桥梁结构PUSH-OVER方法研究
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摘要
Push-over分析方法是近些年来在国外一些发达国家，如美国、日本受到重视的一种结构抗震能力评价的新方法。作为一种结构非线性反应的简化计算方法，在多数情况下它能够得出比静力弹性甚至动力分析更多的重要信息，且操作简便。本文对在桥梁工程应用Push-over分析方法的基本原理、分析步骤以及最新研究进展作了系统论述，并将该方法应用于桥梁结构的抗震性能评价。基于我国《公路工程抗震设计规范》(JTJ 004-89)弹性反应谱，建立了不同场地的地震需求谱。通过具体桥梁实例，进行了结构的Push-over分析得到的能力曲线与非弹性时程分析方法得到的能力曲线平均值进行比较研究，得到了较一致的结果。另外，系统阐述了桥梁结构的P-Δ效应的影响，建立了影响刚度矩阵并进行了严格的理论推导。
系统论述Push-over分析方法的基本原理、分析步骤以及最新研究进展，并将该方法应用于桥梁结构的抗震性能评价。
利用我国规范提供的弹性反应谱，利用Vidic提出的折减系数，建立了不同场地条件的非弹性地震反应需求谱。本文建立的规范非弹性反应谱，可直接应用在实际工程中。
利用需求谱和能力谱法求目标位移，进行桥梁结构的Push-over分析中。利用具体算例比较了push-over方法和时程分析方法建立的能力谱曲线。判断了桥梁结构在不同的地震烈度下的破损极限状态。Push-over方法与时程方法评定的结构破损极限状态结果基本一致。说明了push-over方法具有形象、直观、易于理解的优点。对一定形式的桥梁结构可以用Push-over分析方法进行结构抗震能力评定，其结果准确、可靠。
对桥梁结构的P-Δ效应的影响作了系统阐述。建立了影响刚度矩阵并进行了严格的理论证明。并比较了考虑与不考虑P-Δ效应影响的能力谱曲线，通过对5个钢筋混凝土桥墩进行了计算，说明了P-Δ效应对桥梁的影响与结构的本身物理参数、竖向荷载的大小有关，对于墩顶竖向荷载较大的长细桥墩必须考虑P-Δ效应的影响。
In recent years. Push-over analytical method is regarded as a new evaluation method for seismic resistance capacity of structure in some advanced countries. For example, in USA , Japan and so on. Push-over analysis can get more information than static elastic analysis and it is easy to operate. The basic theories, steps of analysis and the recent achievements about this method are discussed, and the method is applied to evaluate seismic resistance capacity of bridges structure in this paper. The capacity curves obtained by Push-over analysis and inelastic dynamic history analysis method are compared. The results show that Push-over method can replace inelastic dynamic history analysis method to analyze bridge structure under some conditions.
The inelastic response demand spectrum of four site condition is gotten by employed Vidic's strength reduction factors method based on response spectrum of Chinese Code for highway engineering seismic resistance design (JTJ 004-89). The inelastic response demand spectrum can be employed to Calculate real bridges structural seismic resistance capacity.
Target displacement is determined by capacity spectrum method. The capacity curves obtained by Push-over analysis method and inelastic dynamic history analysis method are compared. And the results of Push-over analysis method is nearby the same to inelastic dynamic history method analysis result. So Push-over method can be applied to evaluate bridge structure seismic resistance capacity and damage degree.
The influence of P-A effect of bridges is discussed in detail. The P-A effect is related with bridges structural inhere characteristic by calculating five real bridges. And the P-△ effect must be considered in the slightness pier with heavy loads on top.
