# Handbook of Bottom Founded Offshore Structures

## Part 1. General Features of Offshore Structures and Theoretical Background

### Distributed for Eburon Publishers, Delft

*Handbook*will be a valuable reference for both engineering students and practicing professionals who seek a fundamental understanding of engineering’s underlying theories and technologies. Intended to help offshore engineers acquire and sustain relevant expertise in some notoriously difficult subjects, this installment stimulates reflection on and critical evaluation of the models used and the solutions found. Offshore engineering continues to develop and expand rapidly. While in the public eye its focus has shifted towards subsea and floating developments, bottom founded structures remain the industry’s dependable workhorses, far outnumbering subsea and floating applications. Moreover, the knowledge and technology that have literally pushed the boundaries of offshore engineering into more demanding environments and deeper waters have been largely pioneered by bottom founded structures. As such, the

*Handbook*will be generally applicable to offshore structures of all types.

1. An introduction to offshore engineering

1.1. What is offshore engineering?

1.2. A brief history of offshore oil and gas developments with the characteristics of four periods

1.3. Interactions of offshore engineering with other engineering fields

1.3.1. Civil engineering and naval architecture/shipbuilding

1.3.2. Mechanical engineering

1.3.3. Petroleum engineering

1.3.4. Other disciplines and engineering fields

1.4. Some special features of offshore engineering and offshore structures

1.4.1. Stages in a structure's life cycle

1.4.2. the offshore environment

1.4.3. Health, Safety and Environment

1.5. References

2. Offshore structures standards

2.1. Development of standards during offshore periods 1 and 2

2.2. Development of standards during offshore period 3

2.3. Developments of standards during offshore period 4

2.4. ISO offshore structures standards

2.5. Terminology

2.5.1. General

2.5.2. Terms related to the limit state design format (ISO 19900:2002)

2.5.3. Terms related to the variables used in the design process (ISO 19900:2002)

2.5.4. Other terms for general application (ISO 19900:2002)

2.6. References

3. A classification of offshore structures

3.1. Main classification

3.2. Options for a classification of platforms and structures

3.3. Classification by the manner in which structures resist direct actions

3.3.1. The direct actions

3.3.2. The equilibrium state

3.3.3. The structure's supports

3.3.4. Static vertical actions

3.3.5. Static horizontal actions

3.3.6. Dynamic actions

3.3.7. Classification of structure types

3.4. Definitions of structure types in ISO offshore structures standards

3.5. The worldwide population of offshore structures

3.6. References

Annex 3.A - Examples illustrating the various types of offshore structures

4.Models and modelling

4.1. Introduction

4.2. The modelling process

4.2.1. General

4.2.2. Modelling fluid-structure interaction

4.2.3. Examples of modelling other basic situations

4.3. Main characteristics of models

4.3.1. General

4.3.2. Model attributes

4.3.3. Examples of suitable choices for certain applications

4.3.4. Probabilistic versus deterministic models

4.4. References

Annex 4.A - A generic procedure for the solution of a problem

Annex 4.B - A few words on mechanics

4.B.1. Definition and classification

4.B.2. Mechanics of solids

4.B.3. Mechanics of fluids

4.B.4. Mechanics of soils

Annex 4.C - Use of models in practical applications

5. The offshore environment and environmental actions

5.1. General observations of the offshore environment

5.1.1. Introduction and overview

5.1.2. General aspects of the seabed, the atmosphere and the ocean

5.2. Wind models

5.2.1. The nature of wind

5.2.2. The wind profile

5.2.3. The wind spectrum

5.2.4. Wind actions and action effects

5.3. Current models

5.3.1. The nature of currents

5.3.2. The current profile

5.3.3. Current actions and action effects

5.3.4. Currents in the presence of waves

5.4. Wave models

5.4.1. The nature of waves

5.4.2. Periodic wave models

5.4.3. Random wave models

5.4.4. A comparison of the main features of periodic and random wave models

5.5. Wave spectra

5.5.1. General

5.5.2. Definition of frequency

5.5.3. The wave frequency spectrum

5.5.4. The original one-parameter Pierson-Moskowitz spectrum

5.5.5. The two-parameter Pierson-Moskowitz spectrum

5.5.6. The JONSWAP spectrum

