隔震曲线梁桥三维地震反应分析
|
摘要
随着现代交通体系的快速发展,曲线梁桥得到越来越多的应用。由于曲线梁桥相对与直线梁桥的复杂性与独特性,其抗震设计方法还不完善。本文对隔震曲线梁桥三维地震反应进行了研究,主要包括以下几个内容:
首先,对三维地震动随机过程进行谱特征正交变换,在空间某点定义了一组地震动谱主分量,三个地震动谱主分量在任意时间差时互不相关,利用谱主分量间互不相关的性质,推导出三维地震动随机模拟公式;可以假定某一点上在任意时间差时互不相关的谱特征分量在两点间也互不相关,依此假定建立了两点间不同分量的相干函数模型。
其次,给出曲线坐标系下的隔震曲线梁桥有限元建模方法。首先利用计入翘曲影响的每结点八自由度的曲梁单元,推导出桥墩单元的刚度矩阵、质量矩阵和三个方向地震质量矩阵。然后使用可以模拟铅芯叠层橡胶支座的双向耦合效应的微分型恢复力模型,并用四阶龙格-库塔方法模拟铅芯橡胶支座单元恢复力,由此可得到支座单元的切向刚度矩阵。
最后,编制MATLAB有限元程序与地震动模拟程序,计算某不隔震与隔震三跨连续曲线梁桥在三维地震与单维地震作用下的反应。计算结果表明:相对在单维地震作用下结构地震反应,在三维地震作用下结构可能产生更大地震反应,因此计算曲线梁桥地震反应时应考虑三维地震作用。
As the development of moderm traffic system, curved bridges are adopted more widely. For the complexity and the particularity, research of seismic design of curved bridges is still faultiness. This thesis presents a seismic response study of curved bridges under three-dimensional earthquake excitations. And the major content is as follows:
Firstly, apply the Proper Orthogonal Decomposition of the ground motion processes in the form of a spectral proper transformation (SPT), and the SPT of the 3-V 1-D ground motion processes at each point of the space defines a new set of ground motion processes components, called spectral proper components and uncorrelated for any time lag. Assuming, as seems physically reasonable, that principal components uncorrelated at one single point remain uncorrelated in different points, makes it poffible to obtain a new model of the tow-point coherence function of the different seismic ground motions components so as to complete the statistical model of the 3-V, 4-D seismic ground motions. Embedding the spectral principal components in a Monte Carlo framework, makes this model very attractive for the digital simulation of seismic ground motion.
Secondly, to include the warping effect the curved beam element with eight degrees of freedom is utilized. The element stiffness matrix, element mass matrix and seismic mass matrix in three directions for both girder and pier elements have been derived. The bilateral coupled restoring force model of lead rubber bearings is introduced, and the element stiffness matrix for the bearing element can be derived from this model by the Runge-Kutta method.
Finally, MATLAB program is compiled to conduct time history analysis of a three-span, continuously curved girder bridge under earthquake. Comparisons are made between three-dimensional and single-dimensional responses. It is shown that: the internal forces of structure under the three-dimensional earthquake excitation may be larger than that under the one-dimensional excitation, and seismic analysis considering three-dimensional earthquake motion must be performed for the curved grider beam.
首先,对三维地震动随机过程进行谱特征正交变换,在空间某点定义了一组地震动谱主分量,三个地震动谱主分量在任意时间差时互不相关,利用谱主分量间互不相关的性质,推导出三维地震动随机模拟公式;可以假定某一点上在任意时间差时互不相关的谱特征分量在两点间也互不相关,依此假定建立了两点间不同分量的相干函数模型。
其次,给出曲线坐标系下的隔震曲线梁桥有限元建模方法。首先利用计入翘曲影响的每结点八自由度的曲梁单元,推导出桥墩单元的刚度矩阵、质量矩阵和三个方向地震质量矩阵。然后使用可以模拟铅芯叠层橡胶支座的双向耦合效应的微分型恢复力模型,并用四阶龙格-库塔方法模拟铅芯橡胶支座单元恢复力,由此可得到支座单元的切向刚度矩阵。
最后,编制MATLAB有限元程序与地震动模拟程序,计算某不隔震与隔震三跨连续曲线梁桥在三维地震与单维地震作用下的反应。计算结果表明:相对在单维地震作用下结构地震反应,在三维地震作用下结构可能产生更大地震反应,因此计算曲线梁桥地震反应时应考虑三维地震作用。
As the development of moderm traffic system, curved bridges are adopted more widely. For the complexity and the particularity, research of seismic design of curved bridges is still faultiness. This thesis presents a seismic response study of curved bridges under three-dimensional earthquake excitations. And the major content is as follows:
Firstly, apply the Proper Orthogonal Decomposition of the ground motion processes in the form of a spectral proper transformation (SPT), and the SPT of the 3-V 1-D ground motion processes at each point of the space defines a new set of ground motion processes components, called spectral proper components and uncorrelated for any time lag. Assuming, as seems physically reasonable, that principal components uncorrelated at one single point remain uncorrelated in different points, makes it poffible to obtain a new model of the tow-point coherence function of the different seismic ground motions components so as to complete the statistical model of the 3-V, 4-D seismic ground motions. Embedding the spectral principal components in a Monte Carlo framework, makes this model very attractive for the digital simulation of seismic ground motion.
