双层连续梁桥等效线性化方法隔震分析
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摘要
为了在现行桥梁设计软件上进行连续梁桥的隔震分析,模拟铅芯橡胶隔震支座在地震、温度荷载作用下的非线性,研究了采用等效线性化方法进行桥梁隔震分析的步骤与精度。假设支座初始刚度,加载计算支座的相对位移,并得到支座水平刚度,经过反复迭代得到铅芯橡胶隔震支座的等效刚度。在此基础上将体系简化成线性系统按弹性方法进行计算,以安装了铅芯橡胶隔震支座的双层连续梁桥为例,分别计算等效模型和非线性模型在水平地震、均匀升温、横向风荷载和制动力作用下的响应,并讨论了等效线性化方法计算时的相关问题。与非线性分析结果比较,等效线性化法可以模拟水平地震和温度荷载作用下支座的非线性,结果满足桥梁工程的精度要求。隔震支座在横向风荷载和制动力荷载作用下一般不会屈服,使用第一刚度计算即可。
To analyse seismic isolation of continuous bridge with leadrubber bearings(LRB) by commonly used bridge-design software and simulate the nonlinearity of LRB under seismic and temperature loads,the process and precision of equivalent linear method were studied.First,initial stiffness of the bearings was supposed,and the relative displacement was computed on the special load.Based on the relative displacement and the shearing force of bearings,horizontal stiffness was obtained.And then the equivalent linear stiffness was computed by iterative method.The nonlinear bridge was simplified to equivalent linear system by elasticity methods.Take a double deck bridge with LRB as an example,the reactions of equivalent linear model and nonlinear model under horizontal seism,uniform temperature increase,lateral wind loads and braking force,were calculated and analyzed respectively.The former is computed by elasticity statics methods and the latter is computed by nonlinear statics or dynamics methods.The forces and displacements of pier and girder were obtained by two of them.Meanwhile,a series of problems on equivalent linear method were discussed,such as the astringency of equivalent linear model and the system damping ratio.Compared with nonlinear model,equivalent linear model meets bridge engineering requirements,especially on seismic and temperature load.The LRB are usually not yielding on wind loads and braking force,and in that case,the first stiffness is suitable for bridge design.
To analyse seismic isolation of continuous bridge with leadrubber bearings(LRB) by commonly used bridge-design software and simulate the nonlinearity of LRB under seismic and temperature loads,the process and precision of equivalent linear method were studied.First,initial stiffness of the bearings was supposed,and the relative displacement was computed on the special load.Based on the relative displacement and the shearing force of bearings,horizontal stiffness was obtained.And then the equivalent linear stiffness was computed by iterative method.The nonlinear bridge was simplified to equivalent linear system by elasticity methods.Take a double deck bridge with LRB as an example,the reactions of equivalent linear model and nonlinear model under horizontal seism,uniform temperature increase,lateral wind loads and braking force,were calculated and analyzed respectively.The former is computed by elasticity statics methods and the latter is computed by nonlinear statics or dynamics methods.The forces and displacements of pier and girder were obtained by two of them.Meanwhile,a series of problems on equivalent linear method were discussed,such as the astringency of equivalent linear model and the system damping ratio.Compared with nonlinear model,equivalent linear model meets bridge engineering requirements,especially on seismic and temperature load.The LRB are usually not yielding on wind loads and braking force,and in that case,the first stiffness is suitable for bridge design.
引文
[1]范立础.桥梁抗震[M].上海:同济大学出版社,1997.FAN Li-chu.Earthquake Resistant of Bridges[M].Shanghai:Tongji University Press,1997.
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[3]江宜城,叶志雄,聂肃菲,等.四铅芯橡胶支座显式有限元分析及试验研究[J].中国市政工程,2007(3):41-43.JIANG Yi-cheng,YE Zhi-xiong,NIE Su-fei,et al.Exp-erimental Study of Mechanical Properties of four-lead RubberBearing and Its Explicit Finite Element Analysis[J].ChinaMunicipal Engineering,2007(3):41-43.
[4]熊世树,周正华,王补林.铅芯橡胶隔震支座恢复力模型的分析方法[J].华中科技大学学报(城市科学版),2003,20(2):28-31.XIONG Shi-shu,ZHOU Zheng-hua,WANG Bu-lin.Analysisof Hysteresis Model of Lead-rubber Laminated Bearing[J].Journal of Huazhong University of Science and Technology(Ur-ban Science Edition),2003,20(2):28-31.
[5]王常峰,朱东生,陈兴冲.基于位移的隔震桥梁非迭代设计方法研究[J].世界地震工程,2005,21(3):35-39.WANG Chang-feng,ZHU Dong-sheng,CHEN Xin-chong.R-esearch on Displacement-based Non-iterative Design Method forthe Isolated Bridge[J].World Information on Earthquake En-gineering,2005,21(3):35-39.
[6]孔德怡,李黎,江宜城,等.桥梁隔震设计中几种等效线性化方法比较研究[J].公路交通科技,2008,25(2):73-78.KONG De-yi,LI Li,JIANG Yi-cheng,et al.ComparativeResearch on Equivalent Linearization Methods in Bridge Isola-tion Design[J].Journal of Highway and Transportation Re-search and Development,2008,25(2):73-78.
