Dynamics of Fixed Marine Structures

Dynamics of Fixed Marine Structures, Third Edition proves guidance on the dynamic design of fixed structures subject to wave and current action. The text is an update of the ""UR8"" design guide ""Dynamics of Marine Structures"" with discussion of foundations, wind turbulence, offshore installations, earthquakes, and strength and fatigue. The book employs analytical methods of static and dynamic structural analysis techniques, particularly the statistical and spectral methods when applied to loading and in the calculating dynamic responses. The statistical methods are explained when used to wave, wind, and earthquake calculations, together with the problems encountered in actual applications. Of importance to fixed offshore platforms are the soil properties and foundation covering soil behavior, site investigation, testing, seabed stability, gravity structures, and the use of single piles. Methods of forecasting, measuring, and modeling of waves and currents are also presented in offshore structure construction. Basic hydrodynamics is explained in understanding wave theory, and some description is given to forecasting of environmental conditions that will affect the structures. The effects of vortex-induced vibrations on the structure are explained, and the three methods that can prevent vortex-induced oscillations are given. Wind turbulence or wind loads are analyzed against short natural period or long natural periods of structures. The transportation of offshore platforms, installation, and pile driving, including examples of the applications found in the book, are given as well. The guide is helpful for offshore engineers, designers of inshore jetties, clients needing design and analysis work, specialists related to offshore structural engineering, and students in offshore engineering.

Foreword Preface1 Introduction 1.1 Outline of the contents 1.2 Layout 1.3 Sections which help with the selection of analysis strategy 1.4 Use of the book as a technical reference 1.5 Use of the book as an introductory text2 Dynamics with deterministic loading 2.1 Linear single degree of freedom systems: SDOF 2.1.1 Units 2.2 Oscillation of an SDOF with neither forcing nor damping 2.3 Steady state oscillation of an SDOF with forcing and viscous damping 2.3.1 Steady state solution using real algebra 2.3.2 Dynamic amplification factor 2.3.3 Significance of forcing and natural frequencies 2.3.4 Steady state solution using complex algebra 2.3.5 Complex number representation of response 2.3.6 Steady state response of a non-linear SDOF 2.4 Damped decay and build-up of oscillation 2.4.1 Viscous, damped decay of oscillation 2.4.2 Damping ratio and logarithmic decrement 2.4.3 Response to an impulse 2.4.4 Viscous damped build-up of natural frequency oscillation 2.5 Damping 2.5.1 Hysteretic damping 2.5.2 Friction damping 2.5.3 Typical structural damping 2.6 Modeling multidegree of freedom structures: MDOFs 2.6.1 Natural frequencies of a 2 degree of freedom system 2.6.2 Modeling frame structures 2.6.3 Beam element stiffness 2.6.4 Global axes 2.6.5 Axis transformation 2.6.6 Assembly of global stiffness matrix 2.6.7 Damping 2.6.8 Mass 2.6.9 Supports 2.6.10 Forces applied at nodes 2.6.11 Forces applied to members 2.6.12 Constraints 2.6.13 Joints 2.6.14 Geometric stiffness 2.6.15 Hydrostatic stiffness and effective tension 2.6.16 Modeling continuous structures using plate, shell and brick elements 2.6.17 Substructures 2.7 Static analysis of MDOF structures 2.7.1 Quasi-static analysis 2.8 Steady state solution using complex