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A Simplified Approach to Estimate the Ultimate Longitudinal Strength of Ship Hull

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A Simplified Approach to Estimate the Ultimate Longitudinal Strength of Ship Hull 130 Journal of Marine Science and Technology, Vol. 11, No. 3, pp. 130-148 (2003) A SIMPLIFIED APPROACH TO ESTIMATE THE ULTIMATE LONGITUDINAL STRENGTH OF SHIP HULL Hsin-Chuan Kuo* and Jiang-Ren Chang** Key words: simplified approach, ultimate longitudinal strength, hull girder, “collapse” have been identified as responses to an ex- stiffened panel. cessive hull girder bending moment. These may take place, presumably, with but a single application of load so that the possibility of their occurring must be weighted ABSTRACT against the extreme or worst likely load value. In additions, because aging ships may have suffered dam- In this paper, the calculation of the ultimate longitudinal strength ages due to hull corrosion and fatigue, their structural of the ship hull is revisited. A simplified approach dealing with the longitudinal ultimate strength of ship hull has been developed and an resistance may weaken and further collapse under ap- effective numerical program is implemented based on the individual plied loads even smaller than designed loads. components of ship structures. It is, then, possible to find the ultimate The conventional longitudinal strength calcula- strength of the whole ship structure by evaluating those individual tion for a ship mainly concerns the elastic response of components. Comparisons of numerical results from the proposed hull girder due to an assumed wave load and then, the approach and published literatures are conducted for further validation. Since relative errors of calculations of the current approach to the elastic section modulus of hull girder, which is taken as literature with respect to the experimental data are within 3%, it is the primary surveying index of the longitudinal bending shown that the proposed approach can be adopted for the estimation strength, can be achieved by using the linear bending of the ultimate bending strength of ship hull in sagging or hogging theory. However, this criterion may fail when two ships condition with and without at fully plastic state. In addition, a having identical section modulus with the same materi- comparison between the numerical result and the existing expression for a very large crude carrier also shows that the proposed approach als may have different bending strengths due to differ- is not only as accurate as those published literatures but also more ing resistance to buckling of the compressed parts of available. Therefore, the proposed approach with the numerical girder sections. program is quite suitable to be adopted in the preliminary design of With the full scale structural tests, Vasta [44] ship structure due to its accuracy and simplicity. found that a close correlation between the ultimate bending strength of the hull and the buckling strength of INTRODUCTION the compressed parts of the hull plating exists and proposed that the limiting bending moment of longitu- In the past three decades, a great deal of activity dinally framed hull should be the product of the section has taken place for predicting, in a realistic manner, the modulus and the ultimate stress of plating panels. This sea loads to which the ship hull girder is subjected. The formula is simple; however, it takes no account of main initiative behind these activities is the possible buckling effects from compressed parts. With a com- deficiencies in the standard calculations of the longitu- parison to the conventional elastic bending theory, dinal bending moments, particularly under certain Caldwell [5], therefore, developed the “limit design” circumstances. The ultimate strength of ship structures ideas and introduced the concept of a structural instabil- has been considered very important in the societies of ity strength reduction factor for strength calculations. classification and academic research since the loads However, only calculation with a statical condition of acting on the ship hull are uncertain due to rough seas or loading may not be conformity with the real dynamic unusual loading and unloading of cargoes during loading of the girder. In additions, although the buck- operations. Several potential forms of catastrophic ling effect has been included in calculation, it may not be permissible to replace the distribution of longitudi- Paper Submitted 06/17/03, Accepted 08/12/03. Author for Correspondence: nal compression by an equivalent average ultimate lon- Jiang-Ren Chang. E-mail: [email protected] Associate Professor, Department of System Engineering and Naval gitudinal compression since the buckling phenomenon Architecture, National Taiwan Ocean University, 2, Peining Road, Keelung, depends on the stability of structures and has little or no Taiwan 202. connection with a “mean stress”. Nevertheless, when H.C. Kuo & J.R. Chang: A Simplified Approach to Estimate the Ultimate Longitudinal Strength of Ship Hull 131 the buckling characteristics are found with more re- moment of ships, Hughes [25] proposed a simpler ap- searches in this field, a modification to the formulae proximating method with a rationally based structure will enable the ultimate moment of resistance to be design concept, which does not neglect any reserve of found [5]. Cladwell [5] could be the first one to incor- panel compressive strength until its maximum resis- porate the buckling effects into the ship strength tance has been reached. The accuracy of this method, assessment. Since then, subsequent progress has been based mainly on the panel strength analysis, was dem- made in the fields of buckling as well as final collapse onstrated by a comparison with several experimental studies of structures [6, 11-13, 22, 30], and reliable results and it first led the optimal concept to ship estimates [18, 19, 43] have been emerged for analyzing structural designs. However, ignoring such a contribu- the collapse strength and their post-collapse behaviors. tion of the post-collapse resistance of compressed pan- However, those algorithms, used for calculating the els makes the evaluation of the ultimate strength of a ultimate longitudinal strength of the ship hull girder, redundant structural system impossible. It should be usually differ one another due to their different noted that, in this method, discrete steps from one assumptions, and lack of accurate modeling of the hull element collapse to the next was suggested instead of girder results in unreliable results even in the case of an applying regular small increments of curvature. experimental investigation [32]. By adopting most positive features of the above- Following with Caldwell’s research, Faulker et al. mentioned works with introducing new stress-strain [13] proposed a reasonable method to calculate the relationships, Rahman and Chowdhury [40] developed structural instability strength reduction factor and im- a computing methodology for the ultimate value of the proved formulations became available for critical stress longitudinal bending moment at any cross section of a corresponding to various modes of compression failures. ship or a box girder. The cross section was modeled as Progressive research on post-buckling strength of stiff- one stiffener with its associate effective plating. They ened panels inspired Dow et al. [10] to develop ways of claimed that limit states of these panels, either tensile or estimating average stress-strain characteristics up to compressive, were modeled in an appropriate manner compressive strain. By incorporating buckling behav- since the ultimate strength of the girder section is mainly ior models into an overall analysis of the hull girder as governed by the behavior of panels under compression. the bending curvature increases, Smith [42] also pro- Special attention was also driven to the collapse and posed the incremental curvature procedures to calculate post-collapse behavior of these panels. The computing the derivation of moment-curvature relationship for a program was ever validated by calculating the ultimate complete hull. Although some applications [4, 8] of this longitudinal bending moment of a very large crude approach have demonstrated its general feasibility with carrier (VLCC) which “broke its back” during dis- comparisons to model experiments; however, in our charge of oil in 1980. The ultimate longitudinal strength opinion, some calculating schemes, mainly based on the calculation, which put emphasis on modeling of the finite element formulations, need much time consump- buckling and post-buckling behavior of compressed tion and the plate element strength reached by way of parts of the same actual ship, was also reported [41] and empirical curves might lead to inaccuracy. showed that both the calculation and provision of longi- An engineering approach [4] considering a simpli- tudinal strength are in excess of normal requirements fied analysis model for each individual beam-column for the ship in both hogging and sagging conditions. element was proposed to calculate the strength of the Following with previous studies [4, 18, 19, 41] and hull girder by the linear superposition of individual especially with respect to plate strength and beam- contributions of elements. Based on a flexural-tor- column behavior, Gordo et al. [17] also presented an sional buckling formulation, Adamahak [1] developed approximate assessment of the ultimate longitudinal an approximate method in a computer program and strength of the hull girder. The method was also checked obtained curves of moment-curvature for the calcula- by comparing its predictions with those of Ref. [41] for tion of ultimate
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