*2.2. Analysis of Transverse Seismic Performances of Bearings of the Original Model*

For the through-arch basket-handle bridge, the inclination angle of the arch rib did not increase constantly. Geometrically, the inclination angle was limited by the span, the width and height of the bridge deck, the sagitta, and other factors at the crown of the arch, as shown in Figure 5. The relationship between the inclination angle of the arch rib and these parameters was derived as follows.

**Figure 5.** Axial-stress-envelope diagram of horizontal diagonal bracing between arch ribs of the original model.

The bearings, as the key components connecting the substructure and the superstructure, may be the seismic weak points of the deck-arch bridge. The safety of the bearings was evaluated through the capacity–demand ratio (CDR). The CDR method evaluates the

seismic safety of bridges by comparing the seismic demands and capacities of each key component in the bridge-structure system [46,47]:

$$R\_Q = Q\_\varepsilon / (Q\_{sd}^{\text{max}} + Q\_{dd}) \tag{1}$$

$$R\_{\Delta} = \Delta\_{\mathfrak{c}} / \left(\Delta\_{\mathfrak{s}d}^{\text{max}} + \Delta\_{dd}\right) \tag{2}$$

where *RQ* and *R*<sup>Δ</sup> are the CDR of bearings' shear resistance and deformation, respectively; and *Qc*, *Q*max *sd* , and *Qdd* are the shear bearing capacity, seismic shear demand, and dead-load shear demand on the bearings, respectively; Δ*c*, Δmax *sd* , and Δ*dd* are the deformation capacity of the bearings, the seismic-deformation demand, and the dead-load deformation-demand, respectively. Formula (1) is applicable to the fixed direction of the spherical steel bearings, and Formula (2) is applicable to the FPBs and the moving direction of the spherical steel bearings. The shear capacity of the fixed direction of the spherical steel bearings is taken as 30% of the designed vertical-bearing capacity.

When the CDR is greater than 1, the system is safe. When the CDR is less than 1, the system is not safe. As the top of each pier (column) of the bridge adopts four bearings, the maximum seismic-shear force in each row of bearings was used for a checking calculation when analyzing the transverse seismic performance of the bearings. The CDRs of the bearings of the main bridge are listed in Table 1.

**Table 1.** CDRs of main bridge bearings.


Table 1 shows that the CDR of the bearings of the vault was 0.99, and the CDRs of the bearings of columns 1# and 10# were 0.79, 0.65, 0.63, and 0.80, respectively, which were less than 1; the CDR of the bearings at the tops of the other columns was greater than 1. This shows that the shear capacity of the arch crown and the 1# and 10# spherical steel bearings was insufficient, and that seismic measurements in the transverse direction needed to be undertaken. It is worth noting that these findings were affected by the high and low columns on one side of the side pier of the approach bridge; there was no symmetry in the curves with respect to the arch crown.
