Nonlinear Model for Cable Trusses Based on Polynomial Shape Functions and Energy Approach

Abstract

Biconcave cable trusses are widely utilized in engineering applications, representing an economical solution for large span roofs. The most common modeling approach is via the finite-element method (FEM). Analytical approaches have been proposed for biconcave cable trusses to provide good approximations while reducing the number of variables of the problem, but most of them do not take into account the slackening of cables. The approach proposed in this paper is based on the classical Ritz approach, using polynomial functions to approximate the deformed shape of the cable truss. The equilibrium configuration is found via minimization of total potential energy. The approach is suitable for most load conditions (distributed and concentrated). The model takes into account the nonlinearities attributable to the slackening of both vertical harnesses and bracing cables. The number of variables is reduced compared to a FEM approach, while the results show a good agreement with the FEM solution. This general approach provides a consistent frame from which previously presented closed-form solutions can be derived as particular cases. A previously studied, 60-m-span plane structure is simulated under different load conditions. The results are compared to previous works and to the results of the FEM approach, showing good consistency.