的基础上,用神经网络模型来研究钢筋混凝土梁的抗剪性能。通过对各国规范的抗剪设计方法和神经网络模型预测方法的对比分析,总结得出各国规范的适用性,而且研究表明,本文的神经网络模型具有很好的计算精度,计算结果明显好于各国的经验公式和理论计算方法。
最后,本文在地震工程模拟平台OpenSEES上建立了—榀服役期为10年的十层三跨钢筋混凝土框架纤维模型,对其进行Pushover分析,研究了现浇楼板对结构破坏模式的影响。根据是否考虑现浇楼板效应,分为两种工况,分别进行静力弹塑性分析。分析结果表明：现浇楼板的存在增大柱的转动、减小梁的转动,削弱了设计时所期望的“强柱弱梁”效果,改变了梁柱达到屈服状态与极限状态的先后顺序。
As the service time, the performance of city's existing reinforced concrete buildings continue to deteriorate, affect the safe use of the structure, attenuate its intended function. Study the performance of existing reinforced concrete structures can not only reveal the potential risk, but research also can be directly used to guide the structural design.
In this paper, against the background of having a lot of cities'existing buildings in China, using artificial neural network model and finite element analysis software OpenSEES as a tool, from the materials, components and overall structure of the three levels to study existing concrete structure of the performance of the city.
First, on the basis of summarize and analyze the research results of prediction of concrete strength results concrete strength, using MATLAB neural network toolbox, established the degradation model of concrete strength of existing buildings to study the performance degradation of the existing building materials. The model in this paper mainly considers the degradation of concrete strength with time rules, the results can be used to survey a large area of the seismic performance of existing buildings.
Second, based on a large number of shear test data abroad, using the neural network model to study the components of reinforced concrete beam shear properties. Shear design of the national standard method and neural network prediction method were compared, the results show that this neural network model has good accuracy, its results significantly better than the experience and theoretical calculation formula.
Finally, a three-span and 10 layers reinforced concrete frame was built in OpenSEES with fiber model, by pushover analysis to study the mode of casting slab on the impact of structural damage. Whether to consider casting slab or not, two conditions is divided, and respectively carry on Static Analysis. The presence of cast slab weakened design expected "strong column and weak beam" effect.
Through study of this article, we can effectively reveal degradation laws of existing buildings'material and component, and the affect of cast slab on the seismic capacity of the whole structure.
本文以我国存在大量城市既有建筑为背景,利用人工神经网络模型和非线性有限元分析软件OpenSEES为工具,从材料、构件和整体结构三个层次研究了城市既有混凝土结构的性能。
首先,总结分析国内外有关混凝土强度预测研究成果的基础上,运用MATLAB神经网络工具箱,建立了既有建筑混凝土强度退化的计算模型,研究了既有建筑材料性能退化的情况。本文所建立的模型主要考虑了混凝土强度随时间的退化规律,其成果可用于大面积普查既有建筑的抗震性能。
其次,在收集国外大量抗剪试验数据的基础上,用神经网络模型来研究钢筋混凝土梁的抗剪性能。通过对各国规范的抗剪设计方法和神经网络模型预测方法的对比分析,总结得出各国规范的适用性,而且研究表明,本文的神经网络模型具有很好的计算精度,计算结果明显好于各国的经验公式和理论计算方法。
最后,本文在地震工程模拟平台OpenSEES上建立了—榀服役期为10年的十层三跨钢筋混凝土框架纤维模型,对其进行Pushover分析,研究了现浇楼板对结构破坏模式的影响。根据是否考虑现浇楼板效应,分为两种工况,分别进行静力弹塑性分析。分析结果表明：现浇楼板的存在增大柱的转动、减小梁的转动,削弱了设计时所期望的“强柱弱梁”效果,改变了梁柱达到屈服状态与极限状态的先后顺序。
As the service time, the performance of city's existing reinforced concrete buildings continue to deteriorate, affect the safe use of the structure, attenuate its intended function. Study the performance of existing reinforced concrete structures can not only reveal the potential risk, but research also can be directly used to guide the structural design.
In this paper, against the background of having a lot of cities'existing buildings in China, using artificial neural network model and finite element analysis software OpenSEES as a tool, from the materials, components and overall structure of the three levels to study existing concrete structure of the performance of the city.
