规则梁桥单墩-质点隔震体系地震时程响应半解析法
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摘要
本文基于带集中参数边界条件的分布参数连续梁理论,推导规则隔震梁桥单墩-质点(SCM)地震时程响应的计算步骤。在控制方程边界条件引入等效基础弹簧和墩顶隔震层变形协调条件,解析地获得各阶实模态,用牛顿法搜索各阶频率。为了处理隔震层非比例阻尼产生的耦联效应,由能量法分配各阶实振型的隔震层附加阻尼比,实现体系的实模态近似解耦,应用振型叠加法求解体系的地震时程响应。最后应用该方法对一规则隔震梁桥SCM体系的地震响应进行分析,与有限元时程积分的结果进行比较,表明此方法的有效性。计算结果表明,采用墩顶隔震策略的单墩-质点体系能显著减小结构响应,具有良好的减震效果。
Based on the theory of continuous beam with distributed parameters and with boundary condiction of concentrated parameter,a solving procedure for time-history responses of single column and mass(SCM) systems used to seismic isolated regular bridge is developed.The equivalent foundation spring and the deformation compatibility conditions of the isolation layer at the column top are introduced to the governing equations.The real modes are given analytically,and the frequencies are calculated by the newton method.To handle the coupling effect of non-proportional damping problem,the additional damping of the seismic isolation layer is redistributed to each real mode and thus the system real modal decoupling is derived approximately.Then the mode superposition method can be introduced for solving the time-history response.Finally,the present procedure is applied to study the seismic response of SCM system used to a seismic isolated regular bridge.The comparison with numerical result by the finite element method shows the effectivity of the present method.The solutions also make clear that the structural response can be significantly reduced.Therefore,the seismic isolation strategy at pier top for SCM system shows considerable seismic reduction effectiveness.
Based on the theory of continuous beam with distributed parameters and with boundary condiction of concentrated parameter,a solving procedure for time-history responses of single column and mass(SCM) systems used to seismic isolated regular bridge is developed.The equivalent foundation spring and the deformation compatibility conditions of the isolation layer at the column top are introduced to the governing equations.The real modes are given analytically,and the frequencies are calculated by the newton method.To handle the coupling effect of non-proportional damping problem,the additional damping of the seismic isolation layer is redistributed to each real mode and thus the system real modal decoupling is derived approximately.Then the mode superposition method can be introduced for solving the time-history response.Finally,the present procedure is applied to study the seismic response of SCM system used to a seismic isolated regular bridge.The comparison with numerical result by the finite element method shows the effectivity of the present method.The solutions also make clear that the structural response can be significantly reduced.Therefore,the seismic isolation strategy at pier top for SCM system shows considerable seismic reduction effectiveness.
引文
[1]范立础,王志强.桥梁减隔震设计[M].北京:人民交通出版社,2001.FANG Lichu,WANG Zhiqiang.Seismic reduction and isolation design for bridge[M].Beijing:China Communications Press,2001.(in Chinese)
[2]Constantinou M,Whittaker A,Kalpakidis Y,et al.Performance of seismic isolation hardware under service and seismic loading.MCEER-07-0012.Buffalo,New York:National Center for Earthquake Engineering Research,2007.
[3]Warn G,Whittaker A.Performance estimates for seismically isolated bridges[R].Report of the Multidisciplinary Center for Earthquake EngineeringResearch[R].MCEER-07-0024[M].Buffalo,New York:National Center for Earthquake Engineering Research,2007.
[4]Turkington D,Carr A,Cooke N,et al.Design method for bridges on lead-rubber bearings[J].Journal of Structural Engineering,ASCE,1989,115(12):3017–3030.
[5]Turkington D,Carr A,Cooke N,et al.Seismic design of bridges on lead rubber bearings[J].Journal of Structural Engineering,ASCE,1989,115(12):3000–3016.
[6]Hwang J,Chiou J.An equivalent linear model of lead-rubber seismic isolation bearings[J].Engineering Structures,1996,18(7):528-536.
[7]Hwang J,Chang K,Tsai M.Composite damping ratio of seismically isolated regular bridges[J].Engineering Structures,1997,19(1):55-62.
[8]周锡元,李中锡.规则型隔震桥梁结构的简化分析方法[J].土木工程学报,2001,34(3):53-56.ZHOU Xiyuan.LI Zhongxi.Simplified formulas for seismic-isolation regular Bridge[J].China Civil Engineering Journal,2001,34(3):53-56.(in Chinese)
[9]Guide Specifications for Seismic Isolation Design[S].American Association of State Highway and Transportation Officials,Washington D.C.,CA.1991.
[10]Caltrans Seismic Design Criteria,Version 1.3.California,U.S.A.,2004.
[11]道路橋示方書.同解说[S].V耐震设计编.日本道路协会,1996.
[12]Eurocode 8:Design of Structures for Earthquake Resistance,Part2:Bridges[S].Eurocodes committee,1993.
[13]JTJ004-89公路工程抗震设计规范[S].1990.JTJ004-89 Anti-Seismic Design Code for Highway Engineering[S].1990.(in Chinese)
[14]Hwang J.Evaluation of equivalent linear analysis methods of bridge Isolation[J].Journal of Structural Engineering,Journal of Structural Engi-neering,ASCE,1996,122(8):972-976.
