# Global Analysis of Adjustable Pallet Rack Down-Aisle Frames Using the Generalised Beam Theory
## 1 Introduction  
A global analysis of a cold-formed steel rack structure presents considerable challenges, given the many factors that necessitate consideration, particularly in contrast to the analysis of conventional steel structures. Analyses and design approaches in the scientific literature and standards [1; 2; 3] typically rely on finite element models, ranging from simple 2D beam models to sophisticated 3D shell models. While simple beam models offer advantages such as easy modelling, quick computation, and straightforward result interpretation, their performance is limited since sectional deformations and perforations cannot be directly accounted for. To overcome these limitations, equivalent and/or effective cross-section properties or specific stiffness reduction factors must be employed [1; 3]. In contrast, shell finite element models can simulate rack structure behaviour realistically but at a much higher modelling and computational cost. Furthermore, when shell models are to be applied in the design of such structures and even in research, significant simplifications have to be introduced to maintain efficiency [4]. For instance, simplified modelling of joints is almost obligatory since contacts and looseness are very difficult to include in a global analysis at a reasonable cost. Therefore, it can be concluded that the use of realistic shell models is not the ideal solution either. Alternatively, this study tackles the global analysis of rack structures using the Generalised Beam Theory (GBT). The current state of the art of this theory is not at the level of shell finite element approaches, especially for comprehensive modelling of joints, including aspects such as the mentioned contacts. Nevertheless, one of its advantages lies in the dual nature of GBT beam finite elements, encompassing bothbeam and shell characteristics within the same element. This allows the theory to take advantage of some of the benefits of each element type. Additional positive aspects of the theory will be shown in the paper. This is one of the first in-depth studies devoted to the global analysis of adjustable rack structures using GBT, and it aims to demonstrate the potential future contributions of the theory in this field. Adjustable pallet rack systems are steel structures designed to store products. Figure 0(a) shows that pallet rack systems are composed of uprights, beams and braces (diagonals). Commonly, all these structural members are made of thin-gauge cold-formed steel profiles. The following two horizontal directions are distinguished: (i) the transverse one, referred to as the cross-aisle; (ii) the longitudinal one, termed the down-aisle. The cross-aisle direction is braced; the corresponding braced structures are termed upright frames (Figure 0(a)). Racks can also be braced in the down-aisle direction, but in this study, only unbraced frame racks are considered (Figure 0(a)). Finally, speed-lock beam-to-upright connections are employed to facilitate rack erection based on inserting hooks into upright perforations (tabs), as described in Figure 0(b). The global, member, and joint behaviours of racks are influenced by numerous factors, making them very particular.