Ocean Engineering & Oceanography

Volume 5

Series editors

Manhar R. Dhanak, Florida Atlantic University SeaTech, Dania Beach, USANikolas I. Xiros, New Orleans, USA

More information about this series at http://www.springer.com/series/10524

Srinivasan Chandrasekaran

Dynamic Analysisand Design of OffshoreStructures

123

Srinivasan ChandrasekaranDepartment of Ocean EngineeringIndian Institute of Technology MadrasChennai, Tamil NaduIndia

ISSN 2194-6396 ISSN 2194-640X (electronic)Ocean Engineering & OceanographyISBN 978-81-322-2276-7 ISBN 978-81-322-2277-4 (eBook)DOI 10.1007/978-81-322-2277-4

Library of Congress Control Number: 2015930819

Springer New Delhi Heidelberg New York Dordrecht London© Springer India 2015This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar ordissimilar methodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exemptfrom the relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, express or implied, with respect to the material containedherein or for any errors or omissions that may have been made.

Printed on acid-free paper

Springer (India) Pvt. Ltd. is part of Springer Science+Business Media (www.springer.com)

ToMy parents, teachers, family membersand friends

Preface

Offshore structures are unique in the field of engineering, as they pose manychallenges in the development and conceptualization of design. As innovativeplatform geometries are envisaged to alleviate the encountered environmental loadsefficiently, detailed understanding of their analysis and basic design becomesimportant. Structural dynamics, being an important domain of offshore engineering,require intensive teaching and guidance to illustrate the fundamental concepts, inparticular as applied to ocean structures. With the vast experience of teaching thissubject and guiding research, a humble attempt is made to present the basics in aclosed form, which will be useful for graduate students and researchers. Chapters inthis book are organized such that the reader gets an overall idea of various types ofoffshore plants, basic engineering requirements, fundamentals of structuraldynamics and their applications to preliminary design. Numerical examples andapplication problems are chosen to illustrate the use of experimental, numerical andanalytical studies in the design and development of new structural form for deep-water oil exploration. This book is an effort in the direction of capacity building ofpracticing and consulting offshore structural engineers who need to understand thebasic concepts of dynamic analysis of offshore structures through a simple andstraightforward approach.

Video lectures of the courses available at the following websites: (i) http://nptel.ac.in/courses/114106035; (ii) http://nptel.ac.in/courses/114106036; and (iii) http://nptel.ac.in/courses/114106037, which also substitute the classroom mode ofunderstanding of the contents of this book.

My sincere thanks are due to my professors, colleagues and my students whohave given their valuable input and feedback to develop the contents of this book.In particular, I wish to express my thanks to Mrs. Indira and Ms. Madhavi for theireditorial assistance and graphic art support extended during the preparation ofmanuscript of the book. Author acknowledges the support extended by Centre ofContinuing Education, Indian Institute of Technology Madras for publishing thisbook.

vii

I also owe a lot of thanks to all the authors and publishers who have earlierattempted to publish books on structural dynamics and allied topics, based on whichI developed my concepts on the said subject.

Srinivasan Chandrasekaran

viii Preface

Contents

1 Introduction to Offshore Platforms . . . . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Types of Offshore Platforms. . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Bottom-supported Structures. . . . . . . . . . . . . . . . . . 31.2.2 Compliant Structures . . . . . . . . . . . . . . . . . . . . . . . 71.2.3 Floating Platform . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.3 New-generation Offshore Platforms . . . . . . . . . . . . . . . . . . . 151.3.1 Buoyant Leg Structure (BLS) . . . . . . . . . . . . . . . . . 161.3.2 Triceratops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.3.3 Floating, Storage and Regasification

