A procedure for the static analysis of cable structures following elastic catenary theory

• The elastic catenary element is employed in the analysis of three dimensional cable structures.
• The contemporary presence of slack and taut cables and also compressed elements is admissible.
• The proposed element allows a unitary strategy for the form-finding and the structural analysis under general loading.
• The initializing step for the solution of the non linear system is furnished by the catenary form-finding.

The paper proposes an unitary strategy for the static analysis of general cable nets under conservative loads. A form-finding is first performed in order to initialize the successive non linear analysis. The numerical procedures carried on in both steps, form finding and structural analysis of the net, employ a three dimensional elastic catenary element. Equilibrium conditions at internal nodes and kinematic compatibility at the end nodes of each cable are used to derive the global equations of the net. When the pre-stresses are high and the topology of the net is involved, an accurate initializing solution is essential for the convergence of the successive numeric non linear structural analysis (performed by Newton method). The numerical applications highlight the capability of the proposed procedure to solve three dimensional problems with taut and slack cables, out of plane distributed forces (modeling wind loads), point loads along the cables. The contemporary presence of cables and compression truss elements is also considered testing the effectiveness of the method in the analysis of tensegrity structures.