Secondly, to include the warping effect the curved beam element with eight degrees of freedom is utilized. The element stiffness matrix, element mass matrix and seismic mass matrix in three directions for both girder and pier elements have been derived. The bilateral coupled restoring force model of lead rubber bearings is introduced, and the element stiffness matrix for the bearing element can be derived from this model by the Runge-Kutta method.
Finally, MATLAB program is compiled to conduct time history analysis of a three-span, continuously curved girder bridge under earthquake. Comparisons are made between three-dimensional and single-dimensional responses. It is shown that: the internal forces of structure under the three-dimensional earthquake excitation may be larger than that under the one-dimensional excitation, and seismic analysis considering three-dimensional earthquake motion must be performed for the curved grider beam.
引文
[1]周锡元.地震工程概论.北京:地震出版社, 1985
[2]范立础.桥梁抗震.上海:同济大学出版社, 1996
[3]刘季.在多维地震动复合作用下结构的反应和建筑结构扭转地震效应.哈尔滨建筑工程学院学报, 1986, 2(2): 59-71
[4]李宏男.结构多维抗震理论与设计方法.北京:科学出版社, 1998
[5]李英民,赖明.工程地震动模型化研究综述及展望(Ⅲ).重庆建筑大学建筑工程学院学报, 1998, 20(5): 108-114
[6]李英民,赖明.工程地震动模型化研究综述及展望(Ⅱ).重庆建筑大学建筑工程学院学报, 1998, 20(4): 111-118
[7] Bycroft G. N. White noise representation of earthquakes. Journal of Engineering Mechanics Division,ASCE, 1960, 86(2): 1-16
[8] Tajimi H. A statistical model of determining the maximum response of a struct ure during an earthquake. in: Proc. of t he 2nd WCEE. Toky -Kyoto,Japan: 1960
[9] Kanai K., Semi-empirical formula for the seismic characteristics of the ground, Technical Bulletin of the Earthquake Research Institute: Tokyo,J apan, 1975.
[10] Bolotin V. V. Statistical theory of aseismic design of structures. in: Proc.of t he 2nd WCEE. Tokyo-Kyoto,Japan: 1960. 1365-1374
[11] Penzien J., Watabe M. Characteristics of 3-dimensional earthquake ground motions. Earthquake Engineering and Structural Dynamics, 1975, 3(4): 365-373
[12] Kubo T., Penzien J. Analysis of three-dimensional strong ground motions along principal axes,san fernando earthquake. Earthquake Engineering and Structural Dynamics, 1979, 7(3): 265-278
[13] Kubo T., Penzien J. Simulation of three-dimensional strong ground motions along principal axes,san fernando earthquake. Earthquake Engineering and Structural Dynamics, 1979, 7(3): 279-294
[14] Ghafory-Ashtiany M., Singh M. P. Structural response for six correlated earthquake components. Earthquake Engineering and Structural Dynamics, 1986, 14(1): 103-119
[15] Lopez O. A. Critical response of structures to multicomponent earthquake excitation. Earthquake Engineering and Structural Dynamics, 2000, 29(12): 1759-1778
[16]李宏男.结构多维地震反应.学位论文.北京:国家地震局工程力学研究所, 1990
[17]陈国兴,孙士军,宰金珉.多维相关地震动作用结构地震反应的反应谱法.南京建筑工程学院学报, 1999, (4): 15-23
[18] Wilson E. L. A clarification of the orthogonal effects in three-dimensional seismic analysis. Earthquake Spectra, 1995, 11(4): 659-666
[19] Smeby W., Kiureghian A. D. Mode combination rules for multi-component earthquake excitation. Earthquake Engineering and Structural Dynamics, 1985, 13(1): 1-12
[20] Menun C., Kiureghian A. D. A replacement for the 30%,40% and srss rulls for multicomponent seismic analysis. Earthquake Spectra, 1998, 14(1): 153-163
[21]黄玉平,刘季.双向水平地震动的空间相关性.哈尔滨建筑工程学院学报, 1987, (3): 10-14
[22] Xue S. D. Random vibration analysis of lattice shells subjected to multi-dimensional earthquake inputes. Advances in Structural Dynamics, 2000: 777-784
