The optimum structural design of the hull girder is discussed in this chapter. In the first part, early efforts at optimisation are described: structural optimisation, topology and scantlings optimisation and nonlinear programming. The use of linear and sequential linear programming and its use in the MAESTRO program are described. The need to consider wider issues is discussed and the various single-parameter optimisation criteria described (design for X). Multi-objective optimisation criteria and Pareto optimality are discussed. The background to genetic algorithms and the fundamental theorem of genetic algorithms are presented. Single and multi-objective optimisation using genetic algorithms is described and illustrated with application to a catamaran structure. The analytic hierarchy process used in the ranking of different criteria put forward by stakeholders in an optimum structural design problem is described. This is applied in a case study described in the last part of the chapter that concerns the optimum structural design of a RoPax carrier. In this finite element models are used in the concept design stage to select a topology of the structure as well as the preliminary design stage. A series of criteria selected by a number of stakeholders are used as a basis for the optimisation process.

Chapter 3 provides an introduction to the sea loads that act on ship structures, focusing on environment-related and transient loads. A hypothetical but realistic scenario of a loaded voyage of a bulk carrier is presented, and is used to identify and subsequently classify all loads that act on the hull girder. These are classified as environment-related, hull girder-related, mechanical equipment-related and cargo-related. The sources of environment-related loads are then discussed. These include hydrostatic pressure, wave loads, thermal gradients, ice loads, wind pressure and related variations on a geographic and temporal basis. Transient wave loads are then discussed (bottom slamming, bow flare impact and deck wetting), followed by a discussion on springing. The discussion of slamming includes hydroelastic effects. The need for nonlinear analysis in estimating springing and whipping loads is discussed in the last section of the chapter.

This chapter deals with the linear response of the hull girder to primary loads. The primary structure is defined and vertical bending axial and shear stresses are determined. The theory of shear stresses in open and closed sections is presented. Deflections related to both axial and shear stresses are discussed and hull girder longitudinal bending theory is validated against full-scale measurements. Initial design considerations for longitudinal strength are discussed in relation to rule requirements and the calculation of the section modulus of a transverse section. The combined effect of axial bending and shear-induced axial stresses is discussed and shear lag is defined and calculated. The effective breadth method is described. Horizontal bending of the hull girder is discussed next. The response of the hull girder to torsional loading is discussed next. Torsion theory of thin-walled sections is presented and this leads is applied to the analysis of sections consisting of a number of closed cells subjected to uniform torsion. The last section deals with the determination of critical regions of the hull girder for longitudinal strength with respect to yielding, given that the stress field is multiaxial, longitudinal bending stresses being one component.

The design of ship hulls girders for strength is presented in this chapter. Engineering design is introduced and the tasks of ship structural design discussed. The stages of ship structural design are presented: concept design, preliminary structural design and detail structural design. The concepts of design principles, design criteria and design philosophy are discussed and elucidated. The elastic and plastic design philosophies of ship structures are presented and differentiated. The means to perform rational design of ship structures are listed. The need to perform limit state design of ship structures is discussed and the limit states included in IACS rules mentioned. (serviceability limit state, the ultimate limit state, the fatigue limit state and the accidental limit state). The interaction of limit states is discussed as is that of relevant failure modes. In the last part of the chapter the theoretical basis of the design loads used in the IACS Common Structural Rules is described. The concept of the design sea state is introduced, the use of short-term analysis, the selection of dominant short-term sea states and the identification of dominant load components described. The concept of the equivalent design wave is introduced and in the last section design loads discussed.

In this chapter both hull girder longitudinal bending and torsional loading are treated. Ship-type bodies are considered in both still water and waves (quasi-static loading). The equations for longitudinal bending moment and shear force are obtained. Wave profiles are considered and the use of sectional area curves is illustrated. The balancing procedure of the hull girder on a wave is then described. The various factors that affect longitudinal bending moment and shear force distributions are discussed and reference is made to the Smith effect. Torsional loads are considered next and their generation is described in the case of both closed-deck and open-deck hull forms. Expressions obtained for torsional moments in the past as well as those included in the IACS Common Structural Rules are given. Wave loading of ship hulls is considered and classical linear strip theory is described. The IACS approach to estimating primary longitudinal bending loads and corresponding strength requirements is described. The role of classification societies in ensuring safety and durability is discussed, following which the formulas developed for bending moments and shear forces are presented.

This chapter deals with loads related to the hull structure, the operation of mechanical equipment as well as those related to cargoes. The loads related to the hull structure include hull weight, inertial loads, loads induced during the fabrication process (residual stresses) as well as loads acting during occasional circumstances. These include drydocking, launching, and conversion procedures. Grounding and collision that are undesirable events are also discussed. Loads that are induced by the operation of mechanical equipment are considered, the most important of these being propeller-induced vibration and vibration of the main propulsion machinery. Cargo-induced loads are discussed next. These relate to both cargo and ballast water and include weight, inertial loads and the effect of cargo shifting. Lastly thermal gradients are considered the most important cases being the heating of crude oil using heating coils and ensuring low temperature in the case of gas carriers. The loads acting on the hull girder are summarised in tabular form in which their relative importance is assessed. In the last section load action is described with the principal loads acting on the hull girder discussed as well as the different load systems (primary, secondary and tertiary).

This chapter deals with the application of structural reliability theory in the field of ship structural analysis and design. Sources of uncertainty in the marine environment are discussed, followed by the probability theory dealing with combined loads (still-water bending and wave-induced bending). Three applications of reliability theory are then presented: the development of the IACS reliability-based code for the strength of oil tankers, a comparison of ships designed before and after the introduction of the IACS Common Structural Rules and lastly the risk-based structural design of an oil tanker.

In this chapter the probabilistic modelling of hull girder primary loading and response are presented. In the first part the probabilistic modelling of the sea environment is described. The nature of the sea surface is described in qualitative terms, following which the short-term description is presented. Deterministic modelling is discussed and statistics descriptors of ocean wave records defined. The concept of the wave spectrum is introduced and spectra for moderate and rough sea states described and differentiated, as well as wave spectra for ship design. Ship response to wave loading is discussed. The importance of linear response is underlined and structural considerations described. The basis of extreme value theory is presented and the Fisher-Tippett-Gnedenko theorem is introduced. Extreme as well as combined loads in short-term seas are described. Long-term analysis of sea loads is considered next. Differences with short-term analysis are mentioned and the use of full-scale measurements at sea described. The statistical description of a critical wave height is described using firstly the return period, and probability of occurrence method and secondly the wave height and period approach (scatter diagram). Two methods used to conduct long-term analysis of sea states are described: the long-term cumulative distribution (LTCD) method and the simulation method.

Hull girder vibration is treated in this chapter using mathematical methods (differential equation and energy approach). In the first part elementary vibration theory is presented, progressing from the SDOF system to the undamped vibration of the Timoshenko beam. The energy approach to vibration is presented next. In the next part ship vibration is presented. The types of vibration encountered in ships are discussed and classified, following which the distinguishing features of ship vibration compared to that of a uniform beam are presented. These relate to structural layout, design and operational aspects and the marine environment (added mass effect). In the next section vibration arising from steady-state excitation is described. This concerns vertical, horizontal and torsional vibration. Expressions for natural frequencies in each mode are given. In the case of vertical vibration the differential equations of vibration of a ship hull girder are obtained and expressions for natural frequency included in various publications compared. The differential equations of coupled vertical and horizontal vibration are obtained and springing is discussed. Vibration arising from transient loading is discussed and includes slam-induced whipping and whipping induced by bow flare impact.