Forty years ago this month, the December 1979 issue of Popular Mechanics shows this idea, a version of which comes up every few decades: A bridge connecting Eurasia and America across the Bering Strait.
This design was by California engineer T.Y. Lin and was dubbed the Peace Bridge. It was designed for highway traffic and featured smoothly curved piers to deflect upward advance ice floes. The average water depth over the proposed route was a modest 150 feet, making the project somewhat feasible. This design used 1000 foot prefabricated sections that would be brought to the site by barge.
Lin set the price tag for the bridge at about $3 billion, which he noted was a drop in the bucket compared to the cost of the arms race.
Of course, even if a bridge was put in, there aren’t highways leading anywhere on either side, which would make the purpose of the bridge at least temporarily questionable.