The centre of the deck has a 42mm vertical deflection. The arches deform 30mm at the top points. The top diagonal deforms only 38mm at the centre when its weight is delivered to the arches. The regular deformed values of the arches and the deck confirm a good system for carrying gravity loads.
Diagonal Arch model (linear analysis vs. non linear)
Irregular deformations occur in this situation. The deck is deformed 61/10 ~ 6 times the arch, and 61/42 ~ 1.45 times the case of double arches.
This effect appears due to the fact that the 3D hanger system does not support the deck vertical effectively. The longest inclined hanger has a big sag of 2.042m due to its self weight. Thus, geometric non linear analysis should be applied when the load and deflection are no longer increasing proportionally at the deck location of the long inclining hangers. Prestressed hangers (cables) can be used to increase system stiffness of the hangers and to reduce the vertical deflection of the deck. In this case the vertical component of the hanger force should be equal to the weight of the hanger segment of the deck (multiplied by 9.82m/s2). Knowing the segment weight, one can calculate the tension force F in the hanger needed in the non linear analysis. The hanger in this case must be cable element with an initial prestressing force F as input.
Diagonal Arch with Cross-Ties model, vertical deformed values (m) 123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_
One possible method to reduce the vertical deflection of the hangers is to increase the in-plane stiffness of the hangers by connecting them together with a set of cross-ties as shown in the figure above.
To keep the calculation simple the linear analyse being used. The cross-ties are modelled as beam
elements carrying both tension and compression. No prestressing forces introduced,
i.e. the deflections of the deck and the arches will keep unchanged as the model without the cross-ties.
The vertical deformation of the longest hanger is now reduced by a factor 844/2029=0.42
From a dynamic perspective, the properties of the single hangers are modified by the presence of the lateral constraints that influence their oscillation characteristics too.
