框剪结构沿竖向分段变刚度的连续化递推方法
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摘要
框架剪力墙结构采用传统连续化分析方法估算内力和位移时,需要用到结构参数沿高度不变的假设,但对于高层框剪结构,其刚度往往会沿高度方向发生改变。本文采用递推手段,将连续化方法推广应用于竖向分段变刚度的框架剪力墙结构中。利用位移控制微分方程和连续条件,推导出分段解的递推关系,再通过边界条件得到内力和位移的表达式。4个算例得到的对比结果表明:当竖向分段变刚度递推方法退化用于等刚度时,与传统方法计算结果一致;当刚度变化时,连续化方法计算得到的结构侧移与有限元结果相近。因此,本文提出的竖向分段变刚度的连续化分析方法可以用于快速估算分段变刚度框剪结构的位移和内力,为结构刚度优化奠定基础。
When the traditional continuous analysis method is used to estimate the internal force and displacement of the frame shear wall structure, the assumption that the structural parameters remain constant along the height is needed. However, for high-rise frame-shear wall structure, the stiffness tends to change along the height direction. In this paper, the continuation method is extended to the frame-shear wall structure with vertical piecewise variable stiffness by means of recursion. By using the displacement control differential equation and the continuity condition, the recurrence relation of the piecewise solution is deduced, and the expressions of internal force and displacement are obtained through the boundary condition. The comparison results obtained by the four examples show that: when the recursive method of vertical variable stiffness is degraded to equal stiffness, it is the same as that of the traditional method; when the stiffness changes, the results of the structural lateral displacement using continuous recursive method and finite element method are approximate. As a result, the multi-stage recursive continuation method presented in this paper can be used to estimation displacement and internal force of the frame-shear wall structure with variable stiffness efficiently, which lays a foundation for structural stiffness optimization.
When the traditional continuous analysis method is used to estimate the internal force and displacement of the frame shear wall structure, the assumption that the structural parameters remain constant along the height is needed. However, for high-rise frame-shear wall structure, the stiffness tends to change along the height direction. In this paper, the continuation method is extended to the frame-shear wall structure with vertical piecewise variable stiffness by means of recursion. By using the displacement control differential equation and the continuity condition, the recurrence relation of the piecewise solution is deduced, and the expressions of internal force and displacement are obtained through the boundary condition. The comparison results obtained by the four examples show that: when the recursive method of vertical variable stiffness is degraded to equal stiffness, it is the same as that of the traditional method; when the stiffness changes, the results of the structural lateral displacement using continuous recursive method and finite element method are approximate. As a result, the multi-stage recursive continuation method presented in this paper can be used to estimation displacement and internal force of the frame-shear wall structure with variable stiffness efficiently, which lays a foundation for structural stiffness optimization.
引文
[1] 金问鲁.高层建筑结构的连续化分析[M].北京:中国铁道出版社,1994Jin Wenlu.Continuous analysis of high-rise building structure[M].Beijing:China Railway Press,1994(in Chinese)
[2] 包世华,方鄂华.高层建筑结构设计[M].北京:清华大学出版社,1990Bao Shihua,Fang Ehua.Structural design of high-rise buildings[M].Beijing:Tsinghua University Press,1990(in Chinese)
[3] 朱杰江,徐道远,王颍.框架侧移的连续化模型分析[J].河海大学学报(自然科学版),2001,29(1):12-16Zhu Jiejiang,Xu Daoyuan,Wang Ying.Analysis of frame later displacement using continuum model[J].Journal of Hohai University,2001,29(1):12-16(in Chinese)