[23] Key D. Earthquake design practice for buildings. thomas telford, 1988: 37-39
[24]王君杰.多点多维地震动随机模型及结构的反应谱分析方法.学位论文.北京:国家地震局工程力学研究所, 1992
[25] Hammoutene M., Tiliounine B., Bard P. Y. A two dimensional nonstationary optimized accelerogram scaled for magitude. in: Conditions D. A. S., editor. 10th World Conf. on Earthquake Engineering. Madrid Spain: 1992. 817-821
[26] Naganuma T., Deodatic G., Shinozuka M. Arma models for two-dimensional. Engineering Mechanics,ASCE, 1987, 113(2): 234-251
[27] Wilson E. L., Button M. R. Three-dimensional dynamic analysis for multi-component earthquake spectra. Earthquake Engineering and Structural Dynamics, 1982, 10: 471-476
[28] Lopez O. A., Torres R. The critical angle of seismic incidence and the maximumstructural response. Earthquake Engineering and Structural Dynamics, 1997, 26: 881-894
[29] Hemandez J. J., Lopez O. A. Discussion of "A replacement for the 30%,40% and srss rules for multicomponent seismic analysis" By charles menun and armen der kiureghian. Earthquake Spectra, 1998, 14: 713-715
[30] Skinner R. I., Robinson W. H., Mcvery G. H.工程抗震概论.北京:地震出版社, 1996
[31] Fujita T., Suzuki S., Fujita S. High damping rubber bearings for seismic isolation of buildings (1 st report, hysteretic restoring force characteristics and analytical models). Trans Janpan soc Mech Eng, 1990, (C56): 658-666
[32]唐家祥,刘再华.建筑结构基础隔震.武汉:华中理工大学出版社, 1993
[33] Wen Y. K. Method for random vibration of hysteretic syserm. Journal of the EngineeringMechanics Division,ASCE, 1976, 102(2): 249-263
[34] Park Y. J., Wen Y. K., Anga H. S. Random vibration of hysteretic systems under bi - directional ground motions. Earthquake Engineering and Structural Dynamics, 1986, 14(4): 543-557
[35] Satish N., Reihorn A. M., Constantinou M. C. Torsion in base-isolated structures with elastomeric isolation systems. Journal of Structural Engineering, ASCE, 1993, 119: 2932-2951
[36]张玉良汪洋,张铜生.考虑橡胶垫弹塑性性能及结构阻尼比变化的隔震结构动力分析.工程力学, 2000, 19(2): 58-63
[37] Jenn-Shin H., Ting-Yu H. Experimental study of isolated building under triaxial ground excitations. Journal of structural Engineering,ASCE, 2000, 126: 819-826
[38]朱玉华.建筑结构不同基础隔震系统的试验与分析.学位论文.上海:同济大学, 2001
[39]王建强.基础隔震结构多维及平-扭耦联地震反应分析.学位论文.西安:西安建筑科技大学, 2003
[40] Chen X., Kareem A. Proper orthogonal decom-position-based modeling,analysis and simulation of dynamic wind load effects on structures. Journal of Engineering Mechanics, 2005, 131(4): 325-339
[41] G S., L C. Modal transformation tools in structural dynamics and wind engineering. wind and structures,an international journal, 2000, 3(4): 221-241
[42] G S., F T. A turbulence model based on principal components. Probabilistic Engineering Mechanics, 2002, 17: 327-335
[43] Mb P. Evolutionary spectral and non-stationary processes. Journal of Royal Statasics,Series B, 1965, 27: 204-237
[44] Shinozuka M., Jan C. M. Digital simulation of random processes and its application. sound vib, 1972, 25(1): 111-128
[45] Paola M. D. Digital simulation of wind field velocity. Journal of Wind Engineering and Industrial Aerodynamics, 1998, 74-76: 91-109
[46]克拉夫,彭津.结构动力学.北京:科学出版社, 1981
[47]郭全全,张文芳,吴桂英.中国国家大剧院结构地震分析.工程力学, 2003, 20(2): 43-48
[48] Amin M., Ahs A. Non-stationary stochastic model of earthquake motion. Journal of Engineering Mechanics, 1968: 559-583
[49] Tseng W. S., Penzien J. Seismic response of highway overcrossings. Earthquake Engineering and Structural Dynamics, 1975, 4: 3-24
[50] Cheung Y. K., Cheung M. S. Free vibration of curved and straight beam slab or box-grider bridge. international association for bridge and structure engineering, 1969
