Which is stronger a plank bridge or a arch bridge?

An arch bridge. I think that may have been discovered quite some time ago !!!

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It was - the Romans used arches extensively, in buildings as a well as for bridges. However, the arch is indeed stronger than the plank, or simple beam, bridge because it transmits the loads to its abutments. You can stiffen a beam bridge by fitting it with vertical side-members, or in larger structures, frames (trusses).