<p>During major earthquakes, fault ruptures frequently lead to significant differences in ground motions across the fault trace. As a result, fault-crossing bridges are subjected to complex seismic demands characterized by the combined effects of transient ground shaking and permanent fault displacement. Accurately representing such coupled effects remains a major challenge due to the limited availability of spatially consistent ground motion records and the complexity of the underlying mechanisms. To address this issue, this study evaluates two practical equivalent seismic input frameworks that explicitly incorporate permanent fault displacement while preserving the essential characteristics of ground motions. The seismic excitation is decomposed into two components: (i) dynamic inertial component induced by ground motion without permanent displacement, and (ii) fault-induced relative displacement component between the two sides of the fault, introduced either as a quasi-static input or as a time-dependent dynamic input. Based on this decomposition, the total structural response is obtained through response-level superposition. Four seismic input modes are systematically investigated, including non-uniform excitation (benchmark), uniform excitation, quasi-static equivalent input, and dynamic equivalent input. A three-dimensional finite element model of a simply supported bridge crossing a strike-slip fault is developed in OpenSees to assess the equivalent input frameworks. Results indicate that uniform seismic input significantly underestimates both peak and residual bridge responses, particularly for structural members located near the fault. In contrast, the two equivalent input approaches effectively reproduce the response characteristics of non-uniform excitation, with deviations within acceptable engineering limits. Thereby, the equivalent input frameworks provide a practical yet reliable seismic input representation for both numerical simulations and experimental studies of fault-crossing bridges.</p>