Beam finite element for thin-walled box girders considering shear lag and shear deformation effects

In this paper, a new formulation of beam finite element (B3S) is developed for predicting the performance of shear lag and shear deformation effects in thin-walled single- and multi-cell box girders. The longitudinal warping displacement of each wall of the cross-section is defined as the sum of five deformation modes, i.e., shear lag warping displacement mode, initial shear deformation mode, bending mode, axial mode, and correction mode. Based on the Minimum Potential Energy (MPE) principle with independent descriptions of the displacement fields, the governing differential equations in terms of two generalized displacements, normalized shear lag warping function U(x) and vertical displacement w(x), can be obtained. The proposed beam finite element is refined by selecting closed-form homogeneous solutions of the differential equations as interpolation functions. Besides the nodal Degree Of Freedoms (DOFs) of the conventional beam finite element, the normalized shear lag warping function has been considered as an additional DOF in each node at the element ends to account for the shear lag effect. Moreover, for comparison reasons, the one-dimensional beam finite elements developed based on the Euler-Bernoulli Beam Theory (EBT) and Timoshenko Beam Theory (TBT) have been also introduced. Numerical examples are presented regarding single- or multi-cell box girders with constant or variable depth and the results obtained are compared with those retrieved from the pioneering work or calculated by using solid finite-element models to validate the proposed beam finite element and to demonstrate the wide range of applicability and convenience of using it.