Analysis of Large-Sag Extensible Catenary with Free Horizontal Sliding at One End by Variational Approach

A variational approach for the static equilibrium configuration analysis of a large-sag extensible catenary with free horizontal sliding at one end is developed, considering the virtual work done by the catenary self-weight and the horizontal tension at the free sliding end support. The virtual work of the cable system is expressed in terms of the vertical coordinate, which is a function of the unstrained arc length of the cable. The stationary condition is applied to the virtual work functional to obtain the equilibrium configuration of the catenary. The validity of the variational approach is ensured by Euler’s equation, which is identical to the one derived by the force equilibrium consideration of a catenary segment. The finite element method is used to evaluate the numerical results. A parametric study is performed to demonstrate the effect of axial deformation on the equilibrium configuration of a large-sag extensible free horizontal sliding catenary. The results indicate that as the axial deformation increases, the total arc-length and horizontal span length of the cable also increase. Particularly, the very large-sag catenary configurations are studied and exhibited in this study.