The paper presents the author’s approach to evaluating the dynamic resistance of existing building structures exposed to the action of paraseismic events. The idea of the approach was demonstrated in the example of an existing conveyor bridge, which is an important component of an industrial plant located in an area threatened by the occurrence of mining tremors. A scenario was analysed in which the object’s structure was not adapted to absorb additional dynamic effects. Therefore, it was necessary to determine the load-bearing capacity reserve within which the dynamic effects induced by a mining tremor could be allowed. As part of the analysis, criteria for selecting the authoritative section of the analysed object for further dynamic calculations were established and described in detail. As a result of the implemented evaluation procedure, the limiting values of the ground acceleration components were obtained, which are understood as the resistance of the analysed object in the context of carrying additional dynamic actions induced by a tremor. The determined resistance is included in the ultimate limit state STR framework, which sets the level of strength of particular structures’ components as a criterion. The limit values of the ground acceleration components were calibrated, taking into account other accompanying variable actions according to the Eurocodes guidelines. The study also justified using this approach and provides essential information about dynamic excitation’s most sensitive structural components. Such information can direct the process of retrofit or necessary strengthening of the structure when the evaluated resistance will exceed the intensity of existing or predicted seismic events in the area.