# Numerical Analysis of Reinforcing Effect for Scissors-Type Bridge with Strut Members
## 6 Conclusions  
This paper discussed the reinforcing effect of the strut members to the scissors-type bridge through a theoretical and numerical approach. The advantages of this reinforcing method were evaluated by a statically indeterminate mechanics approach focusing on the reduction of the bending moment which is the dominant sectional force in the scissor structure. Then, we evaluated its applicability to the MB based on the numerical simulation. We considered several reinforcing patterns, which are additional horizontal, vertical, and a combination of horizontal and vertical reinforcing members and tried to seek optimal reinforcing layout and sectional area.  
The following remarks can be made based on the results presented in this paper:  
1. Reducing effect for the bending moment which is the dominant sectional force in the scissor structure was evaluated based on equilibrium equations as a statically indeterminate problem. Two examples indicated that sectional forces in a reinforced scissor structure changed depending on its reinforcing layout and expansion angle. Moreover, the reinforcing effect has a nonlinear relationship between the stress and ratio of extension rigidity (parameter \(\alpha\)).  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Step** & **Additional Member** & **Displacement** & **Bending Moment** & **Configuration** \\ \hline
0 & - & 145.0\% & 137.6\% & \\ \hline
1 & Upper H mem. & 2.3\% & 1.4\% & \\ \hline
2 & Center V mem. & 2.2\% & 1.3\% & \\ \hline
3 & Side V mem. & 1.1\% & 1.3\% & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Optimal reinforcing procedure for three scissors unit model.  
2. Finite element analysis was carried out in order to evaluate the reinforcing effect according to different configurations based on the two-scissors and three-scissors unit model. It can be seen that the horizontal reinforcement to the center is the key reinforcing member for the even number of scissors unit, and the vertical reinforcement to the center is the key reinforcing member for the even number of scissors unit.
3. Although some members do not decrease the value of the axial force by reinforcement, the increment of the maximum axial force was approximately two times in comparison with the initial state at maximum. Thus, increase and decrease of the axial force is not big problem in this research.
4. The most effective reinforcing configuration was the double warren truss (DWT) with the vertical member in a two-unit scissors-type bridge and the DWT without the vertical member in a three-unit scissors-type bridge. Its necessary sectional area was \(\alpha>0.2\) in this numerical discussion.  
The obtained results imply that the scissors-type bridge, including the MB, can enhance its performance by using proper reinforcement of the strut members with necessary in the sectional area. We can design the effective reinforcement configuration for the scissors-type bridges with a small number of scissors units based on this research. We would like to consider further reinforcing effects, e.g., longer bridge spans, and optimization of cross-sectional dimensions in future research.  
Conceptualization, Y.C. and I.A.; methodology, Y.C. and I.A.; software, Y.C.; validation, Y.C. and I.A., investigation, Y.C. and I.A.; resources, Y.C. and I.A.; data curation, Y.C.; writing--original draft preparation, Y.C. and I.A.; writing--review and editing, Y.C. and I.A.; visualization, Y.C.; supervision, I.A.; funding acquisition, Y.C. All authors have read and agreed to the published version of the manuscript.  
This research has been supported by Grant-in-Aid for Early-Career Scientists of Japan Society for the Promotion of Science(JSPS) KAKENHI in 2018-2020.  
Not applicable.  
The authors declare no conflict of interest.