An approximate approach for the natural frequencies of tall buildings with trussed-tube system

Abstract

In this paper, a simple mathematical method, based on a continuous approach, is proposed to determine the natural frequencies and mode shapes of trussed-tube systems in tall buildings. Braces are modelled as transverse springs at specific locations along with the height of the structure. Framed-tube system is idealized as a cantilever beam, representing actual characteristics of the structure. Hamilton’s principle is used in deriving structure’s governing equation of motion. The resulting partial differential equation is then solved by applying the separation of variables method. Applying appropriate boundary conditions, natural frequencies and mode shapes are calculated. Finally, the applicability and accuracy of the solution are investigated through comparison with the results obtained from SAP2000 analysis of the full model. The proposed method is found to be simple and efficient and provides reasonably accurate results in preliminary analysis of tall building structures.