Units (FSRUs) . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 Environmental Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2 Wind Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3 Wave Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.4 Wave Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.5 Current Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.6 Earthquake Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.7 Ice and Snow Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.8 Marine Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.9 Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.10 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.11 Dead Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.12 Live Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.13 Impact Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.14 General Design Requirements . . . . . . . . . . . . . . . . . . . . . . . 432.15 Steel Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.16 Allowable Stress Method . . . . . . . . . . . . . . . . . . . . . . . . . . 452.17 Limit State Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.18 Fabrication and Installation Loads . . . . . . . . . . . . . . . . . . . . 48

ix

2.19 Lifting Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492.20 Load-Out Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502.21 Transportation Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502.22 Launching and Upending Force . . . . . . . . . . . . . . . . . . . . . 532.23 Accidental Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3 Introduction to Structural Dynamics . . . . . . . . . . . . . . . . . . . . . . 633.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.2 Fundamentals of Structural Dynamics . . . . . . . . . . . . . . . . . 643.3 Mathematical Model of Structural System . . . . . . . . . . . . . . 653.4 Single-Degree-of-Freedom Model . . . . . . . . . . . . . . . . . . . . 663.5 Equation of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.5.1 Simple Harmonic Motion Method (SHM Method). . . 673.5.2 Newton’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.5.3 Energy Method. . . . . . . . . . . . . . . . . . . . . . . . . . . 683.5.4 Rayleigh’s Method . . . . . . . . . . . . . . . . . . . . . . . . 683.5.5 D’Alembert’s Principle . . . . . . . . . . . . . . . . . . . . . 69

3.6 Un-damped Free Vibration . . . . . . . . . . . . . . . . . . . . . . . . . 693.7 Damped Free Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.7.1 Viscous Damping . . . . . . . . . . . . . . . . . . . . . . . . . 713.7.2 Coulomb Damping . . . . . . . . . . . . . . . . . . . . . . . . 723.7.3 Under-damped Systems . . . . . . . . . . . . . . . . . . . . . 743.7.4 Critically Damped Systems . . . . . . . . . . . . . . . . . . 753.7.5 Over-damped Systems . . . . . . . . . . . . . . . . . . . . . . 763.7.6 Half Power Method. . . . . . . . . . . . . . . . . . . . . . . . 77

3.8 Forced Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783.8.1 Un-damped Forced Vibration . . . . . . . . . . . . . . . . . 793.8.2 Damped Forced Vibration . . . . . . . . . . . . . . . . . . . 80

3.9 Steady-State Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823.10 Two-Degrees-of-Freedom Model . . . . . . . . . . . . . . . . . . . . . 833.11 Un-damped Free Vibrations and Principal

Modes of Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.12 Multi-degrees-of-Freedom . . . . . . . . . . . . . . . . . . . . . . . . . 893.13 Equation of Motion for Multi-degrees-of-Freedom System . . . 893.14 Influence Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . 913.15 Eigenvalue Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933.16 Dynamic Matrix Method . . . . . . . . . . . . . . . . . . . . . . . . . . 943.17 Dunkerley’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.18 Matrix Iteration Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.19 Stodola’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 963.20 Mode Superposition Method. . . . . . . . . . . . . . . . . . . . . . . . 973.21 Mode Truncation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

3.21.1 Static Correction for Higher Mode Response . . . . . . 983.22 Rayleigh–Ritz Method—Analytical Approach . . . . . . . . . . . . 99

x Contents

4 Damping in Offshore Structures . . . . . . . . . . . . . . . . . . . . . . . . . 1554.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1554.2 Damping Models: Rayleigh Damping . . . . . . . . . . . . . . . . . 157

4.2.1 Example Problem . . . . . . . . . . . . . . . . . . . . . . . . . 1604.3 Caughey Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

4.3.1 Critical Problems Associatedwith Caughey Damping . . . . . . . . . . . . . . . . . . . . . 164

4.3.2 Example Problem . . . . . . . . . . . . . . . . . . . . . . . . . 1644.4 Classical Damping Matrix by Damping Matrix

Superpositioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1664.4.1 Critical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1674.4.2 Example Problem . . . . . . . . . . . . . . . . . . . . . . . . . 167

