Gourile is right that rivets do not pose a fatigue problem as much as bolts would. The railroad industry was the last to let go of rivets for just that reason.
Gourile is also correct that the concern would be fatigue not only around the rivet holes, but also due to the details of the crane support beams. Many "traditional" ways of framing cranes were done for many years before the effects of bad details were understood re: fatigue.
There are two primary culprits that usually occur. One is the use of knee braces that are installed to brace the rail beam longitudinally. The braces develop vertical forces in the beams which produce a lifting force at the column. This is resisted by the web connections to the adjoining beam, resulting in a stress reversal, and therefore, cyclic tensile forces around the web fasteners.
The other issue is the habit of connecting the webs of the beams, at the columns, to the side columns to brace against the lateral forces from the crane. This produces cracking in the webs of the runway beams at the columns. The preferred method of bracing is to attache the beam laterally at the top flange only, taking the lateral force more directly.
Both of these create the potential for cracking in the steel which can be discovered by a number of means...check with local testing labs for the most appropriate method.
Also...the older steel was much more brittle than steels now used, so cracking is not just possible, but probable.