# Numerical Analysis of Reinforcing Effect for Scissors-Type Bridge with Strut Members
## 4 Numerical Results
### Three Scissors Unit Model
#### 4.2.2 In the Case of Lower Reinforcing Patterns (Case 1)  
Figure 13 shows the numerical results which are reinforced in the bottom parts. The left and right figures show BMD and AFD for each numerical case. The maximum and minimum values of contour figures are based on the unreinforced condition (Case 0).  
It is found from Case 1-2 and 1-4 that the deformation of the bridge is decreased greatly by applying the vertical member at the central part. This is because the presence of the vertical members between \(\overline{B_{2}A_{2}}\) and \(\overline{B_{3}A_{3}}\) reduce the bending moment acting on the scissors members. On the other hand, they do not make a dramatic difference in Case 1-1 which has only the horizontal member at a lower hinge place, similar to the two scissors unit model.  
Figure 12: Distribution of sectional forces (response magnification 100 times): (**a**) bending moment distribution; (**b**) axial force distribution.  
.2.3 Effects of Decreasing the Displacement and Sectional Forces Depending on the Reinforcing Layout  
The effects of decreasing the displacement and sectional forces are evaluated by Case 1 to Case 3 according to the position of the reinforcing members. Figures 14 and 15 show the nondimensional value of the central displacement and sectional force for each numerical case divided by the ones in Case 0 without any strut members. Lower, Lower +1, and Lower + Upper in the abscissa axis in both figures show the numerical results of Case 1, 2, and 3. Moreover, in Figure 15a,b, bar graphs colored in blue and purple depict the maximum value in the whole of the model and member \(\overline{B_{2}A_{3}}\).  
It is understood from Figure 14a that Case 1-1 with only the horizontal members and Case 1-3 with the horizontal members and side vertical members increase maximum displacement more than the result of Case 0 without any reinforcement. However, remaining patterns show a high reduction of central displacement. Figure 14b depicts the detail of displacement in small range, and it shows almost a displacement below 1/20 times from the initial state. The highest decrease is obtained in Case 3-3 similar to a double warren truss (DWT) configuration, and its value is smaller than that of Case 3-4 in a fully reinforcement  
Figure 13: Numerical results in lower decks pattern (response magnification 100 times): (**a**) BMD in Case 1-1; (**b**) AFD in Case 1-1; (**c**) BMD in Case 1-2; (**d**) AFD in Case 1-2; (**e**) BMD in Case 1-3; (**f**) AFD in Case 1-3; (**g**) BMD in Case 1-4; (**h**) AFD in Case 1-4.  
pattern. This result implies that side vertical members on the supports are more important in the case of Case 3 with both upper and horizontal members.  
Figure 15a shows that Case 1-1 with only the horizontal members and Case 1-3 with the horizontal members and side vertical members increase the maximum bending moment approximately 1.4 times more than Case 0. However, remaining patterns clearly show a decrease under 1/10 times colored in purple by applying reinforcing members. Furthermore, when looking at the whole of the bridge colored in blue, the maximum bending moment also becomes small due to transmitting forces to another member by the vertical and horizontal member. At this time, the minimum reduction is obtained in Case 3-4.  
Figure 15b shows that the maximum axial force generates near the supporting points in the whole case. These values colored in purple are approximately two times higher than the nonreinforcement state at maximum. That is to say, the axial force does not increase extremely by reinforcing as well as in the two scissors unit model.