CN103615054A

CN103615054A - A buckling-constrained bracing layout method based on cell shear deformation

Info

Publication number: CN103615054A
Application number: CN201310628255.8A
Authority: CN
Inventors: 丁洁民; 赵昕; 张鸿玮; 石涛; 江祥
Original assignee: Architecture Design and Research Institute of Tongji University Group Co Ltd
Current assignee: Architecture Design and Research Institute of Tongji University Group Co Ltd
Priority date: 2013-11-29
Filing date: 2013-11-29
Publication date: 2014-03-05
Anticipated expiration: 2033-11-29
Also published as: CN103615054B

Abstract

The invention relates to a buckling restrained brace arrangement method based on cell shear deformation, which comprises the following steps of: (1) calculating the horizontal earthquake acting force of the structure according to a reaction spectrum or an elastic time-course method; (2) reacting the horizontal earthquake acting force obtained in the step (1) on the structure according to the principle of equivalent static force; (3) extracting deformation of each node of the grid in which the buckling constraint support can be arranged, wherein the deformation comprises the following steps: average horizontal displacement of two nodes at the upper end of the cell, average vertical displacement of two nodes at the left end of the cell and average vertical displacement of two nodes at the right end of the cell; (4) calculating the shearing deformation of the cells; (5) and arranging buckling restrained braces according to the shearing deformation of each cell. Compared with the prior art, the method has the advantages of strong operability, high calculation efficiency and the like.

Description

A buckling-constrained bracing layout method based on cell shear deformation

技术领域 technical field

本发明涉及建筑结构技术领域，尤其是涉及一种消能减震技术中基于区格剪切变形的屈曲约束支撑布置方法。 The invention relates to the technical field of building structures, in particular to a method for arranging buckling-constrained supports based on cell shear deformation in energy dissipation and shock absorption technology. the

背景技术 Background technique

超高层建筑在水平荷载下的变形形式通常是弯剪型，超高层建筑在水平荷载下的变形形式通常是弯剪型，即含有由于梁柱等构件受力产生的变形和由于结构各区格竖向杆件的截面转动产生的变形组成。学者魏琏指出，作为超高层结构的变形限值，层间位移角与剪力墙、梁、柱等结构构件的受力状态的相关性较差。例如图2为某290米高带加强层的超高层结构中柱的三种位移情况，可以看出，柱受到的剪力和弯矩的极值并不是在结构最大层间位移角的位置，并且弯曲变形随着楼层的增大而增大，在高区层间位移角主要由区格之间的弯曲变形为主。因此学者蒋利学提出一个新的参数，即广义剪切变形，可以更好的反应结构的受力特征。 The deformation form of super high-rise buildings under horizontal loads is usually bending-shear type, and the deformation form of super-tall buildings under horizontal loads is usually bending-shear type, that is, it includes the deformation caused by the stress of beams and columns and the vertical deformation of each cell of the structure. Composition of deformations caused by rotation towards the cross-section of the member. Scholar Wei Lian pointed out that as the deformation limit of super high-rise structures, the interstory displacement angle has poor correlation with the stress state of structural components such as shear walls, beams, and columns. For example, Figure 2 shows three displacements of columns in a super high-rise structure with a height of 290 meters and reinforced floors. It can be seen that the extreme values of the shear force and bending moment on the column are not at the position of the maximum interstory displacement angle of the structure. And the bending deformation increases with the increase of the floor, and the displacement angle between floors in the high area is mainly caused by the bending deformation between the cells. Therefore, scholar Jiang Lixue proposed a new parameter, that is, generalized shear deformation, which can better reflect the mechanical characteristics of the structure. the

从屈曲约束支撑的滞回曲线可以看出，其需要达到一定的相对位移才能屈服耗能，并且在相同参数的情况下，屈曲约束支撑耗能的多少由其轴向应变所决定。以往屈曲约束支撑的设计中，原则上BRB(Buckling restrained brace，屈曲约束支撑)应摆在结构受力较大的位置能够使得屈曲支撑在中、大震情况下屈服耗能。现有的工程经验往往将屈曲约束支撑布置在结构层间位移角最大或层间剪力最大的楼层位置，因其层间位移角和水平地震作用力与屈曲约束支撑的耗能大小不能完全成线性关系，所以其屈曲约束支撑的耗能能力往往不能得到最大的发挥，因此要对位置进行大量的尝试和验算，因此寻找受力最大或变形最大的最优布置位置往往需要花费一定的时间。 From the hysteretic curve of the buckling-constrained brace, it can be seen that it needs to reach a certain relative displacement to yield and dissipate energy, and in the case of the same parameters, the amount of energy dissipated by the buckling-constrained brace is determined by its axial strain. In the design of buckling restrained braces in the past, in principle, BRB (Buckling restrained braces) should be placed in the position where the structure is stressed so that the buckling braces can yield and dissipate energy under moderate or large earthquakes. According to the existing engineering experience, the buckling-constrained braces are often placed on the floor where the interstory displacement angle or the interstory shear force of the structure is the largest, because the interstory displacement angle and the horizontal seismic force cannot be completely combined with the energy dissipation of the buckling-constrained braces. Therefore, the energy-dissipating capacity of the buckling-constrained support cannot be maximized. Therefore, a lot of trials and calculations are required for the position. Therefore, it takes a certain amount of time to find the optimal arrangement position with the largest force or deformation. the

发明内容 Contents of the invention

本发明的目的就是为了克服上述现有技术存在的缺陷而提供一种可操作性强、计算效率高的基于区格剪切变形的屈曲约束支撑布置方法。 The purpose of the present invention is to provide a buckling-constrained support arrangement method based on cell shear deformation with strong operability and high calculation efficiency in order to overcome the defects in the above-mentioned prior art. the

