# Global Analysis of Adjustable Pallet Rack Down-Aisle Frames Using the Generalised Beam Theory
## 9 Conclusions  
This paper presented a GBT beam model of a pallet rack down-aisle frame. The model was simplified to a single column to reduce the modelling and computational costs; however, it accounts for the main factors determining the performance of the structure: perforations, beam-to-column and floor joint behaviour, eccentricities with respect to the centroid and shear centre, imperfections, sectional deformations, warping torsion, and geometric nonlinearity (material nonlinearity was not included). The GBT model was validated against a shell finite element simulation. It is noteworthy that despite some significant differences in modelling considerations, particularly regarding joints and perforations, the GBT model demonstrated remarkable agreement with the shell FEM model in terms of sway displacements and section stresses. A parametric study was carried out with the validated GBT model to investigate the effect of imperfections, support conditions and perforations. The main conclusions of the study are as follows:  
1. It was observed that distortional imperfections were needed to trigger the sectional deformations. 2. The effect of the sectional deformations and corresponding imperfections seemed important on individual members, i.e., column segments between beams. Their influence on the horizontal displacements of the joints was minimal. Consequently, the global sway displacement of the structure did not significantly change. 3. The most important effect of activating sectional deformations, achieved by introducing sufficiently large imperfections, was the increase in the warping torsional moment (the commonly known bi-moment) and its corresponding stresses, along with distortional stresses. 4. Modifying the warping support of the floor joint resulted in significant changes to the warping torsional moment and the warping torsional and distortional stresses, but only at the first column level. 5. The introduction of the perforations had a small effect on the global sway displacement. 6. The reduced net area of the perforated members provoked the expected stress increase. 7. In perforated members, while the stress distribution changes depending on the distortional imperfections considered, their influence on the maximum membrane stress is small due to the effects of stress concentration. It is important to emphasise that these concluding remarks are based on a specific structural design with a particular force pattern, predominantly consisting of gravitational loads. It is expected that these results may suffer important changes in other situations. For instance, (i) the role of distortional imperfections in activating the effect of sectional deformations may be less important if triggered by a more realistic GBT modelisation of the joints, or if a higher load level is used, causing the structure to approach the elastic or plastic collapse where sectional deformations become more relevant; (ii) increasing the distance between levels will increase the slenderness of both the individual members and the global structure, leading to greater geometric nonlinear effects in general, and particularly larger sensitivity of the global sway displacements to distortional imperfections and perforations; (iii) the opposite effect will occur if the structure is braced in the down-aisle direction; or (iv) considering higher horizontal loads (such as seismic action) may also change the behaviour concerning sectional deformations and sway displacements. Overall, this article presents only the initial phase of the research and the potential utility of GBT, but there are still aspects to be explored in future studies. Conceptualization: J.B., O.B., M.C. ; Methodology: J.B., O.B., M.C. ; Software: J.B., O.B. ; Investigation: J.B., O.B., M.C., I.L.-R.; Writing--original draft preparation: [PERSON], O.B., M.C. ; Writing--review and editing: I.L.-R.; Supervision: M.C. All authors have read and agreed to the published version of the manuscript. This research received no external funding.