A simple analytic method for computing the natural frequencies and mode shapes of tall buildings

摘要

A simple, yet accurate analytical approach based on energy principles is developed for quick computation of natural frequencies and mode shapes of multistory buildings constructed using framed tube, shear core and double belt trusses systems. The approach here is based on development of a continuum model that would be equivalent, in major motions, to the actual multistory building. Models studied here are cantilever beams with concentrated moments placed at belt truss locations. Governing equation and boundary conditions of the equivalent beam and moment system were derived using the energy method and Hamilton's principle. Separation of variables technique is then applied to model's partial differential equation to obtain the required eigensystem. Robustness and correctness of the proposed method are demonstrated through several numerical examples. Here, 40, 55 and 70-storey tall buildings with combined system of framed tube, shear core and double belt trusses, in which the results obtained from the proposed method, are compared with those obtained from three-dimensional analyses using SAP2000 software. Comparative analyses reveal that the proposed method is simple and efficient; and it provides reasonably accurate results quickly, a feature that is vital during the early stages of building design.