*4.5. Comparative Analysis of Internal-Force Response of Arch Rib*

The CDR is an index to visually express the internal-force response of a section. The CDRs of the out-of-plane bending of the arch rib in the models are shown in Figure 11, and the lifting factor of the safety factor of the arch rib in the models is shown in Table 10,

where positive values mean the CDRs increase and negative values suggest that the CDRs decrease.

**Figure 11.** CDR comparison of out-of-plane bending of arch-rib sections of models. (**a**) Upper chord-arch-rib section. (**b**) Lower-chord arch-rib section.


**Table 10.** CDR-lifting factors for the out-of-plane bending moment.

Figure 11 and Table 10 show that after the FPB was set, the CDRs of the corresponding sections (section codes 1, 2, 7, 12, and 13) greatly improved, regardless of the upper or lower chord, but the CDRs of the adjacent sections (section codes 3, 6, 8, and 11) decreased to a certain extent. That is, the CDRs at the corresponding arch-rib location where the FPB was set rose, but this had an adverse effect on the arch-rib section at the adjacent location of the FPB. In particular, after the FPB was set at the vault, the CDRs of the arch0rib sections at adjacent locations decreased by at least 17%.

As shown in Figure 11 and Table 10, the CDRs of the upper-chord arch-rib section improved by at least 5%, and the CDRs of the 77% section increased by more than 10%. The CDRs of most of the sections of the lower-chord arch rib increased. The arch-foot and arch-crown sections of the upper-chord arch rib and the lower-chord arch rib were the seismic weak points of the arch rib. The CDRs of the arch-rib weak points were improved through the reasonable arrangement of the SBCs.

Figure 11 and Table 10 demonstrate that the CDR of the upper-chord arch-rib section was greatly improved. The CDRs of all the sections increased by more than 8%, and the CDRs of 92% of the sections increased by more than 11%. The CDRs of most of the sections of the lower-chord arch rib increased. Compared with Models 1 and 2, the CDRs of arch-rib weak points can be better improved through the reasonable arrangement of SBCs and FPBs.

#### **5. Conclusions**

Taking a super-long-span CFST with a total length of 788 m as the research object, a non-linear time-history analysis was conducted under E2 excitation in the cross-bridge direction, plus dead-load conditions, and the seismic-design-check calculation was performed according to the seismic response. As a result, the seismic weak points were revealed and the seismic-performance-improvement scheme was explored with a view to proposing a better seismic-performance0improvement scheme for this long-span CFST arch bridge.


**Author Contributions:** D.Y., methodology and finite element analysis; Y.T., drawing and translation; L.G., review and finite element analysis; Z.T., editing and finite element analysis; R.Z., methodology and concepting. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was supported by the Key research and development plans of Guangxi Province (grant no. Guike AB22036007), the Talent Program Project of Chongqing (grant no. cstc2022ycjh bgzxm0133), the Natural Science Foundation of Chongqing (grant no. CSTB2022TIAD-KPX0205), The Natural Science Foundation of China (grant no. 52008064); The Science and Technology Research Program of Chongqing Municipal Education Commission of China (grant no. KJQN202000737); The Postdoctoral Research Program of Chongqing (grant no. 2022CQBSHTB3082); The Postgraduate Research and Innovation Project of Chongqing Jiaotong University (grant no. CYB23247).

**Data Availability Statement:** Data available on request due to restrictions.

**Conflicts of Interest:** The authors declare no conflict of interest.