4.5 Evaluation of Damping from Experimental Results . . . . . . . . 169

5 Hydrodynamic Response of Perforated Offshore Members . . . . . . 1735.1 Fluid–Structure Interaction . . . . . . . . . . . . . . . . . . . . . . . . . 1735.2 Vertical Cylinders in Uniform Flow . . . . . . . . . . . . . . . . . . 1745.3 Flow in Deep Waters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1745.4 Horizontal Cylinder in Uniform Flow . . . . . . . . . . . . . . . . . 1765.5 Horizontal Cylinder in Shear Flow . . . . . . . . . . . . . . . . . . . 1765.6 Blockage Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1765.7 Wave–Structure Interaction (WSI) . . . . . . . . . . . . . . . . . . . . 1775.8 Perforated Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

5.8.1 Wave Forces on Perforated Members. . . . . . . . . . . . 1775.8.2 Wave Forces on Offshore Structures

with Perforated Members . . . . . . . . . . . . . . . . . . . . 1795.8.3 Critical Review. . . . . . . . . . . . . . . . . . . . . . . . . . . 180

5.9 Experimental Investigations on Perforated Cylinders . . . . . . . 1815.10 Experimental Investigations on Perforated TLP Model . . . . . . 1855.11 Numerical Studies on Perforated Cylinders . . . . . . . . . . . . . . 189

5.11.1 Development of the Numerical Models . . . . . . . . . . 189

6 Introduction to Stochastic Dynamics . . . . . . . . . . . . . . . . . . . . . . 2036.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

6.1.1 Mean Value of the Response Process . . . . . . . . . . . 2056.2 Auto-Covariance of the Response Process . . . . . . . . . . . . . . 2076.3 Response Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2086.4 Stochastic Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

6.4.1 Example of Stochastic Modeling . . . . . . . . . . . . . . . 2106.4.2 Example of a Stochastic Process . . . . . . . . . . . . . . . 211

6.5 Return Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2126.6 Safety and Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2136.7 Reliability Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

Contents xi

6.8 Ultimate Limit State and Reliability Approach . . . . . . . . . . . 2156.9 Short-term Reliability of Single Load Effect . . . . . . . . . . . . . 216

6.9.1 Up-Crossing Approach . . . . . . . . . . . . . . . . . . . . . 2166.10 Long-term Reliability of Single Load Effect . . . . . . . . . . . . . 2186.11 Levels of Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2196.12 Reliability Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

6.12.1 Advantages of Reliability Methods (ASC-83) . . . . . . 2206.13 Stochastic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

6.13.1 First-Order Second-Moment Method (FOSM) . . . . . . 2216.13.2 Advanced FOSM . . . . . . . . . . . . . . . . . . . . . . . . . 222

6.14 Fatigue and Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2246.15 Fatigue Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

6.15.1 SN Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2256.16 Miner’s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2276.17 Fatigue Loading and Fatigue Analysis . . . . . . . . . . . . . . . . . 2286.18 Time Domain Fatigue Analysis . . . . . . . . . . . . . . . . . . . . . . 229

6.18.1 Rain Flow Counting . . . . . . . . . . . . . . . . . . . . . . . 2296.19 Deterministic Fatigue Analysis . . . . . . . . . . . . . . . . . . . . . . 2316.20 Spectral Fatigue Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 232

6.20.1 Narrowband Spectrum . . . . . . . . . . . . . . . . . . . . . . 2336.20.2 Broadband Spectrum . . . . . . . . . . . . . . . . . . . . . . . 234

6.21 Stress Concentration Factor (SCF). . . . . . . . . . . . . . . . . . . . 2386.22 Crack Propagation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

6.22.1 Step-by-Step Procedure to Compute the FatigueCrack Propagation. . . . . . . . . . . . . . . . . . . . . . . . . 239

7 Applications in Preliminary Analysis and Design . . . . . . . . . . . . . 2437.1 Free Vibration Response of Offshore Triceratops . . . . . . . . . 2437.2 New Structural Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2447.3 Model Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2457.4 Experimental Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