First, on the basis of summarize and analyze the research results of prediction of concrete strength results concrete strength, using MATLAB neural network toolbox, established the degradation model of concrete strength of existing buildings to study the performance degradation of the existing building materials. The model in this paper mainly considers the degradation of concrete strength with time rules, the results can be used to survey a large area of the seismic performance of existing buildings.
Second, based on a large number of shear test data abroad, using the neural network model to study the components of reinforced concrete beam shear properties. Shear design of the national standard method and neural network prediction method were compared, the results show that this neural network model has good accuracy, its results significantly better than the experience and theoretical calculation formula.
Finally, a three-span and 10 layers reinforced concrete frame was built in OpenSEES with fiber model, by pushover analysis to study the mode of casting slab on the impact of structural damage. Whether to consider casting slab or not, two conditions is divided, and respectively carry on Static Analysis. The presence of cast slab weakened design expected "strong column and weak beam" effect.
Through study of this article, we can effectively reveal degradation laws of existing buildings'material and component, and the affect of cast slab on the seismic capacity of the whole structure.
引文
[1]欧进萍,李惠,吴斌,郭安薪.地震工程灾害与防御：汶川地震建筑震害调查与灾后重建分析报告,2008[C].
[2]赵挺生.旧有建筑物检测与评价[J].工业安全与防尘,1996,3：26-33.
[3]李静,陈龙珠,龙小梅.旧有建筑安全隐患及故障树分析方法[J].工业建筑,2005,35(增刊)：46-49.
[4]何建安.我国建筑工程质量现状与治理[J].建筑技术,1994,21(12)：707-710.
[5]曾华,马洪斌.多龄期钢筋混凝土构件非线性分析[J].低温建筑技术,2009,129(3)：43-44.
[6]张亮,金伟良,鄢飞,宋兆云.基于函数型神经网络的结构耐久性分析[J].工程力学,1998,1998(增刊)：149-154.
[7]李朝旭,王清勤,王理,尹波,豆小宁.既有建筑改造网络交流平台[J].建设科技,2009(16)：80-83.
[8]王恒栋,赵国藩.旧有结构的神经网络评估[J].工业建筑,1996,26(8)：32-34.
[9]王光远.工程结构与系统抗震优化设计的实用方法[M].北京：中国建筑工业出版社,1999.
[10]陈铭建.既有民用建筑安全鉴定方法及工程应用[D].南宁：广西大学,2007.
[11]王子英.既有民用建筑可靠性鉴定及程序设计[D].天津：天津大学,2005.
[12]魏庆晨.已有建筑结构可靠性鉴定的新方法研究[D].南宁：广西大学,2002.
[13]曹茜.钢筋混凝土及预应力混凝土构件受力性能退化模型研究[D].上海：同济大学,2008.
[14]孙彬.在役钢筋混凝土结构的性能退化与抗震性能评估[D].西安：西安建筑科技大学,2006.
[15]姜绍飞.基于神经网络结构优化与损伤检测[M].北京：科学出版社,2002.
[16]姜绍飞,钟善桐.神经网络在结构工程中的应用[J].哈尔滨建筑大学学报,1998,31(6)：129-134.
[17]飞思科技产品研发中心.神经网络理论与MATLAB7实现[M].北京：电子工业出版社,2006.
[18]高大启.有教师的线性基本函数前向三层神经网络结构研究[J].计算机学报,1998,21(1)：80-85.
[19]Mirchandani G, Wei C. On hidden nodes for neural nets[J]. IEEE Trans on Circuits and Systems, 1992,36(5):661-664.
[20]张治国.基于模态分析理论和神经网络的桥梁损伤识别方法研究[D].武汉：武汉理工大学,2005.
[21]刘昭清.基于神经网络的浅埋单跨框架损伤诊断[D].成都：西南交通大学,2005.
[22]刘青峰.神经网络智能诊断系统在混凝土结构中的应用研究[D].湘潭：湘潭大学,2006.
[23]Ren L. Q, Zhao Z. Y. An optimal neural network and concrete strength modeling[J]. Advances in Engineering Software,2002,26(7):117-130.
[24]Dias W. P. S, Pooliyadda S. P. Neural networks for predicting properties of concrete with admixtures[J]. Construction and Buidling Materials,2001,15(7):371-379.
[25]赵复笑,杨殿海,陈宏.基于神经网络的沥青混凝土路面使用性能预测[J].沈阳建筑工程学报：自然科学版,2004,20(2)：121-123.