[7]孔德怡,李黎,江宜城,等.连续梁桥隔震设计与分析若干问题讨论[J].工程抗震与加固改造,2006,28(4):32-36.KONG De-yi,LI Li,JIANG Yi-cheng,et al.Discussion onthe Design and Analysis Problem of Isolated Continuous Bridge[J].Earthquake Resistant Engineering and Retrofitting,2006,28(4):32-36.
[8]郝文化.ANSYS土木工程应用实例[M].北京:中国水利水电出版社,2005.HAO Wen-hua.Apply Example of Civil Engineering by ANSYS[M].Beijing:China Water Power Press,2005.
[9]PARK J G,OTSUKA H.Optimal Yield Level of Bilinear Seis-mic Isolation Devices[J].Earthquake Engineering&Structur-al Dynamics,1999,28(9):941-955.
[10]吴彬,庄军生,臧晓秋.铅芯橡胶支座的非线性动态分析力学参数试验研究[J].工程力学,2004,21(5):144-149.WU Bin,ZHUANG Jun-sheng,ZANG Xiao-qiu.ExperimentalStudy of Mechanical Parameters of Lead-Rubber Bearing byNonlinear Dynamic Analysis[J].Engineering Mechancs,2004,21(5):144-149.
[11]唐家祥,刘再华.建筑结构基础隔震[M].武汉,华中科技大学出版社,1993.TANG Jia-xiang,LIU Zai-hua.Base Seismic Isolation Designof Building Structure[M].Wuhan:Huangzhong University ofScience and Technology Press,1993.
[12]JTJ004-89,公路工程抗震设计规范[S].JTJ004-89,Specifications of Earthquake Resistant Design forHighway Engineering[S].
[2]朱东生,劳远昌,盛大元,等.LRB隔震桥梁的地震反应特点[J].工程力学,2001,18(1):119-125.ZHU Dong-sheng,LAO Yuan-chang,SHENG Da-yuan,etal.The Seismic Response Features of Isolated Bridge with LRB[J].Engineering Mechanics,2001,18(1):119-125.
[3]江宜城,叶志雄,聂肃菲,等.四铅芯橡胶支座显式有限元分析及试验研究[J].中国市政工程,2007(3):41-43.JIANG Yi-cheng,YE Zhi-xiong,NIE Su-fei,et al.Exp-erimental Study of Mechanical Properties of four-lead RubberBearing and Its Explicit Finite Element Analysis[J].ChinaMunicipal Engineering,2007(3):41-43.
[4]熊世树,周正华,王补林.铅芯橡胶隔震支座恢复力模型的分析方法[J].华中科技大学学报(城市科学版),2003,20(2):28-31.XIONG Shi-shu,ZHOU Zheng-hua,WANG Bu-lin.Analysisof Hysteresis Model of Lead-rubber Laminated Bearing[J].Journal of Huazhong University of Science and Technology(Ur-ban Science Edition),2003,20(2):28-31.
[5]王常峰,朱东生,陈兴冲.基于位移的隔震桥梁非迭代设计方法研究[J].世界地震工程,2005,21(3):35-39.WANG Chang-feng,ZHU Dong-sheng,CHEN Xin-chong.R-esearch on Displacement-based Non-iterative Design Method forthe Isolated Bridge[J].World Information on Earthquake En-gineering,2005,21(3):35-39.
[6]孔德怡,李黎,江宜城,等.桥梁隔震设计中几种等效线性化方法比较研究[J].公路交通科技,2008,25(2):73-78.KONG De-yi,LI Li,JIANG Yi-cheng,et al.ComparativeResearch on Equivalent Linearization Methods in Bridge Isola-tion Design[J].Journal of Highway and Transportation Re-search and Development,2008,25(2):73-78.
[7]孔德怡,李黎,江宜城,等.连续梁桥隔震设计与分析若干问题讨论[J].工程抗震与加固改造,2006,28(4):32-36.KONG De-yi,LI Li,JIANG Yi-cheng,et al.Discussion onthe Design and Analysis Problem of Isolated Continuous Bridge[J].Earthquake Resistant Engineering and Retrofitting,2006,28(4):32-36.
[8]郝文化.ANSYS土木工程应用实例[M].北京:中国水利水电出版社,2005.HAO Wen-hua.Apply Example of Civil Engineering by ANSYS[M].Beijing:China Water Power Press,2005.
[9]PARK J G,OTSUKA H.Optimal Yield Level of Bilinear Seis-mic Isolation Devices[J].Earthquake Engineering&Structur-al Dynamics,1999,28(9):941-955.
[10]吴彬,庄军生,臧晓秋.铅芯橡胶支座的非线性动态分析力学参数试验研究[J].工程力学,2004,21(5):144-149.WU Bin,ZHUANG Jun-sheng,ZANG Xiao-qiu.ExperimentalStudy of Mechanical Parameters of Lead-Rubber Bearing byNonlinear Dynamic Analysis[J].Engineering Mechancs,2004,21(5):144-149.
[11]唐家祥,刘再华.建筑结构基础隔震[M].武汉,华中科技大学出版社,1993.TANG Jia-xiang,LIU Zai-hua.Base Seismic Isolation Designof Building Structure[M].Wuhan:Huangzhong University ofScience and Technology Press,1993.
[12]JTJ004-89,公路工程抗震设计规范[S].JTJ004-89,Specifications of Earthquake Resistant Design forHighway Engineering[S].
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