[51] Culver C. G. Natural frequencies of horizontally curved beams. Journal of Structural Division, ASCE, 1967: 134-142
[52]李国豪.曲线箱梁的挠曲扭转分析.上海力学, 1980, 1: 8-16
[53]李国豪,石洞, Heins C. P.曲梁桥地震分析的有限单元法.同济大学学报, 1984, 1: 1-21
[54] Yasaka A. , Mizukoshi K., Izuka M., et al. Biaxial hysteresis model for base isolation devices. in: summaries of technical papers of annual meeting. japan: 1988. 395-400
[55]巴斯K. J.工程分析中的有限元法.傅子智译.:机械工业出版社, 1982
[2]范立础.桥梁抗震.上海:同济大学出版社, 1996
[3]刘季.在多维地震动复合作用下结构的反应和建筑结构扭转地震效应.哈尔滨建筑工程学院学报, 1986, 2(2): 59-71
[4]李宏男.结构多维抗震理论与设计方法.北京:科学出版社, 1998
[5]李英民,赖明.工程地震动模型化研究综述及展望(Ⅲ).重庆建筑大学建筑工程学院学报, 1998, 20(5): 108-114
[6]李英民,赖明.工程地震动模型化研究综述及展望(Ⅱ).重庆建筑大学建筑工程学院学报, 1998, 20(4): 111-118
[7] Bycroft G. N. White noise representation of earthquakes. Journal of Engineering Mechanics Division,ASCE, 1960, 86(2): 1-16
[8] Tajimi H. A statistical model of determining the maximum response of a struct ure during an earthquake. in: Proc. of t he 2nd WCEE. Toky -Kyoto,Japan: 1960
[9] Kanai K., Semi-empirical formula for the seismic characteristics of the ground, Technical Bulletin of the Earthquake Research Institute: Tokyo,J apan, 1975.
[10] Bolotin V. V. Statistical theory of aseismic design of structures. in: Proc.of t he 2nd WCEE. Tokyo-Kyoto,Japan: 1960. 1365-1374
[11] Penzien J., Watabe M. Characteristics of 3-dimensional earthquake ground motions. Earthquake Engineering and Structural Dynamics, 1975, 3(4): 365-373
[12] Kubo T., Penzien J. Analysis of three-dimensional strong ground motions along principal axes,san fernando earthquake. Earthquake Engineering and Structural Dynamics, 1979, 7(3): 265-278
[13] Kubo T., Penzien J. Simulation of three-dimensional strong ground motions along principal axes,san fernando earthquake. Earthquake Engineering and Structural Dynamics, 1979, 7(3): 279-294
[14] Ghafory-Ashtiany M., Singh M. P. Structural response for six correlated earthquake components. Earthquake Engineering and Structural Dynamics, 1986, 14(1): 103-119
[15] Lopez O. A. Critical response of structures to multicomponent earthquake excitation. Earthquake Engineering and Structural Dynamics, 2000, 29(12): 1759-1778
[16]李宏男.结构多维地震反应.学位论文.北京:国家地震局工程力学研究所, 1990
[17]陈国兴,孙士军,宰金珉.多维相关地震动作用结构地震反应的反应谱法.南京建筑工程学院学报, 1999, (4): 15-23
[18] Wilson E. L. A clarification of the orthogonal effects in three-dimensional seismic analysis. Earthquake Spectra, 1995, 11(4): 659-666
[19] Smeby W., Kiureghian A. D. Mode combination rules for multi-component earthquake excitation. Earthquake Engineering and Structural Dynamics, 1985, 13(1): 1-12
[20] Menun C., Kiureghian A. D. A replacement for the 30%,40% and srss rulls for multicomponent seismic analysis. Earthquake Spectra, 1998, 14(1): 153-163
[21]黄玉平,刘季.双向水平地震动的空间相关性.哈尔滨建筑工程学院学报, 1987, (3): 10-14
[22] Xue S. D. Random vibration analysis of lattice shells subjected to multi-dimensional earthquake inputes. Advances in Structural Dynamics, 2000: 777-784
[23] Key D. Earthquake design practice for buildings. thomas telford, 1988: 37-39
[24]王君杰.多点多维地震动随机模型及结构的反应谱分析方法.学位论文.北京:国家地震局工程力学研究所, 1992
[25] Hammoutene M., Tiliounine B., Bard P. Y. A two dimensional nonstationary optimized accelerogram scaled for magitude. in: Conditions D. A. S., editor. 10th World Conf. on Earthquake Engineering. Madrid Spain: 1992. 817-821
[26] Naganuma T., Deodatic G., Shinozuka M. Arma models for two-dimensional. Engineering Mechanics,ASCE, 1987, 113(2): 234-251