本发明的目的可以通过以下技术方案来实现： The purpose of the present invention can be achieved through the following technical solutions:

一种基于区格剪切变形的屈曲约束支撑布置方法，包括以下步骤： A buckling-constrained bracing arrangement method based on cell shear deformation, comprising the following steps:

(1)通过有限元软件根据反应谱或弹性时程法计算结构的各层水平地震作用力； (1) Calculate the horizontal seismic force of each layer of the structure through the finite element software according to the response spectrum or elastic time history method;

(2)根据等效静力的原则，将步骤(1)获得的水平地震作用力反作用于结构上； (2) According to the principle of equivalent static force, react the horizontal seismic force obtained in step (1) on the structure;

(3)提取可布置屈曲约束支撑的区格各节点的变形，包括：区格上端两节点的平均水平位移、区格左端两节点的平均竖向位移和区格右端两节点的平均竖向位移； (3) Extract the deformation of each node of the cell where the buckling restraint support can be arranged, including: the average horizontal displacement of the two nodes at the upper end of the cell, the average vertical displacement of the two nodes at the left end of the cell, and the average vertical displacement of the two nodes at the right end of the cell ;

(4)根据如下区格剪切变形公式计算出区格的剪切变形： (4) Calculate the shear deformation of the cell according to the following cell shear deformation formula:

${γ γ}_{i i} = = \frac{{u u}_{i i} - - {u u}_{i i - - 11}}{{h h}_{i i}} - - \frac{{v v}_{i i} - - {v v}_{j j}}{{I I}_{i i}}$

式中，γ_i为第i层区格的剪切变形，u_i、u_i-1分别为第i层和第i-1层区格上端两节点的平均水平位移，h_i为第i层区格的高，v_i为第i层区格左端两节点的平均竖向位移，v_j为第i层区格右端两节点的平均竖向位移，l_i为第i层区格的宽； In the formula, γ _i is the shear deformation of the i-th layer cell, u _i and u _i-1 are the average horizontal displacements of the upper two nodes of the i-th layer and the i-1th layer cell respectively, h _i is the i-th layer The height of the cell, v _i is the average vertical displacement of the two nodes at the left end of the i-th layer cell, v _j is the average vertical displacement of the two nodes at the right end of the i-th layer cell, l _i is the width of the i-th layer cell;

(5)根据各区格剪切变形的大小布置屈曲约束支撑。 (5) Arrange buckling-constrained supports according to the shear deformation of each cell. the

所述的步骤(1)中，根据反应谱计算结构的水平地震作用力具体为： In the described step (1), the horizontal seismic force of the structure calculated according to the response spectrum is specifically:

将结构设定为m个振型、n个质点的组合，通过以下公式计算每个振型的水平地震作用： Set the structure as a combination of m mode shapes and n particle points, and calculate the horizontal seismic action of each mode type by the following formula:

F_ji＝α_jγ_jX_jiG_i(i＝1，2，3…n，j＝1，2，3…m) F _ji =α _j γ _j X _ji G _i (i=1, 2, 3...n, j=1, 2, 3...m)

${γ γ}_{j j} = = {Σ Σ}_{i i = = 11}^{n no} {X x}_{ji the ji} {G G}_{i i} / / {Σ Σ}_{i i = = 11}^{n no} {X x}_{ji the ji}^{22} {G G}_{i i}$

其中，F_ji为j振型i质点的水平地震作用力标准值；α_j为相应于j振型自振周期的地震影响系数；X_ji为j振型i质点的水平相对位移；γ_j为j振型的参与系数；G_i为集中于质点i的重力荷载代表值。 Among them, F _ji is the standard value of horizontal seismic force of j mode mode i particle; α _j is the seismic influence coefficient corresponding to j mode mode natural vibration period; X _ji is the horizontal relative displacement of j mode mode i particle; γ _j is j is the participation coefficient of mode shape; G _i is the representative value of gravity load concentrated on particle i.

所述的步骤(1)中，根据弹性时程法计算结构的水平地震作用力具体为： In the described step (1), the horizontal seismic force of the structure calculated according to the elastic time-history method is specifically:

单个多自由度结构体系的运动方程为： The motion equation of a single multi-degree-of-freedom structural system is:

$[[M m]] {{\overset{\cdot \cdot \cdot \cdot}{v v}}} + + [[C C]] {{\overset{\cdot \cdot}{v v}}} + + [[K K]] {{v v}} = = {{p p ((t t))}}$

其中，[M]为结构的质量矩阵；[C]为结构的阻尼矩阵；[K]为结构的刚度矩阵；

{v}分别为结构的加速度、速度以及位移；{p(t)}为结构的动力响应。 Among them, [M] is the mass matrix of the structure; [C] is the damping matrix of the structure; [K] is the stiffness matrix of the structure;

{v} are the acceleration, velocity and displacement of the structure respectively; {p(t)} is the dynamic response of the structure.

