Cable-stayed bridges require careful design to prevent significant damage during earthquakes. The best design isolates the tower from the superstructure.
The Chi-Lu Bridge was almost completed (just awaiting a closure pour) when the 1999 Chi Chi Taiwan Earthquake occurred. It is a single tower cable-stayed bridge with two, 120 m (400 ft) spans. The bridge was in an especially vulnerable condition and it suffered a great deal of damage during the earthquake. Several cables were damaged and one pulled out of the tower anchorage. The tower was heavily damaged. The ends of the main spans moved back and forth several feet during the earthquake, severely damaging the supports.
I'm surprised the superstructure could resist the the cable-stay forces with an incomplete superstructure even without an earthquake. However, the superstructure gaps resulted in an unbalanced load, large torsional forces in the tower, and less resistance from the superstructure. There were large cracks and spalls not only to the cover but to the structural concrete in the tower, from the deck all the way to the bottom cables.
I don't think designing the towers of cable-stayed bridges to resist large earthquakes through hinging is a good idea. Even if the tower is able to support the cable stresses after forming a plastic hinge, the bridge wouldn't be functional after the earthquake. Designing the tower to remain elastic and providing dampers to absorb energy from the earthquake would allow the bridge to remain in service.
Cable-Stayed Bridges - Chi Lu Bridge by Mark Yashinsky is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 United States License.