Dynamic analysis of combined system of framed tube and shear walls by Galerkin method using B‐spline functions

Summary In this article, dynamic parameters (natural frequencies and mode shapes) of tall buildings that consist of framed tube and shear walls are obtained using a simple approximate method. The three-dimensional structure is replaced by an equivalent cantilever beam, considering both bending and shear deformations. On the basis of dynamic equilibrium, the governing differential equation of motion is obtained and converted to its corresponding weak form. B-spline functions are then utilized to approximate the weak form and to obtain the final matrix form of the problem. Finally, by applying essential boundary conditions, the natural frequencies and corresponding mode shapes are calculated. To demonstrate the accuracy of the proposed method, numerical examples are solved, and the results are compared with those obtained from SAP2000 computer analysis. The results show that the proposed method is efficient and accurate enough to be used in preliminary design. Copyright © 2014 John Wiley & Sons, Ltd.