运用求解特征值方法得到广义坐标下的方程： Use the method of solving eigenvalues to obtain the equation in generalized coordinates:

$[[M m]] [[Φ Φ]] {{\overset{\cdot &Center Dot; \cdot \cdot}{Y Y}}} + + [[C C]] [[Φ Φ]] {{\overset{\cdot &Center Dot;}{Y Y}}} + + [[K K]] [[Φ Φ]] {{Y Y}} = = {{p p ((t t))}}$

其中，

{Y}分别为结构的广义加速度、广义速度以及广义位移；[Φ]为形函数向量； in,

{Y} are the generalized acceleration, generalized velocity and generalized displacement of the structure respectively; [Φ] is the shape function vector;

将上式乘于任意一个转置向量

得： Multiply the above formula by any transposed vector

have to:

将方程组变为广义坐标下的单自由度体系运动方程，对于第n振型和正则化坐标Y_n有： Change the equation system into a single-degree-of-freedom system motion equation under generalized coordinates, for the nth vibration mode and regularized coordinate Y _n :

${M m}_{n no}^{* *} {\overset{\cdot \cdot \cdot \cdot}{Y Y}}_{n no} + + {C C}_{n no}^{* *} {\overset{\cdot \cdot}{Y Y}}_{n no} + + {K K}_{n no}^{* *} {Y Y}_{n no} = = {P P}_{n no}^{* *} ((t t))$

其中，

为第n振型的广义质量；

为广义阻尼；

为广义刚度；

为广义力，即为水平地震作用力。 in,

is the generalized mass of the nth vibration mode;

is the generalized damping;

is the generalized stiffness;

is the generalized force, that is, the horizontal earthquake force.

所述的步骤(3)中，通过有限元软件的计算数据提取可布置屈曲约束支撑的区格各节点的变形。 In the step (3), the deformation of each node of the cell where the buckling constraint support can be arranged is extracted through the calculation data of the finite element software. the

所述的屈曲约束支撑布置的形式包括单斜撑布置、人字型支撑布置、V型支撑布置或偏心支撑布置。 The form of the buckling-constrained bracing arrangement includes a single-bracing arrangement, a herringbone-shaped bracing arrangement, a V-shaped bracing arrangement or an eccentric bracing arrangement. the

所述的屈曲约束支撑布置在结构的加强层中。 Said buckling restraint braces are arranged in the reinforcement layers of the structure. the

所述的屈曲约束支撑包括金属型阻尼器。 The buckling restraint brace includes a metal type damper. the

采用动力弹塑性方法验证屈曲约束支撑布置的正确性。 The correctness of buckling-constrained brace arrangement is verified by dynamic elastoplastic method. the

与现有技术相比，本发明具有以下优点： Compared with prior art, the present invention has the following advantages:

1、本发明针对屈曲约束支撑的耗能与区格剪切变形之间的联系，根据区格的剪切变形大小布置屈曲约束支撑，本发明方法具有工程应用的可操作性，更好的满足工程建筑发展需要； 1. The present invention aims at the connection between the energy consumption of the buckling-constrained support and the shear deformation of the cell, and arranges the buckling-constrained support according to the shear deformation of the cell. The method of the present invention has the operability of engineering application and better satisfies Engineering construction development needs;

2、本发明采用反应谱或弹性时程方法观察结构局部的区格变形，即剪切变形的变形情况，来推测动力分析下屈曲约束支撑的耗能情况，则能较快找到约束支撑布置的最优位置，节省运算时间，提高效率。 2. The present invention uses the response spectrum or elastic time history method to observe the local grid deformation of the structure, that is, the deformation of the shear deformation, to speculate on the energy consumption of the buckling restraint support under dynamic analysis, and then can quickly find the restraint support arrangement The optimal position saves calculation time and improves efficiency. the

附图说明 Description of drawings

图1为屈曲约束支撑布置方式示意图； Figure 1 is a schematic diagram of the arrangement of buckling-constrained supports;

图2为某超高层柱层间变形、弯曲变形与剪切变形关系图； Figure 2 is a diagram of the relationship between interlayer deformation, bending deformation and shear deformation of a super high-rise column;

图3为本发明的流程示意图； Fig. 3 is a schematic flow sheet of the present invention;

图4为BRB区格变形图； Figure 4 is the BRB grid deformation diagram;

图5为本发明实施例1中某10层框架的三维图和立面图； Fig. 5 is the three-dimensional diagram and the elevation view of a certain 10-layer frame in Embodiment 1 of the present invention;

其中，(4a)为三维图，(4b)为立面图； Among them, (4a) is a three-dimensional map, (4b) is an elevation view;

图6为实施例1中带支撑区格层间变形与弯曲变形； Fig. 6 is the interlayer deformation and bending deformation of the belt support zone lattice in embodiment 1;

图7为本发明实例2中某超高层三维图及立面图； Fig. 7 is a certain super high-rise three-dimensional diagram and elevation view in the example 2 of the present invention;

其中，(7a)为三维图，(7b)为立面图； Among them, (7a) is a three-dimensional map, and (7b) is an elevation view;

图8为本发明实施例2中原区格布置情况； Fig. 8 is the situation of grid layout in the Central Plains in Embodiment 2 of the present invention;

图9为本发明实施例2中替换BRB布置情况； Fig. 9 is the arrangement situation of replacing BRB in embodiment 2 of the present invention;

图10为USA0031地震波； Figure 10 is the USA0031 seismic wave;

图11为本发明实施例2中BC跨区格三种变形图； Fig. 11 is three kinds of deformation diagrams of BC cross-region lattice in the embodiment of the present invention 2;

图12为本发明实施例2中布置三道区格BRB时EF42区格的滞回曲线。 Fig. 12 is the hysteresis curve of the EF42 cell when three cell BRBs are arranged in Example 2 of the present invention. the

具体实施方式 Detailed ways

下面结合附图和具体实施例对本发明进行详细说明。本实施例以本发明技术方案为前提进行实施，给出了详细的实施方式和具体的操作过程，但本发明的保护范围不限于下述的实施例。 The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is carried out on the premise of the technical solution of the present invention, and detailed implementation and specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments. the

