Static, Dynamic and Stability Analysis of Tall Buildings by the Transfer Matrix Method Using Replacement Timoshenko Beam

In this study, an approach is proposed for the analysis of structures that can be represented by the Timoshenko beam model. In this study, the Transfer matrix method, which has been previously developed in the literature for static, dynamic and stability analysis of all types of multi-story buildings, is formulated in this study specifically for the analysis of symmetric buildings consisting of only shear walls or only frames, which can be represented behaviorally as Timoshenko beams. The size of the Transfer matrix, which is 6*6 in the literature by considering all effects in the symmetric state, is obtained as 4*4 due to the characteristics of the systems considered in this study. In the study, firstly, the differential equation system and boundary conditions representing the Timoshenko beam model were obtained in accordance with Hamilton's principle. Then, the element Transfer matrix was obtained by solving the obtained differential equation system. With the presented approach, both static, dynamic and stability analysis can be performed. The most important advantage of the presented method is that the sizes of the matrices used in the analyses are small. With the Transfer matrix method, the size of both the element and the system Transfer matrix is 4*4. At the end of the study, to show the suitability of the presented method with the finite element method, two examples, one consisting of pure walls and the other consisting of pure frames, were solved with the presented approach and the results were evaluated.