matrix algebra 2.9 Natural frequencies of MDOFs 2.9.1 Eigenvalue form 2.9.2 Jacobi method 2.9.3 Householder QR/QL method 2.9.4 Polynomial solution 2.9.5 Vector iteration methods 2.9.6 More complicated methods 2.9.7 Selection of frequency/mode shape calculation method 2.9.8 Some frequencies of commonly used structural elements 2.10 Normal mode (or principal or generalized) coordinates 2.10.1 Forced vibration of MDOF systems 2.10.2 Other uses of principal/generalized coordinates 2.11 Time history solution methods 2.11.1 Convolution integral 2.11.2 Time stepping methods 2.11.3 Central difference (explicit) method 2.11.4 Runge-Kutta (explicit) method 2.11.5 Newmark ß (implicit) method 2.12 Economic solution of large dynamic problems 2.12.1 Separate, simpler model 2.12.2 Guyan reduction or static condensation 2.12.3 Static improvement Notation Bibliography References 3 Statistical and spectral description of random loading and response 3.1 Short term, frequency and sequence independent properties of y(t) 3.1.1 Measures of location 3.1.2 Measures of spread 3.1.3 Probability density function (PDF) 3.1.4 Cumulative distribution function (CDF) 3.1.5 Moments of a PDF 3.1.6 Gaussian (normal distribution) 3.1.7 Non-Gaussian distributions 3.2 Sequence dependent properties of a time history y(t) 3.2.1 Autocovariance 3.2.2 Autocorrelation function Ryy(x) 3.2.3 Autocorrelation coefficient or normalised autocovariance 3.2.4 Time scale 3.3 Fourier analysis and spectra of y(t) 3.3.1 Fourier series 3.3.2 Fourier transform representation of a random time history 3.3.3 Alternative forms of the Fourier transform 3.3.4 The discrete Fourier transform 3.3.5 The Fourier transform pair 3.3.6 Integral form of the Fourier transform pair 3.3.7 Spectral density 3.3.8 Spectral analysis of a dynamic system subject to loading defined by one variable 3.4 Relationship between autocovariance and the energy spectrum 3.5 Short term frequency and sequence independent statistics of simultaneous samples from several time histories: y^t), y2(t) ... 3.5.1 Covariance of yx(t) and y2(t) 3.5.2 Correlation coefficient or normalised covariance 3.5.3 Statistical properties of a + byt(t) + cy2(t) 3.5.4 Statistical properties of y^t) x y2(t) 3.5.5 Joint probability of n random variables 3.5.6 Gaussian multivariate distribution 3.6 Sequence dependent properties of samples from several time histories 3.6.1 Cross-covariance 3.6.2 Cross-correlation coefficient or normalised cross-covariance 3.6.3 Cross-correlation function 3.6.4 Nomenclature 3.7 Cross spectral density and coherence 3.7.1 Cross spectral density 3.7.2 Single-sided cross spectral density 3.7.3 Co- and quad-spectral density 3.7.4 Coherence 3.7.5 Spectral analysis of the response to a summation of random signals 3.8 Relationship between the cross-covariance and the cross-spectrum 3.9 Some further derivations based on spectral properties 3.9.1 Velocity and acceleration spectra 3.9.2 Spectral moments 3.9.3 Bandwidth 3.9.4 Crossing periods and peak distributions 3.9.5 Level crossing periods and the zero crossing period Tz 3.9.6 The crest frequency fc and period Tc 3.9.7 Distribution of amplitudes in a narrow banded spectrum 3.9.8 Rayleigh distribution 3.9.9 Predicting the amplitude exceeded with a given probability or in a given number of cycles 3.9.10 Distribution of the extreme values of a Rayleigh distribution 3.10 Extreme value distributions for environmental data 3.10.1 Types of extreme value distribution 3.10.2 Selection of extreme value distribution 3.10.3 Return period Notation Commonly used symbols Summary Bibliography