Shear deformable doubly- and mono-symmetric composite I-beams

A shear deformable beam element is developed for the coupled flexural and torsional analyses of thin-walled composite I-beams with doubly- and mono-symmetric cross-sections. The present element includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Governing equations and force–displacement relations are derived from the principle of minimum total potential energy. Then the explicit expressions for displacement parameters are derived by applying the power series expansions of displacement components to simultaneous ordinary differential equations. Finally, the element stiffness matrix is determined using the force–displacement relations. In order to verify the accuracy and the superiority of the beam element developed herein, the numerical solutions are presented and compared with the results obtained from the isoparametric beam elements based on the Lagrangian interpolation polynomial, the detailed three-dimensional analysis results using the shell elements of ABAQUS, and the solutions by other researchers.