Even a child building a bridge from popsickle sticks would be uncomfortable with the idea of no support underneath or overhead, whether a crane dropped on it or not.
Wiki --> A truss bridge is a bridge whose load-bearing superstructure is composed of a truss, a structure of connected elements usually forming triangular units. The connected elements (typically straight) may be stressed from tension, compression, or sometimes both in response to dynamic loads. Truss bridges are one of the oldest types of modern bridges. A truss bridge is economical to construct because it uses materials efficiently.
As long as the concrete is in compression (which can be accomplished via pretensioning), the material can be used successfully in truss bridges.
There was a good FR article last month about the first railroad bridge to cross the Mississippi in 1856. See Bridging the Mississippi: The Railroads and Steamboats Clash at the Rock Island Bridge.