To study the effects of the jacking stress level, height and strength ratio of the prestress tendons (λ) on the seismic performance of unbonded prestressed concrete (UPC) beams, six UPC beams and one reinforced concrete (RC) beam were tested under cyclic loads. The hysteretic characteristics, skeleton curves, ductility properties, energy dissipation capacity, strain distribution of reinforcement and self-centering capability of the specimens were studied and discussed. Numerical parameter analysis was also carried out by using OpenSees. The results indicate that three failure modes of UPC beams under cyclic loading were observed, namely the tension-failure mode involving a broken rebar, the compression-failure mode involving concrete crushing and the balanced failure. By considering the influence of the prestress position and magnitude, the modified reinforcing index ω was proposed to determine the failure mode. The ω is suggested to be less than 0.3 to ensure sufficient ductility. The effective stress level is linearly and positively related to the stiffness from cracking to yield K_cr and the ultimate bearing capacity of the UPC beam under cyclic loading. The stiffness of the UPC beam is slightly larger than that of the RC beam before yielding, and significantly greater than that of the RC beam after yielding. Due to the large strength reserve after yielding, the integrated seismic performance of the UPC beam is similar to that of the RC beam. When the λ was unchanged, the increase in the relative height of the prestressed tendons α_h is beneficial for the overall performance factor F, ductility and crack control. The stiffness degradation performance depends on the λ but is independent of the α_h. The total energy dissipation of the non-tensioned UPC specimen was 59% higher than that of the RC beam. The cumulative total energy dissipation of the tensioned UPC specimen was only 13% lower than that of the RC beam with the same number of cycles, indicating that the UPC specimen had a considerable energy dissipation capacity.

This study focuses on a critical aspect of bridge engineering -- the evaluation of cable forces, paying particular attention to the cables that are internally constrained by elastic supports. Detecting these cable forces is important for the safety and stability of bridges. The practical problem introduces a novel mathematical challenge: how to effectively address string vibration equations with one or multiple internal elastic supports,~which remains a theoretical issue not fully solved in engineering. To tackle this, it is necessary to firstly establish an appropriate mathematical model and accurately define initial-boundary value problems. We then formulate the well-posedness of the solution using both classical and weak solution approaches, supplementing the existing numerical results available in engineering. Meanwhile, we attempt to use PINNs (Physics-Informed Neural Networks) instead of traditional FEM (Finite Element Method) in engineering. Consequently, in contrast to the classical solution method, we demonstrate that for a string with finite elastic supports, the weak solution method not only improves mathematical modeling efficiency but also simplifies the process of explaining the well-posedness of the solution.