4.5.4. Torsion of Girder

The girder or abutment features torsion in both the tangential and vertical directions. In this paper, the torsion angle is used to indicate thedegree of torsion. The calculation formula is as follows:

$$\varphi = \frac{\left| u\_i - u\_j \right|\_{\max}}{l\_{ij}} \times \frac{180}{\pi} \tag{5}$$

where *ui* and *uj* is the tangential displacement or vertical displacement of the inner and outer nodes of the girder or abutment,

*lij* is the distance between the inner and outer nodes of the main girder (bridge abutment), where the bridge deck width is 7.2 m.

Calculate the tangential and radial torsion angle of the girder or abutment in the combined case according to the above formula. The specific values are shown in Figure 22.

**Figure 22.** Torsion of the girders. (**a**) Tangential torsion (**b**) Vertical torsion.

It was found that there is a torsion phenomenon in curved bridgesduring earthquakes. After installing seismic mitigation and unseating prevention devices, the tangential torsion of the curved bridge is effectively reduced, but the reduction in the vertical torsion is not large because, for vertical torsion, a certain reduction effect can only be obtained through the overall energy dissipation.

When seismic shock is input along the direction of piers 2 and 3 , it mainly causes the tangential torsion of the beam. When the seismic mitigation and unseating prevention device is installed, the tangential torsion is effectively reduced. To clarify this point, take the outward twist (the short unit is twisted counterclockwise around the Z axis, and the long unit is twisted clockwise around the Z axis) as an example. When the beam is twisted, for SCRB, the outer cable is in a relaxed state, and the inner cable is in a tensioned state, which can provide a large pulling force to the inside of the beam, thereby restricting the torsion of the beam.For case F (the combination of VED and SCRB), not only can the inner SCRB can provide the restraining force to pull the beam together, but the outer VED can also provide the opposite restraining force to push the beam apart.At the same time, it also dissipates part of the seismic energy; therefore, it can effectively reduce the torsion.For case G (the combination of VFD and SCRB), theprinciple is similar to VED.For CASE H (the combination of LRB and SCRB), in addition to SCRB, which can provide constraining force, the horizontal rigidity and damping of the lead rubber bearing can also provide a certain constraining force on the inside and outside, reducing the torsion of the beam. Among several damping devices, LRB and VFD exertstrongereffects on the dissipation ifseismic energy; hence, theyoffer more effective seismic mitigation and unseating prevention.
