Optimal placement of steel diagonal braces for upgrading the seismic capacity of existing structures and its comparison with optimal dampers

In this study, the optimal placement of X steel diagonal braces (SDBs) is presented to upgrade the seismic response of a planar building frame. The optimal placement is defined as the optimal size and location of the SDBs in a frame structure. Steady state response of the structure evaluated at the undamped fundamental natural frequency is defined by means of transfer functions that are independent of initial values and the input excitation. The objective functions are chosen as the amplitude of transfer function of the top displacement and the amplitude of transfer function of the base shear force evaluated at the undamped fundamental natural frequency of the structure. In the optimization procedure, the stiffness parameters of the added braces are described as the design variables. Principal optimality criteria are derived using Lagrange Multipliers Procedure. The obtained nonlinear equations are solved with “Steepest Direction Search Algorithm”. Sensitivities of the objective functions are determined analytically. A simplified algorithm for the state of the base shear force as the objective function is also proposed. The response of the structure is examined for both of the objective functions in terms of the transfer function. Seismic rehabilitation with SDBs is compared to the rehabilitation with viscous dampers. Therefore, a total equivalent stiffness parameter is defined so that the transfer function amplitude of the top displacement of building structure with SDB attains the same value with the transfer function amplitude of the top displacement of building structure with optimal dampers based on the top displacement. The time history analysis is performed using El Centro earthquake ground motion records to demonstrate the validity of the proposed design method. The results of the numerical procedure point out that the proposed procedure based on the transfer function of the base shear force and the top displacement can also be beneficial in the rehabilitation of seismic response of the structures.     

Optimal damper placement based on base moment in steel building frames

A new damper optimization method for finding optimal size and location of the added viscous dampers is proposed based on the elastic base moment in planar steel building frames. A Fourier Transform is applied to the equation of the motion and the transfer function in terms of the fundamental natural frequency of the structures is defined. The transfer function amplitude of the elastic base moment evaluated at the first natural circular frequency of the structure is chosen as a new objective function in the minimization problem. The damper coefficients of the added viscous dampers are taken into consideration as design variables in a steel planar building frame. The transfer function amplitude of the elastic base moment is minimized under an active constraint on the sum of the damper coefficients of the added dampers and the passive constraints on the upper and lower bounds of the added dampers. The optimal damper design presented in this paper is compared with other optimal damper methods based on top displacement, top absolute acceleration and base shear. A ten-storey steel planar building frame is chosen to be rehabilitated with the optimal dampers. The optimal damper allocation is obtained for the transfer function amplitude of the elastic base moment then compared with the other damper optimization methods in terms of the transfer function response. The results of the proposed method show that the method can also be beneficial to decrease both the base moment and the interstorey drift ratios in some frequency regions.     

基于全时程迭代的金属阻尼器减震结构地震响应分析方法研究

准确地估算等效阻尼系数和等效附加刚度对于附加金属阻尼器的减震结构的设计具有实用意义。首先基于等效线性化基本理论推导出等效阻尼系数和等效附加刚度计算公式,并引入全时程迭代的思想,形成一种附加金属阻尼器减震结构的地震响应分析方法。继而通过对3层剪切型结构的地震响应分析,探讨了该计算方法迭代过程的收敛性。最后,通过对3层剪切型结构和8层平面框架结构的地震响应分析,考察了该计算方法的计算精度和可靠性。与现有方法相比,提出的等效阻尼系数和等效附加刚度计算公式物理意义明确,同时考虑了金属阻尼器自身参数和结构动力响应对等效线性化参数的影响,采用的全时程迭代方法具有收敛速度快、计算精度高等优点。     

A general solution for performance evaluation of a tall building with multiple damped and undamped outriggers

