Cable-stayed u-bow bridge

With new materials, cable-stayed bridges have longer than ever span (1.1 km for now), however, still twice shorter as suspended.

My offer is to expand its capabilities with a bow like structure.

The main arc framework (1) could be essentially thinner than a concrete tower of cable-stayed bridges since it is under tension from both sides (internal stayed cables 2 and common stayed cables 4).

The main tensioning cables (2) keep the bow rigid in u like shape and extend the bridge span compare to common cable-stayed structures (5). Some extra support (3) redirects tension from the main arc.

Update 09/2018:
It's is nice to know that this idea was not too far-fetched:
Searching for new bridge forms that can span further

https://www.sciencedaily.com/releases/2018/09/180919083440.htm

Hybrid Cable-stayed-Suspension bridge

There are two main types of cable bridges cable-stayed bridged with tentioned cables and self suported base (like Pont de Normandie) and Suspension bridge (like Golden Gate) with long main cable and suspended cables. 

Cable-stayed are easier to build but they have shorter the span than Suspension bridges. Suspension requires huge anchores (in most cases) and more complicated to build (firs main cable than support). 

http://theconstructor.org/structures/classification-of-steel-bridges/2092/

The longest current cable-stayed Russky Bridge is actually 1.1 km

I offer to join them in hybrid mode to possibly get some extra benefits. 

Stayed cables (1) work for short distance. They are build in first place covering essential part of  the bridge. Futher from the base the angle makes them ineficient. 

The main suspended cable (2) takes the weight of the middle section of the bridge through short suspended cables (3).  The anchors (4) could be smaller and the main cable is thinner. 

 To make bridge a bit more rigid to the side wind vibration amplitude some short extra support (4) could be added to form structures like in extradosed bridges.