References 4 Structural response to random loading 4.1 Wave, wind and earthquake - differences leading to different analysis methods 4.2 Structural response in waves, wind and earthquake 4.2.1 Structural response to a unidirectional sea 4.2.2 Structural response to wind turbulence 4.2.3 Structural response to earthquakes 4.2.4 Structural response to waves, wind and earthquake: summary 4.3 Examples of non-linearities 4.3.1 The effect of non-linear drag loading 4.3.2 The effect of intermittent loading in the splash zone 4.3.3 The effect of non-linear drag for a structure in the wind 4.3.4 The effect of non-linear guy wire behavior on a structure in the wind 4.3.5 The effect of yielding on a structure in an earthquake 4.4 Time history analysis methods 4.4.1 Time history analysis of a structure in a unidirectional sea 4.4.2 Time history analysis of a structure in a spread sea 4.4.3 Time history analysis of a structure in a turbulent wind 4.5 Conclusion Notation References 5 Foundations 5.1 Introduction 5.1.1 Safety factors for foundations 5.2 Introduction to soil behavior 5.2.1 Permeability 5.2.2 Effective stress 5.2.3 Failure of soils 5.2.4 Mohr's circle 5.2.5 Application of Mohr's circle in conjunction with the soil failure criterion 5.2.6 Drained and undrained loading and liquefaction of sands 5.2.7 Consolidation of clays 5.2.8 Soil structure, relative density and clay remolding 5.2.9 Stiffness of soils 5.2.10 Soil damping 5.2.11 Indicative soil properties 5.3 Site investigation and testing 5.3.1 In-situ measurements 5.3.2 Laboratory tests for soil strength 5.3.3 Consolidated-drained (CD) triaxial test 5.3.4 Consolidated-undrained (CU) triaxial test 5.3.5 Unconsolidated-undrained (UU) triaxial test 5.3.6 Unconfined compression test 5.3.7 Differences between soil properties estimated from drained and undrained tests 5.4 Stability of the seabed surface 5.4.1 Scour 5.4.2 Mudslides 5.4.3 Sand waves, dunes, banks, etc. 5.4.4 Subsidence 5.5 Gravity structures 5.5.1 Finite element (FE) methods 5.5.2 Half-space theory 5.5.3 Ultimate capacity of gravity foundations 5.5.4 Piping 5.5.5 Effect of consolidation on bearing capacity 5.5.6 Bearing capacity from published factors 5.5.7 Bearing capacity calculated by the method of slices 5.5.8 More advanced analysis of foundation capacity 5.5.9 Jack-up platforms 5.6 Single piles 5.6.1 Development of lateral force-deflection (p-y) curves 5.6.2 Calculation of Pu 5.6.3 p-y curve for clay 5.6.4 p-y behavior in clay under cyclic conditions 5.5.5 Effect of consolidation on bearing capacity 5.6.6 Compression capacity of piled foundations 5.6.7 Tension capacity 5.6.8 Scour and cavities 5.6.9 Shaft resistance in sand 5.6.10 Shaft resistance in clay 5.6.11 Shaft resistance - displacement (t-z) curves 5.6.12 End bearing capacity of piles 5.6.13 Axial end bearing - displacement (q-z) curves 5.6.14 Torsional moment-rotation curves 5.6.15 Piles in calcareous soils 5.7 Including foundation behavior in global structural analysis 5.7.1 The use of substructuring for the quasi-static analysis of structures on piled foundations 5.7.2 Linearized foundation tangent stiffness for quasi-static analysis of structures on piled foundations 5.7.3 Linearized foundation secant stiffness for dynamic analysis of structures on piled foundations 5.8 Pile groups 5.8.1 Pile group axial capacity 5.8.2 Pile group lateral capacity 5.8.3 Force-deflection analysis of piles in groups Notation References 6 Waves and wave loading 6.1 Introduction 6.2 Waves and currents 6.2.1 Regular waves 6.2.2 Particle motions 6.2.3 Mass transport 6.2.4 Group