Ultimate Strength Assessment of Hull Girder under Cyclic Bending Based on Smith’s Method
Authors: Cui Hu-wei , Yang Ping 
Published: February 2018

Ultimate strength is a critical and fundamental consideration in the design of ship and offshore structures. Accurate assessment of the (residual) ultimate strength of a ship hull is important not only for the initial design, but also for the operation, maintenance, repair, and even for disaster management, rescue, and salvage assessment of the ship hulls. In fact, under ocean wave conditions, the hull girder is likely to withstand extreme cyclic bending. In this article, a simplified method based on Smith's method is proposed to assess the ultimate strength of the ship hulls under extreme cyclic bending. To obtain the nonlinear average stress-average strain relationship (σ-ε curve) of the basic structural element (consisting of a stiffener with its attaching plating) under cyclic in-plane compression and tension, systematic calculations are carried out by using a combination of the Beam-Column analysis and the nonlinear finite element method (NLFEM). By introducing the cyclic σ-ε curves of basic structural elements to a simplified calculation program, which is developed by the authors and based on Smith's method, the ultimate strength of hull girders exposed to extreme cyclic bending is subsequently determined. The ultimate strength of three box girder models and an actual ship are obtained under cyclic bending by using the authors' developed procedures including the simplified calculation program and are compared with the corresponding results from NLFEM calculations and also the box girder experiments.

1. Introduction
Ultimate strength is a critical and fundamental consideration in the design of ship and offshore structures. An appropriate level of the ultimate strength of a ship hull is perhaps its most important guarantee of structural safety. Accurate assessment of the ultimate strength and/ or residual ultimate strength of a ship is pertinent not only for the initial design, but also for the operation, maintenance, repair, and even for disaster management, rescue, and salvage assessment of the ship hulls in accidental situations. Perhaps the first attempt to calculate ship hull girder ultimate strength was by Caldwell (1965), who applied a type of rigid plastic mechanism analysis to evaluate strength. Since then, naval architects have gradually realized various technology developments and advances of importance to the ultimate strength assessment of ship structures. Over the last two decades, the ultimate bearing capacity of ship structures (including plates, stiffened plates, and hull girders) in their many different modes of possible behavior has been widely studied, and a great deal of results developed, which have made possible an increasingly clearer understanding of the ultimate strength behavior of ship structures. However, because of the complexity and importance of the problem, and the need for continuing development is still felt, for example, as described in the 19th International Ship and Offshore Structures Congress (ISSC) report, which emphasizes that (even) "with these developments ultimate strength assessment is now becoming a more important issue to ensure the safety of ship structures."