Static form

The aim of this research is to propose and develop an analytical exact solution for finding the static equilibrium configuration of a catenary before and after incurring defects such as tension loss or a broken dropper. The procedure includes considering the steady-state solution of the dynamic motion equation of the contact wire and the messenger cable. The wire and the cable are considered as tensile Euler–Bernoulli beams. The stiffness matrix of the beam is configured and is used to calculate the dropper's dead load. Progressively, a novel method is proposed to find the equilibrium configuration of the same catenary after the defect. The results prove that the tension loss in the messenger cable is more precarious than the tension loss in the contact wire. The broken dropper causes a significant sag in the sub-span and increases the static forces of the adjacent droppers. A comparison with field measurements justifies the accuracy of the results of the proposed model