velocity CG 6.2.5 Ocean waves 6.2.6 Sea 6.2.7 Swell 6.2.8 Significant wave height and mean zero crossing period 6.2.9 Spectrum 6.2.10 Scatter diagrams 6.2.11 Persistence diagrams 6.2.12 Sea-state cycles 6.2.13 Effect of the seabed on wave characteristics 6.2.14 Shoaling 6.2.15 Diffraction 6.2.16 Refraction 6.2.17 Reflection 6.2.18 Absorption 6.2.19 Wave breaking 6.2.20 Currents 6.3 Measurement 6.3.1 Water surface elevation 6.3.2 Water particle velocities 6.4 Forecasting 6.4.1 General 6.4.2 Extrapolation to extreme values from measurements 6.4.3 Obtaining a long term description of the sea from measurements 6.4.4 Forecasting wave height and period from wind and fetch 6.4.5 Forecasting long term statistics of wave height and period 6.4.6 Forecasting currents 6.4.7 Computer modeling 6.4.8 Joint probability 6.5 Water surface elevation spectra 6.5.1 Introduction 6.5.2 Bretschneider and Pierson-Moscowitz spectra 6.5.3 JONSWAP spectra 6.5.4 Effect of alternative frequency units 6.5.5 Directional spectra 6.5.6 Selection of spectral shape 6.6 Individual wave scatter diagrams 6.6.1 Introduction 6.6.2 The wave height exceedence method 6.6.3 Individual wave height - period joint probability diagrams 6.7 Wave modeling 6.7.1 Introduction 6.7.2 Basic physics 6.7.3 Mathematical manipulations 6.7.4 Wave theories 6.7.5 Regular wave theories 6.7.6 Linear wave theory 6.7.7 Stokes' wave theories 6.7.8 Cnoidal regular theory 6.7.9 Stream function wave theories 6.7.10 Other regular wave theories 6.7.11 Selection of suitable regular wave theory 6.7.12 Irregular (but specified profile) wave theories 6.7.13 Random wave theories 6.7.14 Breaking waves 6.7.15 Wave current interaction 6.8 Hydrodynamic loading 6.8.1 Introduction 6.8.2 Morison's equation 6.8.3 Selection of Cd and Cm 6.8.4 Diffraction 6.8.5 Interference 6.8.6 Wave slam and slap 6.8.7 Structural motion, hydrodynamic added mass and damping 6.9 Analysis of structures subject to extreme and fatigue hydrodynamic loading 6.9.1 Discussion of wave loading on offshore structures 6.9.2 Sine wave fitting and complex number methods 6.9.3 Analysis of wave frequency loading and structural response 6.9.4 Deterministic analysis 6.9.5 Frequency domain spectral analysis 6.9.6 Time domain spectral analysis with linear random wave theory 6.9.7 Time domain spectral analysis - non-linear random wave theory Notation References 7 Vortex-induced forces 7.1 The forces on stationary circular cylinders 7.2 Flow speeds for response of cylinders in steady flow 7.2.1 Critical velocities for cross-flow motion 7.2.2 Critical velocities for in-line motion 7.3 Structural response in steady flow 7.3.1 Harmonic model 7.3.2 Effective mass per unit length: me 7.3.3 Criteria for vortex-induced response 7.3.4 Predictions of amplitude of response of risers 7.4 Vortex shedding in waves 7.4.1 Introduction 7.4.2 A stationary cylinder in waves 7.4.3 Effects of irregular waves, cylinder orientation, wave directionality, currents, roughness and interference 7.4.4 A compliant cylinder in waves 7.5 Devices for preventing vortex-induced oscillations 7.5.1 Strakes 7.5.2 Shrouds 7.5.3 Fairings 7.5.4 Air bubbles 7.5.5 Structural damping devices 7.6 The effect of other flow and structural properties 7.7 Flow calculations 7.7.1 Hydrodynamic damping 7.7.2 Computational flow techniques 7.8 Analysis sequence Notation References 8 Wind turbulence 8.1 Introduction 8.2 The structure of strong winds 8.2.1 Origin of the wind 8.2.2 Weather systems 8.2.3 The atmospheric boundary layer 8.2.4 Atmospheric stability 8.2.5 Equilibrium 8.2.6 Summary 8.3 Statistical