Cost-Effective Marine Fender Design Using an Elastoplastic Support Element: An Investigation
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 147, Issue 5
Abstract
This manuscript investigates the potential cost savings of installing a steel elastoplastic element in series, structurally, with a commercial rubber marine fender. Along with cost savings, the results also provide insight into the design requirements for the elastoplastic element. The approach to the study began with calculating abnormal impact energy for common classes of ships. Using that information, reaction force and required deflection for different levels of plastic deformation were determined. As the level of plastic deformation increases, the requirement for the rubber marine fender decreases. This allows the designer to use a smaller, less expensive, marine fender for a given kinetic energy associated with ship impact. The elastoplastic contribution to energy absorption was estimated using a steel reference element that was tested beyond yield. A Ramberg–Osgood model was fitted to the force-deflection data from the test and then scaled to the anticipated reaction for a full-size ship impact. From this, cost and required deformation of the elastoplastic element were compared. There is a clear trend of cost savings with increasing elastoplastic deformation. The results of the analysis indicate that an elastoplastic element installed in series with a fender might reduce fender costs by several thousand USD to over USD 40,000 per fender. To realize such savings, the full-size elastoplastic element will have to tolerate deflections of 100 to 400 mm while supporting the reaction from a ship coming to rest at berth. Commentary on performance for pre- and post-yield conditions is also provided.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. The following data is available upon request:
•
The spreadsheet of Table 1A.
•
The raw data from the testing of the W6 beam.
Acknowledgments
This study was supported by the Naval Academy Research Council (NARC) program. The NARC is an internal funding program for new faculty at the United States Naval Academy. I would like to express my gratitude to the managers of that program and thank them for supporting my effort. The testing of the W6 specimen took place at the Thomas M. Murray Structures Laboratory at the Virginia Polytechnic Institute and State University (Virginia Tech). I would not have been able to acquire the data for the reference elastoplastic element without the effort and generosity of the staff at the laboratory.
Disclaimer
Strictly for the purpose of discussion and conveyance of original ideas, this manuscript uses actual cost information that was tendered in a hypothetical context. The true cost or cost savings that may be realized by the concept presented here cannot be known until working prototypes have been developed and implemented. The author is not responsible for costs or savings of any actual systems that may result from the topic discussed in this manuscript.
Notation
The following symbols are used in this paper:
- CC
- berth configuration coefficient accounting for the type of dock construction;
- CE
- eccentricity coefficient accounting for the orientation of the ship as it contacts the fender;
- CM
- virtual mass factor accounting for the mass of water moving with the vessel as it impacts the fender;
- CS
- softness coefficient accounting for the relative stiffness between the fender and the hull;
- EA
- abnormal berthing energy;
- EEP
- energy absorbed by the elastoplastic element;
- Efender
- energy used to select a fender for the elastoplastic system;
- EN
- Normal Berthing Energy;
- design energy for fender per manufacturer specifications;
- F
- applied force;
- Fo
- applied force at displacement, δo;
- Fy,reference element
- force at yield for the reference element;
- fEP
- fraction of [(S.F.) − 1] attributed to the rubber marine fender;
- MD
- displacement of the vessel [tonne];
- reaction of rubber marine fender at design displacement;
- r
- fitting constant; ≥1;
- r′
- F − δ model fitting constant; ≥1;
- (S.F.)
- safety factor specified in Trelleborg (2021);
- s.f.
- scale factor for Ramberg–Osgood model;
- VB
- approach velocity of the vessel [m/s];
- α
- fitting constant; ≥0;
- α′
- F − δ model fitting constant; ≥0;
- γ
- shear strain;
- γy
- reference shear strain;
- δ
- displacement of the applied force;
- δo
- displacement of elastoplastic element to fully account for surplus energy;
- δy
- reference displacement;
- τ
- shear stress; and
- τy
- reference shear stress.
References
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PIANC (International Navigation Association). 2002. Guidelines for the design of fender systems. PIANC WG-33. Report of Working Group 33 of the Maritime Navigation Commission. Brussels, Belgium: PIANC.Trelleborg. 2021. “Trelleborg marine systems: Fender application design manual.” Accessed February 4, 2021. https://www.trelleborg.com/en/marine-and-infrastructure/Resources/Design-Manuals-and-Guides.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 147 • Issue 5 • September 2021
Copyright
© 2021 Published by American Society of Civil Engineers.
History
Received: Nov 6, 2020
Accepted: May 10, 2021
Published online: Jul 2, 2021
Published in print: Sep 1, 2021
Discussion open until: Dec 2, 2021
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