考虑竖向地震作用的高桥墩P-Δ效应分析
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摘要
由50年设计基准期的水平地震系数推导出4类桥梁水平地震系数,按一般规律,可求出不同类型桥梁相应的竖向地震系数。选择满足几何边界条件和力学边界条件的变形曲线,用能量方法推导出具有通用性的变形公式,进而可求出墩顶位移与墩底弯矩。与不计P-Δ效应的计算结果相比,考虑P-Δ效应的位移与弯矩都在很大程度上得到放大,特别是在罕遇地震作用下,效果更加明显。对于高柔性桥墩,尚需要考虑高振型和材料非线性的影响。
The lateral earthquake coefficient of four type bridges can be calculated by means of the lateral earthquake factor of 50 years design reference period,then according to common rule,the vertical earthquake coefficient can be found.Utilizing the curve meeting the mechanical and geometrical boundary,the general deformed shape is derived using the energy method,therefore,the maximum displacement of the upper pier and moment of bottom pier can be acquired.Comparing with the displacement and moment getting by different load case,the value of ignoring the P-Δ effect is the minimum,especially with rare strong earthquake.As for high flexible pier,the high mode effect and material nonlinearity also should be taken into account.
The lateral earthquake coefficient of four type bridges can be calculated by means of the lateral earthquake factor of 50 years design reference period,then according to common rule,the vertical earthquake coefficient can be found.Utilizing the curve meeting the mechanical and geometrical boundary,the general deformed shape is derived using the energy method,therefore,the maximum displacement of the upper pier and moment of bottom pier can be acquired.Comparing with the displacement and moment getting by different load case,the value of ignoring the P-Δ effect is the minimum,especially with rare strong earthquake.As for high flexible pier,the high mode effect and material nonlinearity also should be taken into account.
引文
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[5]GB50011-2001,建筑抗震设计规范(2008年版)[S]GB 50011-2001,Code for Seismic Design of Buildings[S](in Chinese)
[6]JTG/TB02-01-2008,公路桥梁抗震设计细则[S]JTG/TB 02-01-2008,Guidelines for Seismic Design ofHighway Bridges[S](in Chinese)
[7]谢礼立,马玉宏,翟长海.基于性态的抗震设防与设计地震动[M].北京,科学出版社,2009Xie Li-li,Ma Yu-hong,Zhai Chang-hai.Performance-based Seismic Design and Design Ground Motion[M].Beijing:The Press of Science,2009(in Chinese)
[8]吕大刚.基于最优设防荷载和性能的抗灾结构智能优化设计研究[D].哈尔滨:哈尔滨建筑大学,1999Lv Da-gang.Optimum Design of Maximum Design Loadand Performance-based Design[D].Harbin:HarbingBuilding University,1999(in Chinese)
[9]周正华,周雍年,卢滔,杨程.竖向地震动特性研究[J].地震工程与工程振动,2003,23(3):25～29Zhou Zheng-hua,Zhou Yong-nian,Lu Tao,YangCheng.Study on Characteristics of Vertical GroundMotion[J].Earquake Engineering and EngineeringVibration,2003,23(3):25～29(in Chinese)
[2]Priestley M J N.Calvi G M,Kowalsky M J.Displacement Based Seismic Design of Structure[M].IUSS Press,2007
[3]程翔云.高桥墩设计计算中的两个问题[J].重庆交通学院学报,2000,19(2):6～10Cheng Xiang-yun.Two Problems in Design andCalculation of High Bridge Piers[J].Journal ofChongqing Jiaotong Institute,2000,19(2):6～10(inChinese)
[4]李睿,董明.考虑P-Δ效应的高墩抗震设计[J].云南工业大学学报,1999,15(1):61～67Li Rui,Dong Ming.Aseismic Response Analysis of HighPier Including the Effect of Geometrical Nonliearity[J].Journal of Yunnan Polytechnic University,1999,15(1):61～67(in Chinese)
[5]GB50011-2001,建筑抗震设计规范(2008年版)[S]GB 50011-2001,Code for Seismic Design of Buildings[S](in Chinese)
[6]JTG/TB02-01-2008,公路桥梁抗震设计细则[S]JTG/TB 02-01-2008,Guidelines for Seismic Design ofHighway Bridges[S](in Chinese)
[7]谢礼立,马玉宏,翟长海.基于性态的抗震设防与设计地震动[M].北京,科学出版社,2009Xie Li-li,Ma Yu-hong,Zhai Chang-hai.Performance-based Seismic Design and Design Ground Motion[M].Beijing:The Press of Science,2009(in Chinese)
[8]吕大刚.基于最优设防荷载和性能的抗灾结构智能优化设计研究[D].哈尔滨:哈尔滨建筑大学,1999Lv Da-gang.Optimum Design of Maximum Design Loadand Performance-based Design[D].Harbin:HarbingBuilding University,1999(in Chinese)
[9]周正华,周雍年,卢滔,杨程.竖向地震动特性研究[J].地震工程与工程振动,2003,23(3):25～29Zhou Zheng-hua,Zhou Yong-nian,Lu Tao,YangCheng.Study on Characteristics of Vertical GroundMotion[J].Earquake Engineering and EngineeringVibration,2003,23(3):25～29(in Chinese)
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