[27] Wilson E. L., Button M. R. Three-dimensional dynamic analysis for multi-component earthquake spectra. Earthquake Engineering and Structural Dynamics, 1982, 10: 471-476
[28] Lopez O. A., Torres R. The critical angle of seismic incidence and the maximumstructural response. Earthquake Engineering and Structural Dynamics, 1997, 26: 881-894
[29] Hemandez J. J., Lopez O. A. Discussion of "A replacement for the 30%,40% and srss rules for multicomponent seismic analysis" By charles menun and armen der kiureghian. Earthquake Spectra, 1998, 14: 713-715
[30] Skinner R. I., Robinson W. H., Mcvery G. H.工程抗震概论.北京:地震出版社, 1996
[31] Fujita T., Suzuki S., Fujita S. High damping rubber bearings for seismic isolation of buildings (1 st report, hysteretic restoring force characteristics and analytical models). Trans Janpan soc Mech Eng, 1990, (C56): 658-666
[32]唐家祥,刘再华.建筑结构基础隔震.武汉:华中理工大学出版社, 1993
[33] Wen Y. K. Method for random vibration of hysteretic syserm. Journal of the EngineeringMechanics Division,ASCE, 1976, 102(2): 249-263
[34] Park Y. J., Wen Y. K., Anga H. S. Random vibration of hysteretic systems under bi - directional ground motions. Earthquake Engineering and Structural Dynamics, 1986, 14(4): 543-557
[35] Satish N., Reihorn A. M., Constantinou M. C. Torsion in base-isolated structures with elastomeric isolation systems. Journal of Structural Engineering, ASCE, 1993, 119: 2932-2951
[36]张玉良汪洋,张铜生.考虑橡胶垫弹塑性性能及结构阻尼比变化的隔震结构动力分析.工程力学, 2000, 19(2): 58-63
[37] Jenn-Shin H., Ting-Yu H. Experimental study of isolated building under triaxial ground excitations. Journal of structural Engineering,ASCE, 2000, 126: 819-826
[38]朱玉华.建筑结构不同基础隔震系统的试验与分析.学位论文.上海:同济大学, 2001
[39]王建强.基础隔震结构多维及平-扭耦联地震反应分析.学位论文.西安:西安建筑科技大学, 2003
[40] Chen X., Kareem A. Proper orthogonal decom-position-based modeling,analysis and simulation of dynamic wind load effects on structures. Journal of Engineering Mechanics, 2005, 131(4): 325-339
[41] G S., L C. Modal transformation tools in structural dynamics and wind engineering. wind and structures,an international journal, 2000, 3(4): 221-241
[42] G S., F T. A turbulence model based on principal components. Probabilistic Engineering Mechanics, 2002, 17: 327-335
[43] Mb P. Evolutionary spectral and non-stationary processes. Journal of Royal Statasics,Series B, 1965, 27: 204-237
[44] Shinozuka M., Jan C. M. Digital simulation of random processes and its application. sound vib, 1972, 25(1): 111-128
[45] Paola M. D. Digital simulation of wind field velocity. Journal of Wind Engineering and Industrial Aerodynamics, 1998, 74-76: 91-109
[46]克拉夫,彭津.结构动力学.北京:科学出版社, 1981
[47]郭全全,张文芳,吴桂英.中国国家大剧院结构地震分析.工程力学, 2003, 20(2): 43-48
[48] Amin M., Ahs A. Non-stationary stochastic model of earthquake motion. Journal of Engineering Mechanics, 1968: 559-583
[49] Tseng W. S., Penzien J. Seismic response of highway overcrossings. Earthquake Engineering and Structural Dynamics, 1975, 4: 3-24
[50] Cheung Y. K., Cheung M. S. Free vibration of curved and straight beam slab or box-grider bridge. international association for bridge and structure engineering, 1969
[51] Culver C. G. Natural frequencies of horizontally curved beams. Journal of Structural Division, ASCE, 1967: 134-142
[52]李国豪.曲线箱梁的挠曲扭转分析.上海力学, 1980, 1: 8-16
[53]李国豪,石洞, Heins C. P.曲梁桥地震分析的有限单元法.同济大学学报, 1984, 1: 1-21
[54] Yasaka A. , Mizukoshi K., Izuka M., et al. Biaxial hysteresis model for base isolation devices. in: summaries of technical papers of annual meeting. japan: 1988. 395-400
[55]巴斯K. J.工程分析中的有限元法.傅子智译.:机械工业出版社, 1982