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 seismic shear of ductile cantilever wall systems in multistorey structures

The distribution of seismic base shear demand among ductile flexural cantilever walls, comprising the lateral load resisting system of a multistorey building, is studied. It is shown that the base shear force demand depends on the sequence of hinge formation at the wall bases, and this in turn depends on the relative wall lengths. Hence, the routine elastic approach in which the shear forces are allocated per relative flexural rigidity or (when some consideration is given to plastic hinge formation) to moment capacity at the wall base, may appreciably underestimate the shear force demand on the walls, particularly the shorter (usually the more flexible) ones. A simple procedure yielding the results of ‘cyclic’ pushover analysis is proposed to predict the peak seismic wall forces for a given total base shear when plastification is confined to the wall base. The effects of plastic hinges developing at higher floors on (1) shear distribution among the walls and (2) the in‐plane floor forces are also considered. Two numerical examples are presented to demonstrate the main points made. Copyright © 2004 John Wiley & Sons, Ltd.     

Frequency analysis of coupled shear wall assemblies

The finite strip procedure is used to predict the free vibration response of both planar and non-planar coupled shear wall assemblies. The solid walls are considered as vertical cantilever strips and a comparison is made between modelling the spandrel beams as discrete beams and as an equivalent continuum with orthotropic plate properties. It is shown that both approaches lead to essentially the same frequencies. The effects of vertical inertial forces and shear deflection are included, and structures considered may have properties that vary with height. The method presented appears to be more versatile than previously published techniques and numerical comparisons with existing methods indicate the predicted results to be accurate.     

Static and seismic limit equilibrium analysis of sliding retaining walls under different surcharge conditions

The static and seismic sliding limit equilibrium condition of retaining walls is investigated, and analytical solutions for the angle of the active slip surface, the critical acceleration coefficient and the coefficient of active earth pressure are provided for different surcharge conditions. In particular, walls retaining a horizontal backfill without surcharge, walls supporting an extended uniform surcharge applied at different distances from the wall and walls supporting a limited uniform surcharge or linear uniform surcharge parallel to the wall are considered in the analysis.The solutions have been derived in the framework of the limit equilibrium approach, considering the effect of the wall through its weight, and accounting for the shear resistance at the base of the wall and the inertia force arising in the wall under seismic conditions.For the wall without surcharge the effect of the vertical component of the seismic acceleration as well as the effects of the inclination of the wall internal face and of the soil–wall friction were also investigated.The angle of the slip plane, the critical seismic acceleration coefficient and the coefficient of active earth pressure are given as functions of dimensionless parameters and the boundary conditions for the applicability of each solution are specified. The influence of soil weight, surcharge conditions and inertia forces on the active earth pressure coefficient is analysed.     

Seismic stability of concrete gravity dams strengthened by rockfill buttressing

Rockfill buttressing resting on the downstream face of masonry or concrete gravity dam is often considered as a strengthening method to improve the stability of existing dam for hydrostatic and seismic loads. Simplified methods for seismic stability analysis of composite concrete-rockfill dams are discussed. Numerical analyses are performed using a nonlinear rockfill model and nonlinear dam-rockfill interface behavior to investigate the effects of backfill on dynamic response of composite dams. A typical 35 m concrete gravity dam, strengthened by rockfill buttressing is considered. The results of analyses confirm that backfill can improve the seismic stability of gravity dams by exerting pressure on the dam in opposition to hydrostatic loads. According to numerical analyses results, the backfill pressures vary during earthquake base excitations and the inertia forces of the backfill are the main source for those variations. It is also shown that significant passive (or active) pressure cannot develop in composite dams with a finite backfill width. A simplified model is also proposed for dynamic analysis of composite dam by replacing the backfill with by a series of vertical cantilever shear beams connected to each other and to the dam by flexible links.     

Seismic shear distribution among interconnected cantilever walls of different lengths

Mid‐rise to high‐rise buildings in seismic areas are often braced by slender reinforced concrete (RC) walls, which are interconnected by RC floor diaphragms. In design, it is typically assumed that the lateral forces are distributed in proportion to the wall's elastic stiffness. Pushover analyses of systems comprising walls of different lengths have, however, shown that large compatibility forces can develop between them, which should be considered in design, but the analyses have also shown that the magnitude of the computed forces is very sensitive to the modelling assumptions. Using the results of a complex shell element model as benchmark, different simple hand‐calculation methods and inelastic beam element models are assessed and improved to yield reliable estimates of the base shear distribution among the individual walls comprising the interconnected wall system. Copyright © 2014 John Wiley & Sons, Ltd.     