[26]Sebastia, Marta, Fernandez. Neural network prediction of unconfined compressive strength of coal fly ash cement mixtures[J]. Cement and Concrete Research,2003,32(2):1137-1146.
[27]中华人民共和国建设部.GB50204-2002混凝土质量检验评定标准[S].北京：中国建筑工业出版社,2002.
[28]A. M. Neville. The fail of concrete compression test specimens [J]. Civil Engineering,1997,24(3):33-34.
[29]韩素芳,麦坤良.C40级普通混凝土试验研究和应用：广东建筑施工技术交流会,北京,2002[C].中国建筑工业出版社.
[30]丁声荣,余巍伟.混凝土的强度预测及其配合比优化设计研究[J].山西建筑,2008,34(34)：1-2.
[31]余雪娟.基于神经网络的混凝土强度预测[J].工程质量,2008,7(A)：40-46.
[32]韩越,张新东.再生混凝土强度预测的神经网络模型[J].混凝土,2008,222(4)：22-26.
[33]陈强,王新刚.人工神经网络在混凝土强度预测中的应用[J].工业建筑,2007,37(增刊)：1013-1016.
[34]崔猛,王新刚.混凝土强度预测的人工智能方法[J].山西建筑,2008,37(27)：99-101.
[35]牛荻涛.混凝土结构耐久性与寿命预测[M].北京：科学出版社,2003.
[36]牛荻涛,王庆霖.一般大气环境混凝土强度经时变化模型[J].工业建筑,1995,25(6)：36-38.
[37]Kani GNJ. How safe are our large RC beams. [J]. ACI,1967, March:128-141.
[38]THurston CW. Kerfeld WJ. Studies of the shear & diagonal tension strength of simply supported RC beams.[J]. ACI,1966, April:451-475.
[39]CSA committee A. CSA A23.3 Design of Concrete Structures[S].
[40]AASHTO LRFD bridge design specifications.2nd ed. Washington (DC):AASHTO[S].2003.
[41]TC Zsutty. Shear strength prediction for separate categories of simple beams tests. [J]. ACI Journal, 1971,68:138-143.
[42]Mphonde AG, Frantz GC. Shear tests of high and low strength concrete beams without stirrups.[J]. ACI,1984, July-August:350-357.
[43]Collins MP, Kuchma D. How safe are our large, lightly reinforced concrete beams, slabs, and footings [J]. ACI Struct,1999,96(4):482-490.
[44]Niwa J, Yamada K, Yokoxawa K, Okamura H. Revaluation of the equation for shear strength of reinforced concrete beams without web reinforcement.[J]. Concr Lib JSCE,1987,9:65-84.
[45]Goth ATC. Prediction of ultimate shear strength of deep beams using neural networks.[J]. ACI Structural Journal,1995,92:28-32.
[46]Sanad A, Saka MP. Prediction of ultimate shear strength of reinforced concrete deep beams using neural networks.[J]. Journal of Structural Engineering,2001,127:818-828.
[47]Cladera A, Mari AR. Shear design procedure for reinforce normal and high-strength concrete beams using artificial neural networks.Part I:Beams without stirrups.[J]. Engineering Structures,2004,26:917-926.
[48]Cladera A, Mari AR. Shear design procedure for reinforce normal and high-strength concrete beams using artificial neural networks.Part II:Beams with stirrups.[J]. Engineering Structures,2004,26:927-936.
[49]Mansour MY, Dicleli M, Lee JY, Zhang J. Predicting the shear strength of reinforced concrete beams using artificial neural networks.[J]. Engineering Structures,2004,26:781-799.
[50]Oreta AWC. Simulating size effect in shear strength of RC beams without stirrups using neural networks.[J]. Engineering Structures,2004,26:681-691.
[51]Seleemah AA. A neural network model for predicting maximum shear capacity of concrete beams without transverse reinforcement.[J]. Canadian Journal of Civil Engineering,2005,32:644-657.
[52]Kim KS, Jung S, Han SE. Prediction of shear strength using artificial neural networks for reinforced concrete members without shear reinforcement[J]. Journal of the Computational Structural Engineering Institute of Korea,2005,18:201-211.
[53]El-Chabib h, Nehdi M, Said A. Predicting shear capacity of NSC and HSC slender beams without stirrups using artificial intelligence[J]. Computers and Concrete,2005,2:69-79.
