剪力墙中断的高层框—剪结构抗震性能分析与工程应用
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摘要
在高层建筑实际设计中,经常遇到这种情况,在结构上部,由于建筑功能的要求或其他原因,要减少剪力墙的尺寸,甚至完全取消。这种断层剪力墙的高层框架-剪力墙结构(简称框-剪结构)是一种新型的高层结构,其特点是采用断层剪力墙来满足现代高层建筑使用功能的要求。剪力墙的变形曲线为悬臂梁型,而框架的变形曲线为剪切型。下部的剪力墙可减少下部框架的内力;而上部的剪力墙则增加上部框架的内力。中断上部剪力墙,减轻上部框架的内力,有其合理性。所以,从力学上来讲,全高剪力墙并不一定是必要的。针对框-剪结构协同工作的受力变形特点,先探讨了框-剪结构中中断部分剪力墙的合理性,提出了可中断剪力墙高度的3个条件:
①剪力墙中断的框-剪结构的顶点侧移不应大于全高剪力墙框-剪结构的顶点侧移;
②剪力墙中断以上框架部分的层间位移角不应大于1.45倍全高剪力墙时的最大层间位移角,因为建筑抗震设计规范(GB50011-2001)规定:框架弹性层间位移角[θe] =1/550,而框-剪的[θe] =1/800,两者比值为1.45;
③剪力墙中断以上的框架部分所承受的楼层地震剪力Vt不应大于全高剪力墙时框架部分所承受最大楼层地震剪力V fmax的n倍,n为剪力墙中断以上部分的框架柱数与全高剪力墙时框架柱数的比值。构造了简明的层单元,一层框-剪结构可只用一个层单元来模拟。应用两种模型:层单元模型、杆系-层模型,采用振型分解反应谱法,分析不同高度和结构刚度特征值的断层剪力墙框-剪结构的地震反应,两种模型给出相近的计算结果。根据可中断剪力墙的高度的3个条件,计算表明:随着刚度特征值的增加,可中断剪力墙的高度随之增加,给出了两者之间的表达式;结构高度对中断剪力墙高度的影响较小。
基于钢筋砼杆件截面的轴力-弯矩-曲率关系,建立了考虑杆件P ??效应和剪切变形,且能分析框架极限状态的非线性有限元法。提出了改进能力谱法,定义了砼框架结构唯一的延性系数,确定Pushover曲线的极限状态点为性能点,通过性能点位于由延性系数所折减的非弹性需求谱曲线上的条件,求出框架所能抵抗的最大地震加速度,评估框架的抗震性能。兼顾承载能力,得出相对受压区高度0.25～0.35,轴压比0.6～0.8的框架,具有较好的抗震性能。
根据所提出的非线性有限元法,将剪力墙当作特别杆单元,对不同高度、配筋、轴压比和刚度特征值的中断剪力墙的框-剪结构进行了极限状态弹塑性分析。根据可中断剪力墙的高度的3个条件,计算表明:相对高度值与配筋和轴压比无关;与结构高度关系较小;随着刚度特征值的增加,相对高度值随之增加,并给出了两者之间的表达式。
Wilson-θ法分为加速度未经过和经过动力平衡方程修正的Wilson -θ①法和Wilson -θ②法;推导了单自由度体系的Wilson -θ①、②法的状态传递算子,由传递算子的谱半径来判断Wilson -θ①、②法的稳定性。Wilson -θ①法的稳定性是无条件的。计算结果表明:Wilson -θ②法的稳定性不是无条件的;并给出了Wilson -θ②法的稳定范围。修正了一些文献中的一个错误:认为Wilson -θ①、②法都是无条件稳定的。
用杆系-层模型和Wilson -θ①法,以及EL Centro地震记录,分析不同高度和结构刚度特征值的断层剪力墙的框-剪结构地震反应。根据可中断剪力墙的高度的3个条件,计算表明:随着刚度特征值的增加,可中断剪力墙的高度随之增加,给出了两者之间的表达式;结构高度对中断剪力墙高度的影响较小。动力时程分析的结果与层单元模型、杆系-层模型和极限状态弹塑性分析结果相近。
In the design of tall building, the dimension of upper part of shear wall would be reduced, and even the upper wall would be cut, due to the architecture demand or other reasons. The frame-shear wall structure with shear wall interruption is a new type of tall building, its characteristic is to meet the function of modern tall building by shear wall interruption. The deformation of shear wall is the type of cantilever bending beam, but the deformation of frame is the type of cantilever shear beam. The lower part of shear wall can decrease the internal forces of lower part of frame; but upper part of shear wall can increase the internal forces of upper part of frame. It may be rational to cut the upper part of shear wall and to reduce the internal forces of the upper frame. Therefore, in the view of mechanics, the full height of wall is not necessarily imperative. Based on the disformation characteristic of the frame-shear wall structure cooperation work, the rationality of the frame-shear wall structure with shear wall interruption is discussed. The 3 conditions of interruptable shear wall height are established:
①The top lateral displacement of the frame-shear wall structure with shear wall interruption is less than top displacement of the frame-shear wall structure with full height shear wall.
