## 6 Conclusions  
Shaking-table tests with multidirectional seismic excitation were carried out on a Y-shaped curved bridge to evaluate seismic performance. The following conclusions were obtained:  
1. The spectral characteristics of the excitation wave, natural vibration characteristics of the bridge, the form of the bridge structure, and constraints at the support directly and indirectly affected the seismic response of an irregular bridge structure, which led to an inconsistent response law. Due to the deviation between the stiffness and mass centers of the bridge, vertical excitation produced structural responses in the other two directions.
2. With unidirectional and multidirectional excitations, the response at the top of the piers was significantly greater in the transverse direction than in the longitudinal direction. The response of piers supporting curved beams was also greater than that of side piers supporting straight girders. For irregular bridges, the seismic design needs to consider horizontally bidirectional seismic inputs.
3. Cracks appeared earlier in the span of a beam with a variable cross-section, and the acceleration response was also the largest. Adding redundant constraints to the beam would reduce the mid-span acceleration response. In most cases, the response to bidirectional excitation was comparable to the response to multidirectional excitation, indicating that a feasible approach to seismic design would be to consider horizontal bidirectional excitation and neglect vertical excitation.
4. Under multidirectional excitation, collisions between the main beam and curved beam were more likely to occur. This suggests that the junction between such beams should have a relatively large expansion joint or improved energy consumption facilities to minimize the risk of collision and any resulting structural damage. However, multidirectional excitation did not increase the collision risk more than bidirectional excitation.
5. The relative displacements of two piers were the same with both bidirectional and multidirectional excitations. This implies that future research can only consider horizontal bidirectional excitation and ignore the influence of vertical excitation.  
Bearing failure and beam falling easily occur around expansion joints, so sufficient lateral constraints should be set and further measures should be taken to prevent piers from colliding. Under multidirectional excitation, seismic wave amplification occurred along the bridge piers, which increased the axial load. Thus, vibration isolation design needs to be carried out to reduce the adverse effects of earthquakes.  
Conceptualization, J.Y. and Z.D.; methodology, J.Y.; software, Q.G.; validation, J.Y., Z.D. and L.T.; formal analysis, Q.G.; investigation, L.T.; resources, Q.G.; data curation, Q.G.; writing--original draft preparation, Z.D.; writing--review and editing, J.Y.; visualization, Q.G.; supervision, Z.D.; project administration, L.T.; funding acquisition, Z.D. All authors have read and agreed to the published version of the manuscript.  
This research was funded by [Natural Science Foundation of Henan Province] grant number [222300420415].  
The authors would like to express their sincere gratitude for the financial support from the Natural Science Foundation of Henan Province (222300420415).  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.