This paper presents a general solution for performance evaluation of a tall building with multiple damped and undamped outriggers. First, general rotational stiffness (GRS) is proposed to model an outrigger that consists of the stiffness of perimeter columns and an outrigger connection and the damping of dampers in an outrigger. By utilizing the dynamic stiffness method, the GRS can be represented by complex stiffness in an outrigger element. To analyze the dynamic characteristics of a tall building with multiple outriggers, a dynamic transcendental equation is obtained from the combination of the GRS and dynamic stiffness method. The structural responses can be calculated through the Fourier transform based on this equation. Moreover, the GRS can also be blended into a finite element (FE) model to generate an augmented state‐space equation for the analysis of the dynamic characteristics and structural responses. Applications to various outriggers are illustrated. In the numerical analysis, good agreements are found between the GRS and the FE that validates the proposed method, and the performances of various outrigger systems are evaluated parametrically. As the results of a tall building with multiple damped or undamped outriggers, the proposed method is capable of providing an optimally parametric design with respect to the position of outriggers, damping, and core‐to‐column and core‐to‐outrigger stiffness ratio. Copyright © 2015 John Wiley & Sons, Ltd.     

超高层主楼与裙房黏滞阻尼器连接减振分析研究

针对上海世茂国际广场裙房(广场)部分由于刚度与质量分布之间的偏心导致扭转变形突出这一问题,采用CANNY程序对主楼和裙房之间黏滞阻尼器连接减振方法开展一系列非线性时程分析,从裙房变形减振效果、主楼变形影响、阻尼器耗能性能等几个方面综合评定该减振方法的有效性。结果表明,在主楼和裙房(广场)之间采用黏滞阻尼器连接这一方法,不仅能有效地控制因扭转效应过大产生的变形,而且对主楼不会产生不利影响,各阻尼器能在设定的范围正常工作。目前这一减振措施已于2005年成功应用到实际工程中。     

消能摇摆钢框架结构抗震性能的影响因素与设计方法

消能摇摆钢框架结构包含主体钢框架结构、摇摆结构和耗能阻尼器三部分。刚度较大的摇摆结构可以使主体钢框架在地震作用下发生均匀的层间变形,抑制薄弱层产生。布设于摇摆结构底部的阻尼器,能够耗散地震动能量,减小整体结构的地震反应,提高结构的抗震性能。文中对消能摇摆钢框架结构抗震性能的影响因素进行参数分析,并基于我国建筑抗震设计规范的原则提出了抗震设计方法。根据消能摇摆钢框架结构的受力机理,提出简化分析模型,通过弹塑性地震反应分析,验证简化模型的有效性。基于简化分析模型对无量纲参数进行参数分析,根据各参数的影响规律得到无量纲参数的建议范围。结合我国“三阶段”抗震设防要求,提出消能摇摆钢框架结构的设计方法,并结合算例进行验证。研究表明,消能摇摆钢框架结构抗震性能良好,设计合理的摇摆结构与阻尼器能够抑制钢框架的薄弱层、减小结构的地震反应。     

金属阻尼器消能减震体系的等阻尼比设计方法

为合理有效地简化金属阻尼器消能减震结构体系的设计,提出了“等阻尼比”的设计原则,在设计性能水准的地震作用下使所有阻尼器自身的等效阻尼比相等,该原则在实际参数设计时可等价于更便于应用的“等延性系数”原则。该原则是一种概念优化设计原则,目的是使所有阻尼器都能充分发挥其阻尼耗能作用,从而以较小的代价来实现预定的减震控制效果。应用该原则可简化等效附加阻尼比的估算,并将金属阻尼器减震体系的刚度参数与阻尼参数进行解耦,使参数的确定过程更简便。基于“等阻尼比”原则,提出了金属阻尼器消能减震体系的实用设计方法,该方法采用以金属阻尼器延性系数和体系刚度特征参数为设计控制参数,以地震作用下层间位移角的性能需求为设计目标,以等效单自由度体系计算位移响应的求解模型。建立了体系等效阻尼比和等效周期的快速估算式,进而给出了两个控制参数的确定方法及阻尼器布置建议。通过对一个钢筋混凝土框架减震结构的设计和性能验算证实了所提方法的可行性与可靠性。     

