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Chapter 1 Introduction
1.1 Introduction
The ship structure is a complex assembly of longitudinally and transversely stiffened plates, frames, brackets, bulkheads, beams, stringers, etc. Ship structures while in service are subjected to various types of loads: static loads, low-frequency loads, high- frequency dynamic loads and impact loads (e.g., Paulling 1988). The ship structure is designed with sufficient strength to sustain loads and deformations throughout its design life of 20-25 years. The bending strength of the ship hull is considered in three forms:
longitudinal strength, transverse strength and torsional strength. The longitudinal strength or the ship hull girder strength is the most fundamental of all and it is necessary to compute that strength accurately. During normal seagoing and approved loading conditions a ship hull sustains smaller applied loads than the design loads without causing buckling or yielding. In rare cases, the applied loads may exceed the capacity and global collapse may occur. Further, due to presence of fabrication related initial imperfections (initial deflections and welding residual stresses), and/or influence of aging processes like corrosion, there could be significant strength reduction as well.
Under longitudinal bending (both in sagging and hogging condition), if the applied loads are high enough, structural members in the hull can undergo buckling in compression and yielding in tension. Nevertheless, these failed (i.e., buckled or yielded) members do carry additional loads beyond the onset of buckling or yielding. The structural effectiveness of such failed members’ decreases and redistribution of internal stresses to the adjacent members occur. As the loads continue to increase, failure of structural members will occur progressively until the hull girder reaches its maximum i.e., ultimate strength. This is the real measure of the hull girder strength. The ship hull can not carry additional load beyond ultimate strength but carries progressively lesser load depending on the properties of the collapsed structural member and loading
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condition. From the structural safety point of view it is therefore necessary to evaluate the ultimate strength accurately.
1.2 Estimation of ultimate strength
Estimation of the hull girder ultimate strength can be approached from three different considerations: (i) fully plastic moment, (ii) initial yield moment, and (iii) instability collapse moment computations. The last one is the most accurate. The plastic moment mode gives an upper bound on the ultimate moment and is never attained in a hull of normal proportions. The initial yield moment mode assumes that buckling does not occur prior to yielding and is computed as the product of the standard elastic section modulus of the ship hull at deck or bottom and the yield strength of the material. Most Classification Society Rules require calculation of the longitudinal strength based on the initial yield moment. The initial yield moment is higher than the true instability collapse moment which considers the buckling and post-buckling strengths of the hull and is always the governing mode of failure.
The determination of the true ultimate strength of a ships’ hull, has become a topic of increased interest to the ship research and design communities. The knowledge of the limiting conditions beyond which a hull girder will fail to perform its function helps in assessing more accurately the true margin of safety between the ultimate capacity of ship hull and the maximum moment acting on it. Assessing the margins of safety more accurately leads to a greater confidence in the design. It may also bring changes in regulations and design requirements with the objective of achieving uniform safety standards among different ships.
1.3 Shortcomings in available methods
Most of the ship structural design criteria and procedures given by Classification Societies are based on the first or initial yield of the hull structures together with buckling checks for structural components and not for the whole hull structure (IRS 2009). Such
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they fail to assess the survivability and safety of aged ship structures, except in rather rudimentary ways. For example, IMO (2000) permits 10% reduction in the required minimum hull girder section modulus as a criterion for new build. Classification Societies set criteria for maximum permissible diminutions for hull structure elements up to 25 %. They assume different linear corrosion growth rate for different elements.
The in-service damages include age-related degradation such as corrosion wastages, fatigue cracking damage and local dents. Corrosion wastage is classified as general corrosion (uniform corrosion) and localized pitting corrosion. The degree of corrosion wastage depends on the corrosion environment which is different for different ship types (e.g. oil tanker, bulk carrier, ore carriers, etc.), the location of structural member (deck, bottom, side shell, etc.) and type of structural member (plates, stiffener web, stiffener flange, etc.). Also, statistics showed that the corrosion process is a random phenomenon. In addition, fabrication induced initial imperfections (initial deflections and welding residual stresses) have considerable negative effect on the ship hull ultimate strength. Also, there can be material changes like softening in the heat affected zone due to fabrication related operations but can be ignored in case of welded steel structures.