[54]El-Chabib h, Nehdi M, Said A. Predicting the effect of stirrups on shear strength of reinforced normal-strength concrete(NSC) and high-strength concrete (HSC) slender beams using artificial intelligence[J]. Canadian Journal of Civil Engineering,2006,33:933-944.
[55]Nehdi M, El-Chabib h, Said A. Evaluation of shear capacity of FRP reinforced concrete beams using artificial neural networks.[J]. Smart Structures and Systems,2006,2:81-100.
[56]ASCE-ACI Committee on Shear Torsion. Recent approaches to shear design of structural concrete[J]. Journal of Structural Engineering,1998,124:1375-1417.
[57]中华人民共和国建设部.GB50010-2002混凝土结构设计规范[S].北京：中国建筑工业出版社,2002.
[58]ACI Committee. Building code requirements for structural concrete (ACI318-02) and commentary (ACI318 R-02).[S].2002.
[59]Commission Of The European Communities. Eurocode No.2:Design of concrete structures-part 1:General rules for buildings.[S].2002.
[60]Society Of Civil Engineers Janpan. Specification for design and construction of concrete structures: Design. [S].1986.
[61]张川,张百胜,黄建锋.钢筋混凝土无腹筋简支梁的抗剪承载力研究[J].重庆建筑大学学报,2005,27(1)：48-52.
[62]于磊,车轶,宋玉普.各国规范无腹筋梁受剪承载力公式比较[J].水利水电科技进展,2009.
[63]高剑飞.OpenSEES:一个专用于土木工程的分析软件[J].四川水利,2007(5)：32.
[64]Silvia Mazzoni, Frank McKenna, Michael H. Scott, Gregory L. Fenves. OpenSees Command Language Manual [M]. Berkeley:Pacific Earthquake Engineering Research Center University of California,2007.
[65]哈尔滨工业大学,大连理工大学,北京建筑工程学院,华北水利水电学院,东南大学.混凝土及砌体结构[M].北京：中国建筑工业出版社,2002.
[66]吴晶晶.基于位移的抗震设计方法中结构局部变形概率分布特征研究[D].重庆：重庆大学,2006.
[67]吕西林,金国芳,吴晓涵.钢筋混凝土结构非线性有限元理论与应用[M].上海：同济大学出版社,1999
[68]吴勇,雷汲川,杨红.板筋参与梁端负弯矩承载力问题的探讨[J].重庆建筑大学学报,2002,24(3)：33-37.
[69]杨溥,李英民,王亚勇.结构弹塑性分析(Pushover)方法的改进[J].建筑结构学报,2000,21(1)：44-50.
[70]候爽,欧进萍.结构Pushover分析的侧向力分布及高阶振型影响[J].地震工程与工程振动,2004,24(3)：89-97.
[2]赵挺生.旧有建筑物检测与评价[J].工业安全与防尘,1996,3：26-33.
[3]李静,陈龙珠,龙小梅.旧有建筑安全隐患及故障树分析方法[J].工业建筑,2005,35(增刊)：46-49.
[4]何建安.我国建筑工程质量现状与治理[J].建筑技术,1994,21(12)：707-710.
[5]曾华,马洪斌.多龄期钢筋混凝土构件非线性分析[J].低温建筑技术,2009,129(3)：43-44.
[6]张亮,金伟良,鄢飞,宋兆云.基于函数型神经网络的结构耐久性分析[J].工程力学,1998,1998(增刊)：149-154.
[7]李朝旭,王清勤,王理,尹波,豆小宁.既有建筑改造网络交流平台[J].建设科技,2009(16)：80-83.
[8]王恒栋,赵国藩.旧有结构的神经网络评估[J].工业建筑,1996,26(8)：32-34.
[9]王光远.工程结构与系统抗震优化设计的实用方法[M].北京：中国建筑工业出版社,1999.
[10]陈铭建.既有民用建筑安全鉴定方法及工程应用[D].南宁：广西大学,2007.
[11]王子英.既有民用建筑可靠性鉴定及程序设计[D].天津：天津大学,2005.
[12]魏庆晨.已有建筑结构可靠性鉴定的新方法研究[D].南宁：广西大学,2002.
[13]曹茜.钢筋混凝土及预应力混凝土构件受力性能退化模型研究[D].上海：同济大学,2008.
[14]孙彬.在役钢筋混凝土结构的性能退化与抗震性能评估[D].西安：西安建筑科技大学,2006.
