自锚式独塔悬索桥竖向弯曲振动基频估算公式
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摘要
为方便计算自锚式独塔悬索桥的竖向自振频率,以塔梁支承体系的独塔自锚式悬索桥为研究对象,采用能量法,推导了该体系的竖向弯曲振动频率公式,最后对此公式可行性进行了算例验证。研究结果表明:文中所推导解析解的竖弯基频计算值与文献解之间的误差能满足初步设计阶段要求;该公式可用于该体系在初步概念设计中选择合理的结构计算参数。
In order to calculate the vertical natural frequencies of self-anchored single tower suspension bridge conveniently,the self-anchored single tower suspension bridge with tower-beam support system was taken as the research object. The formula of the vertical bending vibration frequency of the system was deduced by the energy method. Finally,the feasibility of the proposed formula was verified by the case study. The results indicate that the errors between the calculated values of vertical bending fundamental frequencies of the proposed analytical solutions and those of the literature can meet the requirements of the preliminary design stage,and the proposed formula can be used to select reasonable structural calculation parameters in the preliminary conceptual design of the system.
In order to calculate the vertical natural frequencies of self-anchored single tower suspension bridge conveniently,the self-anchored single tower suspension bridge with tower-beam support system was taken as the research object. The formula of the vertical bending vibration frequency of the system was deduced by the energy method. Finally,the feasibility of the proposed formula was verified by the case study. The results indicate that the errors between the calculated values of vertical bending fundamental frequencies of the proposed analytical solutions and those of the literature can meet the requirements of the preliminary design stage,and the proposed formula can be used to select reasonable structural calculation parameters in the preliminary conceptual design of the system.
引文
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[2]KONSTANTAKOPOULOS T G,RAFTOYIANNIS I G,MICHALTSOS G T. Suspended bridges subjected to earthquake and moving loads[J]. Engineering Structtures,2012,45(2248):223-237.
[3] WESTGATE R,KOO K Y,BROWNNJOHN J,et al. Suspension bridge response due to extreme vehicle loads[J]. Structure and Infrastructure Engineering,2014,10(6):821-833.
[4]FEN Dongming,SUN Hao,FENG M Q. Simultaneous identification of bridge structural parameters and vehicle loads[J]. Computer and Structure,2015,157:76-88.
[5] GUO Tong,LIU Jie,HUANG Lingyu. Investigation and control of excessive cumulative girder movements of long-span steel suspension bridges[J]. Engineering Structures,2016,125(1):217-226.
[6]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,2002.LI Guohao. Stability and Vibration of Bridge Structures[M]. Beijing:China Railway Publishing,2002.
[7]张启伟,冯敏祎.自锚式混凝土悬索桥的动力分析[J].同济大学学报(自然科学版),2004,32(12):1562-1566.ZHANG Qiwei,FENG Minyi. Dynamic analysis of self-anchored concrete suspension bridge[J]. Journal of Tongji University(Natural Science),2004,32(12):1562-1566.
[8]张宏斌,孔宪京,张哲.自锚式悬索桥动力特性分析[J].公路交通科技,2004,21(7):66-69.ZHANG Hongbing,KONG Xianjing,ZHANG Zhe. Research on dynamic performance of self-anchored suspension bridge[J]. Journal of Highway and Transportation Research and Development,2004,21(7):66-69.
[9]王志诚.自锚式悬索桥静动力特性挠度理论研究[D].成都:西南交通大学,2006.WANG Zhicheng. Study on Deflection Theory of Static and Dynamic Characteristics of Self-anchored Suspension Bridge[D]. Chengdu:Southwest Jiaotong University,2006.
[10]张超,黄群君,许莉.考虑主塔刚度影响的三塔自锚式悬索桥竖弯频率计算公式[J].长安大学学报(自然科学版),2014,34(6):100-106.ZHANG Chao,HUANG Qunjun,XU Li. Frequency formulas for vertical vibration of three-tower self-anchored suspension bridge considering tower stiffness influence[J]. Journal of Chang'an University(Natural Science Edition),2014,34(6):100-106.
[11]中交公路规划设计院.公路桥梁抗风设计规范:JTG/T D60-01—2004[S].北京:人民交通出版社,2004.CCCC Highway Consultants Co.,Ltd.. Wind-Resistant Design Specification for Highway Bridges:JTG/T D60-01—2004[S].Beijing:China Communications Press,2004.
[12]王玉田,马宗志,姜福香.独塔空间缆索自锚式悬索桥动力特性研究[J].桥梁建设,2011(4):41-43.WANG Yutian,MA Zongzhi,JIANG Fuxiang. Study of dynamic characteristic of single-tower self-anchored suspension bridges with spatial cables[J]. Bridge Construction,2011(4):41-43.
