An approach to calculate the first mode vibration period for earthquake resistant structural design in case of changing shear and flexural rigidities along height

In our country, which is located on an important earthquake fault line, the long and tiring part of the analysis is seen during calculation under horizontal force. Although these calculations can be concluded quickly and accurately on developing computer programmes, the results are able to be checked using some methods based on acceptance and approximation with engineering approach. The free vibration period is one of the criteria that should be known to ensure that the calculation meets the design criteria of the regulations. Nowadays, the free vibration period is obtained by some computer programmes. In addition to these programs solutions, there are some methods to support that the solution is correct. The differential equation method is a practical and easy method that can be used for this purpose. In this study, it is assumed that the material of structural components is linear elastic, the slabs are infinitely rigid in each plane, there are equal rotations and horizontal displacements at the nodal points of the floor levels, the beam cross-section dimensions are unchanged, and the column and/or shear wall cross-sectional dimensions are changed along the height of the structure. Numerical examples have been solved using this method and the results obtained in MATLAB and SAP2000 computer programs are compared.