A New Approach for Free Vibration Analysis of Thin‐Walled Box Girder Considering Shear Lag Effect

Abstract

The thin-walled box girder (T-WBG) is widely applied in the long-span bridge structures during the past decades due to its lighter self-weight and better mechanical properties. The shear lag effect (SLE), an essential aspect of T-WBG which governs the stress and the deformation, is rather necessary to be revealed properly. The extraordinary issue of T-WBG analysis nowadays is the SLE impact on its dynamical response to external load. This paper proposes an improved finite element method (FEM) to obtain the realistic vibration characteristics of the T-WBG considering the SLE by theory analysis and formula derivation. Firstly, based on the classical plate and shell theory as well as beam theory, the T-WBG was divided into shell subunit for the roof and beam subunit for web and floor, respectively. Secondly, a 3-order polynomial which is consistent with the experiment results was adopted as the axial-displacement interpolation function of the roof subunit, whose nodal displacements parameters were also taken as the basic. Thirdly, the nodal displacement parameters of the web subunit and floor subunit were deduced by the basic according to the principle of deflection consistency. It is shown through a numerical example that the proposed method is much more economical to achieve reasonable accuracy than traditional FEM analysis software when dealing with the free vibration problem of the T-WBG considering the SLE. Besides, it is also observed that the natural frequency values considering the SLE have a trend of decreasing markedly in general, and the influence of SLE on higher-order frequency is more significant than on the lower one under the boundary condition of cantilever supported, while a contrary effect under the boundary condition of simple supported.

Shear Lag Effects on Pedestrian-Induced Vibration and TMD-Based Vibration Control of Footbridges

“…It should be noted that the dynamic responses of such footbridges are much more complicated and important than the static ones, especially when the static behaviour is pre-known. Luo et al [33] proposed a hybrid finite element method to study the dynamic characteristics of the thin-walled box girder by considering the SLE. It was found that the natural frequencies considering the SLE have a general descending trend.…”

“…The aforementioned studies [35][36][37][38][39] indicate that the natural frequencies of the structures might be reasonably altered due to the SLE. However, the existing studies [33][34][35][36][37][38][39] on the dynamic responses of thin-walled box girder considering the SLE were mainly focused on the natural vibration characteristics or free vibration responses. To the best knowledge of the authors, however, there are very few studies related to SLE focusing on the forced vibrations of thin-walled box girder, not to mention the corresponding vibration control measures.…”