桥梁结构地震碰撞分析模型的碰撞刚度计算方法研究
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摘要
针对桥梁结构地震碰撞模拟问题,文中分别推导了基于波动理论的直杆共轴碰撞模型和基于接触单元法的刚体碰撞模型中相应的最大碰撞变形的计算式,并基于二者相等的关系给出了Kelvin模型和Hertz-damp模型中相应碰撞刚度的计算方法,并对所建议方法的合理性和精确度进行了验证分析。研究结果表明,文中建立方法计算的Kelvin模型的碰撞刚度数值明显小于较短主梁的轴向刚度,这一点与以前学者基于实测数据分析得到的结论相一致。数值分析结果表明,相比以前的碰撞刚度计算方法,采用本文建议的方法确定Hertz-damp模型的碰撞刚度时,可以显著提升其碰撞模拟精确度。
In order to study the earthquake-induced bridge pounding,the computation methods of impact stiffness for Kelvin model and Hertz-damp model were theoretically derived based on equating the maximum pounding deformation calculated with the collinear impact model of two rods to that calculated with the rigid-body impact model.Then,the effectiveness of the proposed calculation methods was verified,respectively.The results indicated that the impact stiffness of Kelvin model is obviously smaller than the axial stiffness of the shorter bridge girder,this fact supports previous researchers' comments obtained from the measured data.The numerical analysis results indicated that Hertz-damp model can raise the pounding simulation accuracy with the proposed impact stiffness calculation method.
In order to study the earthquake-induced bridge pounding,the computation methods of impact stiffness for Kelvin model and Hertz-damp model were theoretically derived based on equating the maximum pounding deformation calculated with the collinear impact model of two rods to that calculated with the rigid-body impact model.Then,the effectiveness of the proposed calculation methods was verified,respectively.The results indicated that the impact stiffness of Kelvin model is obviously smaller than the axial stiffness of the shorter bridge girder,this fact supports previous researchers' comments obtained from the measured data.The numerical analysis results indicated that Hertz-damp model can raise the pounding simulation accuracy with the proposed impact stiffness calculation method.
引文
[1]Rosenblueth E,Meli R.The 1985 earthquake:causes andeffects in Mexico City[J].Concrete International,1986,8:23-34.
[2]Otsuka H,Unjoh S,Terayama T,et al.Damage to highwaybridges by the 1995 Hyogoken Nanbu earthquake and theretrofit of highway bridges in Japan[R].Osaka:Third U.S.Japan Workshop on Seismic Retrofit of Bridges,1996.
[3]范立础,李建中.汶川桥梁震害分析与抗震设计对策[J].公路,2009(5):122-128.FAN Li-chu,LI Jian-zhong.Earthquake-induced damageanalysis of bridges in Wenchuan earthquake and seismicdesign counter measures[J].Highway,2009(5):122-128.
[4]李忠献,岳福青,周莉.地震时桥梁碰撞分析的等效Kelvin撞击模型[J].工程力学,2008,25(4):128-133.LI Zhong-xian,YUE Fu-qing,ZHOU Li.Equivalent Kelvinimpact model for pounding analysis of bridges duringearthquake[J].Engineering Mechanics,2008,25(4):128-133.
[5]邓育林,彭天波,李建中.大跨多塔悬索桥纵向地震碰撞反应参数研究[J].振动与冲击,2011,30(4):205-210.DENG Yu-lin,PENG Tian-bo,LI Jian-zhong.Parametricstudy on longitudinal seismic pounding response for a long-span multi-tower suspension bridge[J].Journal of Vibrationand Shock,2011,30(4):205-210.
[6]Muthukumar S,Des Roches R.A Hertz contact model withnon-linear damping for pounding simulation[J].Earthquake Engineering and Structural Dynamics,2006,35(7):811-828.
[7]Taflanidis A A.Optimal probabilistic of seismic dampers forthe protection of isolated bridges against near-fault seismicexcitations[J].Engineering Structures,2011,33:3496-3508.
[8]聂利英,李建中,范立础.地震作用下结构碰撞的模型参数及其影响分析[J].工程力学,2005,22(5):142-146.NIE Li-ying,LI Jian-zhong,FAN Li-chu.Selection ofpounding analysis parameters and its effects on structureunder earthquake[J].Engineering Mechanics,2005,22(5):142-146.
[9]王东升,冯启民,王国新.基于直杆共轴碰撞理论的桥梁地震反应邻梁碰撞分析模型[J].工程力学,2004,21(2):157-166.WANG Dong-sheng,FENG Qi-min,WANG Guo-xin.Analysis model of pounding between adjacent bridge girdersduring earthquakes based on collinear impact between rods[J].Engineering Mechanics,2004,21(2):157-166.
[10]Maison B F,Kasai K.Analysis for type of structural pounding[J].Journal of Structural Engineering,1990,116:957-977.
[11]王军文,李建中,范立础.非规则梁桥伸缩缝处的碰撞对地震反应的影响[J].土木工程学报,2006,39(1):54-59.WANG Jun-wen,LI Jian-zhong,FAN Li-chu.Effect ofpounding at expansion joints on seismic response of irregulargirder bridges[J].China civil engineering journal,2006,39(1):54-59.
[12]Cole G,Dhakal R,Carr A,et al.An investigation of theeffects of mass distribution on pounding structures[J].Earthquake Engineering and Structural Dynamics,2011,40:641-659.
[13]Goldsmith W.Impact:The theory and physical behaviour ofcolliding solids[M].London:Edward Arnold,1960.
[14]Anagnostopoulos S A.Equivalent viscous damping formodeling inelastic impacts in earthquake pounding problems[J].Earthquake Engineering and Structural Dynamics,2004,33(8):897-902.