系统论述Push-over分析方法的基本原理、分析步骤以及最新研究进展，并将该方法应用于桥梁结构的抗震性能评价。
利用我国规范提供的弹性反应谱，利用Vidic提出的折减系数，建立了不同场地条件的非弹性地震反应需求谱。本文建立的规范非弹性反应谱，可直接应用在实际工程中。
利用需求谱和能力谱法求目标位移，进行桥梁结构的Push-over分析中。利用具体算例比较了push-over方法和时程分析方法建立的能力谱曲线。判断了桥梁结构在不同的地震烈度下的破损极限状态。Push-over方法与时程方法评定的结构破损极限状态结果基本一致。说明了push-over方法具有形象、直观、易于理解的优点。对一定形式的桥梁结构可以用Push-over分析方法进行结构抗震能力评定，其结果准确、可靠。
对桥梁结构的P-Δ效应的影响作了系统阐述。建立了影响刚度矩阵并进行了严格的理论证明。并比较了考虑与不考虑P-Δ效应影响的能力谱曲线，通过对5个钢筋混凝土桥墩进行了计算，说明了P-Δ效应对桥梁的影响与结构的本身物理参数、竖向荷载的大小有关，对于墩顶竖向荷载较大的长细桥墩必须考虑P-Δ效应的影响。
In recent years. Push-over analytical method is regarded as a new evaluation method for seismic resistance capacity of structure in some advanced countries. For example, in USA , Japan and so on. Push-over analysis can get more information than static elastic analysis and it is easy to operate. The basic theories, steps of analysis and the recent achievements about this method are discussed, and the method is applied to evaluate seismic resistance capacity of bridges structure in this paper. The capacity curves obtained by Push-over analysis and inelastic dynamic history analysis method are compared. The results show that Push-over method can replace inelastic dynamic history analysis method to analyze bridge structure under some conditions.
The inelastic response demand spectrum of four site condition is gotten by employed Vidic's strength reduction factors method based on response spectrum of Chinese Code for highway engineering seismic resistance design (JTJ 004-89). The inelastic response demand spectrum can be employed to Calculate real bridges structural seismic resistance capacity.
Target displacement is determined by capacity spectrum method. The capacity curves obtained by Push-over analysis method and inelastic dynamic history analysis method are compared. And the results of Push-over analysis method is nearby the same to inelastic dynamic history method analysis result. So Push-over method can be applied to evaluate bridge structure seismic resistance capacity and damage degree.
The influence of P-A effect of bridges is discussed in detail. The P-A effect is related with bridges structural inhere characteristic by calculating five real bridges. And the P-△ effect must be considered in the slightness pier with heavy loads on top.
引文
[1] 胡聿贤著，地震工程学，北京，地震出版社，1988年．
[2] 范立础，桥梁抗震，上海，同济大学出版社，1997年11月，
[3] 范立础、李建中、王君杰，高架桥梁抗震设计，北京，人民交通出版社，2001年4月．
[4] 范立础、卓卫东，桥梁延性抗震设计，北京，人民交通出版社，2001年5月．
[5] M J N普瑞斯特雷等，袁万成等译，桥梁抗震设计与加固[M]，北京，人民交通出版社，1997．
[6] 王姗姗，在多种因素影响下高耸结构的地震反应分析，中国地震局工程力学研究所硕士论文，1999年7月．
[7] 刘红梁，中国地震局工程力学研究所硕士论文，2001年7月．
[8] 叶燎原、潘文．结构静力弹塑性分析(push-over)的原理和计算实例，建筑结构学．2000．21(1)．
[9] 李峻，叶燎原，Push-over分析法及其与非线性动力分析的对比．世界地震工程，1999，15 (2)．
[10] 杨薄等，结构静力弹塑性分析(Push-over)方法的改进，建筑结构学报，2000，21 (44)．
[11] 叶燎原，潘文，结构静力弹塑性分析(push-over)的原理和计算实例，建筑结构学报，2000，21(1)．
[12] 王亚勇，关于设计反应谱、时程法和能量方法的探讨，建筑结构学报，2000，21 (1)
[13] 钱稼茹、罗文斌，建筑结构基于位移的抗震设计[J]，建筑结构，2001，31(4)：3—6．
[14] 何浩祥、李宏男，基于规范弹性反应谱建立需求谱的方法，世界地震工程，2002，18 (3)．
[15] 中华人民共和国交通部部标准《公路工程抗震设计规范》(JTJ 004-89)．北京，人民交通出版社，1990．
[16] 钱培风，结构抗震分析，北京，地震出版社，1983．
[17] 常岭，桥梁的抗震变形能力，工程抗震，1987，4．
[18] 王东升、翟桐等，利用Push-over方法评估桥梁的抗震安全性，世界地震工程，2000，16(2)．
[19] 王东升、郭恩栋、柳春光等，钢筋混凝土圆形截面柱式桥墩抗震性能评价，世界地震工程，2000，16(2)．
[20] 阎贵平、项海帆，具有单排桩基梁式桥墩的实用延性抗震验算方法研究，土木工程学报，1993，26(2)
[21] 中华人民共和国国家标准，建筑抗震设计规范，GB50011-2001，北京，中国建筑工业出版社．
[22] R．W克拉夫、J．彭津著，王光远等译，结构动力学，北京，科学出版社，1983
[23] Pauley T、Priestly M J N，戴瑞同等译，钢筋混凝土和砌体结构的抗震设计[M]，北京，中国建筑工业出版社，1999．
[24] Veletsos A S, Newmark N M. Effect of inelastic behavior on the response of simple system to earthquake motion[C], Proc.2nd world conf. On Earthquake Engineering, 1960,895-912.
