This article is devoted to study of maximum and cancellation phenomena of multi-span railway bridges. For this purpose, six different configurations comprising two and three spans are considered. The governing equation of the beam bridge under moving loads is derived and solved analytically using Duhamel integral method as well as the Newmark Beta method, and the results are validated by those of other studies. Then, the free vibration response of the bridge under one moving load is obtained and the maximum and cancellation speeds are determined. After that, using the free vibration response, the conditions of maximum and cancellation phenomena are estimated and then compared with the results of the forced vibration. For this comparison, the peak values of the forced vibrations are utilized, which include the maximum values of displacement and acceleration along the entire length of the bridge. Based on this comparison, the effective modes are identified, and the contribution of higher modes is investigated. Then, some suggestions are provided to facilitate finding the peak values of displacement and acceleration. Finally, based on the mentioned method, the riskiest trains are recognized accurately. The method and results of this study can detect the challenging conditions of the system more accurately and with fewer calculations.

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