Application of the transfer matrix method for static and dynamic analysis of coupled shear wall buildings using a generalized continuous model

To date, there is no generalized numerical method that efficiently and simply solves both the static and dynamic analysis of buildings while adequately considering local shear deformation, which has been scarcely studied in the literature but is crucial in reducing errors associated with classical continuum models. Therefore, this study proposes a practical solution method, presenting a numerical approach based on the combination of the continuum method and the transfer matrix method to solve the static and dynamic analysis of buildings with both uniform and variable properties. The continuum model used is a generalized sandwich beam derived from the classical sandwich beam, coupled in series with a pure shear beam, and incorporates an additional rotational kinematic field to account for local shear deformation of the walls. The differential equation derived from the variational formulation is of the sixth order with constant coefficients. It is shown that the common equations found in the literature are special cases of the proposed continuum model. The inclusion of local shear deformation, the analytical derivation of transfer matrices, and the proposed solution methods for static and dynamic analysis are the main novelties of this research. Furthermore, it is shown that the relationship between the analytical coefficients of the transfer matrix only needs to calculate eight of its thirty-six coefficients. The results of the numerical applications demonstrate that the proposed method outperforms existing methods in the literature and improves structural safety. This indicates that its practical application by practicing engineers is appropriate for all possible types of behavior.