7.4.1 Free-floating Studies . . . . . . . . . . . . . . . . . . . . . . . 2477.4.2 Free-decay Studies on Tethered Triceratops . . . . . . . 247

7.5 Analytical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2477.6 Empirical Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2497.7 Wave Directionality Effects on Offshore Triceratops . . . . . . . 2507.8 Discussions of Experimental Studies . . . . . . . . . . . . . . . . . . 2507.9 Springing and Ringing Responses of Tension

Leg Platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2567.9.1 Springing and Ringing. . . . . . . . . . . . . . . . . . . . . . 256

7.10 Evolution of Platform Geometry . . . . . . . . . . . . . . . . . . . . 2577.11 Mathematical Development . . . . . . . . . . . . . . . . . . . . . . . . 2587.12 Analytical Model of TLP . . . . . . . . . . . . . . . . . . . . . . . . . . 2597.13 Hydrodynamic Forces on TLP . . . . . . . . . . . . . . . . . . . . . . 262

xii Contents

7.14 Dynamics of Triangular TLP . . . . . . . . . . . . . . . . . . . . . . . 2637.14.1 Mass Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2637.14.2 Stiffness Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 2647.14.3 Damping Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 264

7.15 Ringing Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2657.16 Springing Response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2697.17 Significance of Springing and Ringing Response. . . . . . . . . . 273

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

Contents xiii

Figures

Fig. 1.1 Deep-water drilling semisubmersible with verticalriser storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Fig. 1.2 Bullwinkle steel jacket . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Fig. 1.3 Hibernia gravity base structure . . . . . . . . . . . . . . . . . . . . . 7Fig. 1.4 Lena guyed tower in Mississippi Canyon Block. . . . . . . . . . 9Fig. 1.5 Articulated tower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Fig. 1.6 Tension leg platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Fig. 1.7 Semisubmersible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Fig. 1.8 FPSO platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Fig. 1.9 SPAR platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Fig. 1.10 Different types of ultra-deep-water structures. . . . . . . . . . . . 16Fig. 1.11 Buoyant tower in the fabrication yard. . . . . . . . . . . . . . . . . 17Fig. 1.12 Load out and installed structure in offshore field . . . . . . . . . 18Fig. 1.13 Conceptual view of triceratops. . . . . . . . . . . . . . . . . . . . . . 18Fig. 2.1 Definition of wave parameters . . . . . . . . . . . . . . . . . . . . . . 32Fig. 2.2 Wave theory selection chart (Sarpakaya

and Issacson 1981). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Fig. 2.3 Bottom-supported cylinder . . . . . . . . . . . . . . . . . . . . . . . . 36Fig. 2.4 Lifts under different conditions. a Derrick and structure

on land. b Derrick on land, structure on floating barge.c Derrick and structure in the sea. . . . . . . . . . . . . . . . . . . . 49

Fig. 2.5 Different phases of jacket load-out by skidding . . . . . . . . . . 51Fig. 2.6 Motion of floating objects during installation . . . . . . . . . . . 52Fig. 2.7 View of launch barge and jacket undergoing motion . . . . . . 53Fig. 2.8 Launching and upending. . . . . . . . . . . . . . . . . . . . . . . . . . 53Fig. 3.1 Single-degree-of-freedom model . . . . . . . . . . . . . . . . . . . . 65Fig. 3.2 Free body diagram of single-degree-of-freedom model . . . . . 66Fig. 3.3 Un-damped free vibration of single-degree-of-freedom

model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Fig. 3.4 Damped free vibration of single-degree-of-freedom model. . . 71Fig. 3.5 Displacement of a system in coulomb damping . . . . . . . . . . 72Fig. 3.6 Response of under-damped system. . . . . . . . . . . . . . . . . . . 74Fig. 3.7 Response of critically damped system. . . . . . . . . . . . . . . . . 76

