*4.5. Displacement Response*

### 4.5.1. Displacement at the Short Unit Expansion Joint

We extracted the displacement of each node of the expansion joint and tookthe displacement of each node minus the displacement of the corresponding pier or abutment bottom node at each time. The displacement of the outer node was subtracted from the corresponding pier or abutment bottom, and the displacement of the inner node was subtracted from the corresponding pier or abutment bottom. Subsequently, the maximum absolute value was taken as the peak displacement of each node. We extracted the ra-

dial and tangential peak displacementof the four inner and outer nodes at the short unit expansion joint in all the cases, as shown in Figure 19.

**Figure 19.** Nodal peak displacement of short expansion joints in every case. (**a**) Radial diaplacement (**b**) Tangential displacement.

Figure 19 shows that each combined case exertsan obvious effect on reducing the peak radial tangential displacement of each node at the edge of the short unit expansion joint, and the reduction rate reached more than 45%. Among these, cases G and H producethe greatestseismic mitigation effect. Comparing Figure 19a,b, the peak tangential displacement of the joint at the short unit expansion joint is obviously greater than the peak radial displacement of the joint. The main reason for this is that the ground motion in this paper only considers the input along the direction of piers 2 and 3 , and does not consider the input perpendicular to the horizontal direction. Therefore, the radial displacement of the beam is mainly caused by the torsion of the beam. The tangential displacement is composed of two parts, one of which is caused by the translation of the beam, and the other by the torsion of the beam.

Figure 19b shows that the difference in the tangential displacement ofnodes 3 and 4 in case A is mainly caused by the torsion of the girder. However, after installing the seismic mitigation and unseating prevention devices, the torsional response is effectively reduced, the inward and outward torsion is balanced and essentiallythe same, and the peak tangential displacement ofnodes 3 and 4 also become more consistent.

### 4.5.2. Displacement at the Middle Expansion Joint

We extracted the peak radial and tangential displacement of the four inner and outer nodes of the middle expansion joint under several combined cases, as shown in Figure 20.

Figure 20 shows that the peak seismic mitigation ratio of the radial tangential displacement of each node at the edge of the expansion joint in each combined case also reached more than 40%, and that the damping effect of cases G and H was the greatest. From Figure 20b, it can be seen that the peak tangential displacement of nodes 5,6, 7, and 8 of case A are quite different, mainly due to the torsion of the girder. However, the corresponding peak displacements of the joints in the three combined damping cases F, G and H are all effectively reduced and the difference is not significant. This shows, once again, that through the combined damping optimization design, the torsion of the girder is effectively reduced.

**Figure 20.** Nodal peak displacement of middle expansion joints of every case. (**a**) Radial diaplacement (**b**) Tangential displacement.

### 4.5.3. Displacement at Long Unit Expansion Joint

We extracted the peak radial and tangential displacement of the four nodes on the inner and outer edges of the long unit expansion joint, as shown in Figure 21.

**Figure 21.** Nodal peak displacement of long expansion joints in every case. (**a**) Radial diaplacement (**b**) Tangential displacement.

Figure 21 shows that the long unit expansion joints are similar to the short unit expansion joints. The peak radial and tangential displacements of the joints are effectively reduced, as well as the torsion effect of the girder. The seismic mitigation ratio to the peak tangential displacement is greater than that ofthe peak radial displacement.
