考虑剪力墙剪切变形影响的框架-剪力墙结构分析的传递矩阵法
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摘要
考虑剪力墙剪切变形影响、连梁固结连接条件,利用变分原理,建立框架-剪力墙结构分析模型的微分方程。推导微分方程的初参数解,进而建立适应变刚度结构分析的传递矩阵法,给出均布荷载和倒三角形分布荷载作用的传递矩阵荷载附加项的计算公式,导出顶部集中荷载、顶部集中弯矩、沿高度方向均布荷载和倒三角形分布荷载作用下的挠度、转角、剪力墙弯矩、剪力的计算公式。以2个铰结体系框架-剪力墙为例,对计算公式进行验证。研究结果表明:当连梁等效抗弯刚度为0 k N·m/m时固结体系可退化成铰结体系,当剪力墙抗剪刚度趋于无穷大时,弯剪型剪力墙可退化为不考虑剪切变形的弯曲型剪力墙,因此,本文微分方程可适应于多种模型的计算;采用传递矩阵法分析变刚度框架-剪力墙结构,其计算结果与采用平均刚度法的理论解析解结果较吻合,证明传递矩阵法与平均刚度法都具有可行性,但若提高计算精度,则应采用能考虑变刚度特征的传递矩阵法或有限元法;考虑剪力墙剪切变形影响的本文计算公式所得计算结果与其他公式所得结果有一定差别。
Considering the shear deformation effect of shear wall and the rigid joint condition of connecting beam, a differential equation was presented for the analysis of frame-shear wall structures based on the variational principle. The initial parameter solutions to the differential equation were derived, and the transfer matrix method was put forward to analyze the frame-shear wall structures with variable stiffness. The additional items of calculations of frame-shear wallstructures subjected to the uniformly distributing load and triangularly distributing load were established using transfer matrix method. The deflection, slope, moment and totel shear force were derived for frame-shear wall structures under the concentrated load and concentrated moment on the top, the uniformly distributing load and triangularly distributing load along the height. By using two hinged systems of frame-shear wall structure as the examples, the derived formulae were checked. The results show that when the equivalent flexural stiffness of connecting beam is 0 k N·m/m, the fixed system is degenerated into the hinged system, and when the shear stiffness of shear wall tends to be infinite, the flexural-shear type shear wall is transformed into the flexural type shear wall without the shear deformation effects, so the present differential equation can be used to analyze multi models of frame-shear wall structures. For variable stiffness structures, the calculating results obtained by the present transfer matrix method agree with those of the analytical solutions obtained by the equivalent uniform stiffness, so both methods are feasible. To obtain high precision, the transfer matrix method and finite element method are preferred to adapt to the variable stiffness structures. When the shear deformation effect of shear wall is considered, the results obtained by the presented formulae in this paper differ from those obtained by other formulae.
Considering the shear deformation effect of shear wall and the rigid joint condition of connecting beam, a differential equation was presented for the analysis of frame-shear wall structures based on the variational principle. The initial parameter solutions to the differential equation were derived, and the transfer matrix method was put forward to analyze the frame-shear wall structures with variable stiffness. The additional items of calculations of frame-shear wallstructures subjected to the uniformly distributing load and triangularly distributing load were established using transfer matrix method. The deflection, slope, moment and totel shear force were derived for frame-shear wall structures under the concentrated load and concentrated moment on the top, the uniformly distributing load and triangularly distributing load along the height. By using two hinged systems of frame-shear wall structure as the examples, the derived formulae were checked. The results show that when the equivalent flexural stiffness of connecting beam is 0 k N·m/m, the fixed system is degenerated into the hinged system, and when the shear stiffness of shear wall tends to be infinite, the flexural-shear type shear wall is transformed into the flexural type shear wall without the shear deformation effects, so the present differential equation can be used to analyze multi models of frame-shear wall structures. For variable stiffness structures, the calculating results obtained by the present transfer matrix method agree with those of the analytical solutions obtained by the equivalent uniform stiffness, so both methods are feasible. To obtain high precision, the transfer matrix method and finite element method are preferred to adapt to the variable stiffness structures. When the shear deformation effect of shear wall is considered, the results obtained by the presented formulae in this paper differ from those obtained by other formulae.
引文
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[11]夏桂云,欧见仁.考虑剪力墙剪切变形影响的框架-剪力墙结构分析[J].工程力学,2013,30(6):217-222.XIA Guiyun,OU Jianren.Analysis method of frame-shear wall structures with considering shear deformation effect of shear wall[J].Engineering Mechanics,2013,30(6):217-222.
[12]Smith B S,Coull A.Tall building structures analyis and design[M].New York:Wiley-Interscience,1991:301-327
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[14]胡海昌.弹性力学的变分原理及其应用[M].北京:科学出版社,1981:139-150.HU Haichang.Variational principle in elasticity and its applications[M].Beijing:Science Press,1981:139-150.
