## 4 Results and Discussion
### Vertical Spacing between Bolt Rows  
The first set of case studies considered a steel plate where five hypotheses concerning the vertical spacing between bolt rows are contemplated: 40, 50, 60, 70, and 80 mm. Four steel plate thickness values were combined with each of them: 3, 3.5, 4, and 5 mm. It must be noted that the selected spacing distances comply with the minimum distance to plate edges according to Eurocode 3 [17]. These variations were studied while the horizontal spacing between bolts was kept constant. Figure 3 represents the dimensions and geometrical arrangement of the bolt holes in the plate.  
Equivalent maximum plastic deformation is displayed for the set of case studies in Figure 4. Eurocode 3 [17] requires that this measure does not exceed 5%. Of the 20 cases proposed, 15 complied with the maximum plastic deformation. It can be noted that the 3 mm thick plate complied with the maximum plastic deformation for vertical spacing distances over 60 mm only.  
Figure 5 displays the contour plot of plastic deformation in the joint with the 3 mm thick plate and 70 mm vertical spacing along with the color scale legend. Plastic deformations are located in the contact zone between the bolt and the profile or the metal plate. In the profile web, it can be noticed how the kinematic field of plastic deformations responds to a rotational field with the center at bolt #13. A similar situation is observed in the field of plastic deformations connected to the right component around bolt #20.  
Figure 6 shows, on the one hand, the von Mises stress map of a 3 mm thick plate with 70 mm vertical spacing between bolt rows. This is one of the cases of the previous set that narrowly met the EuroCode specifications. A significant portion of the plate area reached the yield stress of the steel, which is displayed in dark red. On the other hand, the 5 mm thick plate with 80 mm spacing is the case that met specifications the most loosely. In both cases, it was observed that the most stressed areas are those close to the holes vertically outside and horizontally inside (21 and 23).  
The stress state of IPE profiles of the 3 mm thick plate and vertical spacing of 70 mm, one of the designs that met the criteria of EuroCode 3 in an adjusted form, is displayed in Figure 7. It can be observed that the plastic deformation values showed by the color scheme are consistent with the plastic deformations in Figure 5. The von Mises stress distribution  
Figure 4: Equivalent plastic maximum deformation for horizontal spacing of 50–60 mm.  
showed that the joint plates (Figure 6a) have higher load stresses as the dark red areas are greater in the plates than in the profile web.  
Regarding the calculation of bolt shear utilization, it can be observed in Figure 8 that 15 of the 20 cases proposed met the maximum plastic deformation. The case studies with smaller vertical spacing resulted in a peak shear utilization well above the limit (100%), regardless of the plate thickness. On the other hand, the plate thickness did affect the cases with greater vertical spacing. The greater the thickness, the lower the percentage of shear utilization in the bolts. In intermediate values of vertical spacing, the percentages were all stabilized below the limit and are practically the same in each position. There are  
Figure 5: Verification of plastic deformation in joint with 3 mm thick plate with vertical spacing of 70 mm: (**a**) IPE240 web; (**b**) plate.  
Figure 6: von Mises stress distribution in plates with color scale: (**a**) 3 mm thick plate and vertical spacing of 70 mm; (**b**) 5 mm thick plate and vertical spacing of 80 mm. The numbering of bolts is indicated.  
Figure 7: von Mises stress distribution in the web of IPE240 profiles with color scale: (**a**) left end; (**b**) right end.  
13 possible cases out of 20 that met the specifications. The most efficient connections consisted of a 3 mm thick plate with 60 or 70 mm vertical spacing.