Over the past decades, many researchers have studied the energy dissipation system and the vibration control of cable-stayed bridges under earthquake excitations, which includes passive control [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15], active control [8; 9; 14] and semi-active control [7; 8; 9; 10; 16; 17; 18]. As we all know, passive control does not need external energy. In comparison, active control requires external energy; on the basis of structural response and feedback, the optimal control would be achieved by the optimal control algorithm, and then the control force would be imposed on the controlled structure relying on external energy. It is therefore difficult to ensure that a large amount of external energy can be provided during an earthquake if active control is applied to the structure. Instead, passive control may be a reasonable option.  
In engineering practice, the elastomeric bearings and VFDs are usually used alone or simultaneously to control the force and displacement responses, and their effectiveness has already been verified in the transversal direction. However, considering that the cable-stayed bridge may experience large displacement in a longitudinal direction under strong earthquakes, the VFD, though proven to be effective, is difficult to use in the transversal direction [19]. The yielding steel damper (YSD) is another kind of dissipation device, which has the advantages of a lower cost, reliable hysteretic characteristic and a higher initial stiffness that can meet the demand of service load. It has various shapes that can adapt to different structure forms and thus has gained increasing application in recent years, not only in building structures but also in bridge structures [20; 21; 22; 23; 24; 25]. Generally, a YSD's specific form can be classified as E shape [26; 27], C shape [28; 29], X shape [30; 31], triangle shape [19; 20; 21] and pipe shape [24; 25] etc. Some new types of YSD have also been developed in recent years [22; 23; 24; 25; 25], and their effectiveness in reducing the seismic demands of several types of bridges has also been studied [19; 21; 26; 30; 31; 33; 34]. In particular, the application of YSDs in cable-stayed bridges are investigated [19; 20; 21; 28; 35], and one of them has also been verified through the shake table test [19; 28].  
However, the seismic design of YSDs installed in the transverse direction of cable-stayed bridges requires a time-consuming time history analysis. Additionally, the effect of their design parameters (such as the initial yielding strength of YSD) on the seismic reduction of bridges has not been well studied. Additionally, there exists a conflict between reducing seismically induced displacement and seismically induced force simultaneously for cable stayed bridges [12; 13; 26] when the energy dissipation system is adopted.  
This paper aims to obtain a simple and practical method to design YSDs based on the influence of their yielding strength (F\({}_{\rm y}\)) on the seismic responses of the bridge at different locations longitudinally (auxiliary pier, transition pier and tower column). Primarily, a finite element (FE) model should be established based on a real cable-stayed bridge in China. Furthermore, it is necessary to verify the FE model by comparing with the results of shake table test. Then, the FE model would be used to carry out a comprehensive parametric analysis to investigate the influence of F\({}_{\rm y}\) on the seismic responses of the bridge. The theoretically appropriate YSD design would be achieved according to a complicated multivariate function analysis or a simplified single variable function analysis in terms of different designed objectives. In order to develop a practical design method, the YSD working mechanism on the cable-stayed bridge is further investigated, and finally a method is proposed to quickly determine the yield strength of YSDs based on the investigation in this paper.