采用折减刚度系数法计算简支体系地震中动态二阶效应
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摘要
根据简支体系的受力特点,提出采用刚度折减法快速计算非线性动力分析中二阶效应的方法,通过解析法推导出考虑P-δ效应的Euler-Bernoulli梁刚度修正系数,且给出了Timoshenko梁的P-δ效应刚度修正系数。编制相应计算程序,将所得修正系数引入结构Pushover计算和直接积分的非线性动力时程计算,并将该法应用在实际桥梁抗震计算中。各种计算结果与采用增量迭代法的高精度实体单元结果进行了对比分析,结果表明,采折减刚度系数法能够有效、准确地计算结构动态二阶效应;Timoshenko理论中的二阶效应计算要比Euler-Bernoulli理论的更为准确;在地震作用下梁结构中二阶效应会被放大,必须考虑其对结构的影响。
Based on mechanical characters of the simply supported bridges,the method with stiffness correction coefficient for quick calculating the P-δ effect in nonlinear seismic analysis was presented.The stiffness correction coefficient which fits to Euler-Bernoulli beam theory considering the P-δ effect was derived in analytic method.On this basis the stiffness correction coefficient for Timoshenko beam theory was also derived.The stiffness correction coefficient was introduced to the Pushover analysis and the direct integration method of nonlinear dynamic time-history calculation with the compiled program,and the method was applied to the calculation of the bridge seismic resistance.Compared with results using the high precision solid element analysis with increment iteration,it is concluded that(1)the method with tangent stiffness correction coefficient is a simple,effective method to solve the problem with second-order effect;(2) the results in Timoshenko beam theory is more accurate than results in Euler-Bernoulli beam theory;(3)during earthquake,second-order effect of the structure can be magnified,its role should not be neglected.
Based on mechanical characters of the simply supported bridges,the method with stiffness correction coefficient for quick calculating the P-δ effect in nonlinear seismic analysis was presented.The stiffness correction coefficient which fits to Euler-Bernoulli beam theory considering the P-δ effect was derived in analytic method.On this basis the stiffness correction coefficient for Timoshenko beam theory was also derived.The stiffness correction coefficient was introduced to the Pushover analysis and the direct integration method of nonlinear dynamic time-history calculation with the compiled program,and the method was applied to the calculation of the bridge seismic resistance.Compared with results using the high precision solid element analysis with increment iteration,it is concluded that(1)the method with tangent stiffness correction coefficient is a simple,effective method to solve the problem with second-order effect;(2) the results in Timoshenko beam theory is more accurate than results in Euler-Bernoulli beam theory;(3)during earthquake,second-order effect of the structure can be magnified,its role should not be neglected.
引文
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[12]邵长江,钱永久.非一致地震激励下大跨斜拉桥非线性响应计算[J].公路交通科技,2007,24(3):64-67.SHAO Changjiang,QIAN Yongjiu.Analysis on Nonlinear Seis-mic Response of Long-span Cable-stayed Bridge Subjected toAsynchronous Excitation[J].Journal of Highway and Trans-portation Research and Development,2007,24(3):64-67.
[2]PRIESTLEY M.Seismic Design and Retrofit of Bridge Structures[M].New York:Wiley,1996.
[3]TIMOSHENKO S.材料力学[M].天津:天津科学技术出版社,1990.TIMOSHENKO S.Mechanics of Materials[M].Tianjin:TianjinScience and Technology Press,1990.
[4]侯爽,欧进萍.结构pushover分析的侧向力分布及高阶振型影响[J].地震工程与工程振动,2004,24(3):47-53.HOU Shuang,OU Jinping.A Study of Load Pattern Selectionof Pushover Analysis and Influence of Higher Modes[J].Earthquake Engineering and Engineering-Vibration,2004,24(3):47-53.
[5]范立础.桥梁抗震[M].上海:同济大学出版社,1997.FAN Lichu.Bridge Earthquake Resistance[M].Shanghai:Tongji University Press,1997.
[6]GUPTA A,KRAWINKLER H.Dynamic P-delta Effects forFlexible in Elastic Steel Structures[J].Journal of StructuralEngineering,2000,126(1):145-154.
[7]MIRANDA E,BERTERO V V.Evaluation of Strength Reduc-tion Factors for Earthquake-Resistant Design[J].EarthquakeSpectra,1997,10(2):357-379.
[8]KOWALSKY M J.Deformation Limit States for Circular Rein-forced Concrete Bridge Columns[J].Journal of Structural En-gineering,2000,126(8):869-878.
[9]CLOUGH R W,PENZIEN J.结构动力学[M].王光远,译.北京:科学出版社,1985.CLOUGH R W,PENZIEN J.Structure Dynamics[M].WANGGuangyuan,Translated.Beijing:Science Press,1985.
[10]华孝良,徐光辉.桥梁结构的非线性分析[M].北京:人民交通出版社,1997.HUA Xiaoliang,XU Guanghui.Nonlinear Analysis for BridgeStructure[M].Beijing:China Communications Press,1997.
[11]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,1992.LI Guohao.Stability and Vibration of Bridge Structure[M].Beijing:China Railway Publishing House,1992.
[12]邵长江,钱永久.非一致地震激励下大跨斜拉桥非线性响应计算[J].公路交通科技,2007,24(3):64-67.SHAO Changjiang,QIAN Yongjiu.Analysis on Nonlinear Seis-mic Response of Long-span Cable-stayed Bridge Subjected toAsynchronous Excitation[J].Journal of Highway and Trans-portation Research and Development,2007,24(3):64-67.
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