۱- Introduction

۲- Employed higher-order beam theory (HoBT)

۳- Buckling analysis based on HoBT

۴- Finite element formulation

۵- Numerical examples

۶- Conclusions

References

Abstract

When a higher-order or generalized beam theory is used for the buckling analysis of thin-walled beams, the analysis accuracy critically depends on the number and shapes of the cross-sectional modes associated with warping and distortion. In the study, we propose to use the hierarchically-derived cross-sectional modes consistent with the higher-order beam theory for the analysis of pre-buckling stress and buckling load. The proposed formulation is applicable to any box beams subjected to arbitrary loads and general boundary conditions. We demonstrate the effectiveness of the proposed method by performing buckling analyses for axial, bending, torsional, and general loadings. Length-to-height ratios of the beams are also varied from 1 to 100. If up to fifty cross-sectional and rigid-body modes are employed, the calculated buckling loads are found to match favorably those predicted by the shell finite element analysis. In that a unified buckling analysis under general loads is developed for box beams, the present study is expected to contribute towards new possibilities for the efficient buckling analysis of more general box beam structures involving several joints.

Introduction

In contrast to solid beams, thin-walled beams involve global and local buckling modes when they buckle. Local modes involve localized cross-sectional deformations at several points along the beam axis. Specifically, these modes stem from the buckling of the wall plates of a thin-walled beam. A dominant deformation pattern in local modes is distortion, i.e., a sectional in-plane deformation. Cross-sectional deformations of box beams are developed even in global buckling, and thus the classical Euler or Timoshenko beam theories cannot accurately predict the buckling loads and modes of thin-walled beams. The accuracy by these classical beam theories becomes worse especially when the box beams are not long. In the case when a box beam is shorter than a certain length, a local buckling mode appears as the primary buckling mode because the buckling of wall plates forming a box beam is dominant. Prior to proposing a method to accurately predict the buckling phenomenon of thin-walled box beams with a higher-order beam theory, we will review related extant investigations to validate the need for an alternative approach as discussed in the study. If a thin-walled box beam is viewed as a plate structure, a discrete plate model can be employed as in Refs. [1-3]. In the aforementioned studies, a thin-walled beam is considered as an assembly of thin plates having various boundary conditions. Typically, different boundary conditions are considered based on loading and bonding conditions between the wall plates of a box beam. Because they used a plate theory, the analysis was more complicated than that using a (higher-order) beam theory. The finite strip methods were proposed by Refs. [4-8], in which the distortional deformations of the beam section were taken into account. Methods mainly considering warping were also proposed [9-12]. In these methods, nodal displacements at each corner were used as the beam degrees of freedom (DOFs) to describe warping deformation.