Nonlinear numerical assessment of the seismic response of hillside RC buildings

Major damage has been reported in hilly areas after major earthquakes,primarily because of two special conditions:the variation in the seismic ground motion due to the inclined ground surface and the irregularities caused by a stepped base level in the structure.The aim of this study is to evaluate possible differences in the responses of Chilean hillside buildings through numerical linear-elastic and nonlinear analyses.In the first step,a set of response-spectrum analyses were performed on four simplified 2D structures with mean base inclination angles of 0°,15°,30°,and 45°.The structures were designed to comply with Chilean seismic codes and standards,and the primary response parameters were compared.To assess the seismic performance of the buildings,nonlinear static(pushover)and dynamic(time-history)analyses were performed with SeismoStruct software.Pushover analyses were used to compare the nonlinear response at the maximum roof displacement and the damage patterns.Time-history analyses were performed to assess the nonlinear dynamic response of the structures subjected to seismic ground motions modified by topographic effects.To consider the topographic modification,acceleration records were obtained from numerical models of soil,which were calculated using the rock acceleration record of the Mw 8.01985 Chilean earthquake.Minor differences in the structure responses(roof displacements and maximum element forces and moments)were caused by the topographic effects in the seismic input motion,with the highly predominant ones being the differences caused by the step-back configuration at the base of the structures.High concentrations of shear forces in short walls were observed,corresponding to the walls located in the upper zone of the foundation system.The response of the structures with higher angles was observed to be more prone to fragile failures due to the accumulation of shear forces.Even though hillside buildings gain stiffness in the lower stories,resulting in lower design roof displacement,maximum roof displacements for nonlinear time-history analyses remained very close for all the models that were primarily affected by the drifts of the lower stories.Additionally,vertical parasitic accelerations were considered for half the time-history analyses performed here.The vertical component seems to considerably modify the axial load levels in the shear walls on all stories.     

地震荷载作用下兰州地铁隧道结构动力响应

根据《兰州轨道交通1号线一期工程地震安全性评价报告》所给出的100年超越概率63%、10%和2%的场地基岩地震加速度时程,利用有限差分软件进行地下隧道硐室的地震反应分析。在模型底部施加基岩地震动,设置监测点监测衬砌结构的弯矩、轴力及剪力随时间的变化过程,得到100年超越概率63%、10%及2%工况下的隧道结构地震响应。结果表明:隧道衬砌结构最大弯矩位于拱顶处,最大轴力位于拱顶和拱底处,最大剪力位于上侧壁或下侧壁处;隧道结构内力随着超越概率的降低而增大;以超越概率63%的结构最大内力为基准值,在超越概率10%和2%时,弯矩分别增大1.2和1.7倍,轴力分别增大1.3和1.5倍,剪力分别增大1.5和2.9倍,增幅最大。这可能预示着隧道结构在强地震动作用下会发生剪切破坏。     

Analytical models for low-rise buildings with flexible floor diaphragms

The observed behaviour of buildings during earthquakes indicates clearly the importance of the flexibility of floor and roof diaphragms in the response of many structures. This paper presents a new analytical method for the dynamic analysis of some one- and two-storey buildings whose floors may have significant in-plane flexibility. The method begins by treating the floors as bending beams and the walls as shear beams. The equations of motion and the boundary conditions for the floors and the walls are then formulated in one coordinate system and solved exactly to obtain the characteristic equation for the system, which can be solved numerically to obtain the natural frequencies. These, in turn, can be used to determine the mode shapes of the system and the participation factors for earthquake response. Solutions are given for one- and two-storey buildings that resist lateral loads in the transverse direction by two end walls. Perturbation techniques are also applied to simplify further the determination of the fundamental frequency of such single-storey structures. To illustrate the method, a two-storey structure, the Arvin (California) High School Administration Building, damaged in the Kern County earthquake of 1952, has been analysed in its transverse direction. It is seen that the first two modes, dominated by the floor and the roof vibrations, make the largest contributions to the total base shear in the structure.     

