考虑行波效应的二维框架结构的地震响应
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摘要
运用波动方法研究二维框架结构的地震响应.对二维框架结构进行空间离散构造出被研究块体,建立被研究块体的动力学方程,推导空间离散段的段间内力与端部位移关系式;在时间域上交替运用被研究块体动力学平衡方程和段间内力与端部位移关系式进行递推计算,给出结构地震响应分析的波动方法.该方法易于求解考虑行波效应的结构地震响应问题.分别针对水平和竖向地震作用情况,分析了二维框架结构柱的剪力和梁端弯矩的行波效应.结果表明:考虑行波效应时,柱的剪力和梁端弯矩存在增大现象,一些柱的剪力或梁端弯矩甚至出现竖向地震作用比水平地震作用大的现象.框架结构的地震响应应该考虑竖向和水平地震的行波效应.
The wave-based method is presented in this article for the earthquake response of plane frame structure.The spatial discrete segments of plane frame structure are used to form the investigated lumps.The dynamic equations of the investigated lumps and the relations between interior forces and end displacements have been derived.By applying the dynamic equations and the relations alternately in time domain,the wave-based method was presented for seismic response analysis of plane frame structure.The method can be easily used to solve the problem of structural seismic response considering wave passage effect by using the proposed method.Comparisons of the shear forces of columns with the bending moments of beams are carried out for a plane frame structure respectively subjected to horizontal and vertical seismic excitations.It showed that the effect of wave passage may lead the column shear forces and beam-end bending moments to an increase.Some column shear forces and beam-end bending moments caused by the vertical excitations are even greater than those caused by the horizontal excitations.So seismic wave passage effect should be considered for the seismic response analyses of plane frame structure.
The wave-based method is presented in this article for the earthquake response of plane frame structure.The spatial discrete segments of plane frame structure are used to form the investigated lumps.The dynamic equations of the investigated lumps and the relations between interior forces and end displacements have been derived.By applying the dynamic equations and the relations alternately in time domain,the wave-based method was presented for seismic response analysis of plane frame structure.The method can be easily used to solve the problem of structural seismic response considering wave passage effect by using the proposed method.Comparisons of the shear forces of columns with the bending moments of beams are carried out for a plane frame structure respectively subjected to horizontal and vertical seismic excitations.It showed that the effect of wave passage may lead the column shear forces and beam-end bending moments to an increase.Some column shear forces and beam-end bending moments caused by the vertical excitations are even greater than those caused by the horizontal excitations.So seismic wave passage effect should be considered for the seismic response analyses of plane frame structure.
引文
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[11]RAMBABU K V,Allam M M.Response of an open-plane frame to multiple support horizontal seismic excitations with soil–structure interaction[J].Journal of Sound and Vibration,2007,299:388-396.
[12]LIU Tie-lin,LIU Kai-shin,ZHANG Jin-xiang.Unstructured gird method for stress wave propagation in elastic media[J].Comput.Methods Appl Mech.Engrg.,2004,193(23/26):2427-2452.
[2]PAPAZOGLOU A J,ELNASHAI A S.Analytical and field evidence of the damaging effect of vertical earthquake ground motion[J].Earthquake Engineering and Structural Dynamics1996,25:1109-1137.
[3]CHOPRA A K.Dynamics of structures:theory and applications to earthquake engineering[M].2nd edition.Pren-tice-Hall,USA.2001.
[4]SOYLUK K.Comparison of random vibration methods for multi-support seismic excitation analysis of long-span bridges[J].Engineering Structures,2004,26(11):1573-1583.
[5]ZHANG Y H,LI Q S,LIN J H,et al.Random vibration analysis of long-span structures subjected to spatially va-rying ground motions[J].Soil Dynamics and Earthquake Engineering,2009,29(4):620-629.
[6]何庆祥,沈祖炎.结构地震行波效应分析综述[J].地震工程与工程振动,2009,29(1):50-57.HE Qing-xiang,SHEN Zu-yang.Review of structural seismic analysis of traveling wave effects[J].Journal of Earthquake Engineering and Engineering Vibration,2009,29(1):50-57.
[7]JU S H,LIU C W,WU K Z.3D Analyses of buildings under vertical component of earthquakes[J].Journal of Structural Engineering,2000,126(10):1196-1202.
[8]SALAZAR A R,HALDAR A.Structural responses considering the vertical component of earthquakes[J].Com-puters and Structures,2000,74(2):131-145.
[9]周靖,周飞,蔡健,等.脉冲型竖向地震作用下大跨度RC带腋撑框架结构弹塑性动力响应分析[J].工程力学,2010,27(6):113-119.ZHOU Jing,ZHOU Fei,CAI Jian,et al.Seismic elastic-plastic response of long-span RC frame structure with haunched members subjected to pulse-like vertical ground motions[J].Engineering mechanics,2010,27(6):113-119.
[10]李碧雄,邓建辉,王哲.5.12汶川地震底框砖房震害启示[J].西安建筑科技大学学报:自然科学版,2010,42(3):342-347.LI Bi-xiong,DENG Jian-hui,WANG Zhe.Lessons from the performances of masonry structures with ground RC frame suffered5.12Wenchuan earthquake[J].J.Xi′an Univ.of Arch.&Tech:Natural Science Edition,2010,42(3):342-347.
[11]RAMBABU K V,Allam M M.Response of an open-plane frame to multiple support horizontal seismic excitations with soil–structure interaction[J].Journal of Sound and Vibration,2007,299:388-396.
[12]LIU Tie-lin,LIU Kai-shin,ZHANG Jin-xiang.Unstructured gird method for stress wave propagation in elastic media[J].Comput.Methods Appl Mech.Engrg.,2004,193(23/26):2427-2452.
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