## 2 Materials and Methods
### Screening of the Significant Factors in the Load Bridging Model  
The finite element model of the unit load segment used in this paper was a two-dimensional implicit dynamic model presented by [PERSON] et al. (2019). In it, a segment of a unit load, supported on a warehouse storage racking condition across its width, was simulated. This model simplified the packages to non-deformable boxes with frictional contacts. Boxes were defined by density, and loading was conducted through gravitational acceleration. All components of the model were two-dimensional solid elements using plane/strain linear elastic material. The pallet was modeled through a board analog with 3200 quadrilateral elements sized at 2.54 mm for the global seed. Boxes were modeled with a mesh generated from elements sized at 12.7 mm for a total of 6075 elements in the optimal mesh. The solver used was nonlinear, implicit dynamic that allowed for the proper representation of the transient characteristics of the phenomena under study, such as quick box movement, large deflections of the pallet, and nonlinear frictional contacts between each component. This model provided an average prediction accuracy of 8% for unit load segments with three or more columns of packages. [PERSON] et al. (2019) fully describe the finite element model formulation. After the development of the finite element analysis for the unit load segment, multiple factors were identified as necessary inputs for an accurate simulation. The goal of this research endeavor was to understand and characterize the load bridging effect in unit loads. It was hypothesized that not all input variables would have the same degree of influence on load bridging. Screening for the significant factors and interactions, and then simplifying the load bridging model was a key first step towards comprehending the complex interactions occurring among payloads of stacked corrugated boxes. Seven variables were identified as necessary to fully describe the unit load segments being replicated in the finite element model; therefore, these variables were selected as the initial factors for the screening design. The variables were as follows: the number of columns, which corresponds to the payload length divided by the box length; the number of layers, which corresponds to the height of the payload divided by the box  
Figure 1: Steps followed to study the effect of load bridging on racked unit loads. height; the payload height (m); the coefficient of friction between the pallet and the payload (pallet friction); the coefficient of friction between the boxes (box friction); the Young's Modulus of the pallet segment simulator (pallet stiffness, GPa); the total payload weight (kg). All other model inputs were either constants or were derived from the main input variables, such as the material density of the boxes or the specific box dimensions, which depends on the combination of the number of columns, layers, and payload height. Figure 2 shows the unit load segment replicated, graphically depicting each factor. To capture the effects of these variables, values for the study were determined from the trends observed during the model development process in [20]. For the screening design, the unit load segments created consisted of three and five columns, and three and five layers. The coefficient of frictions of the different interactions were selected from a low friction of 0.20 to a high value of 0.60. This covered the ranges of coefficients of friction (CoFs) observed in material handling operations for different common materials [28]. The Modulus of Elasticity of the pallet was selected for an analog of a flexible, plastic pallet of 2.76 GPa and a more rigid, wooden pallet of 8.27 GPa. Pallet stiffness values were estimated based on the expected adjusted bending stiffness rates as developed by [PERSON] et al. [16], with a deflection value of 5 kg/mm for the low stiffness board and 14 kg/mm for the high stiffness board.