Elastic flexural and lateral torsional buckling analysis of frames using finite elements

A stiffness matrix has been developed for the elements of framed systems which are under constant axial force and moment. A global stiffness matrix can be obtained by using this stiffness matrix and the classical finite element techniques. The constant axial force and moment which will be used in the element stiffness matrix are obtained from a preliminary solution. These internal forces are then increased proportionally and new element stiffness matrices are calculated. Due to the increasing external loads excessive displacements, rotations and finally change of directions of these displacements and rotations occur. The external load conditions for this phase, give us the critical buckling load of the system. Within this framework an application is presented for the critical flexural and lateral torsional buckling loads of second-degree parabolic arches. This buckling loads of arches are compared with the specifications of the Eurocode 3, Part 2, Annex D, design of steel structures ENV 1993-1-1 and given some interpretations about the linear and non-linear analysis.