On the force density method for slack cable nets

The design of cable nets and light tenso-structures requires a non conventional mechanical analysis, due either to the various sources of non linearity (large displacements, unilateral behaviour of the cables, non conservative loads) and to the fact that the initial configuration of the cable net is not known, depending on the prestress applied and, in general, on the dead load acting on it. As a consequence, the first problem that the engineer has to face is to determine the initial state of the structure under its own weight compatible with a set of fixed supports (the so called zero state). This problem is known as form finding.The paper examines the force density method for form finding, and it is presented a generalization that uses the exact expressions of the equilibrium derived from the equation of the catenary. The method allows to obtain an exact configuration that may be used as a starting point for subsequent incremental non linear analyses.In the paper it is shown that the use of the exact equilibrium conditions leads to a form finding method that is very similar to the FDM, but yields significant differences in the initial form when the weight of the cables is not negligible. A dimensionless parameter is introduced as degree of freedom of the form.