Damping ratio is a fundamental dynamic parameter of the structure. Recent monitoring of cable-stayed bridges has shown that the damping ratio changes under different operating conditions. In general, the damping ratio of a structure can only be evaluated after the structure is built, and it is still challenging to theoretically calculate the damping ratio of a structure beforehand. To further understand the mechanism of the bridge damping ratio, this paper proposes an evaluation method based on the damping dissipation function. The effects of the initial and modal strain energy of the structure on the damping dissipation are considered. The damping dissipation function of substructures of a laboratory cable-stayed bridge model was tested, and the structural system damping ratio was evaluated. Furthermore, the theoretical discussion and experimental verification of the effect of support friction on the damping ratio were conducted. The results indicate that the damping ratio of the substructure varies with both the vibration amplitude and the initial stress level. Consideration of the initial strain energy during testing the substructure damping dissipation function can lead to more accurate results in the evaluation of the damping ratio of the structural system. In addition, support friction also significantly influences the damping ratio of the longitudinal drift and vertical bending modes of the structure.