In this paper, an analytical approach is presented for the determination of the natural frequencies of tall structures with a combined system of the framed tube, shear core and outrigger-belt truss. It has been assumed that the structure has variable stiffness and mass along the height. The framed tube is modeled as a cantilevered beam with variable box cross section and effects of outrigger-belt truss and shear core on the framed tube system are modeled as a concentrated moment applied at outrigger-belt truss locations. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. By applying the boundary conditions, the integration constants are determined. The mode shape function is approximated by a power series. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for the resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the results of the analysis are compared with those obtained from other references.

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