An incremental formulation of the progressive collapse behavior of ship's hull girder with damages subjected to longitudinal bending is presented based on the Smith's method. The hull girder is modeled as a beam with asymmetric cross section subjected to biaxial bending. The explicit expression of the rotation and translation of the neutral axis due to the buckling and yielding of structural elements is given. The proposed formulation is applied to the residual strength analysis of bulk carriers and a tanker having collision damages at the side structures. Particular focuses are placed on the influence of the rotation of neutral axial on the residual hull girder strength and the solution procedures to obtain the residual strength including the case of biaxial bending.


Ship's hulls may suffer collision or grounding damages, which may threaten safety of ships and surrounding environment. In order to enhance the structural safety of ships and reduce the associated risks, the International Maritime Organization (IMO, 2009) has required in the Goal Based Standard (GBS) to consider the residual strength of the hull girder in specified damaged conditions as one of the functional requirements for the structural rules for bulk carriers and tankers. Ultimate longitudinal bending strength is the most fundamental strength to ensure the safety of ships not only in the intact condition but also in the damaged condition. Many studies have been performed on the assessment of residual bending strength of hull girders with damages. Paik et al. (1998) developed a rapid procedure to identify the possibility of hull girder failure after collision and grounding damages based on the closed-form formulae of the ultimate hull-girder strength and section modulus after the damages. Wang et al. (2002) proposed a similar approach based on the section modulus.

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