②Interstorey drift as a percentage of height above the shear wall interruption is less than 1.45 times of maximum interstorey drift in the structure with full height shear wall, because it is stipulated in code for seismic design of buildings (GB50011-2001): elastic interstorey drift in frame [θe] =1/550; elastic interstorey drift in frame-shear wall structure [θe] =1/800, the ratio between them is 1.45.
③The seismic shear force Vt of frame above the shear wall interruption is less than n times of maximum seismic shear force V fmax of frame in the structure with full height shear wall, n is the ratio of column number above the shear wall interruption to the column number in the structure with full height shear wall.
The concise storey element is fabricated which can model one storey of the frame-shear wall structure. Based on SRSS method, both storey element model and the member-relative storey model are used to analyze the seismic response of frame-shear wall structures with shear wall interruption for different heights and rigidity characteristics. Two models give the similar results. According to 3 conditions of interruptable shear wall height, calculation results indicate: with the increase of the rigidity characteristic, the interruptable shear wall height increases also. The equation between the rigidity characteristic and the interruptable shear wall height is also presented. The height of the structure influences little on the interruptable shear wall height.
Based on the relationship among axial force–bending moment–curvature of the concrete bar section, the nonlinear finite element method considering bar P–Δeffect and shear deformation is established which is able to analyze the ultimate state. The improved capacity spectrum method is put forward, where the unique ductility factor of concrete frame is defined, and the point of ultimate state in pushover curve is regarded as the demand point. On the condition that the demand point locates at the inelastic demand spectrum curve reduced by ductility factor, the maximum seismic spectrum acceleration is obtained to evaluate the seismic behavior of frame. Balancing load carrying capacity, it’s concluded that the frames with 0.25~0.35 relative depth of compressive zone and 0.6~0.8 axial compressive ratios perform benign seismic behavior.
Based on the above nonlinear finite element method, regarding the shear wall as the special bar elements, the frame-shear wall structures with shear wall interruption for different heights, reinforcements, axial compressive ratios and rigidity characteristics are analyzed by static elastic-plastic method. According to 3 conditions of interruptable shear wall height, calculation results indicate: the interruptable shear wall height is not relative to reinforcements and axial compressive ratios, little relative to height of the structure. With the increase of the rigidity characteristic, the interruptable shear wall height increases also. The equation between the rigidity characteristic and the interruptable shear wall height is also presented.
There remain two kinds of Wilson-θmethods, namely, Wilson-θ①and②methods. In Wilson-θ①method, the accelerations are not modified by the dynamic equilibrium equations; in Wilson-θ②method, the accelerations are modified. The amplification matrixes of Wilson-θ①and②methods for single-degree-of-freedom system are derived. The stabilities of Wilson-θ①and②methods are examined by the spectral radii of the amplification matrixes. The stability of Wilson-θ①method is unconditional. The calculation results indicate: the stability of Wilson-θ②method is not unconditional. The stability ranges of Wilson-θ②method are also put forward. The conclusion corrects an error in some references in which both Wilson-θ①and②methods are wrongly considered as unconditional stability.
