ELASTIC FLEXURAL-TORSIONAL BUCKLING ANALYSIS OF DOUBLY-SYMMETRICAL WEB-TAPERED I-BEAMS

In structural steel design, flexural-torsional buckling (FTB) is an important limit state that must be considered, especially in thin-walled members. A thin-walled beam loaded in its plane of symmetry bends in-plane of loading, however, it may fail because of the flexural-torsional buckling, where the beam suddenly deflects and twists out of the loading plane. This type of failure occurs suddenly in members with a much greater in-plane bending stiffness than torsional or lateral bending stiffness. In this paper, the finite element approach in conjunction with the energy method is employed to predict the flexural-torsional buckling loads of a doubly symmetric and web-tapered I-beam. The total potential energy of the flexural-torsional buckling of a beam element is formulated by adding the strain energy to the potential energy of the external forces. To apply the finite element approach, the displacement function of an element is assumed to be cubic polynomials, the variational principle is then applied to the total potential energy equation. Rearrangement of the energy equation leads to the elastic and geometric stiffness matrices. To apply this methodology to the analysis of plane structures, the rotation transportation matrix is applied to both element elastic and geometric stiffness matrices to convert them from the local to a global coordinate system. Through the assembly process of stiffness matrices of each element, with respect to the global degree of freedom, the equilibrium equation of the whole structure is formed, which leads to a generalized eigenvalue problem. In out-of-plane stability problems, in-plane deflections are normally assumed to be neglected if the ratio of the minor axis flexural and torsional stiffness to the major axis flexural stiffness is small. The effects of prebuckling are also required when accurate solutions are needed. Due to the compatibility between the finite element approach and programming, computer technology is utilized in the analysis to extend the application of the method developed in this paper to much more complex structures, which involves enormous computations. Object-oriented technology in C++ is employed to help organize the programming process. Several examples are presented to compare the results to show the efficiency of developed principles.