实施例1 Example 1

如图3所示，一种基于区格剪切变形的屈曲约束支撑布置方法，包括以下步骤： As shown in Figure 3, a buckling-constrained support layout method based on cell shear deformation includes the following steps:

(1)根据反应谱或弹性时程法计算结构的水平地震作用力； (1) Calculate the horizontal seismic force of the structure according to the response spectrum or elastic time history method;

(3)通过有限元软件的计算数据提取可布置屈曲约束支撑的区格各节点的变形，所述的区格为矩形，包括：区格上端两节点的平均水平位移、区格左端两节点的平均竖向位移和区格右端两节点的平均竖向位移； (3) Extract the deformation of each node of the grid that can be arranged with buckling restraint supports through the calculation data of the finite element software. The grid is a rectangle, including: the average horizontal displacement of the two nodes at the upper end of the grid, The average vertical displacement and the average vertical displacement of the two nodes at the right end of the cell;

(4)计算区格的剪切变形； (4) Calculate the shear deformation of the cell;

(5)根据各区格剪切变形的大小布置屈曲约束支撑，最后可采用动力弹塑性方法验证屈曲约束支撑布置的正确性。 (5) According to the size of the shear deformation of each cell, the buckling restraint support is arranged, and finally the correctness of the buckling restraint support arrangement can be verified by using the dynamic elastoplastic method. the

根据区格剪切变形的大小排序，可将区格中原有的钢支撑替代成屈曲约束支撑，可采用单斜撑、人字型或V型支撑布置，也可采用偏心支撑的布置形式，如图1所示。屈曲约束支撑的位置宜布置在结构的加强层，具体位置需根据建筑功能决定。屈曲约束支撑的所需个数需根据结构目标的附加阻尼比以及屈曲约束支撑本身的产品质量决定。 According to the order of the shear deformation of the cells, the original steel supports in the cells can be replaced by buckling-constrained supports, which can be arranged in mono-slant braces, herringbone or V-shaped supports, or in the form of eccentric supports, such as Figure 1 shows. The location of the buckling-restrained brace should be arranged on the reinforced layer of the structure, and the specific location shall be determined according to the building function. The required number of buckling-constrained braces needs to be determined according to the additional damping ratio of the structural target and the product quality of the buckling-constrained braces themselves. the

通常情况下，工程设计中往往采用静力Pushover以及动力弹塑性方法计算消能构件的耗能情况，计算方法虽然较为精确，但耗时较多。本方法运用工程中常用的反应谱或弹性时程方法，观察结构局部的区格变形，即剪切变形的变形情况，来推测动力分析下屈曲约束支撑的耗能情况，则能较快找到约束支撑布置的最优位置，节省运算时间，提高效率。 Usually, static pushover and dynamic elastoplastic methods are often used in engineering design to calculate the energy consumption of energy dissipation components. Although the calculation method is more accurate, it is time-consuming. This method uses the response spectrum or elastic time history method commonly used in engineering to observe the local grid deformation of the structure, that is, the deformation of the shear deformation, to infer the energy consumption of the buckling-constrained support under dynamic analysis, and then find the constraint quickly. The optimal position of support arrangement saves calculation time and improves efficiency. the

结构分析时，振型分解反应谱法考虑般采用多个振型的组合。一般可将质量集中在楼层位置，n个楼层为n个质点，有m个振型。在组合前要分别计算每个振型的水平地震作用及其效应(弯矩、轴力、剪力、位移等)，然后进行内力和位移的振型组合。 In structural analysis, the mode-shape decomposition response spectrum method generally adopts the combination of multiple mode shapes. Generally, the mass can be concentrated on the floor position, n floors are n mass points, and there are m mode shapes. Before the combination, the horizontal seismic action and its effect (bending moment, axial force, shear force, displacement, etc.) of each mode shape should be calculated separately, and then the mode shape combination of internal force and displacement should be carried out. the

根据规范算法，结构j振型i质点的水平地震作用标准值，应按下列公式确定： According to the normative algorithm, the standard value of the horizontal seismic action of the j mode type i particle of the structure should be determined according to the following formula:

F_ji＝α_jγ_jX_jiG_i(i＝1，2，3…n，j＝1，2，3…m) (1) F _ji =α _j γ _j X _ji G _i (i=1, 2, 3...n, j=1, 2, 3...m) (1)

${γ γ}_{j j} = = {Σ Σ}_{i i = = 11}^{n no} {X x}_{ji the ji} {G G}_{i i} / / {Σ Σ}_{i i = = 11}^{n no} {X x}_{ji the ji}^{22} {G G}_{i i} - - - - - - ((22))$

其中，F_ji为j振型i质点的水平地震作用标准值；α_j为相应于j振型自振周期的地震影响系数；X_ji为j振型i质点的水平相对位移；γ_j为j振型的参与系数；G_i为集中于质点i的重力荷载代表值。结构方案确定后上述各参数均为确定值。 Among them, F _ji is the standard value of horizontal seismic action of j mode mode i particle; α _j is the seismic influence coefficient corresponding to j mode mode natural vibration period; X _ji is the horizontal relative displacement of j mode mode i particle; γ _j is j Participation coefficient of mode shape; G _i is the representative value of gravity load concentrated on particle i. After the structural scheme is determined, the above-mentioned parameters are definite values.

水平地震作用效应(弯矩、剪力、轴向力和变形)，当相邻振型的周期比小于0.85时，可按式(3)确定： The horizontal seismic action effect (bending moment, shear force, axial force and deformation), when the period ratio of adjacent mode shapes is less than 0.85, can be determined according to formula (3):

${S S}_{Ek Ek} = = \sqrt{Σ Σ {S S}_{j j}^{22}} - - - - - - ((33))$

式中，S_Ek为水平地震作用标准值的效应；S_j为j振型水平地震作用标准值的效应。 In the formula, S _Ek is the effect of standard value of horizontal seismic action; S _j is the effect of standard value of horizontal seismic action of mode j.