5.5.7. Comparison of Pierson-Moskowitz and JONSWAP spectra

5.5.8. The high frequency tail of the wave frequency spectrum for wind seas

5.5.9. Swell spectra and combined wind sea and swell spectra

5.5.10. The directional spreading function

5.6. Waves with a co-existing current and waves as observed from a moving vessel

5.6.1. General

5.6.2. Waves with a co-existing current: intrinsic and apparent reference frames

5.6.3. Waves as observed from a moving vessel: intrinsic and encounter reference frames

5.7. Models for aerodynamic and hydrodynamic actions

5.7.1. General

5.7.2. Steady flow

5.7.3. Unsteady flow

5.7.4. Arbitrary flow

5.7.5. The inertia action in an ideal fluid

5.7.6. Classification of calculation methods for wave actions

5.8. Hydrodynamic actions on slender members

5.8.1. General

5.8.2. Hydrodynamic actions due to waves at a particular point of a circular cylinder

5.8.3. Correlation between hydrodynamic actions due to waves on circular cylinders at two horizontally separated points

5.8.4. Global wave-induced actions on a structure

5.9. Special environmental actions

5.10. References

Annex 5.A - Analysis of harmonic processes using complex numbers

5.A.1. Complex number representation of cos cot

5.A.2. Complex number representation of sin cot

5.A.3. Vector diagrams and manipulations in the complex plane

5.A.4. Alternative representation

5.A.5. Some further observations

Annex 5.B - Airy water wave formulae

5.B.1. potential flow problem

5.B.2. Velocity potential, dispersion equation and associated relationships

5.B.3. Complex number notation

5.B.4. Wave equations for all water depths and the phase function

5.B.5. Wave equations for all water depths and the phase function

5.B.6. Changes to the wave equations for deep water waves

5.B.7. Changes to the wave equations for shallow water waves

Annex 5.C - Guidance for modelling a structure by equivalent vertical sticks

5.C.1. Introduction

5.C.2. Vertical members

5.C.3. Members in a vertical plane perpendicular to the wave direction

5.C.4. Members in a vertical plane parallel to the wave direction

5.C.5. Members in a horizontal plane

5.C.6. Arbitrarily inclined members

5.C.7. Waves and a simultaneous in-line current

5.C.8. Variable submergence of members around the still water line

5.C.9. The influence of marine growth

5.C.10. Complete stick model

6. The dynamics of structures

6.1. A general introduction to dynamics of structures

6.1.1. Introduction and overview

6.1.2. Characteristics of time-varying applied actions

6.1.3. Characteristics of the body

6.1.4. Characteristics of the responses

6.1.5. The solution of dynamic problems

6.1.6. Organisation of the chapter

6.2. Some observations on dynamic problems for offshore structures

6.3. The single degree of freedom system

6.3.1. Introduction

6.3.2. Forced motions of the one mass-spring system with damper

6.3.3. Free motions of the one mass-spring system with damper

6.3.4. Generalization of the behaviour of the one mass-spring system to the dynamic behaviour of structures in general

6.4. Solving dynamic problems by an equivalent static method

6.5. Multi-degree of freedom systems

6.5.1. Introduction

6.5.2. Two mass-spring systems

6.5.3. The vibrating beam as an example of a lumped mass system with multiple masses

6.6. Continuous systems

6.6.1. Introduction

6.6.2. Lateral free vibrations of a string or cable

6.6.3. Longitudinal and torsional free vibrations of a bar

6.6.4. Free shear vibrations of a beam

6.6.5. Free bending vibrations of a beam

6.6.6. General formulation of the free vibrations of a slender structural component

6.6.7. Normal or generalized coordinates

6.6.8. Forced vibrations of beams

6.6.9. Wave propagation

6.7. Estimation of natural frequencies and mode shapes

6.7.1. Introduction

6.7.2. Illustration of Rayleigh's method for examples of continuous systems

6.7.3. Elementary cases of a vibrating bottom founded offshore structure with a free top end

6.7.4. Elementary cases of a vibrating bottom founded offshore structure with a constrained top end

6.7.5. Some further observations

6.7.6. Natural frequencies of systems supported by a combination of springs

6.7.7. Practical applications and estimating masses and stiffnesses for real structures

6.8. Modal analysis

6.8.1. General

6.8.2. Application to undamped free vibrations

6.8.3. Application to undamped forced vibrations

6.8.4. Application to damped vibrations

6.8.5. Practical application to large structures under broad band excitation with combined quasi-static and dynamic response

