高塔斜拉桥纵桥向高阶振型影响分析
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摘要
地震区斜拉桥多采用漂浮体系的结构体系。在传统的抗震分析中,纵桥向往往简化为单自由度体系以降低计算的复杂性。然而,由于近年来大跨度、高塔斜拉桥的不断涌现,二阶振型的贡献增加,仅考虑一阶振型的单自由度模型是否依然适用值得商榷。因此现选取多座跨径在300 m～1 000 m左右的典型斜拉桥进行分析,研究斜拉桥纵桥向二阶振型随着跨径、塔高以及场地土类型的变化对桥塔塔底弯矩、剪力的贡献。结果表明当斜拉桥桥塔高度超过100 m后,二阶振型对于塔底剪力的贡献基本保持在10%以上,而当塔高超过150 m时,二阶振型对塔底弯矩的贡献也会达到5%以上。为进一步探讨高塔二阶振型的影响,以一座典型斜拉桥为实例,分析其纵桥向二阶振型随主梁质量以及刚度的变化对塔底弯矩、剪力的贡献,研究表明塔梁质量比与塔梁刚度比均是影响二阶振型贡献的重要因素。相比较而言,主梁质量变化对结构的影响更为显著,但在达到一定数值后逐渐减小。
Cable-stayed bridges are often designed as floating systems in seismic area in order to mitigate ther responses induced by the earthquake.The seismic analytical model is commonly simplified as a single DOF system longitudinally.However,as bridge spans become longer and longer,the tower is taller and taller,hence the contribution of the second mode increases and leads to the question that whether first-mode-based single DOF system is still applicable.Based on the seismic analysis of several cable-stayed bridges with variable spans and tower heights,the contribution of second mode to the moment and shear force at the tower bottom in the longitudinal direction is studied.The result shows that the contribution of the second mode becomes non-ignorable when the tower height exceeds 100 m,which increases to over 10% as for the shear force at the tower bottom and over 5% as for moment when the height exceeds 150 m.In order to further investigate this contribution,one of the above practical bridges(Gintang Bridge) is then used to study its variation with the changes of the beam mass and stiffness,which later on were observed to be the most influential factors to the second mode contribution.Compared with the two factors,beam mass plays a more important role to influence the contribution,but they both gradually decreased after certain value.
Cable-stayed bridges are often designed as floating systems in seismic area in order to mitigate ther responses induced by the earthquake.The seismic analytical model is commonly simplified as a single DOF system longitudinally.However,as bridge spans become longer and longer,the tower is taller and taller,hence the contribution of the second mode increases and leads to the question that whether first-mode-based single DOF system is still applicable.Based on the seismic analysis of several cable-stayed bridges with variable spans and tower heights,the contribution of second mode to the moment and shear force at the tower bottom in the longitudinal direction is studied.The result shows that the contribution of the second mode becomes non-ignorable when the tower height exceeds 100 m,which increases to over 10% as for the shear force at the tower bottom and over 5% as for moment when the height exceeds 150 m.In order to further investigate this contribution,one of the above practical bridges(Gintang Bridge) is then used to study its variation with the changes of the beam mass and stiffness,which later on were observed to be the most influential factors to the second mode contribution.Compared with the two factors,beam mass plays a more important role to influence the contribution,but they both gradually decreased after certain value.
引文
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[10]焦驰宇.基于性能的大跨斜拉桥地震易损性分析[D].上海:同济大学,2008.
[11]Mervyn J Kowalsky.Deformation limit states for circu-lar reinforced concrete bridge columns[J].Journal of Structural Engineering,ASCE,2000,126(8):869-878.
[12]Pan Y,Agrawal A K,Ghosn M.Seismic fragillity of continuous steel highway bridges in new york state[J].Journal of Bridge Engineering,2007,12(6):689-699.
[2]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,1996.
[3]Anil K Chopra,Rakesh K Goel.A modal pushover a-nalysis procedure to estimate seismic demands for buildings:theory and prelminary evaluation[R].Pa-cific Earthquake Engineering Research Center,Col-lege of Engineering,University of California Berkeley,2001.
[4]Chopra A K,Goel R K.A modal pushover analysis procedure for estimating seismic demands for build-ings[J].Eartherquake Engineering and Structural Dy-namics,2002,31(3):561-582.
[5]Tatjana Isakovic,Matej Fishinger.Higher modes in simplified inelastic seismic analysis of single column bent viaducts[J].Earthquake Engineering and Struc-tural Dynamics,2006,35:95-114.
[6]Paraskeval T S,Kapposl A J,Sextos A G.Extension of modal pushover analysis to seismic assessment of bridges[J].Earthquake Engineering and Structural Dynamics,2006,35:1269-1293.
[7]李建中,宋晓东,范立础.桥梁高墩位移延性能力的探讨[J].地震工程与工程振动,2005,(1):43-48.
[8]彭凯,李建中,范立础.高墩桥梁考虑墩身高阶振动的水平主导振型[J].震动与冲击,2008,27(7):63-68.
[9]Chang K C,Mo Y L,Chen C C,et al.Lessons learned from the damaged Chi-Lu cable-stayed bridge[J].Journal of Bridge Engineering,ASCE,2004,(4):343-352.
[10]焦驰宇.基于性能的大跨斜拉桥地震易损性分析[D].上海:同济大学,2008.
[11]Mervyn J Kowalsky.Deformation limit states for circu-lar reinforced concrete bridge columns[J].Journal of Structural Engineering,ASCE,2000,126(8):869-878.
[12]Pan Y,Agrawal A K,Ghosn M.Seismic fragillity of continuous steel highway bridges in new york state[J].Journal of Bridge Engineering,2007,12(6):689-699.
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