# Global Analysis of Adjustable Pallet Rack Down-Aisle Frames Using the Generalised Beam Theory
## 1 Introduction
Apart from all the above-mentioned main aspects that influence global analysis of racks, there are others that have attracted the attention of researchers and standardisation committees, such as the residual stresses and partial yielding of the cross-sections [3; 16], particular loading patterns and accidental actions [1; 2; 17], ground-structure interactions [1], and stiffening effects of the pallets [17]. Current design standards for racks offer various approaches to conducting comprehensive global analyses, aiming to account for all considerations presented so far. On the one hand, the most advanced proposals in Europe and America [2; 3] are based on member checks using internal forces determined in beam finite element geometrically nonlinear analysis with imperfections (GNIA). Both in Europe and America, semi-rigid joints have to be included in the model, as well as global sway imperfections (or equivalent horizontal forces) and, depending on the final member checking applied, member imperfections. Analysing down-aisle frames can be carried out separately from the cross-aisle upright systems if the relevant interactions are considered. In Europe, looseness affecting the down-aisle direction can be taken into account through supplementary sway imperfection, and the reduction in stiffness produced by the column perforations is considered through an equivalent cross-section. In America, reduced cross-section area properties are also proposed to cover the effect of perforations [2], and additional stiffness reduction factors are used for all members that contribute to the stability of the structure. The readers are referred to the corresponding standards for detailed information [1; 2; 3]. Noticeably, none of these documents offers clear instructions on torsion when conducting the global analysis, as [PERSON] et al. already pointed out in their studies [7]. Contrarily, the study by [PERSON] et al. in [18], which introduces the Australian design standard for rack design, shows explicit instructions on how to deal with the effects of warping torsion. Furthermore, this standard opens the door to advanced analysis based on shell finite element models to directly determine the ultimate strength of the rack by means of GMNIA. In this manner,perforations, sectional deformations and instabilities, warping torsion effects and eccentricities can be taken into account more realistically. Concerning beam and shell finite element models, it can be considered that the Australian standard is the most innovative and the closest to the current scientific state-of-the-art in relation to the global analysis of racks. In this study, the authors propose an analysis approach based on the GBT. Thanks to the dual nature of the GBT finite elements, torsion and sectional deformations are naturally accounted for, along with perforations [19], without facing the modelling costs associated with shell FEM, particularly concerning joints. Most of the existing global analyses with GBT have been mainly focused on simple portal frames composed of channels or I-sections. The main problem in GBT is to model the joints [20]. This is probably why researchers moved from initial pure GBT frame models [21; 22; 23] to models that combine GBT beam elements for members and shell elements for joints [24; 25]. However, the GBT modelling of joints in racks can be simpler because its nature does not allow for a direct and complete transmission of the torsional warping degree of freedom or local and distortional deformations. This connection is commonly made by means of hooks and tabs, and consequently, the beam warping deformations are just partially transmitted to the column through localised contacts. It seems reasonable to model these connections in a simplified manner when carrying out a global analysis of a pallet rack structure (Only global GBT deformation modes and eccentricities are considered). As a result, the experimentally measured beam-to-column and floor connection stiffness can be directly incorporated into the model, similar to a beam FE model.