6.9. References

7. Response analysis in random seas

7.1. Introduction and overview

7.1.1. General

7.1.2. Organisation of the chapter

7.2. Classification of random processes and random variables

7.3. Relationships between time domain and frequency domain descriptions of random variables - an outline of the theoretical background

7.3.1. Introduction

7.3.2. Representation of a random variable

*x(t)*by Fourier series and determination of its corresponding frequency spectrum

7.3.3. Representation of a random variable

*x(t)*by Fourier transforms and determination of its corresponding frequency spectrum

7.3.4. Correlation functions in the time domain and determination of the corresponding spectral density functions in the frequency domain

7.3.5. Concluding observations

7.4. Short-term statistics

7.4.1. Introduction

7.4.2. The distribution of peak values

7.4.3. The average of the one-

*nth*highest part of all peak values

7.4.4. The distribution of extreme peak values

7.4.5. Time intervals between level crossings and mean periods

7.4.6. An example

7.4.7. Some notes on non-gaussian statistics

7.5. Input-output relationships for linear systems subjected to random excitation

7.6. Long-term statistics

7.6.1. Introduction

7.6.2. The long-term wave climate

7.6.3. Long-term wave statistics

7.6.4. Long-term statistics of a structure’s responses due to wave action

7.6.5. Return periods and probability of encounter

7.6.6. Long-term characterization of the offshore environment in generation and a structure’s corresponding long-term responses

7.7. Transfer functions

7.7.1. General

7.7.2. The transfer function for a one mass-spring system

7.7.3. The transfer function for a multi-degree of freedom system

7.7.4. Transfer function for two (sub)systems in series

7.7.5. Transfer function for two (sub)systems in parallel

7.7.6. Transfer function for a system with a feedback loop

7.7.7. Derivation of transfer functions for general forced responses of an offshore structure

7.7.8. Illustrative examples

7.7.9. Numerical calculations and discretization of resonance peaks

7.8. References

Annex 7.A. Terminology

Annex 7.B. A summary of main points for probability theory

7.B.1. Probability distributions and properties for one random variable

7.B.2. Probability distributions and properties for two and multiple random variables

Annex 7.C. The Weibull distribution

8. Fatigue

8.1. General

8.1.1. Introduction and overview

8.1.2. Organisation of the chapter

8.2. Key features of fatigue damage and its assessment

8.3. Determination of the long-term stress range history for a fatigue assessment

8.3.1. General discussion

8.3.2. Environmental conditions

8.3.3. Global stress analyses

8.3.4. Local geometric stress ranges

8.3.5. Transfer functions and the long-term distribution of geometric stress ranges

8.4. Fatigue resistance

8.5. Fatigue assessments

8.5.1. Palmgren-Miner rule

8.5.2. Counting methods

8.5.3. Variations in the application of the Palmgren-Miner summation

8.5.4. Approximate closed form solution for fatigue damage in a sea state

8.5.5. Simple screening methods

8.6. Summary of important conclusions

8.7. References

9. Structural design and reliability

9.1. Introduction

9.1.1. Structural design in perspective

9.1.2. Basic considerations

9.2. General aspects of structural design

9.2.1. Design situations

9.2.2. Limit states

9.2.3. Design actions

9.2.4. Design resistances

9.2.5. Design criteria

9.3. Working stress design (WSD) and partial factor design (PFD) methods

9.3.1. General

9.3.2. Principles of working stress design (WSD) methods

9.3.3. Principles of partial factor design (PFD) methods

9.4. Structural reliability assessments (SRA)

9.4.1. General

9.4.2. Fundamental formulation of the reliability problem – SRA by level III methods

9.4.3. SRA by level II methods

9.4.4. SRA and level I methods

9.5. Strength checks for WSD and PFD methods

9.6. References

Appendix: Notations and abbreviations

A.1. Coordinate systems

A.2. Symbols

A.3. Abbreviations

Index

**Architecture: **
Architecture--Criticism

**Earth Sciences: **
Oceanography and Hydrology

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