description of turbulence 8.3.1 Turbulence statistics 8.3.2 Turbulence - single point statistics 8.3.3 Turbulence - two point statistics 8.4 Wind data 8.4.1 The mean wind 8.4.2 The turbulent gusts 8.4.3 Non-neutral wind conditions 8.5 Turbulence loads 8.5.1 Aerodynamic loading 8.5.2 Aerodynamic damping 8.6 Calculation of response 8.6.1 Theory 8.6.2 Calculation of response - lattice structures 8.6.3 Calculation of response - single members 8.6.4 Extreme value analysis 8.6.5 Fatigue life analysis 8.7 Choice of method 8.7.1 Comparison of methods 8.7.2 Analysis hints Notation Bibliography References Annex 8A ESDU data items Annex 8B Derivation of theory 8.B.1 Turbulence loads (direct method, ESDU method) 8.B.2 Single-member methods 8.B.3 General methods 9 Installation 9.1 Introduction 9.2 Transportation 9.2.1 Barge motions 9.2.2 Cargo loading and response 9.2.3 Barge flexibility 9.2.4 Slam 9.2.5 Self-floating substructures 9.3 Launch and up-ending 9.3.1 Jacket launch analysis 9.3.2 Analysis method 9.4 Lift 9.4.1 Single degree of freedom lift analysis 9.4.2 Computer analysis of crane dynamic response 9.4.3 Selection of load conditions for analysis 9.5 Docking over a template 9.6 On-bottom stability 9.7 Pile driving 9.7.1 Mathematical analysis 9.8 Installation of gravity structures Notation References 10 Earthquakes 10.1 Introduction 10.2 Design philosophy for earthquake loads 10.3 Theory 10.3.1 The response spectrum method - overview 10.3.2 SDOF lumped-mass system 10.3.3 Derivation of response spectra 10.3.4 Use of response spectra - SDOF structure 10.3.5 MDOF lumped-mass system 10.4 Design data 10.4.1 Accelerograms 10.4.2 Response spectra 10.4.3 Directionality of loading 10.5 Specification of design earthquakes 10.5.1 Earthquake magnitude and intensity 10.5.2 Source evaluation 10.5.3 Source-to-site attenuation 10.5.4 Construction of the response spectrum 10.5.5 Site response analysis 10.5.6 Design data for North Sea sites 10.6 Calculation of structural response 10.6.1 Foundation model 10.6.2 Structure model 10.6.3 Analysis methods 10.6.4 Choice of analysis 10.6.5 Analysis of secondary systems 10.7 Structural configuration for seismic resistance 10.7.1 Global configuration (jacket structures) 10.7.2 Joint detailing (jacket structures) 10.7.3 Gravity structures Annex 10A Sources of accelerogram data Notation Bibliography References 11 Strength and fatigue 11.1 Introduction 11.1.1 Limit states 11.1.2 Safety factors 11.1.3 Unity checks 11.1.4 Non-linear complications with dynamic analysis 11.2 Strength assessment 11.2.1 Local modes of failure (yield, fracture, buckling) 11.2.2 Yield 11.2.3 Buckling 11.2.4 Beam columns 11.2.5 Joint strength 11.2.6 Deterministic quasi-static strength analysis 11.2.7 Frequency domain 'spectral' analysis 11.2.8 Response spectra analysis 11.2.9 Avoiding non-linearities in frequency domain analysis 11.2.10 Possible methods of linearization 11.2.11 Time history analysis 11.3 Fatigue assessment 11.3.1 S-N curves 11.3.2 Miner's rule 11.3.3 Deterministic fatigue analysis 11.3.4 Spectral fatigue analysis 11.3.5 Narrow band spectra 11.3.6 Broad band spectra 11.3.7 Stress concentration factors 11.3.8 Non-linearities which affect spectral fatigue analysis 11.4 Fracture assessment 11.4.1 Brittle fracture 11.4.2 Application of fracture mechanics to fast fracture 11.4.3 Crack propagation 11.5 Overall analysis methods 11.5.1 Dynamic characteristics of environmental loading 11.5.2 Methods of handling the frequency content 11.5.3 Methods of structural analysis 11.5.4 Wave frequency loading 11.5.5 Wave slam and slap 11.5.6 Vortex