Approximate analysis of natural vibrations of coupled shear walls

The continuous connection technique is used to analyse the free vibrations of a system of coupled shear walls. The dynamic equation is expressed in integro-differential form, and the natural modes and frequencies are determined by the Galerkin method. Theoretical results are compared with published experimental data.     

Free vibrations of coupled shear walls

The continuous connection method of analysis is extended to deal with the free vibrations of a coupled shear wall structure. The natural modes and frequencies are determined from the Galerkin technique, and the dynamic response following an imposed lateral displacement is evaluated. A comparison is made between theoretical predictions of natural frequencies and the results from tests on model structures.     

Dynamic properties of planar,coupled shear walls

The paper is a study of the natural frequencies and mode shapes of planar, coupled shear walls, a common lateral resistive element in building construction. The equations of motion are derived for the general case, and the eigenvalue problem associated with free vibrations of equal, constant shear walls is solved, both with and without the inclusion of the inertia of vertical motion. Explicit solutions are presented for the characteristic equation and the mode shapes and the results are illustrated with figures, including an example calculation based on the shear walls of the Mt. McKinley Building, damaged by the Alaskan earthquake of 1964. The results affirm the necessity of including vertical displacement of the shear walls in the analysis of such systems, and suggest that the inertia of vertical motion also must be considered in the analysis for certain ranges of the parameters.     

Inelastic analysis of R/C coupled shear walls

This paper presents a method of analysis capable of calculating the response of an R/C coupled shear wall structure subjected to strong earthquake motion without major complications existing in the method itself. The relative simplicity is achieved while retaining reasonable reliability in the computed response. The reliability of the computed results are tested against 1- the measured responses of a cantilever column member and a 6-storey coupled shear wall system under static cyclic lateral loads; and 2- the measured responses of two coupled shear wall structures which were subjected to simulated earthquake motions on the University of Illinois Earthquake Simulator. The effects of moment-axial force interaction in the wall members on the computed overall responses of the coupled shear wall structures and on the behaviour of each individual wall are discussed.     

并联剪力墙地震反应分析的样条函数方法

本文根据并联剪力墙振型分解的地震反应控制微分方程，构造三次样条基函数，用样条函数方法对并联剪力墙进行地震反应时程分析，建立样条最小二乘法和样条伽辽金法的时程分析计算格式，本文方法所建立的动力刚度矩阵的半带宽仅为4，计算简便，易于编程，是一个简便，有效的分析方法。     

Boundary frame contribution in coupled and uncoupled steel plate shear walls

The steel plate shear wall (SPSW) system is a robust option for earthquake resistance due to the strength, stiffness, ductility and energy dissipation that it provides. Although thin infill plates are efficient for resisting lateral loads, boundary frames that are proportioned based on capacity design requirements add significant structural weight that appears to be one of the factors limiting the use of the system in practice. An alternate configuration, the SPSW with coupling (SPSW‐WC), was explored recently as an option for increasing architectural flexibility while also improving overall system economy and seismic performance. The SPSW‐WC, which extensively employs flexural boundary frame contribution, has shown promise in analytical, numerical and experimental studies, but recent research on uncoupled SPSWs suggests that boundary frame contribution should not be considered for carrying seismic design shear. As a result, in the present study, boundary frame contribution in SPSWs was explored with detailed three‐dimensional finite element models, which were validated against large‐scale SPSW‐WC tests. Six‐story systems were considered, and the study matrix included single and double uncoupled SPSWs along with coupled SPSWs that had various degrees of coupling. Variations in design methodology were also explored. The modeling framework was employed to conduct static monotonic and cyclic pushover analyses and dynamic response history analysis. These analyses demonstrate the beneficial effect of coupling in SPSWs and illustrate the need to consider boundary frame contribution in design of coupled SPSWs. In addition, sharing design shear between the infill plate and the boundary frame is more generally shown to not be detrimental if this sharing is done in the design stage based on elastic analysis and the resulting boundary frame provides adequate secondary strength and stiffness following infill plate yielding. Copyright © 2017 John Wiley & Sons, Ltd.     

Seismic behavior of coupled steel plate shear walls with simple boundary frame connections

The coupled steel plate shear wall (C-SPSW) configuration has been investigated by researchers as a means of improving the overturning stiffness and architectural flexibility of SPSW structures. While C-SPSWs have been shown to exhibit excellent seismic performance, the fabrication cost associated with the high number of moment-resisting connections used in such systems is a potential detraction to their use as an economical solution. Past research has shown that the hysteresis response of SPSWs with simple frame connections is significantly pinched, and as such, most seismic codes prohibit their use in high seismic areas. However, when used in the C-SPSW configuration, a dual system is formed in which the coupling beams not only improve resistance to overturning but also provide substantial lateral strength and energy dissipation capacity. This paper presents an exploration of the potential to improve the economy of C-SPSWs by using the simple boundary frame connections. First, employing the principles of plastic analysis, an attempt is made to quantify the contribution of the coupling beams to the overall lateral load resistance of the system. Then, to evaluate the seismic performance of such C-SPSW systems and allow for the comparison with that of the C-SPSWs with rigid frames, several prototypes are designed and analyzed using a series of nonlinear response history and pushover analyses. The results indicated that the C-SPSWs with simple boundary frames exhibited satisfactory seismic performance comparable with that of the C-SPSWs with rigid frames under both the 10/50 and 2/50 hazard levels, while allowing for reduced fabrication costs.     

