A Direct Method for Buckling Analysis of Single Layer Lattice Structures

Numerous authors have studied the buckling behaviour of single layer lattice structures. Issues such as the buckling analysis in the elastic and plastic ranges, and the effects of imperfections in the failure mechanism of the structure have been investigated. However, there is still an uncertainty at the time of performing the buckling design of individual elements within the structure. This uncertainty stems from the need to approximate the effective length of each individual member. In addition, the approximate design criteria established by the different codes, and in particular Eurocode 3, are generally applicable to planar frames, but uncertain for spatial structures. This paper presents a direct one-step method for the buckling analysis of single layer lattice structures. The method avoids the use of the effective length factor of each individual element. The key point is to perform a non-linear analysis of the structure starting from an initial deformation state that includes the initial imperfections of the elements. Such an initial deformation state is obtained from the first buckling mode of the structure by a suitable scaling procedure based on an energy approach. The resulting initial deformed shape is introduced along with the external loads in a fully non-linear structural analysis that yields the resulting element stresses including the buckling effects. The performance of the method is checked by means of a series of numerical examples. The stiffness characteristics of the connections have been obtained, and included in the analysis, thus showing their influence on the behaviour of the structure.