Abstract
In a framed-tube tall building, shear wall systems are the most efficient structural systems for increasing the lateral load resistance. A novel and simple mathematical model is developed herein which calculates the natural frequencies of such tall buildings. The analyses are based on a continuous model, in which a tall building structure is replaced by an idealized cantilever beam that embodies all relevant structural characteristics. Governing equations and the corresponding eigen-problem are derived based on the energy method and Hamilton’s principle. Solutions are obtained for three examples; using the separation of variables technique implemented in MATLAB. The results are compared to SAP2000 full model analysis; and they indicate reasonable accuracy. The computed natural frequencies for structures 50, 60 and 70 storey buildings were over-estimate 7, 11 and 14 percent respectively. The computed errors indicate that the proposed method has acceptable accuracy; and can be used during the initial stages of designing of tall buildings; it is fast and low cost computational process.
Highlights
Tall building developments have been rapidly increasing worldwide
While these numerical methods are used for final designing, approximate methods are very effective for primary designing
The main aim of this paper is related to calculate the natural frequency of tall buildings that consist of framed tube and shear walls using simple analytical methods
Summary
Tall building developments have been rapidly increasing worldwide. One of the most critical issues in tall buildings is choosing proper structural form to resist lateral loads. In this article, based on a continuum approach and Hamilton’s principle, a simple mathematical method for calculation of natural frequencies of the combined system of the framed tube and shear wall is presented. Kuang (2001) based on continuum method and D’Alembert’s principle achieved governing differential equations of free vibration of structures with the symmetrical shear wall [24]. To fill in the gap, in this study, a simple analytical method for calculating natural frequencies of the combined system of framed tube and shear walls is presented. The main aim of this paper is related to calculate the natural frequency of tall buildings that consist of framed tube and shear walls using simple analytical methods. The results show the ability of the proposed method in comparison with the other methods
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