[25] Vidic T, Fajfar P, Consistent inelastic design spectra: strength and displacement[J], Earthquake Engineering and Structural Dynamics, 1994,25(5):507—521.
[26] Fajfar P, Capacity spectrum method based on inelastic demand spectra[J], Earthquake Engineering and Structural Dynamics, 1999,28(9):979—993.
[27] P.Tsopelas、M.C.Constantinou et al, Evaluation of simplified methods of analysis for yielding structures, 1997, NCEER-97-0012.
[28] Anil k.Chopro、Rakesh k.Goel, Capacity-demand-diagram methods for estimating seismic deformation of inelastic structures: SDF systems, report No.PEER-1999/02.
[29] Eduardo Miranda、M.EERI et al, Evaluation of strength reduction factors for earthquake-resistant design, Earthquake Spectra, August 2000, Vol. 16, No. 2.
[30] J P Moehle、M.EERI, Displacement-based design of RC structures subjected toearthquakes, Earthquake Spectra, 1992, Vol.8,No.3.
[31] Krawinkler H, Pros and Cons of a Push-over Analysis for Seismic Performance, Engineering Structures, VOL.26, pp. 1091-1112.
[32] Helmut Krawinkler, Pros and Cons of a Push-over Analysis of Seismic Performance Evaluation, Engineering Structures, 1998(452～464).
[33] Peter Fajfar et al, A Nonlinear Analysis Method for Performance-Based Seismic Design, Earthquake Spectra, Volume 16, No. 3, August 2000.
[34] M.J.N Priestley, Performance-based seismic design, 12WCEE.
[35] European Prestandard, Eurocode 8[S], CEN, ENV 1998-1-1,1994.
[36] Federal Emergency Management Agency, Guidelines and commentary for the Seismic Rehabilitation of Buildings[S], FEMA273&274, 1998.
[37] Anil K.Chopra et al, Capacity-Demand-Diagram Methods Based on Inelastic Design Spectrum, Earthquake Spectra, November 1999, Volume 15, No. 4.
[38] Gregory A.MacRae, P-Δ effects on single-degree-of-freedom structures in
earthquakes, Earthquake Spectra, 1994, Vol. 10, No.3.
[39] Vojko Kilar et al, Simple Pushover Analysis of Asymmetric Buildings, Earthquake Engineering and Structural Dynamics, VOL. 26 (1997).
[40] Eduardo A fierrro, Performance Design Parameters: Strength vs. Ductility Demand, 12WCEE.
[41] Giuseppe Faella, Evaluation of The R/C Structures Seismic Response By Means of Nonlinear Static Pushover Analyses, 11 WCEE.
[42] Helmut Krawinkler, Pushover Analysis: Why, How, When, and When not to Use It, Structural Engineers Association of California, 1996.
[43] Sigmund A. Freeman, The Capacity Spectrum Method as A Tool for Seismic Design, 11 ECEE.
