Abstract:
To investigate the mechanical behavior of thin-walled box girders with internal diaphragms under torsional loads, a novel box girder beam element (BnCTD) considering the effect of diaphragm stiffness is proposed. Based on the force decomposition method, the torsion of the thin-walled box girder can be divided into rigid torsion and distortion. In the rigid torsion analysis, shearing deformation induced by Saint-Venant torsion and the secondary torsional moment deformation effect are considered, while in the distortion analysis, the effect of secondary distortional moment deformations is incorporated. Using the generalized coordinate method, displacement expressions for the constrained torsion and distortion under torsional loads are unified. The geometric relationship between different types of diaphragms and the main girder deformation is established through deformation compatibility conditions and internal force equilibrium ones. Additionally, a strain analysis method for different diaphragms and the corresponding strain energy expressions are proposed. The governing differential equation for torsion of the thin-walled box girder, accounting for shearing deformations, is derived using the principle of minimum potential energy. The homogeneous solution is employed to construct interpolation functions for the generalized displacements (torsion angle
θ, distortion angle
χ, main torsional rate
η, and main distortional rate
Θ). A new box girder beam element that accounts for the effect of diaphragm stiffness is developed upon the energy variational principle, and the element stiffness matrix and nodal load vector are derived. Numerical examples are provided to validate the computational accuracy and broad applicability of the BnCTD element. The results demonstrate that the BnCTD element can effectively consider the impact of different diaphragm types on the internal forces and deformations of the box girder, accurately reflecting variations in stress distribution, while achieving high computational accuracy with fewer elements compared to solid finite element models, thereby significantly improving computational efficiency. The analysis further reveals that under torsional loads, diaphragms mainly provide stiffness support for distortion deformations. Moreover, as the number of diaphragms increases, the torsional warping stress of the main girder gradually decreases in the vicinity of the diaphragms.