Equivalent stiffness of non-symmetrical cable systems in cable-stayed bridges

Currently the ideal of aesthetically pleasant design in cable-stayed bridges coincides with the search for lighter configurations that unfortunately are more prone than others to instability as they involve slender elements characterized by remarkable geometrical nonlinearities. At a conceptual and preliminary design stage, take into account this complex element interaction can appear an excessive modelling effort. Therefore, subsystems to preliminary size the main elements are commonly used and refined analyses can be postponed at an advanced design stage. The convenience of having at disposal analytical formulations able to include the main structural features while retaining a relatively simple form is thus evident. Within this framework, in the present work the restraining action offered by the cable arrangement to the pylon displacement is evaluated by deriving an expression for its equivalent stiffness. The inherent nonlinearity of long heavy cables associated to their pronounced sag is considered by applying Dischinger's formula. The formulation derived to study the in-plane behaviour of the subsystem that consists out of the pylon and the cables can be extended straightforward to study the out-of-plane behaviour. Finally the equivalent stiffness can be used, either in analytical formulations either in simplified numerical models, to define the critical loads associated to in-plane and out-of-plane buckling and to consequently size and preliminary design the pylon cross-section.