Refined beam finite element model for thin-walled multi-cell box girders considering distortion and secondary distortional moment deformation effect.

• A new one-dimensional beam-type refined finite element accounting for non-uniform distortional warping and shear deformation effect is formulated; • The extra distortional angle is introduced to incorporate the secondary distortional moment deformation effect; • The distortional angle and primary distortional curvature are selected as the degrees of freedom for the establishment of the beam finite elements; • The proposed beam finite elements are desirable to the predictions of distortional behavior of thin-walled single- or multi-cell box girders with constant or variable depth; • The significance of the inclusion of secondary distortional deformation effect on the distortional performance is verified. In this paper, a novel one-dimensional refined beam finite element model (FEM) accounting for non-uniform distortional warping and secondary distortional moment deformation effect (SDMDE) is formulated for the distortional analysis of thin-walled multi-cell box girders with cantilevered flanges. The extra distortional angle is introduced to incorporate SDMDE, and the validity of which is proved through rigorous theoretical derivation. The in-plane and out-plane deformations at any point around the edge of transverse section built upon the distortional center are unified in the same form and described in detail. The governing differential equations in terms of two generalized displacements, distortional angle χ and primary distortional angle curvature Θ , are derived based on the principle of minimum potential energy (MPE) and solved exactly so as to provide non-polynomial shape functions for the establishment of element stiffness matrix and nodal load vector. A series of multi-cell rectangular hollow section (RHS) girders are analyzed and particular extensions are given to single-cell and multi-cell bridge girders with cantilevered flanges. Comparisons to the results generated from corresponding ones provided by pioneering work or shell FEM analyses not only validate the correctness and reliability of the present beam element formulations but also highlight the significance of the inclusion of SDMDE when the cantilevered flanges are arranged. [ABSTRACT FROM AUTHOR]