Friction is an important source of energy dissipation in structural damping. The effect of friction on the damping ratio, however, has not been fully investigated. This paper presents an experimental study of the nonlinear damping ratio induced by friction at bolted joints of a bridge model in the laboratory. The decay responses of the bridge were tested under various bolt configurations and pre-torques. The nonlinear characteristics of the damping ratio were analyzed, and the experimental results were interpreted through numerical simulations. The relationship between damping ratio and amplitude of the Iwan model was derived. The results show that friction induces a nonlinear damping ratio. The damping ratio exhibits two opposite nonlinear characteristics under the influence of bolt joints. The damping ratio may either decrease with decreasing amplitude or may increase, and both of these nonlinear patterns can be elucidated by the Iwan model. Numerical simulations successfully replicate these two nonlinear damping ratios. A case study of an actual steel truss bridge is used to discuss the possible effects of bolt joints on the damping ratio. The results of this paper reveal the nonlinear damping patterns induced by bolt joints and provide an optional model for such structures.