而弹性时程分析应用杜哈默积分求解动力响应，结构分解成N个单自由度体系动力响应，最后叠加即得到整体的结构的响应。而单个多自由度结构体系的运动方程可表示为： The elastic time-history analysis uses the Duhamer integral to solve the dynamic response, and the structure is decomposed into N single-degree-of-freedom system dynamic responses, and finally superimposed to obtain the overall structural response. The motion equation of a single multi-degree-of-freedom structural system can be expressed as:

$[[M m]] {{\overset{\cdot &Center Dot; \cdot &Center Dot;}{v v}}} + + [[C C]] {{\overset{\cdot &Center Dot;}{v v}}} + + [[K K]] {{v v}} = = {{p p ((t t))}} - - - - - - ((44))$

{v}分别为结构的加速度、速度以及位移；{p(t)}为结构的动力响应，结构方案确定后上述各参数均为确定值。 Among them, [M] is the mass matrix of the structure; [C] is the damping matrix of the structure; [K] is the stiffness matrix of the structure;

{v} are the acceleration, velocity and displacement of the structure respectively; {p(t)} is the dynamic response of the structure, and the above parameters are definite values after the structure scheme is determined.

$[[M m]] [[Φ Φ]] {{\overset{\cdot &Center Dot; \cdot \cdot}{Y Y}}} + + [[C C]] [[Φ Φ]] {{\overset{\cdot \cdot}{Y Y}}} + + [[K K]] [[Φ Φ]] {{Y Y}} = = {{p p ((t t))}} - - - - - - ((55))$

其中，

将上式乘于任意一个转置向量

得： Multiply the above formula by any transposed vector

have to:

假定振型对于质量、刚度和阻尼矩阵的正交性，将方程组变为广义坐标下的单自由度体系运动方程，对于第n振型和正则化坐标Y_n有： Assuming that the mode shape is orthogonal to the mass, stiffness and damping matrix, the equations are transformed into a single-degree-of-freedom system motion equation under generalized coordinates. For the nth mode shape and regularized coordinate Y _n :

${M m}_{n no}^{* *} {\overset{\cdot \cdot \cdot \cdot}{Y Y}}_{n no} + + {C C}_{n no}^{* *} {\overset{\cdot \cdot}{Y Y}}_{n no} + + {K K}_{n no}^{* *} {Y Y}_{n no} = = {P P}_{n no}^{* *} ((t t)) - - - - - - ((77))$

其中，为第n振型的广义质量；

为广义阻尼；

为广义刚度；

为广义力，即为水平地震作用力。 in, is the generalized mass of the nth vibration mode;

is the generalized damping;

is the generalized stiffness;

is the generalized force, that is, the horizontal earthquake force.

因此，综上来说，由有限元软件利用反应谱和弹性时程分析方法计算所得出的位移是由各个振型之间的位移通过振型参与系数耦合而成，其与所得到的力之间不成线性关系，因此应用剪切变形的方法不宜直接利用弹性时程分析方法所得出的位移去判断屈曲约束支撑的受力情况，因此需通过力与位移线性相关的等效静力法进行修正，具体方法为，将反应谱或弹性时程波所得出的水平地震作用力应用静力的方式施加在原结构上，所得的力与位移才为线性相关，才能反映出结构应有的特性。 Therefore, in summary, the displacement calculated by the finite element software using the response spectrum and elastic time-history analysis method is formed by coupling the displacement between each mode shape through the mode shape participation coefficient, and the relationship between it and the obtained force Therefore, it is not suitable to directly use the displacement obtained by the elastic time-history analysis method to judge the stress of the buckling-constrained support by using the shear deformation method, so it needs to be corrected by the equivalent static method in which the force and displacement are linearly related. The specific method is to apply the horizontal seismic force obtained by the response spectrum or elastic time-history wave to the original structure in a static manner, so that the obtained force and displacement are linearly correlated, and can reflect the proper characteristics of the structure. the

每个结构区格内的层间变形控制的参数主要有三种：1.层间变形角θ，即层间位移差与层高之比；2.弯曲变形角

即与受力不相关的刚体转动位移；3.剪切变形角γ，即由于区格的剪切变形造成的转角。三者的关系如式(8)所示： There are three main parameters for interstory deformation control in each structural cell: 1. Interstory deformation angle θ, which is the ratio of interstory displacement difference to story height; 2. Bending deformation angle

That is, the rotational displacement of the rigid body that is not related to the force; 3. The shear deformation angle γ, that is, the rotation angle caused by the shear deformation of the cell. The relationship between the three is shown in formula (8):

以某第i层的带BRB的区格为例，如图4所示。则剪切变形可如式(9)所示： Take a cell with a BRB on an i-th layer as an example, as shown in FIG. 4 . Then the shear deformation can be shown as formula (9):

式中，γ_i为第i层区格的剪切变形，u_i、u_i-1分别为第i层和第i-1层区格上端两节点的平均水平位移，h_i为第i层区格的高，v_i为第i层区格左端两节点的平均竖向位移，v_j为第i层区格右端两节点的平均竖向位移，l_i为第i层区格的宽。 In the formula, γ _i is the shear deformation of the i-th layer cell, u _i and u _i-1 are the average horizontal displacements of the upper two nodes of the i-th layer and the i-1th layer cell respectively, h _i is the i-th layer The height of the cell, v _i is the average vertical displacement of the two nodes at the left end of the i-th layer cell, v _j is the average vertical displacement of the two nodes at the right end of the i-th layer cell, l _i is the width of the i-th layer cell.