xv

Fig. 3.8 Response of over-damped system. . . . . . . . . . . . . . . . . . . . 77Fig. 3.9 Half power bandwidth method. . . . . . . . . . . . . . . . . . . . . . 78Fig. 3.10 Damped single degree of freedom under external

excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Fig. 3.11 Steady-state response of damped single-degree-of-freedom

system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Fig. 3.12 Variation of frequency ratio with phase angle for damped

vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Fig. 3.13 Variation of dynamic magnification factor with frequency

ratio for damped vibration. . . . . . . . . . . . . . . . . . . . . . . . . 83Fig. 3.14 Two-degrees-of-freedom system models. a Mass and

stiffness in series; b two pendulums connectedwith a bar of stiffness k . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Fig. 3.15 Spring–mass un-damped two-degrees-of-freedom system. . . . 85Fig. 3.16 Un-damped multi-degrees-of-freedom model . . . . . . . . . . . . 91Fig. 4.1 Damping models a mass proportional damping

b stiffness proportional damping . . . . . . . . . . . . . . . . . . . . 157Fig. 4.2 Rayleigh damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159Fig. 4.3 Example problem 4.2.1. . . . . . . . . . . . . . . . . . . . . . . . . . . 160Fig. 4.4 Example problem 4.3.2. . . . . . . . . . . . . . . . . . . . . . . . . . . 165Fig. 4.5 Example problem 4.4.2. . . . . . . . . . . . . . . . . . . . . . . . . . . 167Fig. 4.6 Free vibration experiment—heave acceleration

of model with perforated column . . . . . . . . . . . . . . . . . . . . 169Fig. 4.7 Free vibration experiment—surge acceleration of model

with perforated column. . . . . . . . . . . . . . . . . . . . . . . . . . . 169Fig. 5.1 Flow in deep waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Fig. 5.2 Experimental setup to study response on perforated

cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181Fig. 5.3 Perforated cylinders considered for the study:

a inner cylinder; b outer cylinder (A); c outer cylinder (B);and d outer cylinder (C) . . . . . . . . . . . . . . . . . . . . . . . . . . 182

Fig. 5.4 Force variation in cylinders (WH = 5 cm). . . . . . . . . . . . . . 183Fig. 5.5 Force variation in cylinders (WH = 25 cm) . . . . . . . . . . . . . 184Fig. 5.6 Front view of TLP model: a without perforated cover;

b with perforated cover . . . . . . . . . . . . . . . . . . . . . . . . . . 185Fig. 5.7 Experimental setup: a components of the model;

b instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186Fig. 5.8 Free surge acceleration with PC. . . . . . . . . . . . . . . . . . . . . 187Fig. 5.9 Free heave acceleration with PC . . . . . . . . . . . . . . . . . . . . 187Fig. 5.10 Surge RAO for 7-cm wave . . . . . . . . . . . . . . . . . . . . . . . . 188Fig. 5.11 Heave RAO for 7-cm wave. . . . . . . . . . . . . . . . . . . . . . . . 188Fig. 5.12 Tether tension variation for 7-cm wave. . . . . . . . . . . . . . . . 188Fig. 5.13 Perforated outer cylinder. . . . . . . . . . . . . . . . . . . . . . . . . . 189

xvi Figures

Fig. 5.14 Perforations along the circumference and length(Chandrasekaran et al. 2014) . . . . . . . . . . . . . . . . . . . . . . . 190

Fig. 5.15 Inner cylinder with perforated outer cylinder . . . . . . . . . . . . 190Fig. 5.16 Domain of inner cylinder generated with volumetric

control (Chandrasekaran et al. 2014) . . . . . . . . . . . . . . . . . 191Fig. 5.17 Domain of inner cylinder with perforated outer cylinder

generated with volumetric control(Chandrasekaran et al. 2014) . . . . . . . . . . . . . . . . . . . . . . . 191

