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    The simple relations to assess residual  hull girder strength are obtained, which may be  used as handy and reliable tools to help make timely decisions in the event  of an emergency.  Kalman et al(2002) investigated the effect of different damage modes of a hull section on the  residual longitudinal strength  of an impaired ship based on elastic theory,  fully plastic resistance moment theory and ultimate bending moment approach, respectively. The practical application of the computational link  between the residual strength contours and ship’s survival is further clarified in given example. Finally, it is suggested that the use of constant, residual strength contours  of  a damaged hull girder section to enhance assessment of a ship’s survival ability when exposed to longitudinal  vertical bending after an accident. Santos et al(2002) presented a probabilistic methodology  for assessing the survivability of damaged passenger  Ro-Ro ships through the identification  of critical damage scenarios. The Static Equivalent Method was used to calculate the critical sea state the ship can survive in a given damage scenario and Monte-Carlo simulation is used to take into account the uncertainties in the ship’s loading condition at the time of  the accident: intact draught, vertical and longitudinal  position of the center  of  gravity and permeability of the Ro-Ro decks.   From above  review  on the residual strength  of the damaged ship, the research on this field mainly focuses on the following two aspects: 1.  Estimating the influence of damaged ship members (such  as damaged panels  and damaged  stiffeners) on the hull girder ultimate strength. 2.  Based  on the empirical and semi-analytical methods, assessing the  residual longitudinal strength of ship after collision and grounding in order to providing handy tools to help make timely decisions in the event of  an emergency  at cost  of accuracy. The objective of this paper is to establish a procedure to evaluate the residual  ultimate hull  girder strength of damaged ship causing  by collision  or grounding  with considering the asymmetry  of cross section and the instantaneous  shift of neutral axis due to the local structure damage. Method and the interaction between the vertical and horizontal bending moment In this research, a simplified progressive  collapse analysis based on the Smith method (Smith, 1977; Dow & smith et al., 1981) is performed. The  stress-strain relationship  of element in the simplified  method is determined on the  basis  of a rational theoretical background.  The vertical bending moment is indeed the most important load effect when considering the hull girder collapse.  However, in many types  of ships, the combined effect of the  vertical and the horizontal bending moments is important especially after the ship is damaged.  As in the  case of biaxial compressive strength of the plates (Guedes Soares, C. & Gordo, J. M. 1996), the nature of the interaction problem requires the solution of two issues. One is the collapse  load in each inpidual mode, which  will be used as  normalizing factor in the interaction formula. The second problem is the interaction formula itself in  order to adequately describe the  combined effect of vertical and horizontal collapse moments. The problem of the interaction relation  for collapse of hull sections  under combined loading was addressed  in a preliminary study by Gordo Soares and  Guedes  (1995)  who analyzed the case of four single skin tankers. Mansour et al  (1995) also studied the  problem although  using a  different method to predict the  collapse load  and a  different interaction formula. Laterly, Gordo and  Guede  Soares (1997) extended their early work by considering five additional tankers with different  configuration  with double hull and with double bottom. Furthermore, in order to cover the range  of  representative hull types, six container ships, are also including in the calculation.
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