[15]Hunt K H,Crossley F R E.Coefficient of restitutioninterpreted as damping in vibroimpact[J].Journal ofApplied Mechanics,1975,42(2):440-445.
[16]Jankowski R.Analytical expression between the impactdamping ratio and the coefficient of restitution in the non-linear viscoelastic model of structural pounding[J].Earthquake Engineering and Structural Dynamics,2006,35(4):517-524.
[17]Malhotra P K.Dynamics of seismic pounding at expansionjoints of concrete bridges[J].Journal of EngineeringMechanics,1998,124(7):794-802.
[18]Gou A X,Li Z J,Li H,et al.Experimental and analyticalstudy on pounding reduction of base-isolated highway bridgesusing MR dampers[J].Earthquake Engineering andStructural Dynamics,2009,38:1307-1333.
[19]Anagnostopoulos S A,Spiliopoulos K V.An investigation ofearthquake induced pounding between adjacent buildings[J].Earthquake Engineering and Structural Dynamics,1992,21(4):289-302.
[2]Otsuka H,Unjoh S,Terayama T,et al.Damage to highwaybridges by the 1995 Hyogoken Nanbu earthquake and theretrofit of highway bridges in Japan[R].Osaka:Third U.S.Japan Workshop on Seismic Retrofit of Bridges,1996.
[3]范立础,李建中.汶川桥梁震害分析与抗震设计对策[J].公路,2009(5):122-128.FAN Li-chu,LI Jian-zhong.Earthquake-induced damageanalysis of bridges in Wenchuan earthquake and seismicdesign counter measures[J].Highway,2009(5):122-128.
[4]李忠献,岳福青,周莉.地震时桥梁碰撞分析的等效Kelvin撞击模型[J].工程力学,2008,25(4):128-133.LI Zhong-xian,YUE Fu-qing,ZHOU Li.Equivalent Kelvinimpact model for pounding analysis of bridges duringearthquake[J].Engineering Mechanics,2008,25(4):128-133.
[5]邓育林,彭天波,李建中.大跨多塔悬索桥纵向地震碰撞反应参数研究[J].振动与冲击,2011,30(4):205-210.DENG Yu-lin,PENG Tian-bo,LI Jian-zhong.Parametricstudy on longitudinal seismic pounding response for a long-span multi-tower suspension bridge[J].Journal of Vibrationand Shock,2011,30(4):205-210.
[6]Muthukumar S,Des Roches R.A Hertz contact model withnon-linear damping for pounding simulation[J].Earthquake Engineering and Structural Dynamics,2006,35(7):811-828.
[7]Taflanidis A A.Optimal probabilistic of seismic dampers forthe protection of isolated bridges against near-fault seismicexcitations[J].Engineering Structures,2011,33:3496-3508.
[8]聂利英,李建中,范立础.地震作用下结构碰撞的模型参数及其影响分析[J].工程力学,2005,22(5):142-146.NIE Li-ying,LI Jian-zhong,FAN Li-chu.Selection ofpounding analysis parameters and its effects on structureunder earthquake[J].Engineering Mechanics,2005,22(5):142-146.
[9]王东升,冯启民,王国新.基于直杆共轴碰撞理论的桥梁地震反应邻梁碰撞分析模型[J].工程力学,2004,21(2):157-166.WANG Dong-sheng,FENG Qi-min,WANG Guo-xin.Analysis model of pounding between adjacent bridge girdersduring earthquakes based on collinear impact between rods[J].Engineering Mechanics,2004,21(2):157-166.
[10]Maison B F,Kasai K.Analysis for type of structural pounding[J].Journal of Structural Engineering,1990,116:957-977.
[11]王军文,李建中,范立础.非规则梁桥伸缩缝处的碰撞对地震反应的影响[J].土木工程学报,2006,39(1):54-59.WANG Jun-wen,LI Jian-zhong,FAN Li-chu.Effect ofpounding at expansion joints on seismic response of irregulargirder bridges[J].China civil engineering journal,2006,39(1):54-59.
[12]Cole G,Dhakal R,Carr A,et al.An investigation of theeffects of mass distribution on pounding structures[J].Earthquake Engineering and Structural Dynamics,2011,40:641-659.
[13]Goldsmith W.Impact:The theory and physical behaviour ofcolliding solids[M].London:Edward Arnold,1960.
[14]Anagnostopoulos S A.Equivalent viscous damping formodeling inelastic impacts in earthquake pounding problems[J].Earthquake Engineering and Structural Dynamics,2004,33(8):897-902.
[15]Hunt K H,Crossley F R E.Coefficient of restitutioninterpreted as damping in vibroimpact[J].Journal ofApplied Mechanics,1975,42(2):440-445.
[16]Jankowski R.Analytical expression between the impactdamping ratio and the coefficient of restitution in the non-linear viscoelastic model of structural pounding[J].Earthquake Engineering and Structural Dynamics,2006,35(4):517-524.
[17]Malhotra P K.Dynamics of seismic pounding at expansionjoints of concrete bridges[J].Journal of EngineeringMechanics,1998,124(7):794-802.
[18]Gou A X,Li Z J,Li H,et al.Experimental and analyticalstudy on pounding reduction of base-isolated highway bridgesusing MR dampers[J].Earthquake Engineering andStructural Dynamics,2009,38:1307-1333.
[19]Anagnostopoulos S A,Spiliopoulos K V.An investigation ofearthquake induced pounding between adjacent buildings[J].Earthquake Engineering and Structural Dynamics,1992,21(4):289-302.
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