半刚性悬挂结构体系减振避震机理及参数优化

提出了一种新型悬挂结构体系--半刚性悬挂结构体系。该结构体系在悬挂楼段与转换层之间设置半刚性层,其间设置减振阻尼装置。通过时域内输入El Centro波、Taft波以及人工波,验证了该体系具有良好的动力响应特性。根据随机振动理论,在复数域内推导了体系的随机振动响应表达式;以主体核筒结构顶点位移和半刚性层的层间位移为目标函数,编制了MATLAB计算程序,对体系中影响结构动力响应的阻尼器的刚度和阻尼、悬挂质量比及半刚性连接的转动刚度等进行参数分析。计算结果表明：该体系能够有效减小地震动力响应,半刚性层的层间位移较大,主体结构顶点位移和悬挂楼层的层间位移较小;对于文中给出的结构算例存在最优参数组合：阻尼器刚度和阻尼分别为1×107/N/m和1×107N•s/m,悬挂质量比取3.0,半刚性连接转动刚度为3.14×104N•m/rad;当半刚性悬挂结构的参数取得最优组合时,主体结构动力响应和半刚性层层间位移均可得到较好的控制,结构的减振避震性能明显提高。     

Iterative step‐by‐step procedure for optimal placement and design of viscoelastic dampers to improve damping ratio

In this study, an iterative step‐by‐step procedure is proposed for optimal placement and design of viscoelastic dampers in order to achieve a target damping ratio based on simple equations and quick estimation. Through the procedure, the dampers are placed one by one in stories with maximum interstory drift at each sequence. Effect of lateral stiffness of added dampers and consequent changes in frequency of the structure as well as changes in damping characteristic of the structure after adding each damper are also considered at each sequence. In order to achieve an economical design, dampers are designed according to the lateral stiffness at each story of the main structure instead of using identical dampers in all stories. During the whole procedure, a time‐history analysis is performed at each sequence. Two numerical examples, including an 8‐story and a 15‐story building, are presented. The results indicate that optimal arrangement of dampers has a considerable influence on reduction of roof displacement up to 25% compared to uniformly distributed arrangement of dampers. In addition, with optimal arrangement, the number of dampers needed to achieve a specific interstory drift is significantly reduced, and the structural damping ratio is improved to a target value, reflecting global optimality of the proposed method.     

Semi‐active control of seismic response of tall buildings with podium structure using ER/MR dampers

A tall building with a large podium structure under earthquake excitation may suffer from a whipping effect due to the sudden change of building lateral stiffness at the top of the podium structure. This paper thus explores the possibility of using electrorheological (ER) dampers or magnetorheological (MR) dampers to connect the podium structure to the tower structure to prevent this whipping effect and to reduce the seismic response of both structures. A set of governing equations of motion for the tower–damper–podium system is first derived, in which the stiffness of the member connecting the ER/MR damper to the structures is taken into consideration. Based on the principle of instantaneous sub‐optimal active control, a semi‐active sub‐optimal displacement control algorithm is then proposed. To demonstrate the effectiveness of semi‐active control of the system under consideration, a 20‐storey tower structure with a 5‐storey podium structure subjected to earthquake excitation is finally selected as a numerical example. The results from the numerical example imply that, as a kind of intelligent control device, ER/MR dampers can significantly mitigate the seismic whipping effect on the tower structure and reduce the seismic responses of both the tower structure and the podium structure. Copyright © 2001 John Wiley & Sons, Ltd.     

往复荷载作用下自复位墙滞回性能研究

将自复位墙简化成刚体,研究了往复荷载作用下自复位墙的滞回性能。通过理论推导,得出往复荷载作用下自复位墙的水平力 转角滞回曲线,给出了各特征点水平力和转角及等效黏滞阻尼系数的表达式,推导了自复位墙保证自复位性能应满足的条件,并提出了自复位墙简化滞回模型。在此基础上,通过参数分析进一步研究了预应力筋及阻尼器设计参数对自复位墙滞回性能的影响。结果表明：自复位墙的转动临界荷载与墙体自重及预应力筋的初始力有关;墙体完全卸载时是否有残余变形与墙体自重、预应力筋初始力及阻尼器屈服力有关;阻尼器屈服力对自复位墙滞回性能影响最大,预应力筋初始力及弹性刚度影响相对较小,阻尼器弹性刚度及布置位置影响最小。     