[15]Tsoplas P,Constantinou M,Kricher C,et al.A.evaluation of simplified methods of analysis for yielding structures[R].Report of the Multidisci-plinary Center for Earthquake Engineering Research(MCEER-97-0012),U.S.A.,1997.
[16]Ramirez O,Constantinou M,Kircher C,et al.Development and Evaluation of Simplified Procedures of Analysis and Design for Sturctures withPassive Energy Dissipation Systems[R].MCEER-00-0010[M].Buffalo,New York:National Center for Earthquake Engineering Research,2001.
[17]Pavlou E,Constantinou M.Response of elastic and inelastic structures with damping systems to near-field and soft-soil ground motions[J].Engi-neering Sturctues,2004,26(9):1217-1230.
[18]彭凯,李建中,范立础.高墩梁桥考虑墩身高阶振动的水平向主导振型[J].振动与冲击,2008,27(7):63-68.PENG Kai,LI Jianzhong,FANG Lichu.Horizontal predominant vibraiton modes of high-pier beam bridge in view of higher-order vibration of piershafts[J].Journal of Vibration and Shock,2008,27(7):63-68.(in Chinese)
[19]Cardone D,Dolce M,Palermo G.Evaluation of simplified methods for the design of bridges with seismic isolation systems[J].Earthquake Spec-tra,2009,25(2):221-238.
[2]Constantinou M,Whittaker A,Kalpakidis Y,et al.Performance of seismic isolation hardware under service and seismic loading.MCEER-07-0012.Buffalo,New York:National Center for Earthquake Engineering Research,2007.
[3]Warn G,Whittaker A.Performance estimates for seismically isolated bridges[R].Report of the Multidisciplinary Center for Earthquake EngineeringResearch[R].MCEER-07-0024[M].Buffalo,New York:National Center for Earthquake Engineering Research,2007.
[4]Turkington D,Carr A,Cooke N,et al.Design method for bridges on lead-rubber bearings[J].Journal of Structural Engineering,ASCE,1989,115(12):3017–3030.
[5]Turkington D,Carr A,Cooke N,et al.Seismic design of bridges on lead rubber bearings[J].Journal of Structural Engineering,ASCE,1989,115(12):3000–3016.
[6]Hwang J,Chiou J.An equivalent linear model of lead-rubber seismic isolation bearings[J].Engineering Structures,1996,18(7):528-536.
[7]Hwang J,Chang K,Tsai M.Composite damping ratio of seismically isolated regular bridges[J].Engineering Structures,1997,19(1):55-62.
[8]周锡元,李中锡.规则型隔震桥梁结构的简化分析方法[J].土木工程学报,2001,34(3):53-56.ZHOU Xiyuan.LI Zhongxi.Simplified formulas for seismic-isolation regular Bridge[J].China Civil Engineering Journal,2001,34(3):53-56.(in Chinese)
[9]Guide Specifications for Seismic Isolation Design[S].American Association of State Highway and Transportation Officials,Washington D.C.,CA.1991.
[10]Caltrans Seismic Design Criteria,Version 1.3.California,U.S.A.,2004.
[11]道路橋示方書.同解说[S].V耐震设计编.日本道路协会,1996.
[12]Eurocode 8:Design of Structures for Earthquake Resistance,Part2:Bridges[S].Eurocodes committee,1993.
[13]JTJ004-89公路工程抗震设计规范[S].1990.JTJ004-89 Anti-Seismic Design Code for Highway Engineering[S].1990.(in Chinese)
[14]Hwang J.Evaluation of equivalent linear analysis methods of bridge Isolation[J].Journal of Structural Engineering,Journal of Structural Engi-neering,ASCE,1996,122(8):972-976.
[15]Tsoplas P,Constantinou M,Kricher C,et al.A.evaluation of simplified methods of analysis for yielding structures[R].Report of the Multidisci-plinary Center for Earthquake Engineering Research(MCEER-97-0012),U.S.A.,1997.
[16]Ramirez O,Constantinou M,Kircher C,et al.Development and Evaluation of Simplified Procedures of Analysis and Design for Sturctures withPassive Energy Dissipation Systems[R].MCEER-00-0010[M].Buffalo,New York:National Center for Earthquake Engineering Research,2001.
[17]Pavlou E,Constantinou M.Response of elastic and inelastic structures with damping systems to near-field and soft-soil ground motions[J].Engi-neering Sturctues,2004,26(9):1217-1230.
[18]彭凯,李建中,范立础.高墩梁桥考虑墩身高阶振动的水平向主导振型[J].振动与冲击,2008,27(7):63-68.PENG Kai,LI Jianzhong,FANG Lichu.Horizontal predominant vibraiton modes of high-pier beam bridge in view of higher-order vibration of piershafts[J].Journal of Vibration and Shock,2008,27(7):63-68.(in Chinese)
[19]Cardone D,Dolce M,Palermo G.Evaluation of simplified methods for the design of bridges with seismic isolation systems[J].Earthquake Spec-tra,2009,25(2):221-238.
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