外文翻译Longitudinal strength of ships with accidentaldamagesGe Wang*, Yongjun Chen, Hanqing Zhang, Hua PengThis paper presents an investigation of the longitudinal strength of ships with damages due to grounding or collision accidents. Analytical equations are derived for the residual hull girder strength and verified with direct calculations of sample commercial ships for a broad spectrum of accidents. Hull girder ultimate strengths of these sample vessels under sagging and hogging conditions are also calculated, based on which correlation equations are proposed. To evaluate a grounded ship, using the section modulus to the deck would be optimistic, while using the section modulus to the bottom would be conservative. On the contrary, to evaluate a collided ship, using the section modulus to the deck would be conservative, while using the section modulus to the bottom would be optimistic. The derived analytical formulae are then applied to a fleet of 67 commercial ships, including 21 double hull tankers, 18 bulk carriers, 22 single hull tankers and six container carriers. The mean values, standard deviations and coefficients of variation for the coefficients in these new analytical formulae are obtained. The ship length exhibits little influence on these coefficients because they are close to the mean values although ship length spans from 150 to 400 m. The ship type shows some influence on the residual strength. Uniform equations are proposed for commercial ships which do not depend on a ship’s principal dim ensions. These formulae provide very handy tools for predicting the residual strength in seconds, without performing step-by-step detailed calculations, an obvious advantage in cases of emergency or salvage operation. r 2002 Elsevier Science Ltd. All rights reserved.Keywords: Residual strength; Hull girder ultimate strength; Section modulus; Damage; Collision;Grounding1. IntroductionTraditionally, ships have been designed to resist all loads expected to arise in their seagoing environment. The objecti ve in structural design has been to maintain a ship’s structural integrity for normal operating conditions. A combination of the most severe loads is usually selected as the nominal design load.Protection of a ship and the cargo it carries from damages incurred by accidents, though an essential issue in the design of watercraft, has been focused on subdividing a ship into compartments. National and international standards (Load Line,MARPOL, SOLAS, Classification Societies’ Rules) have established requi rements or watertight bulkheads and subdivision. Structural strength in collision, grounding or internal accidents (such as an explosion) has attracted very little attention.Public sensation increases each time there is a major loss of ships, cargo and life atsea, or when there is oil pollution from damaged ships. This motivates the development of design procedures and related analysis methods for accidental loads, in particular, the loads due to ship collision or grounding accidents.A ship may collapse after an accident because of inadequate longitudinal strength.However, the consequences of an accident on a ship’s strength are seldom investigated.Although there are some papers published on the residual strength of damaged ship hulls [1,2], this field still remains unexplored.This paper reports on an investigation of the longitudinal strength of damaged ship hulls for a broad spectrum of collision and grounding accidents. Both the hull girder section modulus and hull girder ultimate strength are calculated. We aim to obtain simple relations to assess residual hull girder strength, which may be used ashandy and reliable tools to help make timely decisions in the event of an emergency.Theoretical analyses are presented and analytical formulae are derived. Typical designs of 67 commercial ships, including 21 double hull tankers, 18 bulk carriers, 22 single hull tankers and six container carriers, which have lost portions of bottom shell plating and side shell plating, are analyzed to obtain such simple equations for predicting residual strength of damaged ships.2. Assumptions and analytical methods2.1. Section modulus of hull girdersIt has been a proven practice to use simple beam theory to analyze the global bending of hull girders. Many experiments have confirmed that the bending behavior of ships agrees quite well with the beam theory.The hull girder section modulus indicates the bending strength of the primary hull structures. The calculation of a midship section modulus is a very important step in basic ship design. Structural members that are continuous in the longitudinal direction are included in the calculation of the section modulus. Only members that are effective in both tension and compression are assumed to act as part of the hull girder. The section modulus to the deck or to the bottom is obtained by dividing the moment of inertia by the distance from the neutral axis to the molded deck line at the side or to the base line, respectively.2.2. Ultimate strength of hull girderThe hull girder section modulus is an indicator of initial buckling or initial yielding, which is usually not the state at which the ship achieves its ‘‘true’’ maximum bending capacity. Plates and longitudinals may experience elastic buckling, plastic buckling, post buckling, yielding, and/or fracture in the process of approaching hull girder ultimate strength.The so-called ultimate strength of hull girder corresponds to the maximum bending capacity beyond which the ship will break its back due to extensive yielding and buckling.The continuous improvement of knowledge regarding the