###### Abstract  
Ballastless tracks have a high smoothness, but the corresponding laying requirements are strict. Therefore, the maximum span of cable-stayed bridges that can accommodate ballastless tracks is 392 m. For laying ballastless track structures over larger spans, the deformation characteristics of long-span, cable-stayed bridges under complex loads are incompletely understood, and the interaction between them and long-span track-bridge structures is unclear. The influence of the wavelength of the cosine wave on the track-bridge mapping of different orbital structures was explored. The wavelength characteristics of vertical deformation under complex loads were investigated. The track-bridge integrated model for the cable-stayed bridge was established to analyze the mapping relationship between the rail and the bridge and the wavelength characteristics of deformation. Based on the mapping relationships and the wavelength characteristics of deformation, the train-track-bridge dynamics simulation model was simplified. The results show that, when the minimum wavelength of bridge deformation surpassed 6 m, 10 m, and 16 m, the rail deformation in the ballasted track, the longitudinal-connected track, and the unit slab-type ballastless track accurately mirrored the deformation of the bridge. For the span of bridges ranging from 200 m to 600 m, the wavelength of vertical deformation ranged from 21 to 1270 m under complex loads. During local loads, the vertical deformation below the 200 m wavelength constituted a significant proportion near the pie. Considering the influence of the deformation on the train vibration response, the train-bridge dynamic coupling model can be employed to treat the track structure as a load to reduce the complexity of the model and enhance the calculation efficiency. b 2020 202  
Some scholars have investigated the stiffness of long-span, cable-stayed bridges and girder-rail synergy. [PERSON] et al. [5] systematically summarized the large-span, cable-stayed bridges of railroads constructed in China and put forward the recommended vertical deflection-to-span ratios for the large-span, cable-stayed bridges of railroads and public railways. [PERSON] et al. [6] investigated the effects of structural parameters such as the number of side-span auxiliary piers, the side-to-center span ratio, and the main beam's width-to-span ratio and height-to-span ratio on the stiffness and mechanical properties of cable-stayed bridges. [PERSON] et al. [7; 8; 9] explored the effect of elastic matting stiffness on the deformation of the main beams of large-span, railroad, cable-stayed bridges and the structural deformation of the interlayer of ballasted track slabs on the bridges and found that the uneven deformation of the interlayer between the track slabs and the base slabs could be better managed through the use of rubber matting. Taking a long-span, cable-stayed bridge with a span ranging from 300 m to 1000 m as the research object, [PERSON] et al. [10; 11] established a refined, nonlinear model of large-span, cable-stayed bridge-ballastless track, analyzed the deformation characteristics of the long-span, cable-stayed bridge under the action of train load and temperature, and proposed that the measurement value of the mid-span chord, with a length of 60 m to 40 m, has a better match with the vertical vibration acceleration of the car body. Based on the principle of the midpoint chord measurement method, [PERSON] et al. [12; 13] investigated the relationship between long-wave track irregularity and car body vertical acceleration in high-speed railroads and proposed the 60 m chord control standard of track irregularity under 250-350 km/h. [PERSON] et al. [14] measured the track unevenness statistics of the different wavelength track unevenness and body acceleration relationship; the study shows that, at anything greater than a 200 m wavelength, the effect of the track irregularity on the train body acceleration is negligible.