建筑结构抗震设计方法的新进展
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摘要
在回顾建筑结构抗震设计方法发展历程的基础上,简要地讨论了抗震设计规范中所采用的反应谱振型分解方法的假设条件和存在问题,分析了比例阻尼或经典阻尼理论的适用范围和研究非比例阻尼情况下振型分解理论的必要性。重点介绍:1)建立了实数形式的非比例阻尼的复振型分解理论,给出了适合于规范应用的一般计算公式,指出已有关于比例阻尼的相应计算公式只是其特殊情况;2)成功地将在各国抗震设计规范中广泛应用的CQC方法推广到具有复振型的非比例阻尼系统的一般情况,称为CCQC方法;3)进一步将CCQC方法推广到多维和多点激励的情况(三向输入时称为CCQC3法);4)解决了非比例阻尼系统过阻尼振型地震响应的计算方法,针对系统具有重特征值时情况提出地震响应的相应计算方法;5)考虑到地震地面运动的非平稳特性,发展了随时间变化的完全平方组合CCQC(t)方法;6)提出了一种求解大型复杂结构有限个数低阶复振型的有效方法,减少了目前规范中应用的强逼解耦方法带来的未知误差;7)提出了部分平方组合的概念,研究了初步的判断准则,通过实例分析,初步给出了新方法的适用范围和注意事项,供设计师在实际工作中加以考虑和应用。
The assumption and problem of mode- superposition response spectrum method in the Code for Seismic Design is discussed based on a brief review of the development of seismic design method for building structure.The scope of application for the classical damping theory is analyzed and the necessity of the research on mode- superposition method for non- classical damping is presented.The progress on the mode superposition response spectrum theories are discussed,which includes:1 ) establish the complex mode superposition method (in real form) for the non-classically damped linear system,and provide the general calculation formula for the application of code;2) generalize triumphantly the CQC method to the non- classically damped linear system,the CCQC method be introduced;3) generalize CCQC method to the case of multi - component and multiple- support seismic excitations and deduce corresponding method (for three dimensional input named CCQC3 );4) deduce the formula for non-classically damped system with over- critical damping peculiarity,and give the calculation method of seismic response for the linear system with multiple fold eigenvalues;5) develop the time dependent CCQC (t) algorithm,which considers non-stationary of earthquake ground motion;6) propose a applied and effective method to solve the low order complex vector basis for the large linear non- classically damped system;7) bring forward the concept of Partial Quadratic Combination in order to reduce the calculation amount of CQC and CCQC methods,and study the primary estimation-criterion.
The assumption and problem of mode- superposition response spectrum method in the Code for Seismic Design is discussed based on a brief review of the development of seismic design method for building structure.The scope of application for the classical damping theory is analyzed and the necessity of the research on mode- superposition method for non- classical damping is presented.The progress on the mode superposition response spectrum theories are discussed,which includes:1 ) establish the complex mode superposition method (in real form) for the non-classically damped linear system,and provide the general calculation formula for the application of code;2) generalize triumphantly the CQC method to the non- classically damped linear system,the CCQC method be introduced;3) generalize CCQC method to the case of multi - component and multiple- support seismic excitations and deduce corresponding method (for three dimensional input named CCQC3 );4) deduce the formula for non-classically damped system with over- critical damping peculiarity,and give the calculation method of seismic response for the linear system with multiple fold eigenvalues;5) develop the time dependent CCQC (t) algorithm,which considers non-stationary of earthquake ground motion;6) propose a applied and effective method to solve the low order complex vector basis for the large linear non- classically damped system;7) bring forward the concept of Partial Quadratic Combination in order to reduce the calculation amount of CQC and CCQC methods,and study the primary estimation-criterion.
