Buckling length of a frame member

Abstract

In steel frame design, the definition of buckling lengths of members is a basic task. Computers can be used to calculate the eigenmodes and corresponding eigenvalues for the frames and using these the buckling lengths of the members can be defined using Euler's equation. However, it is not always easy to say, 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 paper, methods to define the buckling length of a specific member is presented. For this assessment, two ideas 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. The behaviour of the methods is shown in several numerical examples. Both methods can be implemented into automated frame design, removing one big gap in the integrated design. This is essential when optimization of frames is considered.