考虑地基及部分楼板变形的框—剪结构分析
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摘要
在框架-剪力墙结构设计中,通常采用楼板在自身平面为刚性的假设。这一假设虽然大大简化了计算工作,但对平面布置不规则的建筑形式,如:个别抗侧力单元的间距很大,楼板刚度变小;建筑平面布置使楼板出现‘瓶颈区’,抗侧力结构沿高度方向有巨大的刚度突变;部分楼板平面形状不规则或有较大的开洞等情况时不能采用此假设,而全部按弹性楼板计算会使计算量很大。若仅对刚度有削弱的楼板考虑为弹性楼板,其它楼板按刚性计算则不仅满足计算精度且减小了计算量。
对于地基变形即结构地基和基础共同作用的问题已经在各种结构设计计算中被广泛讨论。一般的计算方法是考虑地基模型为文克尔地基模型,但该模型具有不能扩散应力和变形的缺陷,不适宜做为高层建筑地基模型。本文考虑到地基土位于地下水以下时形成饱和土,它是一种流体饱和多孔介质,此时的地基宜模拟成各向同性的弹性半无限空间地基模型,而一般高层建筑地基较深,多处于地下水以下,故本文采用弹性半无限空间地基模型来模拟地基变形。
本文主要对考虑地基及部分楼板变形的框-剪结构进行协同、二阶、动力特性和整体稳定的分析。在进行结构协同分析时,我们考虑部分楼板的变形影响,将楼板分成若干个刚性区域,每个刚性区域内的框架和剪力墙分别合并为一个综合框架和一个综合剪力墙,它们之间由刚性连杆连接成一个框-剪单元,综合框架和综合剪力墙均考虑其弯曲和剪切变形,可看作是竖放的铁摩辛柯梁。各个刚性区域间通过弹簧连接,形成空间协同工作体系。对弹性楼板和连梁的作用视为楼层标高处的弹性支撑。考虑上部结构、地基和基础共同作用,认为地基对结构有水平刚度和竖向转动刚度。从而建立考虑地基及部分楼板变形的计算模型。
针对该模型,利用哈密顿力学原理,通过引入的对偶变量,将问题的求解从拉格朗日体系导向哈密顿体系。运用两端边值问题的精细积分法,通过Matlab语言编制计算程序求解结构的状态向量从而得到精确的数值解。最后通过实例分析并与有限元计算对比数据,得到了地基及部分楼板变形对建筑结构协同、二阶、动力特性和整体稳定影响的一些有用结论。整个数值算法具有稳定性高、精度高、收敛快的优点,为研究此类工程问题提供了一种新方法、新途径,有一定的工程参考价值。
The assumption of rigid slab is usually applied in the structural design of frame-shear wall structures, which greatly simplifies the calculation.But the assumption should not be used for the irregular layout of the building, such as: smaller slab stiffness caused by larger individual anti-side force unit spacing; enormous stiffness mutation of anti-side structure along the height direction due to the'bottleneck area' of building floor layout; some floor slabs with irregular shape or a larger open hole. However, great calculation amount is got by assumption of all elastic slab.If the floors with weakened stiffness are considered as flexible floor and others rigid, the computing accuracy is meeted and computational complexity is reduced.
The combined effect of the foundation and base has been widely discussed in a variety of structural design calculations. Winkler foundation model is generally used. But it is not appropriate as a model of high-rise building foundation because the model cannot describe the spread of stress and deformation. The foundation soil at the groundwater below is saturated soil, which is a fluid-saturated porous media.So the foundation is analoged into isotropic elastic semi-infinite space foundation model.For the high-rise building foundations is deeper generally, most in the groundwater below, so semi-infinite elastic foundation model is used to simulate spatial deformation of the foundation in this paper.
The frame-shear structure of coordination, the second order, the dynamic properties analysis and the overall stability analysis were performed mainly considering the deformation of the foundation and part of floor. In the cooperative analysis study of structure, the slab is divided into a number of rigid regions by the part of the deformation of floor slab. The framework and the wall within each rigid region were merged into a comprehensive framework and an integrated wall respectively, which were formed into frame-shear wall unit. Integrated framework and an integrated wall are regared as Timoshenko beam placed vertically considering bending and shear deformation. Various rigid regions were connected through the spring to form a collaborative work space system. The elastic floors and coupling beams were regarded as the elastic support of the floor elevation. The foundation of the structure has horizontal and vertical and rotation bound by considering the common role among the upper part of the structure, the foundation and basis. Thus the calculation model was set up to consider part of the foundation and slab deformation.