引文
[1] 周锡元.抗震性能设计与三水准设防.土木水利,2003,30(5) :21-32．
[2] 李刚,程耿东.基于性能的结构抗震设计-理论、方法与应用[M].科学出版社,2004．
[3] 建筑工程抗震性能设计通则(CECS 160:2004(试用)).中计划出版社,2004．
[4] Rayleigh, Lord. Theory of Sound[M]. New York, 1945．
[5] Caughey T K. Classical normal modes in damped linear dynamic systems[J]. J. Appl. Mech. , 1960, 27(2) : 269-271．
[6] Caughey T K, O' Kelley M E J. Classical normal modes in damped linear dynamic systems[J]. J. Appl. Mech., 1965, 32:583-588．
[7] Clough R W, Penzien, J. Dynamics of structures[M]. 1993．
[8] Cornwell R E, Craig R R, Johnston C P. On the appliacation of the mode acceleration method to structural dynamics problem[J]. Earthq. Eng. Struct. Dyn, 1983, 11: 679-688．
[9] Nour-Humid B, Clough R W. Dynamic analysis of structures using Lanczos co-ordinates[J]. Earthq. Eng. Struct. Dyn, 1984,12 : 365-377．
[10] 吴鸿庆,任侠.结构有限元分析[M].北京:中国铁道出版社,2000．
[11] Wilson E L , Yuan M, Dickens J M. Dynamic analysis by direct superposition of Ritz vectors[J]. Earthq. Eng. Struct. Dyn, 1982, 10: 813-821．
[12] Roesset J, Whitman R V, Dobry R. Modal analysis for structures with foundation interaction[J]. J. Struct. Div. , ASCE, 1973, 99 : 399-416．
[13] Warburton G, B, Soni S R. Errors in response calculations for non-classically damped structures[J]. Earthq. Eng. Struct. Dyn, 1977, 5(3) , 365-376．
[14] Foss F K. Co-ordinates which uncouple the linear dynamic systems[J]. J. App. Mech. , ASME, 1958, 24,361-364．
[15] Velesos A S, Ventura C E. Modal analysis of non-classically damped linear systems[J]. Earthq. Eng. Struct. Dyn, 1986,14(2) , 217-243．
[16] Igusa T, Kiureghian A D, Sackman J L. Modal decomposition method for stationary response of non-classically damped systems[J]. Earthq. Eng. Struct. Dyn, 1984, 12(1) , 121-136．
[17] 周锡元.一般有阻尼线性体系地震反应的振型分解方法[M].地震出版社,1992．
[18] Hurty W C, Rubinstein M F. Dynamics of structures[M]. Prantice-Hall, New Jersey, 1994．
[19] Tsai H C, Kelly J M. Non-classical damping in dynamic analysis of base-isolated structures with internal equipment[J]. Earthq. Eng. Struct. Dyn, 1988, 16(1) , 29-43．
[20] Skinner R I, Robinson W H, McVerry G H. An introduction to seismic isolation, 1993 : 151-159．
[21] 周锡元,董娣等.非正交阻尼线性振动系统的复振型地震响应叠加分析方法[J].土木工程报,2003,36(5) :30-36．
[22] Xi-Yuan Zhou,Rui-Fang Yu,Di Dong.Complex mode superposition algorithm for seismic responses of non-classically damped linear system[J].Journal of Earthquake Engineering,2004,8 (4) :597-641．
[23] 周锡元,俞瑞芳,非比例阻尼线性系统基于规范反应谱的CCQC法[J].工程力学,2006,23(2) :10-17．
[24] Wilson E L,Kiureghian A D.A replacement for SRSS method in seismic analysis[J].Earthq.Eng.Struct.Dyn.,1981,9: 187-192．
[25] Kiureghian A D,Yutaka N.CQC modal combination rule for high-frequency modes[J].Earthq.Eng.Struct.Dyn.,1993,22 (11) :943-956．
[26] Morante M,Wang Y,et al.Evaluation of modal combination methods for seismic response spectrum analysis.Transactions of the 15~(th) International Conference on Structural Mechannics in Reactor Technology,K06/2,1999
[27] 周锡元,高晓安,马东辉.在结构地震反应完全平方组合公式中振型相关系数的简化[J].北京工业大学学报,2004,39(4) :441-445．
[28] Wilson E L,Button M R.Three-dimensional Dynamic Analysis for Multi-component Earthquake Spectra[J].Earthq.Eng. Struct.Dyn.,1982,10:471-476．
[29] Smeby W,Kiurghian A D.Modal combination rules for multicomponent earthquake excitation[J].Earthq.Eng.Struct.Dyn., 1985,13:1-12．
[30] Lopez O A,Chopra A K,Hernandez J J.Evaluation of combination rules for maximum response calculation in multi-component seismic analysis[J].Earthq.Eng.Struct.Dyn.,2001,30: 1379-1398．
[31] Hernandez J J,Lopez O A.Evaluation of combination rules for peak response calculation in three-component seismic analysis [J].Earthq.Eng.Struct.Dyn.,2003,32:1585-1602．
[32] Yu R F,Wang L,Liu H,Zhou X Y,The CCQC3 method for multi-component seismic responses of non-classically damped irregular structures.2005 America Structures Congress,ASCE. No.6064,New York.