因此，

为该第i层层间变形，若楼层有刚性楼板假定，其值等于层间位移角，而为区格两端点的竖向变形差与区格长度的比值，即该区格弯曲变形。由此可以得到区格内屈曲约束支撑的轴向变形值Δl为： therefore,

is the interstory deformation of the i-th floor, if the floor has a rigid floor assumption, its value is equal to the interstory displacement angle, and is the ratio of the vertical deformation difference between the two ends of the cell to the length of the cell, that is, the bending deformation of the cell. From this, the axial deformation value Δl of the buckling-constrained support in the cell can be obtained as:

$Δl Δl = = \frac{{l l}_{i i} \cdot &Center Dot; {h h}_{i i}}{\sqrt{{l l}_{i i}^{22} + + {h h}_{i i}^{22}}} {γ γ}_{i i} - - - - - - ((1010))$

因此，若已知整体结构中所有带屈曲约束支撑区格的尺寸，计算出区格剪切变形值，即可知道屈曲约束支撑的轴向变形。因此可以从位移层面上得到结构摆放屈曲约束支撑的最佳位置。 Therefore, if the dimensions of all the cells with buckling-constrained supports in the overall structure are known, and the shear deformation values of the cells are calculated, the axial deformation of the buckling-constrained supports can be known. Therefore, the optimal position of the structure to place the buckling restraint support can be obtained from the displacement level. the

以一10层三跨框架为例，如图5所示。层高为3m，边柱1000mm×1000mm，中柱600mm×600mm，梁250mm×600mm，X向两个立面从下至上依次都布置500×200×10×16截面的钢支撑。总共10×2＝20道支撑。反应谱和弹性时程分析采用X向单方向输入。 Take a 10-story three-span frame as an example, as shown in Figure 5. The storey height is 3m, the side columns are 1000mm×1000mm, the central columns are 600mm×600mm, the beams are 250mm×600mm, and the two facades in the X direction are arranged with steel supports of 500×200×10×16 sections from bottom to top. A total of 10×2=20 supports. Response spectrum and elastic time history analysis use X-direction input. the

应用反应谱方法，将所得出的水平地震作用力通过等效侧向力的方法施加到结构上。图6为带支撑区格的剪切变形和层间变形，可以看出区格的弯曲变形随着楼层的增高而增高，而剪切变形一开始增大，之后一直变小。 Applying the response spectrum method, the obtained horizontal seismic force is applied to the structure by the method of equivalent lateral force. Figure 6 shows the shear deformation and interstory deformation of the grid with support. It can be seen that the bending deformation of the grid increases with the increase of the floor, while the shear deformation increases at the beginning and then decreases all the time. the

其所有区格尺寸相同，则比较其剪切变形位移角即可得到屈曲约束支撑变形的大小排列，将剪切变形按绝对值从大到小的顺序排列，如表1所示。可以看出最大出现在3层，其次是2和4层。 All the cell sizes are the same, and the size arrangement of the buckling-constrained support deformation can be obtained by comparing the shear deformation displacement angles, and the shear deformations are arranged in descending order of absolute value, as shown in Table 1. It can be seen that the largest occurrence is at layer 3, followed by layers 2 and 4. the

表1带支撑区格剪切位移情况 Table 1 Shear displacement of grid with support

则在X向支撑上分别任意布置一道、两道、三道屈曲约束支撑来替代普通钢支撑，屈曲约束支撑屈服力设为500kN，地震波采用Elcentro波，为保证屈曲约束支撑都能屈服，最大地震加速度选用150gal。持时为4s，则耗能最优布置情况如表2所示： One, two, and three buckling-constrained supports are arbitrarily arranged on the X-direction support to replace the ordinary steel support. The yield force of the buckling-constrained support is set to 500kN, and the seismic wave uses Elcentro waves. In order to ensure that the buckling-constrained support can yield, the maximum earthquake Acceleration selects 150gal. If the duration is 4s, the optimal arrangement of energy consumption is shown in Table 2:

表2各种BRB布置耗能情况 Table 2 Energy consumption of various BRB layouts

注：耗能单位为kN·mm Note: The unit of energy consumption is kN mm

从表中可以看出，耗能最大的排序组合基本上符合剪切位移从大到小的顺序，由于反应谱等效静力存在的一些拟合误差，但用剪切变形的大小来判断屈曲约束支撑摆放的最优位置是可行的。 It can be seen from the table that the sorting combination with the largest energy consumption basically conforms to the order of shear displacement from large to small, due to some fitting errors in the equivalent static force of the response spectrum, but the size of the shear deformation is used to judge the buckling The optimal position of constraint support placement is feasible. the

