New method of estimating natural frequency of tall pyramidal buildings for tube-in-tube and tube with shear wall systems

The need for adequate and appropriate living and working spaces and population density and the increasing cost of land and use of high-rise buildings requires growing research on these structures. The tube system is one of the most suitable structural systems for high-rise buildings. The purpose of this study was to obtain one of the most important dynamic properties, namely the natural frequency (ω) for a number of tall buildings with a pyramidal tube system. A tube-in-tube approximate method for analyzing and calculating the natural frequency of a combined pyramidal tube system with shear wall pyramid is presented. The size of the pyramid angle of the tube frame varies with the length (height) of the structure. The proposed method enables us to calculate the natural frequency of vertical and curved tall buildings with the help of computer programming. The models were analyzed using finite element form and mathematical analytical method. The results show that the investigated method correctly calculates the natural frequency and is in good agreement with the finite element results and has better compatibility with pyramidal angle structures with higher altitude, and the resulting computational error is much lower. The results of the proposed mathematical model provide an easy-to-use method for understanding the dynamic properties of structures and the effects of angle-frequency variations. Furthermore, this analytical method has the least error for tube systems with tube-in-tube and the highest error for shear wall pyramidal systems.