Equivalent Timoshenko linear beam model for the static and dynamic analysis of tower buildings

A continuous Timoshenko linear beam model immersed in a three-dimensional space is introduced to study the static and dynamic behavior of tower buildings. A schematization of the building as a periodic system with rigid floors connected by deformable elements (columns and shear walls) is considered. The rigid floors are endowed with six degrees of freedom (three displacements and three rotations). The constitutive equations of the equivalent beam (coarse model) are identified from a discrete model of the three-dimensional frame (fine model) via a homogenization procedure. A complete linear constitutive law is obtained, with axial force coupled with bending and shear force coupled with torsion. The first aim is to investigate the relative importance of the macro-shear and macro-bending contributions to the deformation of the building. Then, the ability of the coarse model to reproduce the local stress distribution of the fine model is checked. Finally, the representativeness of the coarse model for the detection of the natural frequencies of the fine model is analyzed.