A novel box girder beam element considering equivalent shear deformation freedom of corrugated steel webs

To investigate the influence of diaphragms on the bending forces and deformations of composite box girders with corrugated steel webs (CBG-CSWs), a novel box girder beam element named TBT-CSW, which incorporates the equivalent shear deformation degree of freedom of the CSWs, was proposed. Based on the mechanical characteristics and deformation compatibility of CBG-CSWs, a geometric relationship expression between the equivalent bending rotation and the equivalent shear deformation was established. Addressing the difference in bending shear flow distribution between the side webs and central webs in multi-cell CBG-CSW sections, a formula for determining the equivalent shear deformation coefficient of CSWs was proposed based on the principle of equivalent shear strain energy. The governing differential equations, considering the effects of equivalent bending rotation and equivalent shear deformation, were derived using the principle of minimum potential energy. Their homogeneous solutions were employed to construct interpolation functions for the generalized displacements (vertical deflection, equivalent shear deformation of CSWs, and equivalent bending rotation). Based on the energy variational principle, a two-node, six-degree-of-freedom box girder element (TBT-CSW) was developed, capable of accounting for the influence of end and intermediate diaphragms on the equivalent shear deformation of corrugated steel webs. The element stiffness matrix and equivalent nodal load vector were also derived. Numerical examples validated the computational accuracy and broad applicability of the TBT-CSW beam element. Research results show that, compared to the traditional TBTS beam element, the TBT-CSW beam element achieves up to a 30.8% higher accuracy in stress calculation at critical locations. End diaphragms have a minor influence on the global internal forces and deformation of the girder, but significantly affect the stress distribution in the adjacent flanges. The arrangement of intermediate diaphragms, however, markedly alters the local internal force distribution within the girder cross-section, increases the degree of static indeterminacy, and leads to significant changes in the stress at the top and bottom surfaces of the flanges, while the mid-surface stress remains relatively stable. As the number of intermediate diaphragms increases, the vertical deflection of the girder gradually decreases, but the overall internal force distribution remains essentially unchanged.