Coupled Shear Walls Research Articles

Considérations sismiques des murs de refend ductiles avec ouvertures

This paper describes the results of an analytical study of linear and nonlinear behaviour of ductile coupled shear walls with openings, under seismic loading. The walls in a typical building were studied and assumed to be ductile. They were designed, calculated, and detailed in compliance with the National Building Code of Canada 1990 (NBC) and the Canadian concrete code CAN3-A23.3-M84. The results of the elastic analysis show, as expected, that the concentrated force at the top specified by the NBC does not accurately simulate upper-mode effects, at least for this type of structure. A spectral analysis covering the five first modes, as described in the NBC, seems more suitable for coupled shear walls with openings with a period of more than 1.5 s approximately. The results of the nonlinear analysis show that application of the overstrength factor to the wall as recommended by CAN3-A23.3 greatly improves its behaviour and prevents tensile failure of the wall, although it does not always guarantee the desired sequence of plastification in the case of severe earthquakes. Application of the factor does, nonetheless, limit plastification of the wall to lower levels and keeps rotational ductility in beams and walls to a reasonable level. Key words: coupled shear walls, openings, reinforced concrete, ductility, overstrength factor, earthquake, building codes.[Journal translation]

Formulation of transition elements for the analysis of coupled wall structures

The formulations of transition elements are presented for the numerical modeling of the transition regions of coupled wall structures. These transition elements solve the incompatibility related to different degrees of freedom between beam and wall element in finite element analysis for transition regions. The stiffness matrix of the transition element with the nodal types of plane stress element is derived from the exact stiffness matrix of the Hermitian beam element, based on the kinematic and force constraints between beam and wall element. That is, a transition element can be described as the quasibeam element which is replaced by an equivalent plane stress element, keeping equal the basic behavior of the beam element. Similarly, the stiffness matrices of transition zone elements which are directly connected to transition elements in transition regions can be derived from the equivalent constraint conditions. These transition elements are classified as three types according to the location and number of the nodes of each transition element. Also, a coupled shear wall model as the numerical example is presented in order to illustrate the characteristics and efficiencies of these transition elements.

Assessing the damping properties of coupled wall structural systems

AbstractIn this paper, the global response of the coupled shear wall assemblies will be studied at two different limit states. The primary objective of this investigation is to establish upper and lower bounds on the level of the damping that will be induced in the system due to yield excursions and energy dissipation of the structural members.

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

AbstractFor 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.

CYCLIC BEHAVIOUR OF CONNECTING BEAMS IN REINFORCED CONCRETE SLIT SHEAR WALLS.

The connecting beams in slit shear walls are generally much shorter than those in ordinary coupled shear walls and may therefore behave quite differently. In order to investigate the shear behaviour of such short connecting beams, two series of shear tests, one on monotonic behaviour and the other on cyclic behaviour, were carried out. Altogether, 24 specimens were tested. The results of the monotonic shear tests have been reported in an earlier paper. This paper presents some additional information on the ductility of the beams as revealed by the monotonic shear tests, and the results of the cyclic shear tests. From the cyclic shear tests, the cracking and failure characteristics, reinforcement stress distribution, stiffness and strength degradations, ductility and damping capacity of the connecting beams are studied. The results are useful for evaluating the seismic performance of reinforced concrete slit shear walls. (A)

A Knowledge‐Based Design Tool to Assist in Preliminary Seismic Design

Abstract: Many structural engineers only rarely need to be concerned with seismic design. It is a relatively difficult process that can involve advanced analytical techniques and concepts such as ductility which are not normally encountered except in this context. A prototype Seismic Design Assistant (SDA) has been developed specifically to assist, advise, and guide design engineers engaged in the preliminary seismic design of reinforced concrete buildings (with coupled shear walls). Available seismic design methods are reviewed, and a particular method is outlined that incorporates sophisticated analytical procedures to enable ductility requirements to be satisfied. This method provides the basis of the knowledge base employed within the SDA. The prototype design tool has been implemented on a Sun workstation using Quintec‐Prolog, Quintec‐Flex, and Fortran 77. Details are presented of the architecture of the SDA, of the knowledge representation that has been employed, and of the integration of traditional procedural software within a knowledge‐based approach.