[15]芮筱亭,贠来峰,陆毓琪.多体系统传递矩阵法及其应用[M].北京:科学出版社,2008:23-100.RUI Xiaoting,YUN Laifeng,LU Yuqi.Transfer matrix method of multibody system and its applications[M].Beijing:Science Press,2008:23-100.
[16]龙驭球.弹性地基梁的计算[M].北京:高等教育出版社,1981:6-67.LONG Yuqiu.Calculation of elastic foundation beam[M].Beijing:Higher Education Press,1981:6-67.
[2]包世华.新编高层建筑结构[M].北京:中国水利水电出版社,2001:151-193.BAO Shihua.Newly edited high-rise building structures[M].Beijing:China Water Power Press,2001:151-193.
[3]王崇昌,马克俭,粟秀文.高层建筑钢筋混凝土剪力墙结构分析[M].贵阳:贵州人民出版社,1989:290-303.WANG Chongchang,MA Kejian,SHU Xiuwen.Analysis of reinforced concrete shear wall structures in high-rising building structures[M].Guiyang:Guizhou People’s Press,1989:290-303.
[4]司林军.变刚度框架-剪力墙结构静动力分析的初参数解[D].南宁:广西大学土木建筑工程学院,2006:9-37.SI Linjun.The initial parameter method for static and dynamic analysis of frame shear-wall structures with variable stiffness[D].Nanling:Guangxi University.College of Civil Engineering and Architecture,2006:9-37.
[5]郭乐工,郭乐宁.框架-剪力墙结构的侧向刚度分析[J].郑州大学学报(工学版),2010,31(1):20-22.GUO Legong,GUO Lening.Lateral stiffness analysis on frame-shear wall structures[J].Journal of Zhengzhou University(Engineering Science Edition),2010,31(1):20-22.
[6]孟焕陵.高层建筑结构的体系判别、合理刚度及扭转计算研究[D].长沙:湖南大学土木工程学院,2006:32-94.MENG Huanling.Research on system judgment,reasonable stiffness and torsion calculation of tall building structures[D].Changsha:Hunan University.School of Civil Engineering,2006:32-94.
[7]Capuani D,Merli M,Savoia M.Dynamic analysis of coupled shear wall-frame systems[J].Journal of Sound and Vibration,1996,192(4):867-883.
[8]Topkaya C,Kurban C O.Natural periods of steel plate shear wall systems[J].Journal of Constructional Steel Research,2009,65(3):542-551.
[9]唐兴荣.框架剪力墙结构考虑剪力墙剪切变形时的内力和位移[J].苏州城建环保学院学报,1996,9(3):20-29.TANG Xingrong.Internal forces and deflections of frame-shear wall structures with consideration of shear deformation of shear walls[J].Journal of Suzhou Institute of Urban Construction and Environmental Protection,1996,9(3):20-29.
[10]郭猛,姚谦峰,袁泉.框架-密肋复合墙结构剪力分担率计算方法研究[J].工程力学,2011,28(2):141-146.GUO Meng,YAO Qianfeng,YUAN Quan.Calculation method for the shear-sharing ratio of frame-composite wall structure[J].Engineering Mechanics,2011,28(2):141-146.
[11]夏桂云,欧见仁.考虑剪力墙剪切变形影响的框架-剪力墙结构分析[J].工程力学,2013,30(6):217-222.XIA Guiyun,OU Jianren.Analysis method of frame-shear wall structures with considering shear deformation effect of shear wall[J].Engineering Mechanics,2013,30(6):217-222.
[12]Smith B S,Coull A.Tall building structures analyis and design[M].New York:Wiley-Interscience,1991:301-327
[13]夏桂云,李传习.考虑剪切变形影响的杆系理论与应用[M].北京:人民交通出版社,2008:1-41.XIA Guiyun,LI Chuanxi.Frame structure theory and its applications including shear deformation effects[M].Beijing:China Communications Press,2008:1-41.
[14]胡海昌.弹性力学的变分原理及其应用[M].北京:科学出版社,1981:139-150.HU Haichang.Variational principle in elasticity and its applications[M].Beijing:Science Press,1981:139-150.
[15]芮筱亭,贠来峰,陆毓琪.多体系统传递矩阵法及其应用[M].北京:科学出版社,2008:23-100.RUI Xiaoting,YUN Laifeng,LU Yuqi.Transfer matrix method of multibody system and its applications[M].Beijing:Science Press,2008:23-100.
[16]龙驭球.弹性地基梁的计算[M].北京:高等教育出版社,1981:6-67.LONG Yuqiu.Calculation of elastic foundation beam[M].Beijing:Higher Education Press,1981:6-67.