Optimum viscous dampers for stiffness design of shear buildings

The problem in this paper is to find the optimum sets of story stiffnesses and of damping coefficients of the dampers of an elastic planar shear building with viscous dampers (SBVD model) subject to constraints on maximum interstory drifts due to a set of spectrum-compatible earthquake motions, on upper bounds for each damping coefficient of dampers, and on the sum of damping coefficients of dampers. Two basic characteristics of an ordered set of optimum SBVD designs have been disclosed: (1) greater damping coefficients are distributed within the specified upper bounds among the dampers placed on stories with greater interstory drifts; (2) the effect on stiffness reduction of the optimization of the damping coefficients of dampers from an initial design of an SBVD model with uniform dampers is greater when non-uniform maximum interstory drifts with larger differences between the minimum and maximum values are specified. A design guideline for the effective configuration of viscous dampers for stiffness design of an SBVD model is proposed.     

Seismic design of a tall building with energy dissipation damper for the attenuation of torsional vibration

This paper reports a structural design method of a 100 m tall building using passive energy dissipation dampers, which made the unique architectural form of the building structurally feasible. This tall building will have 21 floors above ground and three basement floors, and will be an educational facility in the city of Osaka. The shape of the building is a unique combination of a rectangular parallelepiped and a quadrangular pyramid with a spacious atrium and a spherical hall inside. The main structure is composed of rigid steel frames, and the outer ones are equipped with dampers. The passive energy dissipation dampers applied to this project are mild steel plates with honeycomb‒shaped openings and capable of large elasto‒plastic deformation. They are expected to perform good energy absorption during earthquakes. As they are installed between vertical spans inside columns, they are consistent with the architectural planning. A structural problem caused by torsional vibrations in the event of an earthquake would be serious if the complex form of the building had not been considered. One of the major objectives of implementing such dampers is the stiffness and strength enhancement that adjusts and reduces the torsional vibrations to the normal level commonly encountered in a standard tall building design process. Time‒history analysis is carried out using a dynamic model to examine the structural performance of the building, which proves that the building is kept intact even under a large earthquake whose peak velocity is 50 cm s⁻¹. © 1998 John Wiley & Sons, Ltd.     

改进遗传算法的结构调谐质量阻尼器风振控制的优化设计

为获得带调谐质量阻尼器(TMD)的建筑结构在随机风荷载作用下基于舒适度及动力可靠度的TMD装置的最优参数,在获得与舒适度相关的结构一阶模态加速度风振响应的解析解的基础上,根据随机过程极值理论,获得受控结构平均最大风振位移的解析解;然后,定义结构在设置TM,和不设置TMD的平均最大风振位移之比作为减振效果指标,并以之为优...     

被动耗能减震结构基于能力谱法的抗震设计方法研究

结合我国抗震设计规范,提出被动耗能减震结构基于能力谱法的抗震设计方法。在该方法中,结构的性能水平用层间位移角限值予以量化,以简化方法计算速度相关型阻尼器的等效阻尼比。该法首先对经过初步设计的建筑结构进行推覆分析以评估其抗震性能,然后依据性能目标要求选择阻尼器的参数和数量,并对设置阻尼器的结构再次进行推覆分析以检验层间位移角是否满足性能目标要求。通过算例,介绍用该方法对钢筋混凝土规则框架进行消能减震设计的设计过程。实例分析表明,提出的被动耗能减震结构基于能力谱法的抗震设计方法是可行的,并且与非线性动力分析得出的平均结果吻合较好。     

High‐performance control of wind‐induced vibration of high‐rise building via innovative high‐hardness rubber damper

