A new semi-analytical method is developed for the analysis of interactions between the subgrade and the foundation and the superstructure of the super tall building bundled-tube structure by threedimensional model which is a combination of stiffened-thin-wall tubes on semi-infinite elastic body.
The subgrade is idealized as a semi-infinite elastic body, and the rigidities of the elastic body pertinent to various deformations of the foundation have been expressed as analytical equations
, with which the reactions between the foundation and subgrade can be quantified expediently.
The foundation is taken as a part of the superstructure. In fact, the foundation is the extension of the superstructure toward the underground. The only difference is the size, since in most cases the foundation must be large enough to make the soil stable.
The superstructure and its foundation of the super tall building bundled-tube structure are simplified equivalently and continuously to a combination of stiffened-thin-wall tubes on semiinfinite elastic subgrade. Then discretization is made by some nodal lines, the unknown functions defined on the lines are used as primary unknowns, and interpolating functions are implemented between the lines. So the displacement field of the computing model can be expressed by the unknown functions. After using the principle of minimum potential energy, the governing equations will then be obtained, which is actually a group of ordinary differential equations. Therefore, analysis of a tall building structure will be changed into the solution of the boundary problem of a group of ordinary differential equations that can be solved by the precise and powerful Ordinary Differential Equation Solver—COLSYS
, a kind of computational software.
The interactions between the subgrade and the foundation and the superstructure of a super tall building bundled-tube structure due to static loadings are analyzed by the method based on the model. The numerical results show that the analytical model is reasonable and feasible. Therefore, a practicable method for the global analysis of the super tall building bundled-tube structure is obtained, and some valuable conclusions are acquired through analyzing the computing results as well.