Abstract: For the dynamic demand assessment of bridge structures under ship impact loading, it may be prudent to adopt analytical models which permit rapid analysis with reasonable accuracy. Herein, a nonlinear dynamic macro-element is proposed and implemented to quantify the demand of bridge substructures subjected to ship collisions. In the proposed nonlinear macro-element, a combination of an elastic-plastic spring and a dashpot in parallel is employed to describe the mechanical behavior of ship-bows with strain rate effects. Based on the analytical model using the proposed macro-element, a typical substructure under 5000 deadweight tonnage (DWT) ship collision is discussed. Our analyses indicate that the responses of the structure using the nonlinear macro-element agree with the results from the high resolution model, but the efficiency and feasibility of the proposed method increase significantly in practical applications. Furthermore, comparisons between some current design codes (AASHTO, JTGD60-2004, and TB10002.1-2005) and the developed dynamic analysis method suggest that these design codes may be improved, at least to consider the effect of dynamic amplification on structural demand.

Key words: Nonlinear macro-element, Ship-bridge collision, P-a curve, Dynamic demand, Design codes

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