shedding loading 11.5.7 Wind loading 11.5.8 Earthquake loading Notation References12 Examples 12.1 Analyses of a single pile platform 12.1.1 Modeling method 12.1.2 Preliminary estimate of natural period 12.1.3 Foundation model: p-y curves 12.1.4 Time history dynamic analysis 12.1.5 Secant stiffness, linearized foundation, for frequency domain dynamic analysis 12.1.6 Linear frequency domain analysis 12.1.7 Comparison of time and frequency domain analysis 12.1.8 Fatigue analysis 12.1.9 Semi-probabilistic fatigue analysis 12.1.10 Spectral fatigue analysis 12.1.11 The 2.5 second rule 12.1.12 Comparison of fatigue analysis methods 12.2 Dynamic response of a jack-up platform 12.2.1 Problem definition 12.2.2 Outline methodology 12.2.3 Estimation of natural period 12.2.4 Selection of extreme regular wave 12.2.5 Wave theory 12.2.6 Regular wave loading 12.2.7 Structural analysis of static response to regular wave plus current 12.2.8 Results of regular wave analysis 12.2.9 Spectrum for random wave, frequency domain, spectral analysis 12.2.10 Selection of linear wave theory 12.2.11 Calculation of wave particle kinematics at a range of depths and wave periods 12.2.12 Combination of particle velocities with spectrum to determine the rms velocity and linearized drag force equation at any location 12.2.13 Mode shape and the consistent natural period 12.2.14 Hydrodynamic and structural damping 12.2.15 Spectral calculation of additional dynamic response to loading in the vicinity of the structural natural period 12.2.16 Frequency multiplying effects 12.2.17 Wind force on the structure 12.2.18 Summation of the separately calculated deflections 12.3 Vortex shedding example 12.3.1 Basic data 12.3.2 Calculation of mode 1 frequency and mode shape 12.3.3 Calculation of mode 1 reduced velocity, stability parameter and response 12.3.4 Calculation of mode 2 frequency and mode shape 12.3.5 Calculation of mode 2 reduced velocity, stability parameter and response 12.3.6 Calculation of mode 3 frequency and mode shape 12.3.7 Combination of in-line and cross-flow response 12.3.8 Vortex shedding in waves 12.3.9 Wave synchronized vortex shedding References 12.4 Wind turbulence example 12.4.1 Extreme response analysis Static design Direct method ESDU method WINDSPEC method Summary 12.4.2 Fatigue life analysis Omnidirectional analysis (u-component only) Directional analysis (u-component only) Directional analysis (u and v-components) Summary 12.5 Earthquake example 12.5.1 Modeling 12.5.2 Member stiffness matrix 12.5.3 Formation of global stiffness matrix 12.5.4 Deflection under a static horizontal force 12.5.5 Mass matrix 12.5.6 Polynomial method for the calculation of natural frequencies 12.5.7 Vector iteration method for the calculation of mode shapes 12.5.8 Generalized mass for each mode 12.5.9 Spectral displacement and acceleration for each natural frequency 12.5.10 Response to horizontal ground acceleration 12.5.11 Response to vertical ground motion 12.5.12 Summation of directions 12.5.13 Static coefficient method References Appendix A Complex number representation of amplitude and phase A. 1 Plotting on the complex phase - phasor diagrams A. 2 Calculations using 0° and -90° loading and response as real and imaginary parts A. 3 e A. 4 Negative frequencies A. 5 Complex number multiplication and division A. 6 Complex number inversion: 1/Z A. 7 Phase lead and lag Appendix B The Gamma Function Appendix C Consistent units Appendix D Stiffness matrix of a 3-d beam element Appendix E Useful data and formulas Index

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