*2.4. Seismic Internal Force Response Analysis of Arch Rib Section*

The seismic performance of the CFST arch bridge first depends on the seismic performance of the CFST main arch ring, so this paper focuses on the internal force of the arch-rib section. As the left and right arch ribs are symmetrical and their internal forces are similar, to save space, only the internal-force response of the right arch rib section was analyzed. When studying the axial force and the out-of-plane bending moment and in-plane bending moment of the arch-rib section, the maximum and minimum internal forces were considered and expressed in maximum and minimum working conditions, respectively. When analyzing the shear force on an arch rib section, only the most unfavorable situation was considered. The calculated results of internal-force seismic response of the arch rib are shown in Figure 6.

**Figure 6.** Internal-force envelope of an arch-rib section of the original model. (**a**) Axial-force demand. (**b**) Shear demand. (**c**) Out-of-plane bending-moment demand. (**d**) In-plane bending -moment demand.

Figure 6a illustrates that the axial-force difference between the arch foot of the upperchord arch rib and the crown section of the upper-chord arch rib was small, and that the axial-force distribution was relatively uniform; the axial force of the arch-foot section of the lower-chord arch rib was greater than that of the arch-crown section of the lower-chord arch rib. It can be seen from Figure 6b that, except at the arch foot, the shear force on the upper-chord arch-rib section was greater than that on the lower-chord arch-rib section, and the shear force at the arch crown of the upper-chord arch rib was much larger than that at the arch crown of the lower-chord arch rib. Figure 6c,d indicate that the bending moment in

the upper-chord arch -rib section was greater than that -n the lower-chord arch-rib section, except at the arch foot.

Transverse seismic conditions mainly affect the out-of-plane bending moment of archbridge structures, so we focus on the out-of-plane bending performance here. The axial force affects the flexural capacity of the member, and the out-of-plane bending moment of the section determines the flexural demand of the section. In this paper, a CDR method is used to evaluate the out-of-plane bending performance of the arch-rib section:

$$R\_{\rm M} = M\_{\rm c}^{\rm min} \,/\left(M\_{\rm e}^{\rm max} + M\_{\rm d}^{\rm max}\right) \tag{3}$$

In Formula (3), *R*<sup>M</sup> is the CDR of the bending resistance of the arch rib, *M*min <sup>c</sup> is the bending capacity of the section, and *M*max <sup>e</sup> and *M*max <sup>d</sup> are the bending-moment demands of the section under the combined working conditions of seismic and dead loads, respectively. The fiber model in XTRACT software was used to calculate the bending capacity of the section. The steel-structure material adopted the strain-hardening model, and the confined concrete used a Mander model.

The CDRs of the out-of-plane bending of key sections of the main arch rib were calculated, and the results are shown in Table 2.


**Table 2.** CDR of out-of-plane bending of arch-rib section of the original model.

The CDRs of key arch sections under the most unfavorable working conditions are shown in Table 2. The CDRs of the upper-chord arch-rib section were much smaller than those of the lower-chord arch-rib section, and the CDRs of the arch crown and arch foot were smaller than those of the other sections. Therefore, the arch-rib sections of the upper chord, the arch crown of the lower chord, and the arch foot are the weak points in this arch bridge. The CDRs of the upper-chord arch-rib section, the arch crown of the lower chord, and the arch foot of the lower chord should be increased through the implementation of seismic measures.