实施例2 Example 2

如图7所示，某超高层建筑，结构高度为300米，共68层，根据研究表明，将加强层中的钢支撑用消能器代替，形成耗能减震层，此种做法不占用建筑的使用空间，并且在中大震下可以发挥耗能屈曲约束支撑，保护结构主体结构安全。有利于模型在11，12，26，27，41，42，57，58设有环带桁架，截面尺寸为600mm×600mm×40mm×60mm，研究的思路是用等刚度的屈曲约束支撑代替桁架，因其各层高度不全相同，因此取尺寸相同的区格12，27，42，58层X向的区格进行研究，以便比较。图8为原区格布置情况；图9为替换BRB布置情况。区格的尺寸为10500mm×3600mm，采用动力弹塑性分析进行耗能研究，结构型钢梁的连梁采用FEMA塑性绞梁，柱、墙采用纤维单元，屈曲约束支撑采用软件自带的BRB单元，结构阻尼比取0.05。由于结构基本对称，因此地震波采用X向输入，并且研究X向上的支撑优化布置。 As shown in Figure 7, a super high-rise building has a structural height of 300 meters and a total of 68 floors. According to research, the steel supports in the reinforced layer are replaced by energy dissipators to form an energy-dissipating and shock-absorbing layer. This method does not occupy The use space of the building, and under moderate and large earthquakes, it can exert energy-dissipating buckling restraint supports to protect the safety of the main structure of the structure. It is beneficial for the model to have ring-belt trusses at 11, 12, 26, 27, 41, 42, 57, and 58, with a cross-sectional size of 600mm×600mm×40mm×60mm. Because the heights of each layer are not all the same, the X-direction cells of the 12th, 27th, 42nd, and 58th layers of the same size cells are used for research for comparison. Figure 8 shows the layout of the original cell; Figure 9 shows the layout of the replaced BRB. The size of the grid is 10500mm×3600mm, and the energy consumption research is carried out by dynamic elastoplastic analysis. The connecting beam of the structural steel beam adopts FEMA plastic twisted beam, the column and wall adopt fiber element, and the buckling restraint support adopts the BRB element that comes with the software. The structural damping ratio is taken as 0.05. Since the structure is basically symmetrical, the seismic wave is input in the X direction, and the optimal arrangement of the supports in the X direction is studied. the

为方便示意，后将区格命名为AB42等，意为AB跨第42层区格。动力时程波采用适合本模型场地类别的天然波USA0031，如图10所示，调整成中震进行分析，加速度时程最大值设为150gal，时程设为6秒。 For the convenience of illustration, the cell is named AB42, etc., which means that AB spans the 42nd layer cell. The dynamic time-history wave adopts the natural wave USA0031 suitable for the site category of this model, as shown in Figure 10, which is adjusted to moderate earthquakes for analysis. The maximum acceleration time history is set to 150gal, and the time history is set to 6 seconds. the

将结构用此条天然波进行弹性时程分析，所得的水平地震作用力反作用于结构中，得出区格之间的剪切变形，例如BC跨，将跨中所有区格的层间变形、弯曲变形和剪切变形取出，如图11所示。可看出加强层层间位移角角最大则为第四加强层区，但剪切变形最大的位置为第一、二加强层区。 Use this natural wave to analyze the elastic time history of the structure, and the obtained horizontal seismic force reacts in the structure to obtain the shear deformation between the cells. For example, in the BC span, the interstory deformation, Bending deformation and shear deformation are taken out, as shown in Figure 11. It can be seen that the interlayer displacement angle of the reinforcement layer is the largest in the fourth reinforcement layer area, but the positions with the largest shear deformation are the first and second reinforcement layer areas. the

将总共20个所要研究的区格，将剪切变形最大的十个区格按照从大到小的顺序排列如下表3所示，将一至六道屈曲约束支撑的结果，通过最优布置进行祝贺的方式计算耗能，整理如表4所示。再利用以往工程经验，将屈曲约束支撑布置在第四区，即层间位移角最大的加强区，以及层间剪力最大的加强区，即第一区，在这两个区内分别布置1至6道屈曲约束支撑时最优的布置进行统计，如表5所示。可以看出，跟表4相比，通过以往的经验还计算出的耗能水平，效果没有此方法得出的耗能高，因此可证明此算法具有一定的优越性。 Arrange a total of 20 cells to be studied, and arrange the ten cells with the largest shear deformation in order from large to small, as shown in Table 3 below, and congratulate the results of one to six buckling restraint supports through the optimal arrangement Energy consumption is calculated according to the method, as shown in Table 4. Then, using previous engineering experience, the buckling-constrained braces are arranged in the fourth area, that is, the reinforced area with the largest interstory displacement angle, and the reinforced area with the largest interstory shear force, that is, the first area. In these two areas, 1 The optimal layout of the six buckling-constrained supports is counted, as shown in Table 5. It can be seen that compared with Table 4, the energy consumption level calculated by previous experience is not as high as that obtained by this method, so it can be proved that this algorithm has certain advantages. the

另外，此算法可以判断EF跨中，四个区由于剪切变形值都很小，因此在此跨中布置屈曲约束支撑耗能较低，如表6所示。原因为EF跨之间的区格由于结构在从1层到42层之间都设置了柱间支撑，支撑约束了区格的变形，造成EF跨间以及高区的AB跨区格剪切变形都较小，从而将屈曲约束支撑布置在这些位置，耗能效果并不理想，滞回曲线不饱满，如图12所示。因此在实际布置中，应尽量避免布置在这些位置。 In addition, this algorithm can judge that in the mid-span of EF, since the shear deformation values in the four areas are very small, the energy consumption of buckling-constrained supports in this mid-span is low, as shown in Table 6. The reason is that the grids between the EF spans are equipped with inter-column supports from the 1st floor to the 42nd floor, and the supports constrain the deformation of the grids, resulting in shear deformation of the grids between the EF spans and the AB spans in the high area. are small, so that the buckling restraint supports are arranged at these positions, the energy dissipation effect is not ideal, and the hysteresis curve is not full, as shown in Figure 12. Therefore, in the actual layout, these positions should be avoided as much as possible. the

表3带支撑区格剪切位移情况 Table 3 The shear displacement of the grid with support

表4各种BRB布置最优耗能情况 Table 4 Optimal energy consumption of various BRB arrangements

注：耗能单位为kN·mm Note: The unit of energy consumption is kN mm

表5根据层间剪力与层间位移角布置最优耗能情况 Table 5 Arrangement of optimal energy consumption according to interstory shear force and interstory displacement angle