Taking the parallel Timoshenko beams as calculation model, using Hamiltonian mechanics, by introducing the dual variables, the solution of the problem was oriented from the Lagrangian system to Hamiltonian system. The precise integration method of two end boundary conditions was adopted to realize the high-precision numerical solution of the system by means of computer progrmmers with Matlab. Finally, through examples of analysis and comparison with finite element data , some useful conclusions on the impact of synergies and second power characteristics and the overall stability by the deformation of foundation and floor of structure. The high stability , high precision and quick convergence are the advantage of the numerical algorithm,which must have reference value to the project since it provided a new method, new ways for the study of such works.
对于地基变形即结构地基和基础共同作用的问题已经在各种结构设计计算中被广泛讨论。一般的计算方法是考虑地基模型为文克尔地基模型,但该模型具有不能扩散应力和变形的缺陷,不适宜做为高层建筑地基模型。本文考虑到地基土位于地下水以下时形成饱和土,它是一种流体饱和多孔介质,此时的地基宜模拟成各向同性的弹性半无限空间地基模型,而一般高层建筑地基较深,多处于地下水以下,故本文采用弹性半无限空间地基模型来模拟地基变形。
本文主要对考虑地基及部分楼板变形的框-剪结构进行协同、二阶、动力特性和整体稳定的分析。在进行结构协同分析时,我们考虑部分楼板的变形影响,将楼板分成若干个刚性区域,每个刚性区域内的框架和剪力墙分别合并为一个综合框架和一个综合剪力墙,它们之间由刚性连杆连接成一个框-剪单元,综合框架和综合剪力墙均考虑其弯曲和剪切变形,可看作是竖放的铁摩辛柯梁。各个刚性区域间通过弹簧连接,形成空间协同工作体系。对弹性楼板和连梁的作用视为楼层标高处的弹性支撑。考虑上部结构、地基和基础共同作用,认为地基对结构有水平刚度和竖向转动刚度。从而建立考虑地基及部分楼板变形的计算模型。
针对该模型,利用哈密顿力学原理,通过引入的对偶变量,将问题的求解从拉格朗日体系导向哈密顿体系。运用两端边值问题的精细积分法,通过Matlab语言编制计算程序求解结构的状态向量从而得到精确的数值解。最后通过实例分析并与有限元计算对比数据,得到了地基及部分楼板变形对建筑结构协同、二阶、动力特性和整体稳定影响的一些有用结论。整个数值算法具有稳定性高、精度高、收敛快的优点,为研究此类工程问题提供了一种新方法、新途径,有一定的工程参考价值。
The assumption of rigid slab is usually applied in the structural design of frame-shear wall structures, which greatly simplifies the calculation.But the assumption should not be used for the irregular layout of the building, such as: smaller slab stiffness caused by larger individual anti-side force unit spacing; enormous stiffness mutation of anti-side structure along the height direction due to the'bottleneck area' of building floor layout; some floor slabs with irregular shape or a larger open hole. However, great calculation amount is got by assumption of all elastic slab.If the floors with weakened stiffness are considered as flexible floor and others rigid, the computing accuracy is meeted and computational complexity is reduced.
The combined effect of the foundation and base has been widely discussed in a variety of structural design calculations. Winkler foundation model is generally used. But it is not appropriate as a model of high-rise building foundation because the model cannot describe the spread of stress and deformation. The foundation soil at the groundwater below is saturated soil, which is a fluid-saturated porous media.So the foundation is analoged into isotropic elastic semi-infinite space foundation model.For the high-rise building foundations is deeper generally, most in the groundwater below, so semi-infinite elastic foundation model is used to simulate spatial deformation of the foundation in this paper.
The frame-shear structure of coordination, the second order, the dynamic properties analysis and the overall stability analysis were performed mainly considering the deformation of the foundation and part of floor. In the cooperative analysis study of structure, the slab is divided into a number of rigid regions by the part of the deformation of floor slab. The framework and the wall within each rigid region were merged into a comprehensive framework and an integrated wall respectively, which were formed into frame-shear wall unit. Integrated framework and an integrated wall are regared as Timoshenko beam placed vertically considering bending and shear deformation. Various rigid regions were connected through the spring to form a collaborative work space system. The elastic floors and coupling beams were regarded as the elastic support of the floor elevation. The foundation of the structure has horizontal and vertical and rotation bound by considering the common role among the upper part of the structure, the foundation and basis. Thus the calculation model was set up to consider part of the foundation and slab deformation.
Taking the parallel Timoshenko beams as calculation model, using Hamiltonian mechanics, by introducing the dual variables, the solution of the problem was oriented from the Lagrangian system to Hamiltonian system. The precise integration method of two end boundary conditions was adopted to realize the high-precision numerical solution of the system by means of computer progrmmers with Matlab. Finally, through examples of analysis and comparison with finite element data , some useful conclusions on the impact of synergies and second power characteristics and the overall stability by the deformation of foundation and floor of structure. The high stability , high precision and quick convergence are the advantage of the numerical algorithm,which must have reference value to the project since it provided a new method, new ways for the study of such works.
引文
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