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Modeling of the unsymmetrical hysteretic behavior is verified by pseudodynamic test results. It is shown that influence of vertical inertia force can not be neglected when e/h (e=eccentricity, h=pier height) is relatively large. A parametric study shows that under Level 2 accelerograms, steel bridge piers with intermediate eccentricity (e/h around 0.1\uff5e0.2) are susceptible to highest maximum displacement; And eccentricity definitely leads to higher residual displacement level than centrally loaded steel bridge 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