[4] Chan Chun-Man,Liu Peng.Design optimization of practical tall concrete buildings using hybrid optimality criteria and genetic algorithms[A].Eighth International Conference on Computing in Civil & Building Engineering[C].Stanford,California,2000,August,14-16,2000:263-270
[5] 黄世敏,魏琏,程绍革,等.地震区框架-剪力墙结构最优剪力墙数量的研究[J].工程抗震,2003,(1):1-5Huang Shimin,Wei Lian,Cheng Shaoge,et al.A Study on the optimal quantity of shear walls for frame-shear wall structures in earthquake zone[J].Earthquake Resistant Engineering,2003,(1):1-5(in Chinese)
[6] 方德平,王全凤.变刚度框剪结构地震反应的层单元分析[J].建筑结构,2005,35(11):36-38Fang Deping,Wang Quanfeng.Story element analysis method to earthquake response of frame interrupted shear wall structure[J].Building Structure,2005,35(11):36-38(in Chinese)
[7] Atik M,Badawi MM,Shahrour I,et al.Optimum level of shear wall curtailment in wall-frame buildings:the continuum model revisited [J].Journal of Structural Engineering,2014,140(1):896-912
[8] 中国建筑科学研究院建筑结构研究所.高层建筑结构设计[M].北京:科学出版社,1982Institute of Building Structures.China Academy of Building Research structural design of high-rise buildings[M].Beijing:Science Press,1982(in Chinese)
[9] 傅学怡.实用高层建筑结构设计[M].北京:中国建筑工业出版社,1992Fu Xueyi.Practical high-rise building structure design[M].Beijing:China Construction Industry Press,1992(in Chinese)
[10] 钱稼茹,赵作周,叶列平.高层建筑结构设计(第二版)[M].北京:中国建筑工业出版社,2012Qian Jiaru,Zhao Zuozhou,Ye Lieping.Structural design of high-rise buildings(Second Edition)[M].Beijing:China Construction Industry Press,2012(in Chinese)
[11] 赵西安.高层建筑结构实用设计方法(第三版)[M].上海:同济大学出版社,1998Zhao Xi’an.Practical design method for high-rise building structures(Third Edition)[M].Shanghai:Tongji University press,1998(in Chinese)
[2] 包世华,方鄂华.高层建筑结构设计[M].北京:清华大学出版社,1990Bao Shihua,Fang Ehua.Structural design of high-rise buildings[M].Beijing:Tsinghua University Press,1990(in Chinese)
[3] 朱杰江,徐道远,王颍.框架侧移的连续化模型分析[J].河海大学学报(自然科学版),2001,29(1):12-16Zhu Jiejiang,Xu Daoyuan,Wang Ying.Analysis of frame later displacement using continuum model[J].Journal of Hohai University,2001,29(1):12-16(in Chinese)
[4] Chan Chun-Man,Liu Peng.Design optimization of practical tall concrete buildings using hybrid optimality criteria and genetic algorithms[A].Eighth International Conference on Computing in Civil & Building Engineering[C].Stanford,California,2000,August,14-16,2000:263-270
[5] 黄世敏,魏琏,程绍革,等.地震区框架-剪力墙结构最优剪力墙数量的研究[J].工程抗震,2003,(1):1-5Huang Shimin,Wei Lian,Cheng Shaoge,et al.A Study on the optimal quantity of shear walls for frame-shear wall structures in earthquake zone[J].Earthquake Resistant Engineering,2003,(1):1-5(in Chinese)
[6] 方德平,王全凤.变刚度框剪结构地震反应的层单元分析[J].建筑结构,2005,35(11):36-38Fang Deping,Wang Quanfeng.Story element analysis method to earthquake response of frame interrupted shear wall structure[J].Building Structure,2005,35(11):36-38(in Chinese)
[7] Atik M,Badawi MM,Shahrour I,et al.Optimum level of shear wall curtailment in wall-frame buildings:the continuum model revisited [J].Journal of Structural Engineering,2014,140(1):896-912
[8] 中国建筑科学研究院建筑结构研究所.高层建筑结构设计[M].北京:科学出版社,1982Institute of Building Structures.China Academy of Building Research structural design of high-rise buildings[M].Beijing:Science Press,1982(in Chinese)
[9] 傅学怡.实用高层建筑结构设计[M].北京:中国建筑工业出版社,1992Fu Xueyi.Practical high-rise building structure design[M].Beijing:China Construction Industry Press,1992(in Chinese)
[10] 钱稼茹,赵作周,叶列平.高层建筑结构设计(第二版)[M].北京:中国建筑工业出版社,2012Qian Jiaru,Zhao Zuozhou,Ye Lieping.Structural design of high-rise buildings(Second Edition)[M].Beijing:China Construction Industry Press,2012(in Chinese)
[11] 赵西安.高层建筑结构实用设计方法(第三版)[M].上海:同济大学出版社,1998Zhao Xi’an.Practical design method for high-rise building structures(Third Edition)[M].Shanghai:Tongji University press,1998(in Chinese)