注：耗能单位为kN·mm，括号内为与最优布置耗能之间的比值。 Note: The energy consumption unit is kN mm, and the ratio between the energy consumption and the optimal layout is in the brackets. the

表6EF跨耗能情况 Table 6 EF cross energy consumption situation

Claims

1. A buckling restraint support layout method based on cell shear deformation, characterized in that, comprising the following steps:

(1) Calculate the horizontal seismic force of each layer of the structure through the finite element software according to the response spectrum or elastic time history method;

(2) According to the principle of equivalent static force, react the horizontal seismic force obtained in step (1) on the structure;

(3) Extract the deformation of each node of the grid where buckling restraint supports can be arranged in the structure, including: the average horizontal displacement of the two nodes at the upper end of the grid, the average vertical displacement of the two nodes at the left end of the grid, and the average vertical displacement of the two nodes at the right end of the grid. to the displacement;

(4) Calculate the shear deformation of the cell according to the following cell shear deformation formula:

{γ γ}_{i i} = = \frac{{u u}_{i i} - - {u u}_{i i - - 11}}{{h h}_{i i}} - - \frac{{v v}_{i i} - - {v v}_{j j}}{{I I}_{i i}}

In the formula, γ _i is the shear deformation of the i-th layer cell, u _i and u _i-1 are the average horizontal displacements of the upper two nodes of the i-th layer and the i-1th layer cell respectively, h _i is the i-th layer The height of the cell, v _i is the average vertical displacement of the two nodes at the left end of the i-th layer cell, v _j is the average vertical displacement of the two nodes at the right end of the i-th layer cell, l _i is the width of the i-th layer cell;

(5) Arrange buckling-constrained supports according to the shear deformation of each cell.

2. a kind of buckling-constrained bracing arrangement method based on cell shear deformation according to claim 1, is characterized in that, in described step (1), according to the horizontal seismic force of response spectrum calculation structure is specifically:

The structure is set as a combination of m mode shapes and n particle points, and the horizontal seismic action of each mode shape is calculated by the following formula:

F _ji =α _j γ _j X _ji G _i (i=1, 2, 3...n, j=1, 2, 3...m)

{γ γ}_{j j} = = {Σ Σ}_{i i = = 11}^{n no} {X x}_{ji the ji} {G G}_{i i} / / {Σ Σ}_{i i = = 11}^{n no} {X x}_{ji the ji}^{22} {G G}_{i i}

Among them, F _ji is the standard value of horizontal seismic force of j mode mode i particle; α _i is the seismic influence coefficient corresponding to j mode mode natural vibration period; X _ji is the horizontal relative displacement of j mode mode i particle; γ _j is j is the participation coefficient of mode shape; G _i is the representative value of gravity load concentrated on particle i.

3. a kind of buckling-constrained bracing arrangement method based on cell shear deformation according to claim 1, is characterized in that, in described step (1), calculate the horizontal seismic force of structure according to elastic time-history method concrete for:

The motion equation of a single multi-degree-of-freedom structural system is:

[[M m]] {{\overset{\cdot &Center Dot; \cdot &Center Dot;}{v v}}} + + [[C C]] {{\overset{\cdot &Center Dot;}{v v}}} + + [[K K]] {{v v}} = = {{p p ((t t))}}

Among them, [M] is the mass matrix of the structure; [C] is the damping matrix of the structure; [K] is the stiffness matrix of the structure;

Use the solve eigenvalue method to obtain the equation in generalized coordinates:

[[M m]] [[Φ Φ]] {{\overset{\cdot \cdot \cdot &Center Dot;}{Y Y}}} + + [[C C]] [[Φ Φ]] {{\overset{\cdot &Center Dot;}{Y Y}}} + + [[K K]] [[Φ Φ]] {{Y Y}} = = {{p p ((t t))}}

in,

Multiply the above formula by any transposed vector

have to:

Change the equation system into a single-degree-of-freedom system motion equation under generalized coordinates, for the nth vibration mode and regularized coordinate Y _n :

{M m}_{n no}^{* *} {\overset{\cdot &Center Dot; \cdot \cdot}{Y Y}}_{n no} + + {C C}_{n no}^{* *} {\overset{\cdot &Center Dot;}{Y Y}}_{n no} + + {K K}_{n no}^{* *} {Y Y}_{n no} = = {P P}_{n no}^{* *} ((t t))

in, is the generalized mass of the nth vibration mode;

is the generalized damping;

is the generalized stiffness;

is the generalized force, that is, the horizontal earthquake force.

4. A method for arranging buckling-constrained supports based on cell shear deformation according to claim 1, characterized in that, in the step (3), the buckling-constrained supports can be arranged through the calculation data extraction of finite element software The deformation of each node of the grid.

5. A buckling-constrained bracing arrangement method based on cell shear deformation according to claim 1, characterized in that, the forms of the buckling-constrained bracing arrangement include single-bracing arrangement, herringbone-shaped bracing arrangement, V type support arrangement or eccentric support arrangement.

6 . The method for arranging buckling-constrained braces based on cell shear deformation according to claim 1 , wherein the buckling-constrained braces are arranged in the reinforcement layer of the structure. 7 .

7 . The method for arranging buckling-constrained supports based on cell shear deformation according to claim 1 , wherein the buckling-constrained supports include metal dampers. 8 .

8. A buckling-constrained bracing arrangement method based on cell shear deformation according to claim 1, characterized in that the correctness of the buckling-constrained bracing arrangement is verified by a dynamic elastoplastic method.