behavior of hull girders and structural members has led to the development of various methods.ISSC 2000 Special Task Committee VI.2 [4] reviews the state-of-the-art technology for predicting hull girder ultimate strength. The committee conducted extensive benchmark calculations and assessed the uncertainties involved in these approaches.Among all groups of approaches (closed-form formulae, simplified analytical methods and nonlinear FEM simulations), the simplified analytical methods are favored by most analysts. These approaches save modeling time; they generally account for fabrication imperfections and provide reliable results. Extensive related studies have placed simplified methods as the first choice when one tries to calculate ultimate hull girder strength. A program of this kind, ALPS/ISUM[3], is used in this investigation.2.3. Extent of damages2.3. Extent of damagesEvery accident is different. The resulting damage also varies. Accidents require many parameters to describe the damage a ship sustains after an accident. A comprehensive description can easily fill a couple of pages or more, even though not all of the data is necessary for calculating hull girder strength. For simplicity, this paper uses definitions that are convenient for calculation but retain the main characteristics of accidental damages.For a grounding, it is assumed that the bottom shell and the attached bottom longitudinals are lost. No girders are assumed to be damaged after a grounding. This study investigates a broader range of bottom loss, up to 80% of ship breadth, to simulate minor to severe grounding damages.For a collision, it is assumed that the side shell and the attached longitudinals are lost. The damage starts from the deck at the side and extends downward. The deck stringer plate and longitudinal bulkhead that attach to the damaged side are assumed to be intact after an accident. A broad range of side shell loss, ranging from 5% to about 40% of ship depth, is considered.The assumptions mentioned above help to simplify the definition of damages. Only one parameter is used to describe the damage. Introduction of additional parameters is avoided. The focus is on shell plating, the first barrier from water flooding. Structures attached to the damaged shell are not considered with the assumption that they may be approximated by ‘‘smearing’’ as equivalent thickness of shell.There exist other assumptions with regard to damage extents. In the ABS Guide for assessing hull-girder residual strength [5], a grounding damage includes bottom girders attached to the damaged bottom shell to a certain depth; collision damage includes deck stringer plate and slope bulkhead plating attached to the damaged side shell plating for a specified extent. Paik et al. [1] defined collision and grounding damages according to this ABS Guide. For sensitivity studies, they analyzed 0.8 to 1.2 times the specified damage extents described in the ABS Guide. Wang et al. [2] analyzed a broad range of bottom damage, spanning from minor to substantial damage. Wang et al. also investigated cases where there is damage in bottom girders in additional to damage to the bottom shell.2.4. Presentation of resultsTwo means are used to indicate the longitudinal bending strength of a ship hull: hull girder section modulus and ultimate hull girder strength. Section modulii to thedeck and bottom, and ultimate bending strengths of hull girder under sagging and hogging are calculated and presented in dimensionless format; all are compared with their values at intact condition.Bottom damage is expressed as a percentage of the ship’s breadth. Side damage extent is expressed as a percentage of the ship’s depth.The investigation is focused on midship sections of typical commercial ships. Sections beyond midship are not analyzed in this paper but the same analysis may be performed on those sections readily.3. Simple equations for the residual section modulusFig. 1 is a sketch of a transverse section, which characterizes the geometry of a ship and ignores many details. This transverse section may be a double hull tanker, a bulk carrier, a container carrier, a single hull tanker or any other type of ship. The shaded area is the assumed damage caused by either collision or grounding accident.For an intact hull, the cross-sectional area, height of neutral axis above the base line, distance of the deck at the side to the neutral axis, moment of inertia and section modulus are A; z0; z1; I and eSMT0; respectively. The section modulii to the deck and the bottom, eSMdkT0 andeSMbtmT0; have been used by the industry to indicate the hull girder strength.ΔA is the cross-sectional area of the lost structure. Its center is c from the neutral axis of the intact hull. The c is positive when the center of the damaged area ΔA isabove the neutral axis. The shift of neutral axis Δz0 isWhereThe neutral axis moves away from the lost area. The moment of inertia of thedamaged hull becomesSubstituting Eq. (1) into Eq. (2) givesThe section modulus to a location of distance z from the neutral axis when z is abovethe neutral axis becomesSubstituting Eq. (1) into Eq. (3) and replacing eSMT0 with I=z into the aboveequation givesAn expansion of this equation by neglecting higher order terms of r gives theexpression for dimensionless section modulus for z above the neutral axisThrough a similar process, the following equation is derived for z below the neutralaxis:Eqs. (1)–(8) are applicable to general cases where there is an area loss in a transverse section.中文翻译:船舶危险状态下的纵向强度计算---Ge Wang*, Yongjun Chen, Hanqing Zhang, Hua Peng摘要此文将提到关于船舶在搁浅和碰撞两种危险状况下的调查报告。