Based on the member-relative storey model, Wilson-θ①method and EL Centro ground motion record, the seismic response if frame-shear wall structures with shear wall interruption for different heights and rigidity characteristics are analyzed by time history method. According to 3 conditions of interruptable shear wall height, calculation results indicate: with the increase of the rigidity characteristic, the interruptable shear wall height increases also. The equation between the rigidity characteristic and the interruptable shear wall height is also presented. The height of the structure influences little on the interruptable shear wall height. The conclusion of dynamic time history analysis is similar to the conclusions of storey element model, the member-relative storey model and static elastic-plastic method.
①剪力墙中断的框-剪结构的顶点侧移不应大于全高剪力墙框-剪结构的顶点侧移;
②剪力墙中断以上框架部分的层间位移角不应大于1.45倍全高剪力墙时的最大层间位移角,因为建筑抗震设计规范(GB50011-2001)规定:框架弹性层间位移角[θe] =1/550,而框-剪的[θe] =1/800,两者比值为1.45;
③剪力墙中断以上的框架部分所承受的楼层地震剪力Vt不应大于全高剪力墙时框架部分所承受最大楼层地震剪力V fmax的n倍,n为剪力墙中断以上部分的框架柱数与全高剪力墙时框架柱数的比值。构造了简明的层单元,一层框-剪结构可只用一个层单元来模拟。应用两种模型:层单元模型、杆系-层模型,采用振型分解反应谱法,分析不同高度和结构刚度特征值的断层剪力墙框-剪结构的地震反应,两种模型给出相近的计算结果。根据可中断剪力墙的高度的3个条件,计算表明:随着刚度特征值的增加,可中断剪力墙的高度随之增加,给出了两者之间的表达式;结构高度对中断剪力墙高度的影响较小。
基于钢筋砼杆件截面的轴力-弯矩-曲率关系,建立了考虑杆件P ??效应和剪切变形,且能分析框架极限状态的非线性有限元法。提出了改进能力谱法,定义了砼框架结构唯一的延性系数,确定Pushover曲线的极限状态点为性能点,通过性能点位于由延性系数所折减的非弹性需求谱曲线上的条件,求出框架所能抵抗的最大地震加速度,评估框架的抗震性能。兼顾承载能力,得出相对受压区高度0.25～0.35,轴压比0.6～0.8的框架,具有较好的抗震性能。
根据所提出的非线性有限元法,将剪力墙当作特别杆单元,对不同高度、配筋、轴压比和刚度特征值的中断剪力墙的框-剪结构进行了极限状态弹塑性分析。根据可中断剪力墙的高度的3个条件,计算表明:相对高度值与配筋和轴压比无关;与结构高度关系较小;随着刚度特征值的增加,相对高度值随之增加,并给出了两者之间的表达式。
Wilson-θ法分为加速度未经过和经过动力平衡方程修正的Wilson -θ①法和Wilson -θ②法;推导了单自由度体系的Wilson -θ①、②法的状态传递算子,由传递算子的谱半径来判断Wilson -θ①、②法的稳定性。Wilson -θ①法的稳定性是无条件的。计算结果表明:Wilson -θ②法的稳定性不是无条件的;并给出了Wilson -θ②法的稳定范围。修正了一些文献中的一个错误:认为Wilson -θ①、②法都是无条件稳定的。
用杆系-层模型和Wilson -θ①法,以及EL Centro地震记录,分析不同高度和结构刚度特征值的断层剪力墙的框-剪结构地震反应。根据可中断剪力墙的高度的3个条件,计算表明:随着刚度特征值的增加,可中断剪力墙的高度随之增加,给出了两者之间的表达式;结构高度对中断剪力墙高度的影响较小。动力时程分析的结果与层单元模型、杆系-层模型和极限状态弹塑性分析结果相近。
In the design of tall building, the dimension of upper part of shear wall would be reduced, and even the upper wall would be cut, due to the architecture demand or other reasons. The frame-shear wall structure with shear wall interruption is a new type of tall building, its characteristic is to meet the function of modern tall building by shear wall interruption. The deformation of shear wall is the type of cantilever bending beam, but the deformation of frame is the type of cantilever shear beam. The lower part of shear wall can decrease the internal forces of lower part of frame; but upper part of shear wall can increase the internal forces of upper part of frame. It may be rational to cut the upper part of shear wall and to reduce the internal forces of the upper frame. Therefore, in the view of mechanics, the full height of wall is not necessarily imperative. Based on the disformation characteristic of the frame-shear wall structure cooperation work, the rationality of the frame-shear wall structure with shear wall interruption is discussed. The 3 conditions of interruptable shear wall height are established:
①The top lateral displacement of the frame-shear wall structure with shear wall interruption is less than top displacement of the frame-shear wall structure with full height shear wall.
