Vintage photo from Clermont County Historical Society
Photo uploaded by Rick Shelton
View this photo at clermont-county-history.org
BH Photo #515926
I wish I could help more with this, but I'm just settling into middle age, so despite rumors to the contrary I wasn't around when this happened. :)
Without any other sources, either date could be correct.
I don't know if this is something you would want to pursue, but there was a similar steel truss to this one several miles away that carried Round Bottom Road over the same East Fork. It was taken down in the mid 80's. Unfortunately, I have no personal history with it so that's all I can give you.
I added both dates in for future reference. Even if it did go down in 1913, a three-year replacement timeline would have been entirely plausible given the magnitude of destruction from the flood. With counties having to replace dozens of bridges all at once, the process of rebuilding them all probably took years.
Also to point out that while it would probably take a tornado to wreck an iron truss due to its open nature, a covered bridge would have been lots more susceptible to simple straight-line wind damage. Thus, the "cyclone" may or may not have been an actual tornado, which may explain why it was never reported as such. Then again, as Nathan mentioned, weather forecasting and analysis wasn't anything like it is today in 1913 and/or 1915.
The Clermont County Historical Society still shows 1915 as the date of the " cyclone ". Obviously one of the dates is in error. With the build date of 1916 for the steel truss, I guess it would depend on how long they waited to replace the bridge.
In Ohio, I would assume by default that any bridge lost in 1913 was associated with that storm system, which did include tornadic elements. I don't see any recorded tornados in Ohio, but keep in mind in 1913 weather forecasting wouldn't have been as thorough as today. Some tornados might have occurred but not been officially recorded, while other damaging events like straight line winds might have been misinterpreted by local news agencies as tornados. I have speculated that the nature of the storm that destroyed the Chester, Illinois bridge in the 1940s might not be accurately described as well, as many sources described it as "windstorm of tornadic force" rather than a true tornado. Yet I find it hard to imagine that a bridge of such mass would be taken down by straight line winds, especially given the lack of collapses of similar bridge types elsewhere. Note this is all pure speculation from an untrained amateur weather nerd (me).
Lost Bridges says this one was destroyed in 1913....
Given the time frame, I wonder if the cyclone that took it down was connected to the flood of 1913 or the storms that caused it?