In this study an approximate method based on the continuum approach and transfer matrix method for static and dynamic analyses of symmetric wall‐frame buildings is presented. The whole structure is idealized as a sandwich beam in this method. Initially the differential equation of this equivalent sandwich beam is written; shape functions for each storey can then be obtained by the solution of differential equations. By using boundary conditions and storey transfer matrices obtained from these shape functions, system modes and periods can be calculated. The reliability of the study is shown using several examples. A computer program has been developed in MATLAB and numerical samples have been solved for demonstration of the reliability of this method. The results of the samples show the agreement between the present method and other methods given in the literature. Copyright © 2007 John Wiley & Sons, Ltd.
In multi-storey buildings, unforeseen foundation rotations can change the building’s behavior. Therefore, these effects should be taken into account in the analysis. In the studies conducted in the literature, the impact of the rotation of the foundation on the building behavior under static loads has been investigated. In this study, an approach is proposed to determine the dynamic behavior of buildings under the effect of foundation rotation, regardless of the type of bearing system. The multi-storey building was modeled as an equivalent flexural-shear beam in the study. In the study, the axial displacements of the columns, which are neglected in the flexural-shear beam model, are also considered, which is different from the literature. The equation of motion representing the dynamic analysis of the equivalent flexural-shear beam was solved with the help of the Differential Transform Method. The period coefficients, effective mass ratio and peak displacement coefficient for five cases were determined and plotted. A code was prepared using Matlab for the analysis with the Differential Transform Method. As a result of the study, the dynamic characteristics obtained depending on the dimensionless building behavior coefficient have been graphed. Using the given graphs, the dynamic characteristics of the buildings under the effect of foundation rotation can be determined quickly and practically. The method presented in this study can be used for Response spectrum analysis of all systems with pure shear beam, pure bending beam and bending-shear beam behavior. In addition, an approach has been proposed to consider [Formula: see text] effects within the scope of the study. The results obtained in the study were interpreted, and the impact of rotation on dynamic characteristics was discussed. At the end of the study, for the convenience of the presented method, two examples, one for wall-frame and the other for frame systems, were solved with the proposed method, and the results were compared with the SAP2000 program.
In this study, an approximate method based on the continuum approach and transfer matrix method for free vibration analysis of multi bay coupled shear walls is presented. In this method the whole structure is idealized as sandwich beam. Initially the differential equation of this equivalent sandwich beam is written then shape function for each storey can be obtained by the solution of differential equations. By using boundary conditions and storey transfer matrices which are obtained by these shape functions, system modes and periods can be calculated. Reliability of the study is shown with a few examples. A computer program has been prepared in MATLAB computer algebra system and numerical samples have been solved for demonstration of the reliability of the method. The results of the samples display the convergence of the present method to the other methods used in literature.
Differential Quadrature Method (DQM) is a powerful method which can be used to solve numerical problems in the analysis of structural and dynamical systems. In this study the governing equation which represents the free vibration of coupled shear walls is solved using the DQM method. A one-dimensional model has been used in this study. At the end of study various examples are presented to verify the accuracy of the method.
SUMMARYIn this study an approximate method based on the continuum approach and transfer matrix method for static and dynamic analyses of multi-bay coupled shear walls is presented. The whole structure is idealized as a sandwich beam in this method. Initially the differential equation of this equivalent sandwich beam is written, then shape functions for each storey can be obtained by the solution of differential equations. By using boundary conditions and storey transfer matrices which are obtained by these shape functions, system modes and periods can be calculated. Reliability of the study is shown with a few examples. A computer program has been developed in MATLAB and numerical samples have been solved for demonstration of the reliability of this method. The results of the samples display the agreement between the present method and the other methods given in the literature.
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