[33] Kiureghian A D,Neuenhofer A.A response spectrum method for multiple-support seismic excitations.Report No.UCB/EERC-91/08． Earthquake Engineering Research Center,University of California Berkeley.1991．
[34] Berrah M,Kausel E.Response spectrum analysis of structures subjected to spatially varying motion[J].Earthq.Eng.Struct. Dyn.,1992,21:713-740．
[35] Clough R W,Mojtahedi S.Earthquake response analysis considering non-proportional damping[J].Earthq.Eng.Struct.Dyn., 1976,4:489-498．
[36] Warburton G.B.Soil-structure interaction for tower structures [J].Earthq.Eng.Struct.Dyn.,1978,6,535-556．
[37] Duncan P E,Eatock Tayloy R.A note on the dynamic analysis of non-proportionally damped systems[J].Earthq.Eng.Struct. Dyn.,1979,7:99-105．
[38] Ibrahimbegovic A.and Wilson E L Simple numerical algorithm for the mode superposition analysis of linear structural systems with nonproportion damping[J].Computers and Structures,1989, 33:523-533．
[39] 俞瑞芳,周锡元.大型非比例阻尼线性系统的地震反应复振型分析方法[J].计算力学学报(待刊).
[40] 俞瑞芳,周锡元.非比例阻尼线性系统考虑过阻尼影响的复振型分解法[J].建筑结构学报,2006,27(1) :50-59．
[41] 篮天,张毅刚,大跨度屋盖结构抗震设计[M],中国建筑工业出版社,北京,2000．
[42] 俞瑞芳,周锡元,非比例阻尼线性体系地震响应的部分平方组合(CPQC)法[J].土木工程学报(审稿中).
[43] Xiyuan Zhou,Ruifang YU.Mode superposition method of nonstationary seismic responses for non-classically damping linear system[J].Journal of Earthquake Engineering (in review).
[2] 李刚,程耿东.基于性能的结构抗震设计-理论、方法与应用[M].科学出版社,2004．
[3] 建筑工程抗震性能设计通则(CECS 160:2004(试用)).中计划出版社,2004．
[4] Rayleigh, Lord. Theory of Sound[M]. New York, 1945．
[5] Caughey T K. Classical normal modes in damped linear dynamic systems[J]. J. Appl. Mech. , 1960, 27(2) : 269-271．
[6] Caughey T K, O' Kelley M E J. Classical normal modes in damped linear dynamic systems[J]. J. Appl. Mech., 1965, 32:583-588．
[7] Clough R W, Penzien, J. Dynamics of structures[M]. 1993．
[8] Cornwell R E, Craig R R, Johnston C P. On the appliacation of the mode acceleration method to structural dynamics problem[J]. Earthq. Eng. Struct. Dyn, 1983, 11: 679-688．
[9] Nour-Humid B, Clough R W. Dynamic analysis of structures using Lanczos co-ordinates[J]. Earthq. Eng. Struct. Dyn, 1984,12 : 365-377．
[10] 吴鸿庆,任侠.结构有限元分析[M].北京:中国铁道出版社,2000．
[11] Wilson E L , Yuan M, Dickens J M. Dynamic analysis by direct superposition of Ritz vectors[J]. Earthq. Eng. Struct. Dyn, 1982, 10: 813-821．
[12] Roesset J, Whitman R V, Dobry R. Modal analysis for structures with foundation interaction[J]. J. Struct. Div. , ASCE, 1973, 99 : 399-416．
[13] Warburton G, B, Soni S R. Errors in response calculations for non-classically damped structures[J]. Earthq. Eng. Struct. Dyn, 1977, 5(3) , 365-376．
[14] Foss F K. Co-ordinates which uncouple the linear dynamic systems[J]. J. App. Mech. , ASME, 1958, 24,361-364．
[15] Velesos A S, Ventura C E. Modal analysis of non-classically damped linear systems[J]. Earthq. Eng. Struct. Dyn, 1986,14(2) , 217-243．
[16] Igusa T, Kiureghian A D, Sackman J L. Modal decomposition method for stationary response of non-classically damped systems[J]. Earthq. Eng. Struct. Dyn, 1984, 12(1) , 121-136．
[17] 周锡元.一般有阻尼线性体系地震反应的振型分解方法[M].地震出版社,1992．
[18] Hurty W C, Rubinstein M F. Dynamics of structures[M]. Prantice-Hall, New Jersey, 1994．
[19] Tsai H C, Kelly J M. Non-classical damping in dynamic analysis of base-isolated structures with internal equipment[J]. Earthq. Eng. Struct. Dyn, 1988, 16(1) , 29-43．