Fig. 5.18 Simulation of inner cylinder (Chandrasekaran et al. 2014). . . 192Fig. 5.19 Simulation of inner cylinder with perforated outer cylinder

(Chandrasekaran et al. 2014) . . . . . . . . . . . . . . . . . . . . . . . 192Fig. 5.20 Force on inner cylinder (WH = 10 cm; WP = 1.6 s)

in numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 193Fig. 5.21 Force on inner cylinder with perforated outer cylinder

in numerical simulation (WH = 10 cm; WP = 1.6 s) . . . . . . 193Fig. 5.22 Comparison of forces on inner cylinder with and

without perforated outer cylinder . . . . . . . . . . . . . . . . . . . . 194Fig. 5.23 Horizontal velocity variation for various percentages

of perforation with wave steepness 0.0051 . . . . . . . . . . . . . 196Fig. 5.24 Horizontal velocity variation for various percentages

of perforation with wave steepness 0.0103 . . . . . . . . . . . . . 196Fig. 5.25 Horizontal velocity variation for various percentages

of perforation with wave steepness 0.0164 . . . . . . . . . . . . . 197Fig. 5.26 Horizontal velocity at mean sea level for various

wave steepness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198Fig. 5.27 Change in horizontal velocity between sections

and perforation ratio 11 %, and H/L 0.0962 . . . . . . . . . . . . 198Fig. 5.28 Change in horizontal velocity between sections

and steep wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199Fig. 5.29 Change in horizontal velocity between sections

and medium steep wave . . . . . . . . . . . . . . . . . . . . . . . . . . 199Fig. 5.30 Change in horizontal velocity between section

and low-steep wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200Fig. 6.1 Amplitude amplification for various damping ratios . . . . . . . 210Fig. 6.2 Typical S–N curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226Fig. 6.3 Spatial definition of notch, hot spot and surface

in a plane surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228Fig. 6.4 Hot spot stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228Fig. 6.5 Example of rain flow counting . . . . . . . . . . . . . . . . . . . . . 230Fig. 7.1 Details of the scaled model . . . . . . . . . . . . . . . . . . . . . . . . 246Fig. 7.2 Model installed in the wave flume . . . . . . . . . . . . . . . . . . . 247Fig. 7.3 Analytical model of single BLS, free-floating triceratops,

and tethered triceratops. . . . . . . . . . . . . . . . . . . . . . . . . . . 248Fig. 7.4 Components of triceratops. . . . . . . . . . . . . . . . . . . . . . . . . 252

Figures xvii

Fig. 7.5 Plan and elevation of the scaled model . . . . . . . . . . . . . . . . 253Fig. 7.6 Instrumentation for different wave approach angles . . . . . . . 253Fig. 7.7 Surge/sway RAOs of triceratops . . . . . . . . . . . . . . . . . . . . 254Fig. 7.8 Heave RAOs of triceratops . . . . . . . . . . . . . . . . . . . . . . . . 254Fig. 7.9 Pitch/Roll RAOs of BLS . . . . . . . . . . . . . . . . . . . . . . . . . 255Fig. 7.10 Pitch/Roll RAO’s of deck . . . . . . . . . . . . . . . . . . . . . . . . . 255Fig. 7.11 Schematics of springing and ringing. . . . . . . . . . . . . . . . . . 256Fig. 7.12 Frequency range of TLPs relative to dominant

wave frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257Fig. 7.13 a PM spectrum for wave height elevation. b Impact wave

profile with impact wave at t = 10 s.c Non-impact wave profile . . . . . . . . . . . . . . . . . . . . . . . . 260

Fig. 7.14 a Plan and b elevation of example TLP . . . . . . . . . . . . . . . 261Fig. 7.15 Response of square TLPs to impact waves.

a Response of TLP1. b Response of TLP2.c Response of TLP3. d Response of TLP4. . . . . . . . . . . . . . 266