[15]姜绍飞.基于神经网络结构优化与损伤检测[M].北京：科学出版社,2002.
[16]姜绍飞,钟善桐.神经网络在结构工程中的应用[J].哈尔滨建筑大学学报,1998,31(6)：129-134.
[17]飞思科技产品研发中心.神经网络理论与MATLAB7实现[M].北京：电子工业出版社,2006.
[18]高大启.有教师的线性基本函数前向三层神经网络结构研究[J].计算机学报,1998,21(1)：80-85.
[19]Mirchandani G, Wei C. On hidden nodes for neural nets[J]. IEEE Trans on Circuits and Systems, 1992,36(5):661-664.
[20]张治国.基于模态分析理论和神经网络的桥梁损伤识别方法研究[D].武汉：武汉理工大学,2005.
[21]刘昭清.基于神经网络的浅埋单跨框架损伤诊断[D].成都：西南交通大学,2005.
[22]刘青峰.神经网络智能诊断系统在混凝土结构中的应用研究[D].湘潭：湘潭大学,2006.
[23]Ren L. Q, Zhao Z. Y. An optimal neural network and concrete strength modeling[J]. Advances in Engineering Software,2002,26(7):117-130.
[24]Dias W. P. S, Pooliyadda S. P. Neural networks for predicting properties of concrete with admixtures[J]. Construction and Buidling Materials,2001,15(7):371-379.
[25]赵复笑,杨殿海,陈宏.基于神经网络的沥青混凝土路面使用性能预测[J].沈阳建筑工程学报：自然科学版,2004,20(2)：121-123.
[26]Sebastia, Marta, Fernandez. Neural network prediction of unconfined compressive strength of coal fly ash cement mixtures[J]. Cement and Concrete Research,2003,32(2):1137-1146.
[27]中华人民共和国建设部.GB50204-2002混凝土质量检验评定标准[S].北京：中国建筑工业出版社,2002.
[28]A. M. Neville. The fail of concrete compression test specimens [J]. Civil Engineering,1997,24(3):33-34.
[29]韩素芳,麦坤良.C40级普通混凝土试验研究和应用：广东建筑施工技术交流会,北京,2002[C].中国建筑工业出版社.
[30]丁声荣,余巍伟.混凝土的强度预测及其配合比优化设计研究[J].山西建筑,2008,34(34)：1-2.
[31]余雪娟.基于神经网络的混凝土强度预测[J].工程质量,2008,7(A)：40-46.
[32]韩越,张新东.再生混凝土强度预测的神经网络模型[J].混凝土,2008,222(4)：22-26.
[33]陈强,王新刚.人工神经网络在混凝土强度预测中的应用[J].工业建筑,2007,37(增刊)：1013-1016.
[34]崔猛,王新刚.混凝土强度预测的人工智能方法[J].山西建筑,2008,37(27)：99-101.
[35]牛荻涛.混凝土结构耐久性与寿命预测[M].北京：科学出版社,2003.
[36]牛荻涛,王庆霖.一般大气环境混凝土强度经时变化模型[J].工业建筑,1995,25(6)：36-38.
[37]Kani GNJ. How safe are our large RC beams. [J]. ACI,1967, March:128-141.
[38]THurston CW. Kerfeld WJ. Studies of the shear & diagonal tension strength of simply supported RC beams.[J]. ACI,1966, April:451-475.
[39]CSA committee A. CSA A23.3 Design of Concrete Structures[S].
[40]AASHTO LRFD bridge design specifications.2nd ed. Washington (DC):AASHTO[S].2003.
[41]TC Zsutty. Shear strength prediction for separate categories of simple beams tests. [J]. ACI Journal, 1971,68:138-143.
[42]Mphonde AG, Frantz GC. Shear tests of high and low strength concrete beams without stirrups.[J]. ACI,1984, July-August:350-357.
[43]Collins MP, Kuchma D. How safe are our large, lightly reinforced concrete beams, slabs, and footings [J]. ACI Struct,1999,96(4):482-490.
[44]Niwa J, Yamada K, Yokoxawa K, Okamura H. Revaluation of the equation for shear strength of reinforced concrete beams without web reinforcement.[J]. Concr Lib JSCE,1987,9:65-84.
[45]Goth ATC. Prediction of ultimate shear strength of deep beams using neural networks.[J]. ACI Structural Journal,1995,92:28-32.