Dynamic soil–structure interaction of coupled shear walls by boundary element method

For a class of civil engineering structures, that can be accurately represented by ‘coupled shear walls’ (CSWs), a discrete model for the analysis of the dynamic interaction with the underlying soil is proposed. The CSWs, with one or more rows of openings, rest on a rigid foundation embedded in the elastic or viscoelastic half-space. A hierarchical finite element model based on an equivalent continuum approach is adopted for the structure. A frequency-domain boundary element method is used to represent the half-space. Finally, the set of equations governing the response of the coupled soil-structure system to harmonic lateral loads acting on the structure is also given. The frequency deviation effect with respect to the fixed-base structure and the effects of radiation and material damping in the soil are presented for different characteristics of the structure and different soil properties.     

基于能力设计原理的双肢剪力墙极限承载力研究

通过对双肢剪力墙的静力推覆分析(Push-over分析)揭示其极限状态的多种形式并提出连梁强度折减系数K,对在理想极限状态下的连梁剪力超强进行折减,得出对应于不同极限状态下连梁对墙肢轴力的改变量,可用于双肢剪力墙结构超强的整体计算,为带转换层的高层建筑转换结构的能力设计提供了理论基础。     

上部再生混凝土双肢剪力墙抗震性能试验研究

进行了3个1∶4缩尺的四层双肢剪力墙模型抗震性能的对比试验,连梁跨高比为1.5。模型1为普通混凝土双肢剪力墙,模型2为全再生混凝土双肢剪力墙,模型3为底部两层普通混凝土、上部两层再生混凝土双肢剪力墙。分析了各双肢剪力墙的承载力、延性、刚度、滞回特性、耗能及破坏特征。结果表明:与普通混凝土双肢剪力墙相比,全再生混凝土双肢剪力墙的抗震性能略差,底部两层普通混凝土、上部两层再生混凝土的双肢剪力墙与普通混凝土双肢剪力墙抗震性能接近。建立了再生混凝土双肢剪力墙的承载力计算模型,计算结果与试验结果吻合较好。     

Free vibrations of open-section shear walls

The coupled torsional-flexural vibration of open-section shear walls, braced by connecting beams at each floor level, is analysed on the basis of Vlasov's theory of thin-walled beams. The basic dynamic equations and boundary conditions are derived from Hamilton's principle, and a numerical solution obtained by the Ritz-Galerkin method. In addition to the primary torsional and flexural inertias, secondary effects due to rotatory and warping inertia forces have also been taken into account. The method is suitable for both rigid and flexible base conditions. A series of numerical examples is presented in which analytical results are compared with available experimental data, and the effects of secondary inertia forces, base flexibility and connecting beams upon the vibration characteristics of such shear walls are examined for two different structural forms.     

Modelling hysteretic behaviour of coupled walls for dynamic analysis

Modelling techniques for dynamic inelastic response analysis of coupled wall structures are investigated. Emphasis is placed on effects of parameters defining the force-displacement hysteresis loop. Specifically, effects of axial force-moment interaction, strength reduction, shear yielding, pinching, reloading and unloading branches of hysteresis loops are considered. Effects of modelling parameters on selected response quantities are investigated and discussed in detail. A 20-storey coupled wall structure was selected for dynamic analysis. Ranges of parameters characterizing force-displacement hysteresis loops were obtained from laboratory tests under slowly reversed static loading. Previously recorded strong motion accelerograms were used as input motions. Results indicate that wall axial forces and beam strength reduction can have significant effects on response envelopes. Moderate variations in unloading and reloading branches of hysteresis loops and pinching appear to have little effect on dynamic response.     

钢筋混凝土剪力墙非线性动力分析模型

介绍了目前常用的钢筋混凝土剪力墙的几种非线性动力分析模型,并对模型涉及的各元件的滞回特性及有关参数的取值作了简要讨论。提供的力学模型和滞回特性可供钢筋混凝土剪力墙、框－墙结构和、钢－混凝土混合结构的非线性动力分析时采用。     

A regularized fiber element model for reinforced concrete shear walls

Reinforced concrete shear walls are used because they provide high lateral stiffness and resistance to extreme seismic loads. However, with the increase in building height, these walls have become slenderer and hence responsible of carrying larger axial and shear loads. Because 2D/3D finite element inelastic models for walls are still complex and computationally demanding, simplified but accurate and efficient fiber element models are necessary to quickly assess the expected seismic performance of these buildings. A classic fiber element model is modified herein to produce objective results under particular loading conditions of the walls, that is, high axial loads, low axial loads, and nearly constant bending moment. To make it more widely applicable, a shear model based on the modified compression field theory was added to this fiber element. Consequently, this paper shows the formulation of the proposed element and its validation with different experimental results of cyclic tests reported in the literature. It was found that in order to get objective responses in the element, the regularization techniques based on fracture energy had to be modified, and nonlinearities because of buckling and fracture of steel bars, concrete crushing, and strain penetration effects were needed to replicate the experimental cyclic behavior. Thus, even under the assumption of plane sections, which makes the element simple and computationally efficient, the proposed element was able to reproduce the experimental data, and therefore, it can be used to estimate the seismic performance of walls in reinforced concrete buildings. Copyright © 2016 John Wiley & Sons, Ltd.     

