Equivalent single layer approach for ultimate strength analysis of box girder under bending load

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The objective of this study is to assess the ultimate strength of box girder using equivalent single layer (ESL) approach. Box girders, composed of stiffened panels, are subjected to a four-point bending load for the ultimate strength analysis. The results of ESL were validated using FEM and experiments. Modeling of ESL includes a single plate with the same stiffness as the actual stiffened panel topology, as opposed to traditional FEM modeling and test specimen, where the stiffener is explicitly modeled. For ESL approach, VUGENS subroutine in Abaqus software is used to define the non-linear stiffness properties. Material and geometric non-linearities were considered during simulations. The ESL stiffness matrix was derived from unit cell simulations under six loading conditions. In this case, a unit cell is a periodic structure that represents the entire stiffened panel model. Contact interaction is utilized to simulate the controlled movement of a hollow cylinder contacting a box girder, a precise modeling approach essential for comprehensive analysis. The explicit dynamic analysis is used to allow the large deformation and non-linear material behavior on stiffened panels. The effect of initial imperfection, residual stress, and stiffener slenderness on the ultimate strength was studied. The ultimate strength of a box girder is determined by its maximum bending moment. According to the results, the ESL model achieves results similar to the traditional FEM model and experiment. The accuracy of ESL to FEM in the ultimate strength assessment varies depending on the magnitude of residual stress and initial imperfection applied to the stiffened panel.

Original languageEnglish
Article number116535
JournalOcean Engineering
Publication statusPublished - 15 Jan 2024


  • Box girder
  • Equivalent single layer
  • Finite element method
  • Ultimate strength
  • VUGENS subroutine


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