Fig. 7.16 Response of equivalent triangular TLPs to impact waves(T0 per tether same). a Response of TLP1. b Responseof TLP2. c Response of TLP3. d Response of TLP4 . . . . . . . 267

Fig. 7.17 Response of equivalent triangular TLPs to impact waves(total T0 same). a Response of TLP1. b Response of TLP2.c Response of TLP3. d Response of TLP4. . . . . . . . . . . . . . 268

Fig. 7.18 Response of square TLPs to non-impact waves.a Response of TLP1. b Response of TLP2.c Response of TLP3. d Response of TLP4. . . . . . . . . . . . . . 270

Fig. 7.19 Response of equivalent triangular TLPs to non-impact wave.a Response of TLP1. b Response of TLP2.c Response of TLP3. d Response of TLP4. . . . . . . . . . . . . . 271

Fig. 7.20 Response of equivalent triangular TLPs to non-impactwaves (total T0 same). a Response of TLP1.b Response of TLP2. c Response of TLP3.d Response of TLP4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

xviii Figures

Tables

Table 1.1 Offshore jacket platforms constructed worldwide . . . . . . . . . 4Table 1.2 Gravity platforms constructed worldwide

(Courtesy: Pennwell Publishing Co.) . . . . . . . . . . . . . . . . . . 6Table 2.1 Forces on members of different geometric shapes

using Froude–Krylov theory. . . . . . . . . . . . . . . . . . . . . . . . 37Table 2.2 Numerical values of C1–C4 . . . . . . . . . . . . . . . . . . . . . . . . 37Table 2.3 Typical live load values used in platform design

(Graff 1995). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Table 2.4 Impact factor for live loads . . . . . . . . . . . . . . . . . . . . . . . . 43Table 2.5 Coefficient for resistance to stresses . . . . . . . . . . . . . . . . . . 45Table 2.6 Load factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Table 2.7 Conditions specified for various limit states . . . . . . . . . . . . . 47Table 4.1 Results of free vibration experiment . . . . . . . . . . . . . . . . . . 170Table 5.1 Flow regimes in uniform flow . . . . . . . . . . . . . . . . . . . . . . 174Table 5.2 Reduced velocity range . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Table 5.3 Geometric details of cylinders considered for the study . . . . . 182Table 5.4 Hydrodynamic forces for 25 cm wave height (N) . . . . . . . . . 183Table 5.5 Force reduction in inner cylinder . . . . . . . . . . . . . . . . . . . . 184Table 5.6 Details of TLP model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185Table 5.7 Comparison of mass of acrylic and aluminum

perforated covers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186Table 5.8 Results of free-vibration experiment . . . . . . . . . . . . . . . . . . 187Table 5.9 Average surge response reduction . . . . . . . . . . . . . . . . . . . . 188Table 5.10 Details of cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190Table 5.11 Details of perforations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190Table 5.12 Forces on inner cylinder (WH = 10 cm) . . . . . . . . . . . . . . . 194Table 5.13 Forces on inner cylinder with perforated

outer cylinder (WH = 10 cm) . . . . . . . . . . . . . . . . . . . . . . . 194Table 6.1 Merits and demerits of FOSM of reliability . . . . . . . . . . . . . 222Table 6.2 Rain flow counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231Table 6.3 C conversion table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239Table 6.4 Fatigue crack propagation . . . . . . . . . . . . . . . . . . . . . . . . . 239

xix

Table 7.1 Mass properties of free-floating and tethered . . . . . . . . . . . . 245Table 7.2 Details of prototype and model of free-floating

and tethered triceratops . . . . . . . . . . . . . . . . . . . . . . . . . . . 246Table 7.3 Natural periods of the structure. . . . . . . . . . . . . . . . . . . . . . 249Table 7.4 Details of model and prototype of free-floating