Static inelastic analysis of RC shear walls

A macro-model of a reinforced concrete (RC) shear wall is developed for static inelastic analysis. The model is composed of RC column elements and RC membrane elements. The column elements are used to model the boundary zone and the membrane elements are used to model the wall panel. Various types of constitutive relationships of concrete could be adopted for the two kinds of elements. To perform analysis, the wall is divided into layers along its height. Two adjacent layers are connected with a rigid beam. There are only three unknown displacement components for each layer. A method called single degree of freedom compensation is adopted to solve the peak value of the capacity curve. The post-peak stage analysis is performed using a forced iteration approach. The macro-model developed in the study and the complete process analysis methodology are verified by the experimental and static inelastic analytical results of four RC shear wall specimens. Supported by: National Natural Science Foundation of China, Grant number 59895410     

Seismic resistance of precast concrete shear walls

The earthquake resistance of stacked precast concrete simple shear walls found typically in Large Panel buildings of the cross-wall type is studied. Physical model testing on a small shaking table facility and analytical techniques are compared. Results of the testing of four models to failure portrayed the non-linear effects of rocking and shear slip that were assumed in several analytical studies but were never before measured experimentally. The physical model studies are supplemented with an independent mathematical analysis using a modified version of the dynamic, non-linear computer code Drain 2–D. Correlation of the analytical and experimental results show that the computer study can be used to predict the overall shear wall response. Results of the small scale model and the mathematical model studies indicate that the simple shear wall behaves in a non-linear manner, even for low magnitudes of base acceleration. Non-linear effects, usually concentrated in only one or two joints, reduced force levels and increased displacements. The four small scale models that were tested withstood high magnitudes of base acceleration without collapse.     

Approximate frequency analysis of shear wall frame structures

The finite strip method is used to determine the natural frequencies of shear wall frame buildings. The structure can be modelled in two different ways. In the first approach both the shear walls and the frames are idealized simply as an assemblage of finite strips of varying thicknesses with given or computed properties, while in the second approach the shear walls are still idealized as a series of finite strips, but the frames are regarded as a number of long columns which are interconnected with each other or with finite strips through the horizontal beams. Numerical results obtained from both models indicate good agreement with finite element solutions. The proposed models can be applied to a wide range of shear wall frame assemblies and are therefore more versatile than most existing models.     

Probabilistic development of shear strength model for reinforced concrete squat walls

In order to reconcile the larger scatter and avoid the biased estimate from deterministic predictions for the shear strength of reinforced concrete (RC) squat structural walls, a probabilistic shear strength model is developed in this paper based on the strut‐and‐tie model and the generalized likelihood uncertainty estimation (GLUE) method. The strut‐and‐tie model is used to derive an appropriate function form for the probabilistic shear strength model, where four unknown model parameters (e.g. k₁, k₂, k₃ and k₄) are defined carefully to guarantee them having a clear physical‐based meaning so that the corresponding prior distribution ranges can be specified reasonably. Then, the GLUE method is adopted to estimate the posterior cumulative distribution of k₁, k₂, k₃ and k₄ with an available experimental database. Furthermore, to demonstrate the stability of the estimated posterior cumulative distribution, the sensitivity of three major aspects in GLUE method is investigated. Finally, based on the estimated cumulative distribution of k₁, k₂, k₃ and k₄, the developed probabilistic shear strength model is simplified as a mean prediction model and a standard deviation prediction model for facilitate using in engineering practice. Therefore, with the developed probabilistic shear strength model, not only can the squat structural walls be designed in confidence, but the accuracy of those deterministic predictions can be evaluated in a probabilistic manner. Copyright © 2016 John Wiley & Sons, Ltd.     

钢筋混凝土剪力墙的变形能力及基于性能的抗震设计

影响钢筋混凝土剪力墙变形能力的主要因素包括高宽比r、轴压比n、边缘约束构件约束程度等.本文首先建立了钢筋混凝土剪力墙端部约束构件的配箍特征值λvw、轴压比n、高宽比r与剪力墙极限位移Δuw之间的关系,即λvw-n-r-Δuw关系,然后通过7个研究机构所进行的钢筋混凝土剪力墙试验对该关系进行了验证.在此关系的基础上,本文提出了钢筋混凝土剪力墙基于性能的抗震设计方法.根据本文方法,设计者可以在已知层间位移角需求θ及确定损伤指标Dw的情况下对剪力墙端部约束构件进行配箍.本文最后通过一算例详细介绍了该方法的设计过程.