[2] 范立础，桥梁抗震，上海，同济大学出版社，1997年11月，
[3] 范立础、李建中、王君杰，高架桥梁抗震设计，北京，人民交通出版社，2001年4月．
[4] 范立础、卓卫东，桥梁延性抗震设计，北京，人民交通出版社，2001年5月．
[5] M J N普瑞斯特雷等，袁万成等译，桥梁抗震设计与加固[M]，北京，人民交通出版社，1997．
[6] 王姗姗，在多种因素影响下高耸结构的地震反应分析，中国地震局工程力学研究所硕士论文，1999年7月．
[7] 刘红梁，中国地震局工程力学研究所硕士论文，2001年7月．
[8] 叶燎原、潘文．结构静力弹塑性分析(push-over)的原理和计算实例，建筑结构学．2000．21(1)．
[9] 李峻，叶燎原，Push-over分析法及其与非线性动力分析的对比．世界地震工程，1999，15 (2)．
[10] 杨薄等，结构静力弹塑性分析(Push-over)方法的改进，建筑结构学报，2000，21 (44)．
[11] 叶燎原，潘文，结构静力弹塑性分析(push-over)的原理和计算实例，建筑结构学报，2000，21(1)．
[12] 王亚勇，关于设计反应谱、时程法和能量方法的探讨，建筑结构学报，2000，21 (1)
[13] 钱稼茹、罗文斌，建筑结构基于位移的抗震设计[J]，建筑结构，2001，31(4)：3—6．
[14] 何浩祥、李宏男，基于规范弹性反应谱建立需求谱的方法，世界地震工程，2002，18 (3)．
[15] 中华人民共和国交通部部标准《公路工程抗震设计规范》(JTJ 004-89)．北京，人民交通出版社，1990．
[16] 钱培风，结构抗震分析，北京，地震出版社，1983．
[17] 常岭，桥梁的抗震变形能力，工程抗震，1987，4．
[18] 王东升、翟桐等，利用Push-over方法评估桥梁的抗震安全性，世界地震工程，2000，16(2)．
[19] 王东升、郭恩栋、柳春光等，钢筋混凝土圆形截面柱式桥墩抗震性能评价，世界地震工程，2000，16(2)．
[20] 阎贵平、项海帆，具有单排桩基梁式桥墩的实用延性抗震验算方法研究，土木工程学报，1993，26(2)
[21] 中华人民共和国国家标准，建筑抗震设计规范，GB50011-2001，北京，中国建筑工业出版社．
[22] R．W克拉夫、J．彭津著，王光远等译，结构动力学，北京，科学出版社，1983
[23] Pauley T、Priestly M J N，戴瑞同等译，钢筋混凝土和砌体结构的抗震设计[M]，北京，中国建筑工业出版社，1999．
[24] Veletsos A S, Newmark N M. Effect of inelastic behavior on the response of simple system to earthquake motion[C], Proc.2nd world conf. On Earthquake Engineering, 1960,895-912.
[25] Vidic T, Fajfar P, Consistent inelastic design spectra: strength and displacement[J], Earthquake Engineering and Structural Dynamics, 1994,25(5):507—521.
[26] Fajfar P, Capacity spectrum method based on inelastic demand spectra[J], Earthquake Engineering and Structural Dynamics, 1999,28(9):979—993.
[27] P.Tsopelas、M.C.Constantinou et al, Evaluation of simplified methods of analysis for yielding structures, 1997, NCEER-97-0012.
[28] Anil k.Chopro、Rakesh k.Goel, Capacity-demand-diagram methods for estimating seismic deformation of inelastic structures: SDF systems, report No.PEER-1999/02.
[29] Eduardo Miranda、M.EERI et al, Evaluation of strength reduction factors for earthquake-resistant design, Earthquake Spectra, August 2000, Vol. 16, No. 2.
[30] J P Moehle、M.EERI, Displacement-based design of RC structures subjected toearthquakes, Earthquake Spectra, 1992, Vol.8,No.3.
[31] Krawinkler H, Pros and Cons of a Push-over Analysis for Seismic Performance, Engineering Structures, VOL.26, pp. 1091-1112.
[32] Helmut Krawinkler, Pros and Cons of a Push-over Analysis of Seismic Performance Evaluation, Engineering Structures, 1998(452～464).
[33] Peter Fajfar et al, A Nonlinear Analysis Method for Performance-Based Seismic Design, Earthquake Spectra, Volume 16, No. 3, August 2000.
[34] M.J.N Priestley, Performance-based seismic design, 12WCEE.
[35] European Prestandard, Eurocode 8[S], CEN, ENV 1998-1-1,1994.
[36] Federal Emergency Management Agency, Guidelines and commentary for the Seismic Rehabilitation of Buildings[S], FEMA273&274, 1998.
[37] Anil K.Chopra et al, Capacity-Demand-Diagram Methods Based on Inelastic Design Spectrum, Earthquake Spectra, November 1999, Volume 15, No. 4.
[38] Gregory A.MacRae, P-Δ effects on single-degree-of-freedom structures in
earthquakes, Earthquake Spectra, 1994, Vol. 10, No.3.
[39] Vojko Kilar et al, Simple Pushover Analysis of Asymmetric Buildings, Earthquake Engineering and Structural Dynamics, VOL. 26 (1997).
[40] Eduardo A fierrro, Performance Design Parameters: Strength vs. Ductility Demand, 12WCEE.
[41] Giuseppe Faella, Evaluation of The R/C Structures Seismic Response By Means of Nonlinear Static Pushover Analyses, 11 WCEE.
[42] Helmut Krawinkler, Pushover Analysis: Why, How, When, and When not to Use It, Structural Engineers Association of California, 1996.
[43] Sigmund A. Freeman, The Capacity Spectrum Method as A Tool for Seismic Design, 11 ECEE.