Dowel connections securing roof-diaphragms to perimeter walls in historic masonry buildings and in-field testing for capacity assessment

In the seismic retrofit of existing masonry constructions, global interventions are often needed to inhibit the onset of local mechanisms and to engage the whole building box-like structural behaviour. Such interventions are represented by perimeter ties and roof and floor diaphragms. This paper considers the roof diaphragm strengthening solution and investigates the use of stud connections securing the roof thin-folded shell to the perimeter walls. Stud connections serve the dual purpose of collecting and transferring the out-of-plane inertia forces of the masonry walls to the roof diaphragm, as well as transferring the diaphragm reaction forces to the shear walls. Specific detailing of the stud connection and the adoption of an improved lime-mortar overlay on the top of the masonry walls are proposed to improve the connection strength; without such improvements, the connection capacity would be jeopardised by the reduced shear resistance of the masonry wall due to the absence of significant vertical confining action at the roof level. The intervention entirely changes the behaviour of the connection and significantly reduces shear stresses on the masonry wall. The structural behaviour of the connection is analysed and discussed. Emphasis is made on the conceptual design of laboratory and in-field test procedures and testing frames in order to replicate the boundary conditions in real applications. In-situ tests may help during the design of the roof thin-folded shell system and allow for the efficiency assessment of the connections prior to the final intervention, thereby proving the actual feasibility of the retrofit solution.     

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。     

错位转换层位置对高层建筑竖向构件受力性能影响的研究

作为一种新型转换层结构——错位转换层结构,其竖向位置的移动对高层结构在水平地震作用下竖向构件受力性能有何影响目前尚未见文献报道。采用有限元程序对高层带错位转换层结构进行了水平地震作用下的时程反应和反应谱分析．分析了上部转换层和下部转换层相对位置保持不变的情况下．整体改变错位转换层位置对结构地震作用、剪力及竖向构件内力的影响。分析研究发现。错位转换层整体位置的竖向移动对结构整体剪力、上部转换层下承托墙肢内力、上部转换层框支剪力墙内力影响不大．但对落地剪力墙、上部转换层下框支柱和下部转换层梁托柱内力有较大影响。     

The dynamics of interstructural connection to prevent pounding

This paper examines the dynamic implications of connecting closely neighbouring structures for the purpose of eliminating pounding during earthquakes. To prevent this destructive contact the structures are connected by a link and beam system which transmits the connection forces to the floors of the structures. Four specific cases are used as examples of the effects. The coupled system is modelled as a combined mass and stiffness matrix problem which allows the traditional methods for analysis. The mode shapes and natural frequencies for these cases are examined, and it is shown that the general response characteristics can be derived from the coupled system's frequencies and modes. Estimates of the fundamental frequency of the coupled system are derived. Both the harmonic and earthquake response are examined for the four cases. In all circumstances the linkage reduces the relative overlap deflection of the structures at large amplitudes, but it also increases the base shear on the stiffer of the two structures at excitation frequencies below the fundamental frequency. It is shown that bounds on the base shear are derivable from the change in the fundamental frequencies. The dependence of the response characteristics on the stiffness of the coupling beam is also examined.     

A generalized continuum method for dynamic analysis of asymmetric tall buildings

The paper presents a continuum method for dynamic analysis of asymmetric tall buildings with uniform cross-section in which the horizontal stiffness is provided by shear walls and columns of arbitrary shape and layout, coupled by horizontal beams. The equations of motions are formulated in variational terms, including axial strain energy. Numerical solutions, obtained by using finite time differences and infinite polynomials, are presented for the response of a twenty-storey building with six shear walls to an impact load and earthquake accelerations. It is shown that omission of the axial deformations results in a substantially distorted pattern of behaviour, some of its effects being:

• 1 Overestimation of the bending stiffness of the coupled shear walls, with corresponding changes in their stiffness ratios.
• 2 Underestimation of the periods of the principal modes, with a corresponding change in the dynamic response.
• 3 Distortion of the magnitude, form, time of onset and coupling of the maximum displacements.
• 4 Pronounced change in the shear force and moment diagrams for the shear walls, the beams and the building as a whole.

