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
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