In this paper, new formulations to calculate equivalent damping ratios used in equivalent linear analysis of seismic-isolated structures, specifically isolated with lead-rubber bearings (LRBs), are proposed. These formulations are capable of incorporating the variation in LRB hysteretic behavior due to reduced bearing strength as a function of lead core heating. To quantify the accuracy of the proposed equations in predicting the maximum isolator displacements (MIDs), MIDs obtained from an extensive number of nonlinear time history analyses (NTHAs) were compared with predicted ones. NTHAs were conducted with two sets of near-field ground motions recorded at different soil conditions. It was found that different formulations are needed to calculate the equivalent LRB damping ratios for the two considered ground motion sets. It was also found that the proposed equations result in highly accurate MID estimations, regardless of isolator characteristics, soil properties, or seismicity levels.