     

Analytical predictions of the seismic response of friction damped timber shear walls

A new concept for the earthquake resistant design of timber shear wall structures is proposed. By providing friction devices in the corners of the framing system of the shear wall, its earthquake resistance and damage control potential can be enhanced considerably. During severe earthquake excitations, the friction devices slip and a large portion of the seismic energy input is dissipated by friction rather than by inelastic deformation of the sheathing-to-framing connectors. A simple numerical model is developed and results of inelastic time-history dynamic analyses show the superior performance of the friction damped timber shear walls compared to conventional shear wall systems. The proposed friction devices act both as safety valves by limiting the inertia forces transmitted to the structure, and as structural dampers by dissipating a significant portion of the seismic energy input. The devices can be used in any configuration of the framing system to accommodate architectural or construction requirements. The damping system may also be conveniently incorporated in existing timber shear wall buildings to upgrade significantly their earthquake resistance.     

Dynamic analysis of a beam resting on an elastic half-space with inertial properties

This work gives a semi-analytical approach for the dynamic analysis of beams and plates resting on an elastic half-space with inertial properties. Such calculations have been associated with significant mathematical challenges, often leading to unrealizable computing processes. Therefore, this paper presents a detailed analysis of Green's function defining surface displacements of such a space in the contact zone with structures, which allows determination of reactive forces and other physical magnitudes. The obtained solutions can be applied to (i) study dynamic interaction between soil and structures, (ii) determine transient wave fields caused by a seismic source, and (iii) assess numerical computations with different numerical methods programs. Natural frequencies, natural shapes, and the dynamic response of a beam due to external harmonic excitation are determined. Eigenfrequencies and Eigenshapes are presented. Validation with a Boussinesq problem illustrates the inertia effect on the results of the dynamic analysis.     

Free vibration of frame shear wall structures on flexible foundations

The finite strip method is used to study the effect of an elastic foundation on the natural frequencies of coupled frame shear wall structures. The solid wall in the structure is divided into several strip elements, the column is treated as a line element and the effect of the connecting beams is dealt with through the compatibility matrices which transfer their structural properties to the adjacent strip or line elements. The comparison functions which satisfy the boundary conditions of being free at the top and being spring supported at the bottom are used for the displacement field in the longitudinal direction. A series of numerical examples is presented to show the accuracy and applicability of the proposed method.     

Vibrations of timoshenko beam-columns on two-parameter elastic foundations

A finite element procedure is developed for analysing the flexural vibrations of a uniform Timoshenko beam-column on a two-parameter elastic foundation. The beam-column is discretized into a number of simple elements with four degrees of freedom each. The governing matrix equation for small-amplitude, free vibrations of the beam-column on the elastic foundation is derived from Hamilton's principle. Several numerical examples are provided to show the effects of axial force, foundation stiffness parameters, partial elastic foundation, shear deformation and rotatory inertia on the natural frequencies of the beam-column.     

Dynamic response of a pair of walls retaining a viscoelastic solid

Making use of a previously reported, simple, approximate method of analysis, a critical evaluation is made of the dynamic pressures and forces induced by horizontal ground shaking on a pair of infinitely long, parallel walls retaining a uniform viscoelastic solid. The walls are presumed to be rigid but elastically constrained against rotation at their base. The effects of both harmonic and earthquake-induced excitations are examined. The accuracy of the method is assessed by comparing its predictions for the special case of fixed-based walls with those obtained by an exact method, and comprehensive numerical data are presented which elucidate the underlying response mechanisms, and the effects and relative importance of the parameters involved. The parameters examined include the characteristics of the ground motion, the ratio of the distance between walls to the height of the contained material, and the flexibility of the rotational wall constraints. In addition to valuable insights into the responses of the systems investigated, the results presented provide a convenient framework for the analysis of more complex systems as well.     

Vibration of cylindrical shells with clamped ends

A general method is outlined for the determination of natural frequencies of cylindrical shells with any boundary conditions when the effects of rotatory inertia and transverse shear deformation are included in the analysis. This is applied to cylindrical shells with both ends clamped. It is shown that the inclusion of these effects tends to have a greater effect upon frequencies of cylindrical shells with clamped ends than it does for corresponding shells with simply supported ends, for which numerical results are available. The authors suggest an empirical relation, which together with the latter results enables rapid estimates to be made of the effects of rotatory inertia and shear deformation on the frequencies of a wide range of cylindrical shells with clamped ends. An assessment of the accuracy of the theory with these effects included is made by comparing frequencies with values from a three-dimensional elasticity theory, but this comparison has to be restricted to cylindrical shells with simply supported ends.