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.

Hydroelastic problems involve dynamically coupled, structurally elastic, hydrodynamic systems. The fluid can have many effects such as added inertia, additive hydrostatic stiffness, increased system damping, or external excitation (e.g. wave impact, variable current forces, etc.). This chapter illustrates some of the aspects of hydroelastic problems by deriving fundamental relationships and discussing a specific example - ship springing. Springing vibration is differentiated from whipping vibration by the source of excitation. Springing is excited by synchronous matching of the natural frequency with the incident wave encounter frequency while whipping is transient vibrations due to impact/slam loads. A well-developed energy method - the Rayleigh-Ritz method - is applied in the determination of fluid-structure resonance. For general marine vibrations, energy methods may be used when free surface effects are small or negligible. Fluid inertia effects are calculated using strip theory and Lewis form coefficients. Limitations of strip theory are discussed. A spherical globe mounted on a flexible pole submersed in water is given as an example of a hydroelastic system.

The analysis in this chapter of marine platform motions is directly applicable to any floating system such as ships, offshore platforms, floating wind turbines, or wave energy devices. The basic underlying model is the classic linear spring-mass-damper system. The mass will be augmented by the added mass of the fluid; the damping will be the result of the dissipation of energy by waves; the linear spring will be due to hydrostatic effects plus any external stiffness such as mooring lines; and the exciting forces are due to incident waves. Depending on the body shape and mass distribution, the equations of motion can be dynamically/statically coupled. Wave excitation is comprised of Froude-Krylov and diffraction components. Solutions to the equations of motion in the frequency domain are expressed as RAO’s. The RAO is a linear operator representing the dynamic response of a system (e.g. displacement, acceleration, bending moment, etc.) per unit input, typically the incident wave amplitude. Once the rigid body dynamics are expressed as RAO’s, other quantities or dynamics of interest may be determined, e.g. relative motion, dynamic bending and shear.