A simple mathematical model for approximate analysis of tall buildings

Abstract

The focus of this article is to present a new and simple mathematical model that may be used to determine the optimum location of a belt truss reinforcing system on tall buildings such that the displacements due to lateral loadings would generate the least amounts of stress and strain in building’s structural members. The effect of belt truss and shear core on framed tube is modeled as a concentrated moment applied at belt truss location, this moment acts in a direction opposite to rotation created by lateral loads. The axial deformation functions for flange and web of the frames are considered to be cubic and quadratic functions respectively; developing their stress relations and minimizing the total potential energy of the structure with respect to the lateral deflection, rotation of the plane section, and unknown coefficients of shear lag, the mathematical model is developed. The proposed model shows a good understanding of structural behavior; easy to use, yet reasonably accurate and suitable for quick evaluations during the preliminary design stage which requires less time. Numerical examples are given to demonstrate the ease of application and accuracy of the proposed modeled.