An equivalent continuum approach for coupled shear walls

This paper presents a continuum approach for the analysis of coupled shear walls. The rows of openings are modelled as homogeneous layers with elastic moduli defined through an energy balance condition, and the local deformations at the junctions between wall and lintel beams are taken into account. Hence, an equivalent continuous beam is obtained which is analysed by a displacement-based approach. The proposed model allows for the evaluation of the remarkable role played by the shear strains on the wall deformation and for the analysis of shear walls with many rows of openings without any additional computational effort. Various numerical examples are developed and the results obtained turn out to be more accurate than those given by classical methods.

Finite Element Model for Seismic RC Coupled Walls Having Slender Coupling Beams

A finite element model capable of tracing the nonlinear response of coupled shear walls to earthquake motions is proposed. The walls are idealized as an assembly of quadrilateral elements with three degrees of freedom, two translational and one-rotational, at each corner, and nonlinearities, such as cracking, crushing of concrete, and yielding of steel, are included in the model. The coupling beams are idealized as line elements, and the nonlinearities are confined to element ends through inelastic experimentally based moment-rotation relationships. Allowance has been made for stiffness degradation and bond slippage. The rotational degree of freedom to the plane stress element makes the compatibility of rotations at the coupling-beam-wall interface possible, the evaluation of coupling beams rotation straightforward and the mathematical model elegant. The model was applied to trace the response of two coupled shear walls tested elsewhere and the results achieved were in good agreements with experimental results.

Free vibrations of coupled walls by transfer matrices and finite element modelling of joints

A transfer matrix analysis of coupled shear walls is combined with finite element models for joint flexibility. Every joint is considered as a single rectangular element with a displacement model that is consistent with the kinematic constraints imposed by the adjacent beams. The derivation of the element stiffness is based on plane stress elasticity. The overall problem can be solved for the static and free vibrational response of coupled shear walls on flexible foundations. Assessment of its performance and comparison with simpler models for joint deformation is accomplished through the determination of natural frequencies and modes of vibration for a range of previously tested or analysed specimens. Having established the accuracy of the proposed high-order finite element joint model, the effect of joint flexibility on higher frequencies and modes of vibration is then assessed.

Analogies with shear effect in the structural analysis

The characteristics and/or parameters of improved equivalent beams for several structural members are given. By means of analogy with the shear effect and as part of the theory of equivalences, closed from expressions, tables and diagrams for non-prismatic beams, bridge decks, piles and coupled shear walls are presented. The results obtained for dynamic behaviour of a coupled shear wall, built in or founded on piles, are also presented.

Nonlinear dynamic analysis of damped structures using the transfer matrix technique

A conceptually simple and computationally efficient numerical model, based on the transfer matrix formulation is proposed for the prediction of nonlinear dynamic responses of a coupled shear wall structure incorporating damping. With the transfer matrix method, damping is introduced into the formulation through the field and station transfer matrices using the constitutive law. The effect of damping on the responses of a vibrating beam is incorporated into the station transfer matrix while those of the walls are incorporated into the field transfer matrix. The nonlinear behaviour is approximated as a sequence of successively changing linear systems over a short time interval. The transfer matrix formulation adopts established models of material behaviour in dealing with the inelastic beam element deformation and load reversals. The dynamic solution assumes constant properties within short time increments, and relies on the kinematic relationships of the Wilson θ method.

Estimating Seismic Base Shears of Tall Wall‐Frame Buildings

An approximate method for determining the seismic base shear of high‐rise building structures on the basis of the preliminary design information is presented. The method is based on the generalized representation of the family of shear‐flexure cantilevers by the coupled‐wall theory, and is applicable to nontwisting structures consisting of any combination of walls and frames that are uniform with height. Such structures include coupled shear walls, walls connected by beams to columns, and wall‐frame structures. The static and dynamic behavior as well as the geometric and material properties of shear‐flexure cantilevers are fully described in terms of two nondimensional characteristic parameters. A decoupled eigenvalue approach is used to evaluate the base shear coefficients corresponding to the first two periods of free vibration. The derivation of the method as well as a comparison of its results with those obtained by earlier approximate methods and by a discrete finite element dynamic analysis are give...

Stiffened, Coupled Shear Walls

Based on the continuum approach, a general analysis is presented for a pair of laterally loaded, coupled shear walls, supported on either rigid or flexible foundations, with one or two stiffening beams at arbitrary positions on the height. Closed solutions are given for the three common load cases; a uniformly distributed load, a triangularly distributed load, and a point load at the top, simulating both wind and earthquake actions. Numerical examples show that structural performance can be improved considerably by the addition of two stiffening beams, the greatest benefits being achieved when the beams are located at roughly one‐third and two‐thirds of the height, when the structure is supported on rigid foundations. The corresponding optimum position for a single stiffening beam is between 0.4 and 0.5 of the height of the structure. The optimum beam positions occur at lower levels if the structure is supported on flexible foundations.

