Thin‐Walled Multicell Box‐Girder Finite Element

A thin‐walled‐box‐girder finite element that can model extension, flexure, torsion, torsional warping, distortion, distortional warping, and shear lag effects was developed using an extended version of Vlasov's thin‐walled beam theory. The element has two end nodes, but it has besides the six nodal degrees of freedom of a conventional beam element, additional degrees of freedom to account for torsional warping, distortion, distortional warping, and shear lag. The governing differential equation pertaining to each action was used to derive the exact shape functions and the stiffness matrix and nodal load vector of the element. An orthogonalization procedure was employed to uncouple the various distortional and shear lag modes. A numerical example was solved that compared the proposed method with the facet‐shell finite element analysis, with good agreement between the two sets of results.