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Shock and Vibration
Volume 2014 (2014), Article ID 201425, 19 pages
Research Article

Ship Bow Force-Deformation Curves for Ship-Impact Demand of Bridges considering Effect of Pile-Cap Depth

1Department of Bridge Engineering, College of Civil Engineering, Hunan University, Changsha 410082, China
2State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China

Received 13 August 2013; Accepted 3 December 2013; Published 13 March 2014

Academic Editor: Vadim V. Silberschmidt

Copyright © 2014 Wei Fan and Wancheng Yuan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Since static analysis procedures in the vessel impact-resistant design codes neglect dynamic amplification effects related to bridge mass, ship-impact responses of bridges may be potentially underestimated. For this reason, several dynamic vessel-impact analysis techniques had been recently proposed, where a force-deformation curve was employed to model the vessel bow stiffness. Most of the recent works mainly focused on the force-deformation curves of the barge bows rather than the ship bows. In this paper, a high-resolution finite element model is developed to obtain the ship bow force-deformation curves. The global and local characteristics of the ship bow force-deformation curves are discussed based on the finite element crush analyses between the ship bows and the rigid walls. Effect of pile-cap depth on the force-deformation curves (rather than only impact forces) is studied in detail, and the corresponding empirical equations are developed using an energy ratio method. Finally, a practical example of ship-bridge collision is investigated to validate the force-deformation curves considering the effect of pile-cap depth. It is found from the case study that the effect of pile-cap depth plays an important role in quantifying structural demand under impact loads. The case study also indicates that the developed equations are reasonable in practical applications.