Buckling length assessment with finite element approach

In the design of steel frames, the consideration of stability and buckling is an important issue. It can be done in multiple ways. If the concept of buckling length is used, widely used procedure is to calculate the eigenmodes and corresponding eigenvalues for the frame and by using them define buckling length of the members with the well-known Euler's equation. However, it maybe difficult to tell, which eigenmode should be used for the definition of the buckling length of a specific member. Conservatively, the lowest positive eigenvalue can be used for all members. In this contribution, two methods to define the buckling length of a specific member are considered. The first one uses geometric stiffness matrix locally and the other one uses strain energy measures to identify members taking part in a buckling mode. Compared to simplified approaches presented in literature the approaches based on the finite element discretization have certain advantages. First, the method is applicable to any kind of distributed loading. Secondly, also tapered members can be handled with the technique. Moreover, the out-of-plane buckling behavior and with suitable element the lateral buckling loads can be also be assessed. The applicability and features of the methods are shown in a numerical 3D example. Both methods can be relatively easily implemented into automated frame design procedure. This is essential when optimization of frames is considered.