and tethered triceratops . . . . . . . . . . . . . . . . . . . . . . . . . . . 251Table 7.5 Natural period of the structure(s) . . . . . . . . . . . . . . . . . . . . 252Table 7.6 Geometric properties of square TLPs considered . . . . . . . . . . 262Table 7.7 Natural wave periods and frequencies of equivalent

triangular TLPs with T0 per tether same. . . . . . . . . . . . . . . . 262Table 7.8 Values of coefficients for interpolation of Cm . . . . . . . . . . . . 262

xx Tables

Notations

qa Mass density of airCw Wind pressure coefficienth Phase anglev(t) Gust componentFD Drag forceFL Lift forcevz Wind speed at elevation of z m above MSLV10 Wind speed at 10 m above MSLFg Average gust factorLu Integral length scaleδ Surface drag coefficient/logarithmic decrementxp Peak frequencyr2z Variance of U(t)H Wave heightk Wave lengthd Water depthη Wave surface elevationk Wave numberx Wave circular frequencyf Cyclic frequencyq Density of fluidCd Drag coefficientsCm Inertia coefficientsDx Distance between the column membersS0 Intensity of earthquakexg Natural frequency of the groundng Damping of the ground�F0 Force amplitude on the structuref(t) Excitation force[k] Stiffness

xxi

[m] Mass element[c] Damping elementW Vertical loadx0 Initial displacements_x0 Initial velocitiesωn Natural frequencyA Areaµ Coefficient of absolute viscosityxd Damped vibration frequencyξ Damping ratioCc Critical dampingt Time periodpo Amplitude of varying load f(t)aij Flexibility influence coefficientx::

Accelerationm* Generalized massω* Generalized frequencyU/S UpstreamD/S DownstreamY Depth of immersionCBF Blockage factorS Center to center distance of the cylinderD Diameter of the cylinderT DraftFB Total buoyancya Area of perforationd Water depthg Acceleration due to gravityHFXðxÞ The transfer functionhFX(t) Impulse response functionCX(s) Auto-covarianceRX(s) Auto-correlationFm(m) Cumulative distribution function{fm(m)} Probability density functionPf Probability of failureHs Significant wave heightTp Spectral peak perioduc Current velocityuw Mean wave speedG(x) Performance functionβHL Reliability indexsg Stress range in each groupng Number of cycles in each groupDRC Fatigue damage estimated by range counting

xxii Notations

DRFC Rain flow countingDLCC Level crossing countingDPC Peak countingDNB Narrow band approximationng Number of cyclesD Total damageσ StressVCG Vertical center of gravityAw Water plane areaΔ DisplacementGMLa Lateral meta-centric heightsGMLo Longitudinal meta-centric heightsI Moment of InertiaRAO Response amplitude operator

Notations xxiii

About the Author

Srinivasan Chandrasekaran is a faculty member of the Department of OceanEngineering at Indian Institute of Technology Madras, Chennai, India. He hasteaching, research and industrial experience of about 23 years during which he hassupervised many sponsored research projects and offshore consultancy assignmentsboth in India and abroad. His areas of current research are dynamic analysis anddesign of offshore platforms, development of geometric forms of compliant offshorestructures for ultra-deep water oil exploration and production, sub-sea engineering,rehabilitation and retrofitting of offshore platforms, structural health monitoring ofocean structures, seismic analysis and design of structures and risk analyses, andreliability studies of offshore and petroleum engineering plants. He has also been avisiting fellow under the invitation of Ministry of Italian University Research toUniversity of Naples Federico II, Italy, for a period of 2 years during which heconducted research on advanced nonlinear modeling and analysis of structuresunder different environment loads with experimental verifications. He has published110 research papers in international journals and refereed conferences organized byprofessional societies around the world. He has also authored three textbooks whichare quite popular among graduate students of civil and ocean engineering. He is amember of many national and international professional bodies and delivered manyinvited lectures and keynote addresses in the international conferences, workshopsand seminars organized in India and abroad.

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