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.     

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.     

Approximate natural frequencies for coupled shear walls

An approximate yet accurate formula is proposed for the natural frequencies of coupled shear walls under continuous medium assumptions. First the deflected shape of the structure is represented as the sum of two components: one due to flexural cantilever action and one due to shear-flexure cantilever action. The natural frequencies of the latter two systems are then combined in Dunkerley's formula to yield the approximate frequency of the structure.     

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.     

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.     

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。     

On the coupled torsional and sway vibrations of a class of shear buildings

This paper is concerned with the free vibrations of a restricted class of multi-storey shear buildings in which inertial coupling exists between the torsional and the two sway vibrations. The restrictions imposed are that (a) the shear centres of all storeys lie on a vertical straight line, (b) the principal axes of shear are in the same directions in all storeys, (c) the centres of mass of all floors lie on another vertical straight line, (d) the radius of gyration about the shear centre of every floor mass is the same and (e) the ratios of the two shear stiffnesses to the torsional stiffness do not vary from storey to storey. In consequence of the last restriction it is proved that the 3n natural frequencies, normal modes and generalized masses, where n is the number of storeys, are expressible very simply in terms of products of the three natural frequencies, normal modes and generalized masses of the single-storey, three-dimensional building formed by removing everything above the first floor, with the n natural frequencies, normal modes and generalized masses of a certain n-storey, two-dimensional shear frame. In the special case of a uniform building, a simple closed form solution, valid for any number of storeys, is given.     

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 non-radial vibrations of the earth

Summary Earthquake shear waves with period around 12.2 min have been lately reported byM. Båth (1958), who suggests that these might be due to torsional vibrations of the whole mantle on some axis through the centre of the earth. An attempt has been made here to put forward a theory which accounts for such vibrations. The general elastokinetic equation for a heterogeneous isotropic medium is solved for a free spherical shell overlying a liquid core, and the solution is investigated for the first two modes. The frequency equation is solved for a shell and the limiting cases of a full sphere and an infinitely thin shell. Application is then made for various approximate mantle models, and periods are found which are in fair agreement with the observed. It is then shown that if the rigidity of the core is taken into consideration a closer agreement with the observed might be attained.

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Zusammenfassung Seismische Transversalwellen mit einer Periode von rund 12.2 min sind neulich vonM. Båth (1958) beobachtet worden, der vermutet, dass sie Torsionsschwingungen des ganzen Erdmantels um eine Achse durch das Erdzentrum sind. Ein Versuch wird hier gemacht eine Theorie für solche Schwingungen zu entwickeln. Die allgemeine elastokinetische Gleichung für ein heterogenes, isotropisches Medium wird für eine freie, sphärische Schale über einem flüssigen Kern gelöst, und die Lösung wird für die zwei ersten Schwingungsformen untersucht. Die Frequenzgleichung wird für eine Schale und für die Grenzfälle einer ganzen Sphäre und einer unendlich dünnen Schale gelöst. Die Lösungen werden dann auf verschiedene, approximative Mantel-Modellen angewendet, und Perioden werden gefunden, die ziemlich gute Übereinstimmung mit der beobachteten Periode zeigen. Es wird danach gezeigt, dass, falls die Righeit des Erdkerns in Betracht gezogen wird, eine noch bessere Übereinstimmung mit der beobachteten Periode erreicht wird.

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This research was supported by Eng.Herbert E. Linden of Beverly Hills, California.     

Torsional and coupled vibrations of embedded footings

An approximate analytical solution is presented for torsional vibrations of footings partially embedded into a semi-infinite medium or a stratum. Simple formulas derived for pure torsional motion make it possible to apply a correction for the effect of embedment to the known solutions of surface footings. The solution completes an approach to the analysis of all modes of footing vibrations, including the coupled modes. The approach to coupled modes is illustrated by the solution of coupled response involving horizontal translation, rocking and torsion. Formulas are presented for stiffness and damping coefficients that can be used in the analysis of embedded footings or structures supported by such footings Field experiments were conducted with concrete footings featuring circular, square and rectangular bases and variable embedment depths. The experimental results were compared with theoretical predictions of pure torsional vibrations.     

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.     

Natural vibrations of shear wall buildings on flexible supports

A shear wall building is considered as an assembly of plane and curvilinear shear walls tied together by floor slabs to act as a composite unit. Based on this conception and the continuous medium approach, the governing dynamic equations and boundary conditions are derived from energy principles, using Vlasov's theory of thin-walled beams. All primary and secondary inertia forces, as well as the influence of elastic foundation flexibility, have been taken into consideration. A numerical solution of the dynamic equations is achieved by employing the Ritz-Galerkin technique, yielding both natural frequencies and mode shapes. The technique is applicable to buildings containing coupled and non-coupled, open section shear walls oriented in plan in any arbitrary manner. The use of the method is illustrated by the example of a complex building with unsymmetric plan, and the analytical natural frequencies of two shear wall building models are compared with those obtained experimentally by other investigators.     

The effect of column mass on shear building vibrations

In the usual assignment of mass for shear building models, the mass of the columns is lumped with the mass of the floor at each floor level. In order to account for frequencies of modes higher than N in an N-storey building, however, additional column masses must be identified. In this note, such additional masses are located at the mid-height of each column, and the characteristics of the shapes and frequencies of the resulting higher mode set are investigated.     

组合剪力墙的抗震研究与发展

剪力墙是高层建筑结构中的核心抗侧力部件,研制抗震性能好的剪力墙,是建筑抗震设计的关键技术之一。组合剪力墙包括不同材料和不同结构形式的组合,可以发挥不同材料和不同结构形式各自的优势,使剪力墙的延性和耗能能力得以提高,从而改善其抗震性能。本文对国内外一些新型组合剪力墙的抗震研究工作进行了归纳总结,并对其发展作一展望。