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.

The different types of uncertainty and the theories developed to account for them are presented in this chapter. The concepts of risk and reliability are introduced and defined following which basic probability ideas are discussed. The methods used to determine structural reliability are described (the direct integration method, Level II reliability methods and the Level I method). Level II reliability methods include the mean value first-order second-moment method and variants of it based on the Hasofer-Lind reliability index used in the case of nonlinear limit state functions and the Rackwitz-Fiessler procedure that has to be followed in the case of non-normal distributions. The Level I reliability method is discussed and the approach followed to determine partial safety factors described. In the next section fuzzy logic and fuzzy set theory are described. They are introduced by distinguishing between classical logic and fuzzy logic, following which fuzzy sets and fuzzy inference are described. In the last section the steps in the fuzzy inference system are presented and examples of such systems mentioned.

The nonlinear response of the hull girder to global loads is treated in this chapter. These include torsional loads, the result of major damage leading to loss of longitudinal strength of part of the hull girder, and hull girder collapse. In the case of torsional loads, of critical importance is the position of the shear centre, and this depends on hull girder geometry (closed or open section). The effect of structural arrangements is then described in relation to longitudinal warping. The effect of discontinuities is discussed and design issues are considered. Combined and coupled horizontal bending and torsion are treated next. The next section deals with the determination of reserve strength of the hull girder following damage. The approach followed by a classification society to calculating residual strength is described and the use of IACS Common Structural Rules in calculating residual strength of oil tankers is presented. The topic of the last part of the chapter is the ultimate strength of the hull girder in longitudinal bending. The need to calculate ultimate strength is discussed, followed by the calculation of ultimate strength using a simplified, upper bound approach. Progressive collapse analysis is presented and this allows for the gradual spread of elasto-plastic behaviour in individual stiffened plate elements of the hull girder.