②Interstorey drift as a percentage of height above the shear wall interruption is less than 1.45 times of maximum interstorey drift in the structure with full height shear wall, because it is stipulated in code for seismic design of buildings (GB50011-2001): elastic interstorey drift in frame [θe] =1/550; elastic interstorey drift in frame-shear wall structure [θe] =1/800, the ratio between them is 1.45.
③The seismic shear force Vt of frame above the shear wall interruption is less than n times of maximum seismic shear force V fmax of frame in the structure with full height shear wall, n is the ratio of column number above the shear wall interruption to the column number in the structure with full height shear wall.
The concise storey element is fabricated which can model one storey of the frame-shear wall structure. Based on SRSS method, both storey element model and the member-relative storey model are used to analyze the seismic response of frame-shear wall structures with shear wall interruption for different heights and rigidity characteristics. Two models give the similar results. According to 3 conditions of interruptable shear wall height, calculation results indicate: with the increase of the rigidity characteristic, the interruptable shear wall height increases also. The equation between the rigidity characteristic and the interruptable shear wall height is also presented. The height of the structure influences little on the interruptable shear wall height.
Based on the relationship among axial force–bending moment–curvature of the concrete bar section, the nonlinear finite element method considering bar P–Δeffect and shear deformation is established which is able to analyze the ultimate state. The improved capacity spectrum method is put forward, where the unique ductility factor of concrete frame is defined, and the point of ultimate state in pushover curve is regarded as the demand point. On the condition that the demand point locates at the inelastic demand spectrum curve reduced by ductility factor, the maximum seismic spectrum acceleration is obtained to evaluate the seismic behavior of frame. Balancing load carrying capacity, it’s concluded that the frames with 0.25~0.35 relative depth of compressive zone and 0.6~0.8 axial compressive ratios perform benign seismic behavior.
Based on the above nonlinear finite element method, regarding the shear wall as the special bar elements, the frame-shear wall structures with shear wall interruption for different heights, reinforcements, axial compressive ratios and rigidity characteristics are analyzed by static elastic-plastic method. According to 3 conditions of interruptable shear wall height, calculation results indicate: the interruptable shear wall height is not relative to reinforcements and axial compressive ratios, little relative to height of the structure. With the increase of the rigidity characteristic, the interruptable shear wall height increases also. The equation between the rigidity characteristic and the interruptable shear wall height is also presented.
There remain two kinds of Wilson-θmethods, namely, Wilson-θ①and②methods. In Wilson-θ①method, the accelerations are not modified by the dynamic equilibrium equations; in Wilson-θ②method, the accelerations are modified. The amplification matrixes of Wilson-θ①and②methods for single-degree-of-freedom system are derived. The stabilities of Wilson-θ①and②methods are examined by the spectral radii of the amplification matrixes. The stability of Wilson-θ①method is unconditional. The calculation results indicate: the stability of Wilson-θ②method is not unconditional. The stability ranges of Wilson-θ②method are also put forward. The conclusion corrects an error in some references in which both Wilson-θ①and②methods are wrongly considered as unconditional stability.
Based on the member-relative storey model, Wilson-θ①method and EL Centro ground motion record, the seismic response if frame-shear wall structures with shear wall interruption for different heights and rigidity characteristics are analyzed by time history method. According to 3 conditions of interruptable shear wall height, calculation results indicate: with the increase of the rigidity characteristic, the interruptable shear wall height increases also. The equation between the rigidity characteristic and the interruptable shear wall height is also presented. The height of the structure influences little on the interruptable shear wall height. The conclusion of dynamic time history analysis is similar to the conclusions of storey element model, the member-relative storey model and static elastic-plastic method.
引文
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