High‐hardness viscoelastic rubber dampers are used to upgrade both the habitability environment and the structural safety in high‐rise buildings subjected to wind disturbances. While most of usual viscoelastic dampers have limitation on temperature and frequency dependencies, etc., the proposed high‐hardness viscoelastic rubber dampers possess many unprecedented properties. High hardness, large stiffness, small temperature and frequency dependencies are examples of such properties. Mechanical modelling of the proposed high‐hardness viscoelastic rubber dampers is introduced first, and the wind‐induced response of high‐rise buildings with and without the proposed high‐hardness viscoelastic rubber dampers is computed under dynamic horizontal loads derived from wind tunnel tests. It is shown that high‐rise buildings with the proposed high‐hardness viscoelastic rubber dampers exhibit extremely smaller wind‐induced responses (both along‐wind and cross‐wind responses) than those without such dampers. In particular, a remarkable reduction of acceleration has been achieved owing to sufficient hysteresis even in the small strain range. It is concluded that the proposed high‐hardness viscoelastic rubber dampers can upgrade the habitability environment of building structures dramatically. Copyright © 2008 John Wiley & Sons, Ltd.     

Comparison of distribution methods for viscous damping coefficients to buildings

A simple and convenient method often adopted by practising engineers designing supplemental viscous dampers to a building is to calculate damping coefficients of viscous dampers corresponding to a desired added damping ratio. To facilitate the design, various methods for distributing damping coefficients along the height of the building are compared in the study. In the article, two non-repetitive distribution methods are proposed and compared with some often adopted methods and a repetitive simplified sequential search algorithm. Numerical studies of three planar frames in which two are vertically irregular have indicated that all distribution methods may result in similar seismic responses if added damping ratio are the same. Nevertheless, compromising among a few design factors such as the total added damping coefficient, maximum damper force at one storey, total added damper force, control of storey drift and total computational efforts, one of the two proposed methods distributing the damping coefficient only to ‘efficient storeys’ may provide one of the better choices for the practical design of viscous dampers.     

减震装置的移位原理及其在黏滞阻尼减震结构设计中的应用

现有消能减震结构的设计方法在确定减震关键参数及其空间分配时需要繁琐的迭代试算.为解决此问题,基于减震结构消能减震装置的"移位"原理,提出了减震结构的系统化设计方法,可高效地实现减震结构中阻尼器的参数确定与分配.基于广义单自由度理论提出了减震主自由度的概念,进而发现了减震结构中消能减震装置的"移位"原理,即若要将减震装置...     

Simplified optimal design of MDOF structures with negative stiffness amplifying dampers based on effective damping

This paper presents a study on multi‐degree‐of‐freedom (MDOF) structures equipped with a negative stiffness amplifying damper (NSAD). The NSAD not only preserves the negative stiffness feature of negative stiffness devices (NSDs) but also achieves prominent damping magnification effect, substantially reducing a NSD's requirement for high additional damping, which is used to contain the increased displacements resulting from the reduction in overall stiffness of a system. The dynamic equations of MDOF systems with NSADs are described in state–space representation, and the effective damping and frequencies are parametrically studied. Then, a simple optimization method is proposed. A study of the 20‐storey benchmark building shows that NSADs are the most efficient of supplemental devices in reducing interstorey drifts compared with viscous dampers (VDs) and viscoelastic dampers (VEDs) with the same supplemental damping coefficient. For instance, when compared with that of VEDs, the maximal peak interstorey of NSADs can be further reduced by about 30%. In terms of reducing acceleration responses, NSADs perform much better than VDs and VEDs owing to their negative stiffness feature. Partially arranged, NSADs are best implemented at the storeys that have smaller interstorey drift responses. This is because the negative stiffness preserved by NSADs significantly reduces the interstorey drift of storeys without NSADs.     

高层建筑几种风振控制方式的设计方法

本文提出了高层建筑三种风振控制方式(拉索,挡风板和可调质量阻尼器)的一个改进的设计方法。文中:建立了脉动风的成型滤波器,导得了基于结构层间位移、速度和加速度反应的扩展二次型目标函数的控制规律,实现了高层建筑强度,刚度和舒适度的控制要求,提出了消极控制的具体设计方法,采用了一种简单而实用的自适应控制方法,使主动控制得到实现。