[46]Sanad A, Saka MP. Prediction of ultimate shear strength of reinforced concrete deep beams using neural networks.[J]. Journal of Structural Engineering,2001,127:818-828.
[47]Cladera A, Mari AR. Shear design procedure for reinforce normal and high-strength concrete beams using artificial neural networks.Part I:Beams without stirrups.[J]. Engineering Structures,2004,26:917-926.
[48]Cladera A, Mari AR. Shear design procedure for reinforce normal and high-strength concrete beams using artificial neural networks.Part II:Beams with stirrups.[J]. Engineering Structures,2004,26:927-936.
[49]Mansour MY, Dicleli M, Lee JY, Zhang J. Predicting the shear strength of reinforced concrete beams using artificial neural networks.[J]. Engineering Structures,2004,26:781-799.
[50]Oreta AWC. Simulating size effect in shear strength of RC beams without stirrups using neural networks.[J]. Engineering Structures,2004,26:681-691.
[51]Seleemah AA. A neural network model for predicting maximum shear capacity of concrete beams without transverse reinforcement.[J]. Canadian Journal of Civil Engineering,2005,32:644-657.
[52]Kim KS, Jung S, Han SE. Prediction of shear strength using artificial neural networks for reinforced concrete members without shear reinforcement[J]. Journal of the Computational Structural Engineering Institute of Korea,2005,18:201-211.
[53]El-Chabib h, Nehdi M, Said A. Predicting shear capacity of NSC and HSC slender beams without stirrups using artificial intelligence[J]. Computers and Concrete,2005,2:69-79.
[54]El-Chabib h, Nehdi M, Said A. Predicting the effect of stirrups on shear strength of reinforced normal-strength concrete(NSC) and high-strength concrete (HSC) slender beams using artificial intelligence[J]. Canadian Journal of Civil Engineering,2006,33:933-944.
[55]Nehdi M, El-Chabib h, Said A. Evaluation of shear capacity of FRP reinforced concrete beams using artificial neural networks.[J]. Smart Structures and Systems,2006,2:81-100.
[56]ASCE-ACI Committee on Shear Torsion. Recent approaches to shear design of structural concrete[J]. Journal of Structural Engineering,1998,124:1375-1417.
[57]中华人民共和国建设部.GB50010-2002混凝土结构设计规范[S].北京：中国建筑工业出版社,2002.
[58]ACI Committee. Building code requirements for structural concrete (ACI318-02) and commentary (ACI318 R-02).[S].2002.
[59]Commission Of The European Communities. Eurocode No.2:Design of concrete structures-part 1:General rules for buildings.[S].2002.
[60]Society Of Civil Engineers Janpan. Specification for design and construction of concrete structures: Design. [S].1986.
[61]张川,张百胜,黄建锋.钢筋混凝土无腹筋简支梁的抗剪承载力研究[J].重庆建筑大学学报,2005,27(1)：48-52.
[62]于磊,车轶,宋玉普.各国规范无腹筋梁受剪承载力公式比较[J].水利水电科技进展,2009.
[63]高剑飞.OpenSEES:一个专用于土木工程的分析软件[J].四川水利,2007(5)：32.
[64]Silvia Mazzoni, Frank McKenna, Michael H. Scott, Gregory L. Fenves. OpenSees Command Language Manual [M]. Berkeley:Pacific Earthquake Engineering Research Center University of California,2007.
[65]哈尔滨工业大学,大连理工大学,北京建筑工程学院,华北水利水电学院,东南大学.混凝土及砌体结构[M].北京：中国建筑工业出版社,2002.
[66]吴晶晶.基于位移的抗震设计方法中结构局部变形概率分布特征研究[D].重庆：重庆大学,2006.
[67]吕西林,金国芳,吴晓涵.钢筋混凝土结构非线性有限元理论与应用[M].上海：同济大学出版社,1999
[68]吴勇,雷汲川,杨红.板筋参与梁端负弯矩承载力问题的探讨[J].重庆建筑大学学报,2002,24(3)：33-37.
[69]杨溥,李英民,王亚勇.结构弹塑性分析(Pushover)方法的改进[J].建筑结构学报,2000,21(1)：44-50.
[70]候爽,欧进萍.结构Pushover分析的侧向力分布及高阶振型影响[J].地震工程与工程振动,2004,24(3)：89-97.