## 4 Discussion
### Discussion on the Load Bridging Effects and Trends by Each Significant Factor
#### 4.1.4 Effect of the Package Friction Coefficients on the Bending Ratio of a Board  
The friction coefficient of the packages was observed to be a factor that when increased, tended to reduce the bending response of the boards. The rate of change was more pronounced for larger boxes when there was a larger contact area between the boxes. This can be clearly observed in Figure 13. Furthermore, the friction coefficient for the  
Figure 11: Effect of payload height (mm) on board bending ratio by pallet friction, box friction, and number of columns.  
packages were modeled differently for the horizontal and the vertical box surfaces. These components do not affect the bending response equally. Increasing the friction properties of the vertical package surfaces generated a reduction in the bending of the boards for most of the studied scenarios (Figure 14). Alternatively, changes on the frictional properties of the horizontal box surfaces only generated a change in board deflection for unit loads with large boxes (Figure 15). As seen in Figure 10a, the unit load with three columns presented a rotational motion of the boxes. Increasing the horizontal friction between boxes reduced this motion and affected the resulting deflection by decreasing it. Unit loads where the aspect ratio or other factors already prevented rotational motion were not affected by changes in the horizontal CoFs.  
The effect of changes in package friction coefficients can be observed for a commonly used unit load scenario. The unit load is supported on a 1200 mm \(\times\) 1000 mm wooden pallet (0.45 pallet friction) and contains 340 mm \(\times\) 250 mm \(\times\) 400 mm corrugated boxes made of kraft paper (average box friction of 0.45) that are stacked three high (1200 mm total height). By changing the friction of the packages on the vertical surfaces from a coefficient of 0.30 to 0.60, while keeping the horizontal friction fixed at 0.45, it decreases the experienced deflection by 50.4%. The same scenario but with smaller 170 mm \(\times\) 125 mm \(\times\) 400 mm corrugated boxes (in six columns) generated a deflection reduction of only 15%. Alternatively, fixing the vertical friction at 0.45 but increasing the horizontal friction coefficient from 0.30 to 0.60 can reduce the deflection by 22.1% for large boxes but does not generate any significant change in unit loads carrying small boxes.  
A feature that could impact the overall effect of package friction on the bending of a unit load is the application of containment mechanisms. Methods such as stretch wrapping can restrain the boxes and prevent any rotation or displacement. The increased unitizing forces increase the overall load bridging effect and could potentially reduce the deflection experienced by the unit load. By not considering stretch wrapping or other containment methods commonly utilized, this model provides a conservative estimation of the load  
Figure 12: Effect of pallet friction coefficient on board bending ratio by payload height (mm), box friction, and number of columns.  
bridging effect. Further refinements can be developed in order to take into account all of the many possible modifications available for unit loads.  
Figure 14: Effect of the friction coefficient of the vertical surface of the packages on board bending ratio by pallet friction, payload height (mm), and number of columns, with a fixed coefficient of friction of the horizontal surface of 0.45.  
Figure 13: Effect of the friction coefficient of packages on board bending ratio by pallet friction, payload height (mm), and number of columns.