A harmonic approach to the non-uniform torsion of box girder with edge cantilevers by fully considering the secondary torsional moment deformation effect

Abstract

The restrained torsion analysis of open and purely closed cross-section thin-walled beams has been well addressed by applying the classical Vlasov and Benscoter non-uniform torsion theory, respectively. However, the warping torsion of the thin-walled box girder with wide overhanging slabs has to date received relatively less attention, although it exhibits notable and complicated shear lag phenomena. In this paper, a semi-analytical approach based on the harmonic analysis is presented to consistently take into account the secondary torsional moment deformation effect (STMDE) in edge cantilevers and closed cell of the box girder. The non-uniform warping and the associated strain field are reasonably determined by fulfilling the following requirements as (i) the longitudinal local equilibrium, (ii) the traction-free boundary conditions, and (iii) the shear flow continuity at joints connecting wall branches of the cross section. The advantage of the proposed method lies in that regardless of the applied loading and boundary conditions each harmonic term of the state variables can be manually determined to save a large amount of computing resources and time. Convergence study shows that the resulted Fourier series of state variables can be made converged if only first few terms are retained. Some benchmark problems, which primarily focus on thin-walled box girders having single- and multi-cellular cross sectional shapes under typical constraints and applied torques, are solved to demonstrate the reliability of the harmonic approach for non-uniform torsion of the box girder with edge cantilevers. It is shown by comparing with the results of shell finite element analysis that the semi-analytical solutions by the harmonic approach generally have better accuracy than the numerical results using 3D beam element with seven nodal degrees of freedom and analytical results by classical thin-tube theory (TTT).