[20] Skinner R I, Robinson W H, McVerry G H. An introduction to seismic isolation, 1993 : 151-159．
[21] 周锡元,董娣等.非正交阻尼线性振动系统的复振型地震响应叠加分析方法[J].土木工程报,2003,36(5) :30-36．
[22] Xi-Yuan Zhou,Rui-Fang Yu,Di Dong.Complex mode superposition algorithm for seismic responses of non-classically damped linear system[J].Journal of Earthquake Engineering,2004,8 (4) :597-641．
[23] 周锡元,俞瑞芳,非比例阻尼线性系统基于规范反应谱的CCQC法[J].工程力学,2006,23(2) :10-17．
[24] Wilson E L,Kiureghian A D.A replacement for SRSS method in seismic analysis[J].Earthq.Eng.Struct.Dyn.,1981,9: 187-192．
[25] Kiureghian A D,Yutaka N.CQC modal combination rule for high-frequency modes[J].Earthq.Eng.Struct.Dyn.,1993,22 (11) :943-956．
[26] Morante M,Wang Y,et al.Evaluation of modal combination methods for seismic response spectrum analysis.Transactions of the 15~(th) International Conference on Structural Mechannics in Reactor Technology,K06/2,1999
[27] 周锡元,高晓安,马东辉.在结构地震反应完全平方组合公式中振型相关系数的简化[J].北京工业大学学报,2004,39(4) :441-445．
[28] Wilson E L,Button M R.Three-dimensional Dynamic Analysis for Multi-component Earthquake Spectra[J].Earthq.Eng. Struct.Dyn.,1982,10:471-476．
[29] Smeby W,Kiurghian A D.Modal combination rules for multicomponent earthquake excitation[J].Earthq.Eng.Struct.Dyn., 1985,13:1-12．
[30] Lopez O A,Chopra A K,Hernandez J J.Evaluation of combination rules for maximum response calculation in multi-component seismic analysis[J].Earthq.Eng.Struct.Dyn.,2001,30: 1379-1398．
[31] Hernandez J J,Lopez O A.Evaluation of combination rules for peak response calculation in three-component seismic analysis [J].Earthq.Eng.Struct.Dyn.,2003,32:1585-1602．
[32] Yu R F,Wang L,Liu H,Zhou X Y,The CCQC3 method for multi-component seismic responses of non-classically damped irregular structures.2005 America Structures Congress,ASCE. No.6064,New York.
[33] Kiureghian A D,Neuenhofer A.A response spectrum method for multiple-support seismic excitations.Report No.UCB/EERC-91/08． Earthquake Engineering Research Center,University of California Berkeley.1991．
[34] Berrah M,Kausel E.Response spectrum analysis of structures subjected to spatially varying motion[J].Earthq.Eng.Struct. Dyn.,1992,21:713-740．
[35] Clough R W,Mojtahedi S.Earthquake response analysis considering non-proportional damping[J].Earthq.Eng.Struct.Dyn., 1976,4:489-498．
[36] Warburton G.B.Soil-structure interaction for tower structures [J].Earthq.Eng.Struct.Dyn.,1978,6,535-556．
[37] Duncan P E,Eatock Tayloy R.A note on the dynamic analysis of non-proportionally damped systems[J].Earthq.Eng.Struct. Dyn.,1979,7:99-105．
[38] Ibrahimbegovic A.and Wilson E L Simple numerical algorithm for the mode superposition analysis of linear structural systems with nonproportion damping[J].Computers and Structures,1989, 33:523-533．
[39] 俞瑞芳,周锡元.大型非比例阻尼线性系统的地震反应复振型分析方法[J].计算力学学报(待刊).
[40] 俞瑞芳,周锡元.非比例阻尼线性系统考虑过阻尼影响的复振型分解法[J].建筑结构学报,2006,27(1) :50-59．
[41] 篮天,张毅刚,大跨度屋盖结构抗震设计[M],中国建筑工业出版社,北京,2000．
[42] 俞瑞芳,周锡元,非比例阻尼线性体系地震响应的部分平方组合(CPQC)法[J].土木工程学报(审稿中).
[43] Xiyuan Zhou,Ruifang YU.Mode superposition method of nonstationary seismic responses for non-classically damping linear system[J].Journal of Earthquake Engineering (in review).
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