Initial deflections can be initial deflection of plating between support member (stiffener/longitudinals), column type deflection of stiffeners and sideways initial deflections of stiffeners. Available statistics showed that both the magnitude and shape of initial deflections are random in nature. Incase of welding residual stresses, magnitude and its pattern are random. Replacement of damaged or corroded members and dry docking can be expensive. Furthermore, available data show that deleterious factors (corrosion loss, initial deflections and residual welding stresses) are random in nature.
The reviewed literature does not show enough studies on this subject, as has been critically appraised in Chapter 2. The present study evaluates the effects of these random imperfections and ageing effects due to corrosion wastage on the hull girder strength.
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1.4 Scope and objective of the present investigation The scope of the present investigation is restricted to:
• Only vertical bending moment is considered in the estimation of the ultimate hull girder strength. Effects of horizontal bending moment, shear force and torsion are neglected.
• It is assumed that structural members collapse locally between two adjacent frames neglecting the overall deformation behaviour of the structure. Initial deflection of plating between two stiffeners is accounted only and those of stiffeners are ignored.
• The initial deflection shape is restricted to buckling mode shape and only initial deflection magnitude is random. Only magnitude of the welding residual stresses is considered to be random and the fixed idealized distribution pattern is assumed. Only material yield strength is assumed to be random and softening of heat affected zone is ignored.
• Only general corrosion in longitudinal members of ship hull is considered while studying the in-service damage of the hull girder and other corrosion forms like pitting corrosion, grooving corrosion and weld metal corrosion are ignored. Other types of in- service damage agents like fatigue cracks, mechanical local dents due to permanent set are not taken into account.
• Randomness in the geometrical properties (e.g. dimensions, gross thickness) is ignored. Also, randomness in the Young’s modulus is not accounted in the material properties.
• Only bulk carriers and oil tankers are analysed in this thesis, although the methodology can be applied to other types of ships as well.
The main objective of the present investigation is to obtain accurate estimates of the random ultimate bending strength of ship hull girders by:
(i) developing more realistic models of progressive collapse behaviour of the transverse sections
(ii) incorporating fabrication-related initial imperfections in the model and associated
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(iii) incorporating corrosion loss during service including the effects of random initiation time, random corrosion rates and spatial randomness in the corrosion loss process obtained from actual survey data.
1.5 Outline of thesis
Chapter 2 of this thesis reviews and presents a critical appraisal of the existing methods (based on direct calculation, progressive collapse analysis, finite element analysis and idealized structural unit methods) for estimation of ultimate hull girder strength of a ship subjected to longitudinal bending. Analytical and empirical based formulations for analysis of un-stiffened plate and stiffened plates are reported. Various time dependent models of general corrosion growth (empirical and phenomenological) are reported in detail. The effect of corrosion loss on hull girder ultimate strength is reviewed.
Chapter 3 describes the detailed methodology adopted in this study which involves a Simplified Incremental-Iterative Method (a form Smith’s method) with advanced stress-strain relationship developed for plating between two stiffeners. This proposed derivation accounts the effects of initial imperfections both initial deflection and residual stresses. Accordingly, stress-strain relationship for stiffened plates for different modes of failure is modified. The effect of randomness in initial imperfections and yield strength, including statistical dependence in these parameters among the structural elements of the hull, is investigated. Detailed numerical examples involving two benchmark hull structures are presented.
Chapter 4 presents a study on temporal and spatial aspects of random corrosion in ship structural elements. Data on corrosion diminution of five existing bulk carrier are collected and analyzed. Statistics of corrosion initiation time (coating life) and random growth law parameters are determined. Properties of the random corrosion field are investigated based on corrosion data from topside tank platings.
Finally, Chapter 5 summarises concluding remarks from the present study and recommendations to drive the future study are given.
