Simplified Analysis of Bundled-Tube Structures

A simplified method is presented for the analysis of bundled tube structures subjected to lateral loads. The rigidly-jointed perimeter and interior web frame panels are replaced by equivalent orthotropic plates, whose properties are chosen to represent both the axial and shearing deformation characteristics of the frames. The force and stress distributions in the substitute panels are assumed to be represented with sufficient accuracy by polynomial series in the horizontal coordinates, the coefficients of the series being functions of the height only. The unknown functions are determined from the principle of least work. The influence of stiffer corner columns is included in the analysis. By incorporating simplifying assumptions regarding the form of stress distribution in the frame panels, the structural behaviour can be reduced to the solution of a single second-order linear differential equation, enabling closed-form solutions to be obtained for the standard load cases of a uniformly distributed load, a triangularly distributed load, and a point load at the top. Solutions may then be obtained from design curves.