# Numerical Analysis of Reinforcing Effect for Scissors-Type Bridge with Strut Members
## 4 Numerical Results
### Two Scissors Unit Model
#### 4.1.2 In the Case of Lower Reinforcing Patterns (Case 1)  
Figure 8 shows numerical results which are reinforced in bottom parts. The left and right figures show BMD and AFD for each numerical case. It is found from Case 1-2 and 1-4 that the maximum bending moment decreases greatly due to restraining the deformation of the bridge by applying the vertical member at the central part. On the other hand, they do not made a dramatic difference in Case 1-1 which has only the horizontal member at the lower hinge place and Case 1-3 which sets on the vertical member at both ends because these reinforcing patterns cannot reduce the deflection of the MB1.0 directly. Now, let us consider the reinforcing effects by focusing on the high bending members (\(\Lambda^{\prime}\)-shaped members) in Case 0. Figure 9 shows the sectional distribution of member \(\overline{B_{1}A_{2}}\). The longitudinal axis depicts the change in sectional forces in each case, and the abscissa axis depicts the attention point along with the member axis direction. Point \(B_{1}\) and central pivot show \(x=0\) mm and 2150 mm in the figure. Figure 8: 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. When looking at Figure 9a, it is found that the maximum axial force of 2 kN in Case 0 was increased by the strut member except Case 1-3. However, these increments of the axial force are not a big problem because the effect of the bending moment is decreased greatly from the initial state. When looking at Figure 9b, Case 1-1 is unable to decrease the bending moment, but the maximum value increases 1.5 times from Case 0 according to the increment of self-weight. However, it is understood that the bending moments are basically decreased by applying a vertical member at least. Figure 9c shows detail of the bending moment distribution for each case. It is found that the minimum bending moment is obtained in Case 1-4. From the above, it is clear that the vertical reinforcing members can reduce the maximum bending moment approximately 1/20-1/30 times in comparison to the initial state. Figure 9: Change of sectional force distributions for member \(\overline{B_{1}A_{2}}\) in Case 1: (**a**) AFD; (**b**) BMD; (**c**) Close-up of BMD. .1.3 Effects of Decreasing the Displacement and Sectional Forces Depending on the Reinforcing Layout  
Effects of decreasing the displacement and sectional forces are evaluated by Case 1 with the bottom horizontal members and Case 3 with the upper and bottom horizontal members. Figures 10 and 11 show the nondimensional value of displacement and sectional force for each numerical case divided by ones in Case 0 without any strut members. Lower and Lower + Upper in the abscissa axis in both figures show the numerical results of Case 1 and 3. Moreover, in Figure 11a,b, bar graphs colored in blue and purple depict the maximum value in the whole of the model and '\(\Lambda\)'-shaped members. It is understood from Figure 10a that of every reinforcing pattern, only the horizontal member without the vertical member (Case 1-1 and Case 3-1) and Case 1-3 increase the maximum displacement more than the result of Case 0. It is seen that reinforcing effects of the lower horizontal member are few. However, the remaining patterns show decreasing one by setting on the vertical member. Figure 10b depicts the detail of displacement in a small range, and it shows almost a displacement below 1/10 times from the initial state. A high effect of decreasing is obtained in Case 3-4. Figure 11a shows that of every reinforcing pattern, only the horizontal member without the vertical member (Case 1-1 and Case 3-1) and Case 1-3 increase the maximum bending moment approximately 1.2-1.5 times more than Case 0. However, the remaining patterns clearly show decreasing one under 1/10 times by applying the vertical member.