框架结构侧移曲线的泛函推导和目标位移确定
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摘要
直接基于位移的抗震设计方法要求在设计之初确定结构各楼面处的目标侧移以便将多自由度体系转化为单自由度。基于Hamilton原理,从能量的理论出发建立了关于框架结构侧移曲线的泛函,通过数学中的变分原理推导了该侧移曲线,并指出了数学原理与力学中能量观点的联系,使得框架结构侧移曲线有了可靠的数学理论基础。最后提出了按该侧移曲线确定结构目标侧移的方法并通过算例说明了该方法的可行性。文中提出的侧移曲线适用于刚度沿高度分布较均匀的框架结构。
In direct displacement-based seismic design of buildings,the target lateral displacement on storys should be determined at first to transform MDF into SDF.According to the Hamilton principle,the functional about lateral displacement curve has been established from potential energy.The curve is deduced with variation calculus and energy opinions in mechanics,which are confirmed with math theory,through which the reliable theoretical basis of the lateral displacement curve of a frame structure is given.At last,determination method of target lateral displacement is suggested and the practicability of the method is shown through an example.The lateral displacement curve proposed in this paper can be applied to frame structures with regular stiffness distribution along the height direction.
In direct displacement-based seismic design of buildings,the target lateral displacement on storys should be determined at first to transform MDF into SDF.According to the Hamilton principle,the functional about lateral displacement curve has been established from potential energy.The curve is deduced with variation calculus and energy opinions in mechanics,which are confirmed with math theory,through which the reliable theoretical basis of the lateral displacement curve of a frame structure is given.At last,determination method of target lateral displacement is suggested and the practicability of the method is shown through an example.The lateral displacement curve proposed in this paper can be applied to frame structures with regular stiffness distribution along the height direction.
引文
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[4]Priestley MJ N.Displacement based approaches to rational limit stats design of new structures[C]//Proceedings of XI ECEE-Invited Lectures,Paris,1998.
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[6]蒋欢军,李培振.钢筋混凝土框架结构的最大地震位移形状曲线[J].同济大学学报:自然科学版,2008,36(5):581-585.Jiang Huanjun,Li Peizhen.Maximum seismic displacement profiles of reinforced concrete frames[J].Journal of Tongji University(Nature Sci-ence),2008,36(5):581-585.
[7]梁兴文,黄雅捷,杨其伟.钢筋混凝土框架结构基于位移的抗震设计方法研究[J].土木工程学报,2005,38(9):53-60.Liang Xingwen,Huang Yajie,Yang Qiwei.Displacement-based seismic design method of RC frames[J].China Civil Engineering Journal,2005,38(9):53-60.
[8]梁兴文,史庆轩.混凝土结构设计[M].北京:科学出版社,2004.Liang Xingwen,Shi Qingxuan.Concrete Structure Design[M].Beijing:Science Press,2004.
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[10]Medhekar MS,Kennedy D TL.Displacement-based seismic design of building-theory[J].Engineering Structures,2000,22(3):201-209.
[11]Medhekar MS,Kennedy D TL.Displacement-based seismic design of building-application[J].Engineering Structures,2000,22(3):210-221.
[12]门进杰,史庆轩,周琦.框架结构基于性能的抗震设防目标和性能指标的量化[J].土木工程学报,2008,41(9):76-82.Men Jinjie,Shi Qingxuan,Zhou Qi.Performance-based seismic fortification criterion and quantified performance index for reinforced concreteframe structures[J].China Civil Engineering Journal,2008,41(9):76-82.
[2]Goel R K,Chopra AK.Improved direct displacement-based design procedure for performance-based seismic design of structures[C]//Proceedingsof Structures Congress,2001.
[3]Chopra AK,Goel R K.Evaluation of a NSP estimate seismic deformation:SDF systems[J].Journal of Structural Engineering,2000,126(4):482-490.
[4]Priestley MJ N.Displacement based approaches to rational limit stats design of new structures[C]//Proceedings of XI ECEE-Invited Lectures,Paris,1998.
[5]Karavasilis TL,Bazeos N,Beskos D E.Maximum displacement profiles for the performance-based seismic design of plane steel moment resistingframes[J].Engineering Structures,2006,28(1):9-22.
[6]蒋欢军,李培振.钢筋混凝土框架结构的最大地震位移形状曲线[J].同济大学学报:自然科学版,2008,36(5):581-585.Jiang Huanjun,Li Peizhen.Maximum seismic displacement profiles of reinforced concrete frames[J].Journal of Tongji University(Nature Sci-ence),2008,36(5):581-585.
[7]梁兴文,黄雅捷,杨其伟.钢筋混凝土框架结构基于位移的抗震设计方法研究[J].土木工程学报,2005,38(9):53-60.Liang Xingwen,Huang Yajie,Yang Qiwei.Displacement-based seismic design method of RC frames[J].China Civil Engineering Journal,2005,38(9):53-60.
[8]梁兴文,史庆轩.混凝土结构设计[M].北京:科学出版社,2004.Liang Xingwen,Shi Qingxuan.Concrete Structure Design[M].Beijing:Science Press,2004.
[9]铁摩辛柯S,盖尔J.材料力学[M].北京:科学出版社,1990.Timoshenko S.,Gere J.Material Mechanics[M].Beijing:Science Press,1990.
[10]Medhekar MS,Kennedy D TL.Displacement-based seismic design of building-theory[J].Engineering Structures,2000,22(3):201-209.
[11]Medhekar MS,Kennedy D TL.Displacement-based seismic design of building-application[J].Engineering Structures,2000,22(3):210-221.
[12]门进杰,史庆轩,周琦.框架结构基于性能的抗震设防目标和性能指标的量化[J].土木工程学报,2008,41(9):76-82.Men Jinjie,Shi Qingxuan,Zhou Qi.Performance-based seismic fortification criterion and quantified performance index for reinforced concreteframe structures[J].China Civil Engineering Journal,2008,41(9):76-82.
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