大跨拱桥水平地震行波反应计算的一致反应谱方法
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摘要
针对大跨度拱桥具有对称性的特点,把水平地震行波作用下拱桥地震反应计算的动力方程分解为正、反对称半拱桥的一致地震反应计算的2个动力方程,并提出了考虑行波效应的输入地震正、反对称分量反应谱的新概念。应用与场地类型有关的实际地震记录,讨论了不同地震行波正、反对称分量反应谱的特点。数值分析结果表明,地震行波正、反对称分量具有与原地震波相同形状的反应谱。在建立地震行波正、反对称分量加速度幅值衰减关系的基础上,与常规的一致反应谱方法相结合,建立了大跨度对称拱桥水平地震行波反应计算的一致反应谱方法。算例结果表明,这一方法的精度与目前地震一致输入下反应谱方法的计算精度相当,可使得计算工作大为简化,且便于工程应用。此方法同样适用于拱桥竖向地震行波反应计算。
Regarding to the nature of long-span arch bridge′s symmetry,the dynamic equation for seismic response analysis of the arch bridge under horizontal travelling seismic wave excitation was decomposed into two dynamic equations for consistent seismic response analysis of symmetrical and asymmetrical semi-arch bridges.A new concept of symmetrical and asymmetrical component response spectra for travelling seismic wave was developed.The spectrum features of the symmetrical and asymmetrical components of travelling seismic wave were discussed by using actual earthquake records considering different types of site.Numerical analysis results show that the spectra of symmetrical and asymmetrical components of the travelling seismic wave have same shape with that of original seismic wave.Based on establishing the acceleration amplitude′s attenuation relations of the symmetrical and asymmetrical components of travelling seismic wave and combining with the consistent seismic design spectra in current codes,the consistent response spectrum method for horizontal seismic travelling wave response analysis of the long-span symmetrical arch bridges was suggested.The results of numerical example demonstrate that the calculation precision of the suggested method has a same level with the consistent response spectrum method being applied currently in engineering.The calculation can be significantly simplified so that the method is easy to use in engineering.The method can also be applied to the case of the dynamic response analysis of arch bridge under vertical seismic travelling wave excitation.
Regarding to the nature of long-span arch bridge′s symmetry,the dynamic equation for seismic response analysis of the arch bridge under horizontal travelling seismic wave excitation was decomposed into two dynamic equations for consistent seismic response analysis of symmetrical and asymmetrical semi-arch bridges.A new concept of symmetrical and asymmetrical component response spectra for travelling seismic wave was developed.The spectrum features of the symmetrical and asymmetrical components of travelling seismic wave were discussed by using actual earthquake records considering different types of site.Numerical analysis results show that the spectra of symmetrical and asymmetrical components of the travelling seismic wave have same shape with that of original seismic wave.Based on establishing the acceleration amplitude′s attenuation relations of the symmetrical and asymmetrical components of travelling seismic wave and combining with the consistent seismic design spectra in current codes,the consistent response spectrum method for horizontal seismic travelling wave response analysis of the long-span symmetrical arch bridges was suggested.The results of numerical example demonstrate that the calculation precision of the suggested method has a same level with the consistent response spectrum method being applied currently in engineering.The calculation can be significantly simplified so that the method is easy to use in engineering.The method can also be applied to the case of the dynamic response analysis of arch bridge under vertical seismic travelling wave excitation.
引文
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[10]谢礼立,翟长海.最不利设计地震研究[J].地震学报,2003,25(3):250-261.Xie L L,Zhai Ch H.Study on the most unfavorableground motions in seismic design[J].ACTA Seis-mologica Sinica,2003,25(3):250-261.
[2]Zerva A.Response of multi-span beams to spatially in-coherent seismic ground motions[J].Earthquake Engi-neering and Structural Dynamics,1990,19(6):819-832.
[3]Nazmy A S,Abdel-Ghffor A M.Effect of ground mo-tion spatial variability on the response of cable-stayedbridges[J].Earthquake Engineering and StructuralDynamics,1992,21(1):1-20.
[4]Hao H.Arch response to correlated multiple excita-tions[J].Earthquake Engineering and Structural Dy-namics,1993,22(5):389-404.
[5]屈铁军,王前信.多点输入地震反应分析研究的进展[J].世界地震工程,1993,9(1):30-36.Qu T J,Wang Q X.Progress in seismic response a-nalysis under multi-support inputs[J].World Earth-quake Engineering,1993,9(1):30-36.
[6]Harichandran R S,Hawwari A,Sweidan B N.Re-sponse of long-span bridges to spatially varying groundmotion[J].Journal of Structural Engineering,1996,122(5):476-484.
[7]楼梦麟,邸龙.地震行波激励下单层柱面网壳反应分析[J].结构工程师,2005,21(5):48-52.Lou M L,Di L.Response analysis of single layer cylin-drical reticulated shell under seismic wave-passage excita-tions[J].Structural Engineers,2005,21(5):48-52.
[8]李强.水平多点输入下大跨度拱桥地震反应分析[D].上海:同济大学,2007.Li Q.Seismic response analysis of the long-span archbridge under the horizontal multiple-support excitation[D].Shanghai:Tongji University,2007.
[9]楼梦麟,高珊.多点激励下拱桥竖向地震反应的简化计算方法[J].防灾减灾工程学报,2009,29(6):638-643.Lou M L,Gao Sh.The simplified method for the ver-tical seismic response analysis of the arch bridge underthe multiple-support excitation[J].Journal of DisasterPrevention and Mitigation Engineering,2009,29(6):638-643.
[10]谢礼立,翟长海.最不利设计地震研究[J].地震学报,2003,25(3):250-261.Xie L L,Zhai Ch H.Study on the most unfavorableground motions in seismic design[J].ACTA Seis-mologica Sinica,2003,25(3):250-261.
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