Early tied‐arch bridges cannot satisfy the current traffic load demand due to their load grades and maintenance levels. Also, these tied‐arch bridges have accumulated structural damage with increasingly prominent safety risks. In order to accurately evaluate the characteristics of tied‐arch bridges’ structural‐influenced lines and identify damage of their arch ribs and suspenders, two analytical solutions are derived and established in this paper for the thrust‐influenced lines of parabola and catenary two‐hinged arches with a tie beam. A new method and an index for identifying damage of arch ribs and suspenders of tied‐arch bridges are proposed. The results of numerical simulation in this paper verified that the proposed analytical solution has good analytical accuracy in practice on those two‐hinged nonflat arches. With the use of equivalent thrust‐influenced line difference curvature, the effectiveness of damage identification and the verification method were verified on the tie beam, suspender, and arch rib of plane tie arch structure as well as the suspender and arch rib of tied‐arch bridges in this research. Furthermore, combining with grey relation analysis, the noise immunity of the proposed index method can be verified. Also, thrust‐influenced line recognition based on VMD (variational mode decomposition) is introduced, and a practical process of bridge health assessment based on the quasistatic‐influenced line loading of three‐axle heavy vehicles is established. Theoretical analysis and numerical verification show that the calculated error of the analytic solution of two‐hinged arches with a rise‐span ratio greater than 1/8 is less than 9.57%, and the error decreases with the increase of the rise‐span ratio. Therefore, it can be applied to the calculation and analysis of tied‐arch bridges with a rise‐span ratio range between 1/4 and 1/5. With the equivalent thrust‐influenced line index proposed in this paper, the damage of suspenders and arch ribs of tied‐arch bridges can be accurately located. It has been found that the proposed method is more effective to identify the damage of suspenders than the damage of arch ribs does, showing good noise immunity. In summary, this research has provided theoretical support for arch bridge design and evaluation. Combining with existing bridge‐monitoring methods, the new bridge damage identification method proposed in this paper has the prospect of realizing the normal health status assessment of existing tied‐arch bridges.

There is no analytical solution to the deflection influence line of catenary hingeless arches nor an explicit solution to the deflection influence line difference curvature of variable section hingeless arches. Based on the force method equation, a deflection influence line analytical solution at any location before and after structural damage is obtained, and then an explicit solution of the deflection influence line difference curvature of the structural damage is obtained. The indexes suitable for arch structure damage identification are presented. Based on analytical theory and a finite element model, the feasibility of identifying damage at a single location and multiple locations of an arch bridge is verified. This research shows that when a moving load acts on a damaged area of an arch structure, the curvature of the deflection influence line difference will mutate, which proves theoretically that the deflection influence line difference curvature can be used for the damage identification of hingeless arch structures. This research has provided theoretical support for hingeless arch bridge design and evaluation. Combined with existing bridge monitoring methods, the new bridge damage identification method proposed in this paper has the potential to realize normal health status assessments of existing arch bridges in the future.