Matrix Force Analysis of Thin-Walled Structures

The Bernoulli's hypothesis of plane cross sections remaining perpendicular to the deformed center line does not adequately approximate the deformation due to the torsion of a long prismatic shell (or thin-walled structure with open cross section). Due to the warping, the pure torsion gives rise to the occurrence of normal stresses in longitudinal direction. In order to simplify the analysis, a specific design model standing in between a long shell and a classical beam is introduced. The matrix force method proves to be a powerful tool for the analysis of such thin-walled members. The flexibility, transformation, and equilibrium matrices are derived. Two different techniques of matrix force method are presented in detail. Through a limiting process (when the torsional rigidity approaches zero) it is shown that the suggested procedure presents the generalization of the method used in the case of solid beam assemblages.