预应力桥梁竖向振动特性和地震反应分析
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摘要
基于模态摄动法和振型叠加法,建立了预应力桥梁竖向地震反应分析的计算方法.通过2个典型工程实例分析,讨论了桥梁竖向地震反应分析中的几个问题.算例结果表明:①预加力使桥梁的自振频率升高,影响主要体现在低阶自振频率上,随着振型阶序的增加,预加力的影响变小.对于20m和32m跨度的预应力桥梁来说,竖向基频分别升高5.3%和6.3%,而第5阶竖向频率升高只有1%左右.②在地表波作用下预应力梁跨中截面弯矩减小约30%和25%,预加力提高了桥梁的抗震能力.③竖向地震反应中高阶振型的贡献可以忽略.④7度设防烈度下,在预应力桥梁跨中截面弯矩的荷载组合效应中,竖向地震作用效应所占比例分别达24.56%和26.15%,8度设防烈度时所占比例分别为38.93%和41.46%,说明在这类预应力桥梁抗震设计中应考虑竖向地震反应的影响.
Based on the modal perturbation method and the mode superposition method,an approach is established for the vertical seismic response analysis of the prestressed bridges.Several problems met in the vertical seismic response analysis of the prestressed bridge are illustrated by a case study of two simply-support prestressed bridges.Some conclusions are drawn on the basis of the numerical results.The natural frequencies increase when the preloading is applied to the bridge.The preloading effect mainly focuses on the lower natural frequencies and the effect becomes smaller when the modal order is higher.The fundament frequencies of the prestressed bridges with 20 m and 32 m span increase respectively by about 5.3% and 6.3% and its fifth modal frequency only increases by about 1%.The moments of the middle-span section of the prestressed bridges decrease by about 30% and 25% under the excitation of site ground wave.The contributions of high-order modes can be neglected for the vertical seismic responses of the bridges.The ratio factors of the vertical seismic response in the total response of the middle-span section moment of the prestressed bridges are 24.56% and 26.15% when earthquake fortification intensity is at level 7,and 38.93% and 41.46% when earthquake fortification intensity is at level 8.This means that the influence of the vertical responses should be taken into consideration in the seismic design of the prestressed bridges.
Based on the modal perturbation method and the mode superposition method,an approach is established for the vertical seismic response analysis of the prestressed bridges.Several problems met in the vertical seismic response analysis of the prestressed bridge are illustrated by a case study of two simply-support prestressed bridges.Some conclusions are drawn on the basis of the numerical results.The natural frequencies increase when the preloading is applied to the bridge.The preloading effect mainly focuses on the lower natural frequencies and the effect becomes smaller when the modal order is higher.The fundament frequencies of the prestressed bridges with 20 m and 32 m span increase respectively by about 5.3% and 6.3% and its fifth modal frequency only increases by about 1%.The moments of the middle-span section of the prestressed bridges decrease by about 30% and 25% under the excitation of site ground wave.The contributions of high-order modes can be neglected for the vertical seismic responses of the bridges.The ratio factors of the vertical seismic response in the total response of the middle-span section moment of the prestressed bridges are 24.56% and 26.15% when earthquake fortification intensity is at level 7,and 38.93% and 41.46% when earthquake fortification intensity is at level 8.This means that the influence of the vertical responses should be taken into consideration in the seismic design of the prestressed bridges.
引文
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[4]楼梦麟,洪婷婷.预应力梁横向振动分析的模态摄动法[J].工程力学,2006,23(1):107.LOU Menglin,HONG Tingting.Mode perturbation method forlateral vibration analysis of prestressed beam[J].EngineeringMechanics,2006,23(1):107.
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[2]Miyamoto A,Tei K,Nakamura H,et al.Behavior ofprestressed beam strengthened with external tendons[J].Journal of Structural Engineering,ASCE,2000,126(9):1030.
[3]刘宏伟,张伟,庄惠平.预加力对梁的动力影响分析[J].黑龙江科技学院学报,2002,12(3):37.LIU Hongwei,ZHANG Wei,ZHUANG Huiping.Analysis ofdynamic effect of prestressed force on beam[J].Journal ofInstitute of Science and Tecnology,2002,12(3):37.
[4]楼梦麟,洪婷婷.预应力梁横向振动分析的模态摄动法[J].工程力学,2006,23(1):107.LOU Menglin,HONG Tingting.Mode perturbation method forlateral vibration analysis of prestressed beam[J].EngineeringMechanics,2006,23(1):107.
[5]中国科学技术咨询服务中心预应力技术专家组.预应力工程实例应用手册(桥梁结构篇)[M].北京:中国建筑工业出版社,1996.Pretressed Technique Expert Group of Science and TechnologyConsultative Center of China.Handbook of applications ofpretressed technique in engineering(bridge structure)[M].Beijing:China Architecture&Building Press,1996.
[6]Timoshenko S,Young D H,Weaver W Jr.Vibration problems inengineering[M].4th ed.New York:John Wiley&Sons Inc,1974.
[7]石树中,沈建文,楼梦麟.基岩场地强地面运动加速度反应谱统计特征[J].同济大学学报:自然科学版,2002,30(11):1300.SHI Shuzhong,SHEN Jianwen,LOU Menglin.Static features ofresponse spectra of acceleration of strong ground motion at rocksites[J].Journal of Tongji University:Natural Science,2002,30(11):1300.
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