Flexure-Torsion Coupled Vibrations for Tall Building Structures Considering the Effects of Vertical Loads

Abstract

A significant characteristic in the development of tall buildings in recent Chinais the complication of the structural systems due to architectural reasons. The triple resisting systems consisting of shear walls, frames, and thin-walled cores with stepped parameters or setbacks are viable structural systems in tall buildings. This chapter presents a simplified analytical method for the analysis of the coupled vibrations for these systems with stepped parameters considering the effects of vertical loads based on several assumptions. These assumptions include that floors are rigid in their plane and perfectly flexible out of plane; the building masses and vertical loads are stepped with height, lumped masses, and concentrated loads may have on the connection and boundary places; and mass centroids of each floor are in a straight line. The systems are considered as generalized composite stepped cross-section cantilever, which consist of shear walls and thin walled cores, and the frames are treated as continuous elastic support that provide two transverse springs, and one torsional spring for the cantilever. The corresponding flexure-torsion coupled vibration differential equations considering the effects of vertical loads are derived. There are two sets of equations for the upper and lower parts of the structures. Solving these differential equations with their boundary conditions and connecting conditions between the upper and lower parts by ODE Solver, the natural frequencies and normal modes can be obtained.