Nonlinear Dynamics of Coupled Shear Walls Using Transfer Matrices

An application of the transfer‐matrix technique to the nonlinear dynamic analysis of coupled shear walls is presented. Through the proposed method, the problem is reduced to a tractable size without the imposition of severe uniformity conditions on the structure. The dynamic response is determined by a step‐by‐step numerical approach in which the properties of the structural elements are updated according to the current state of deformation and yield. The transfer‐matrix formulation adopts established models of material behavior in dealing with inelastic beam deformation and load reversals. The dynamic solution assumes constant properties within short time increments, and relies on the kinematic relationships of the Wilson‐θ method. Damping has also been taken into account through a simple viscous model. The effectiveness and accuracy of the method, as well as its potential for further development, are assessed by comparing its predictions with measured displacements of model structures subjected to vario...

RC‐Coupled Shear Wall Structures. I: Analysis of Coupling Beams

The structural behavior of reinforced concrete coupled shear wall structures is greatly influenced by the behavior of their coupling beams. Flexure and shear are the two main modes of failure of reinforced concrete coupling beams. The behavior of coupling beams in the shear mode of failure, known as diagonal splitting, is represented by a mathematical model, and a method for the ultimate strength analysis is presented. The proposed method of analysis for RC coupling beams is used to verify the results of nine beams tested by a previous investigator.

RC Coupled Shear Wall Structures. II: Ultimate Strength Calculations

Three modes of failure of reinforced concrete coupled shear wall structures, observed in microconcrete models of 15‐story structures, are described. A method is proposed to predict the mode of failure and the ultimate strength of coupled shear wall structures. The method is based on the evaluation of the strengths of the coupling beams and the walls at failure. Two lateral load cases have been considered: a point load at the top and a four‐point equivalent triangular distribution. The proposed analysis and the test results are compared.

Dynamic behavior of coupled shear wall through analytical models

The dynamic behavior of a symmetrical, non-twisting coupled shear wall under lateral dynamic loads is presented. The analysis is made on idealized models of the actual structure. The modelling technique is based on two methods: (a) the wide column frame method and (b) the flexible beam frame method. The analysis is based on the plane frame technique, in which all of the components of the real structure are idealized as members which have continuous distribution of stiffness and mass along their length. Thus, the model has an infinite number of degrees of freedom. The advantages of these models are their simplicity and ease of computeration using a small computer. The technique of modelling is demonstrated through a numerical example.

Analysis of coupled shear walls using high order finite elements

In this work finite element solutions for coupled shear walls and other approximate methods are compared. Ten different finite elements, which belong to four different families of elements, are used to solve three examples. For each example several meshes are used for the analysis. It is concluded that the use of high order Lagrange type elements yields the best results, with instant convergence, for the simplest and coarsest mesh possible for the representation of the shear wall geometry and loading.

Stiffened Coupled Shear Walls

A method of analysis (based on the continuum approach) is derived for investigating the beneficial effect of a stiffening beam, which may be positioned somewhere along the structural height, on laterally loaded coupled shear walls. It is shown that the incorporation of a stiffening beam into coupled shear walls will reduce considerably the maximum shear force in the lintel beams and the base moment in the walls and the top drift of the structure. It was found that stiffening beam should be positioned at a level about 0.4 of the structural height for achieving the greatest reduction in the maximum shear force in the lintel beams and about 0.5 of the height for achieving the minimum top deflection, depending on the flexural stiffness of the lintel beams.

Behaviour of nonlinear coupled shear walls with flexible bases

This paper examines the importance of base flexibility on the nonlinear behaviour of coupled shear walls subjected to pseudo-static lateral loading. The classic continuum method is adopted, with the base flexibility modelled by effective rotational and vertical elastic stiffnesses, Kθ and Kv, respectively. Since the magnitudes of these stiffnesses depend on the properties of the supporting soil and also on the characteristics of the foundation itself, different soils as well as the type of foundation are considered. The latter consists of separate footings under each wall as well as a single combined foundation under the coupled walls. In general, the results show that base flexibility becomes especially important for the overall lateral stiffness at all load levels, whereas internal stresses are affected in only the lower portion of the structure for service loading. Key words: shear walls, coupled, nonlinear, continuum method, flexible bases, separate footings, combined foundation.