Elastic flattening of box beams under bending moment (The Brazier effect of rectangular tubes)

Abstract

In this study, a formula describing on the flattening phenomenon when a bending moment acts on a box beam was derived considering the cross-sectional deformation. Calculation results obtained using the derived formula were then compared with results acquired using the finite element method (FEM). The case of a bending moment acting on a box beam composed of four thin plates that permits cross-sectional deformation along the longitudinal direction was investigated with the following assumptions: the boundaries of these plates is are simply supported, an equally distributed load acts on these plates, and the width along the neutral line of the plates is retained after deformation. Furthermore, on the basis of the coupling of the deflections of adjacent plates and the thin plate theory, the moment of inertia of cross section was obtained as a function of the curvature of the box beam. A formula relating the bending moment to the curvature is was then derived. Calculation results from this derived formula were compared with FEM results modeling only the cross section using generalized plane strain elements. For box beams with a square cross section, the maximum moments and curvatures calculated from the derived formula were within 5% of the FEM results. This indicates that it is important to consider the reduction in the cross section that accompanies the bending of the plates. Regarding general box beams with a rectangular cross section, the influence of the aspect ratio of the cross section was found to be considerably larger in the FEM results than in the derived formula. The reason for this difference may be that plates do not satisfy the abovementioned assumptions regarding the boundary and load conditions of the plates; however, confirming this remains a task for future work.