[13]李洪泉,赵明帅,陈彦江.独塔自锚式悬索桥车桥耦合振动响应研究[J].重庆交通大学学报(自然科学版),2015,34(3):1-6.LI Hongquan,ZHAO Mingshuai,CHEN Yanjiang. Research on vehicle-bridge coupling vibration of self-anchored suspension bridge with single-tower[J]. Journal of Chongqing Jiaotong University(Natural Science),2015,34(3):1-6.
[14]邱景,李光凤,沈锐利.自锚式悬索桥与上承式拱桥组合体系桥梁稳定性研究[J].重庆交通大学学报(自然科学版),2012,31(1):1-5.QIU Jing,LI Guangfeng,SHENG Ruili. Stability study of selfanchored and arch-suspension combination bridge[J]. Journal of Chongqing Jiaotong University(Natural Science),2012,31(1):1-5.
[2]KONSTANTAKOPOULOS T G,RAFTOYIANNIS I G,MICHALTSOS G T. Suspended bridges subjected to earthquake and moving loads[J]. Engineering Structtures,2012,45(2248):223-237.
[3] WESTGATE R,KOO K Y,BROWNNJOHN J,et al. Suspension bridge response due to extreme vehicle loads[J]. Structure and Infrastructure Engineering,2014,10(6):821-833.
[4]FEN Dongming,SUN Hao,FENG M Q. Simultaneous identification of bridge structural parameters and vehicle loads[J]. Computer and Structure,2015,157:76-88.
[5] GUO Tong,LIU Jie,HUANG Lingyu. Investigation and control of excessive cumulative girder movements of long-span steel suspension bridges[J]. Engineering Structures,2016,125(1):217-226.
[6]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,2002.LI Guohao. Stability and Vibration of Bridge Structures[M]. Beijing:China Railway Publishing,2002.
[7]张启伟,冯敏祎.自锚式混凝土悬索桥的动力分析[J].同济大学学报(自然科学版),2004,32(12):1562-1566.ZHANG Qiwei,FENG Minyi. Dynamic analysis of self-anchored concrete suspension bridge[J]. Journal of Tongji University(Natural Science),2004,32(12):1562-1566.
[8]张宏斌,孔宪京,张哲.自锚式悬索桥动力特性分析[J].公路交通科技,2004,21(7):66-69.ZHANG Hongbing,KONG Xianjing,ZHANG Zhe. Research on dynamic performance of self-anchored suspension bridge[J]. Journal of Highway and Transportation Research and Development,2004,21(7):66-69.
[9]王志诚.自锚式悬索桥静动力特性挠度理论研究[D].成都:西南交通大学,2006.WANG Zhicheng. Study on Deflection Theory of Static and Dynamic Characteristics of Self-anchored Suspension Bridge[D]. Chengdu:Southwest Jiaotong University,2006.
[10]张超,黄群君,许莉.考虑主塔刚度影响的三塔自锚式悬索桥竖弯频率计算公式[J].长安大学学报(自然科学版),2014,34(6):100-106.ZHANG Chao,HUANG Qunjun,XU Li. Frequency formulas for vertical vibration of three-tower self-anchored suspension bridge considering tower stiffness influence[J]. Journal of Chang'an University(Natural Science Edition),2014,34(6):100-106.
[11]中交公路规划设计院.公路桥梁抗风设计规范:JTG/T D60-01—2004[S].北京:人民交通出版社,2004.CCCC Highway Consultants Co.,Ltd.. Wind-Resistant Design Specification for Highway Bridges:JTG/T D60-01—2004[S].Beijing:China Communications Press,2004.
[12]王玉田,马宗志,姜福香.独塔空间缆索自锚式悬索桥动力特性研究[J].桥梁建设,2011(4):41-43.WANG Yutian,MA Zongzhi,JIANG Fuxiang. Study of dynamic characteristic of single-tower self-anchored suspension bridges with spatial cables[J]. Bridge Construction,2011(4):41-43.
[13]李洪泉,赵明帅,陈彦江.独塔自锚式悬索桥车桥耦合振动响应研究[J].重庆交通大学学报(自然科学版),2015,34(3):1-6.LI Hongquan,ZHAO Mingshuai,CHEN Yanjiang. Research on vehicle-bridge coupling vibration of self-anchored suspension bridge with single-tower[J]. Journal of Chongqing Jiaotong University(Natural Science),2015,34(3):1-6.
[14]邱景,李光凤,沈锐利.自锚式悬索桥与上承式拱桥组合体系桥梁稳定性研究[J].重庆交通大学学报(自然科学版),2012,31(1):1-5.QIU Jing,LI Guangfeng,SHENG Ruili. Stability study of selfanchored and arch-suspension combination bridge[J]. Journal of Chongqing Jiaotong University(Natural Science),2012,31(1):1-5.