In bidirectional ductile end diaphragm systems (EDSs) in which buckling restrained braces (BRBs) are used as the hysteretic devices to provide ductile responses to earthquake excitations, BRBs that connect the abutments to the bridge's superstructure span across the expansion joints. Therefore, these BRBs should not only be designed to resist significant forces from seismic excitations, but would also be expected to accommodate the displacements due to the expansion or contraction of the bridge as a consequence of temperature changes. Such displacement demands on the BRBs would produce cyclic stresses and strains in the BRB's core plate, and the BRB must be designed to ensure that the low-cycle fatigue of the BRB is prevented over the design life of the bridge (or periodically replaced if having shorter low-cycle fatigue life). In the absence of such a consideration, BRBs would have to be connected to the abutment in series with lock-up devices to allow thermal expansion and contraction of the bridge under normal conditions but engaged during earthquakes, which is not a desirable detail. In this study, the low-cycle fatigue analyses of BRBs across bridge expansion joints are performed by subjecting a bridge to temperature changes from various cities to determine recommended design parameters. Resulting from these analyses, the minimum ratio of BRBs' core plate yielding length over total bridge length is recommended as 3% to avoid low-cycle fatigue over 75 years of thermal changes on the bridge superstructure.