Ground motions at sites close to a fault are sometimes affected by forward directivity, where the rupture energy arrives at the site in a form of a very short duration pulse. These pulses impose a heavy demand on structures located in the vicinity of the fault. In this research, a probabilistic seismic demand analysis (PSDA) for a self-centering bridge is carried out. The bridge columns consisted of unbonded, post-tensioned, concrete-filled, fiber-reinforced polymer tubes. A bridge model was developed and non-linear time history analyses were performed. Three different methodologies that used spectral accelerations to predict structural responses were used, and a time-domain approach was used for PSDA. In addition to the three approaches, a time-domain PSDA methodology was also used. The results of the PSDA from the four approaches are compared, and the advantages of using the time-domain methodology are discussed. The results of the PSDA showed that for a site located very close to the fault (6 km in this study), earthquakes having a magnitude (Mw) as small as 6.5 can be significantly hazardous because the periods of pulses generated by small magnitude earthquakes coincide with the periods of the bridge. Since small magnitude events occur with greater frequency than large magnitude events, they can have important contributions to risk.