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NONLINEAR DYNAMIC BEHAVIOUR OF OFFSHORE GUYED TOWER

By

Risheendra Singh Bisht

Thesis Submitted To The Indian Institute Of Technology, Delhi

For The Award Of The Degree Of DOCTOR OF PHILOSOPHY

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DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY

NEW DELHI 110016 JUNE 1994

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CERTIFICATE

This 1 s to certify that the thesis entWed,.. Non'inear dynamic behaviour of O什shore Guyed Towert',.being submitted by Risheendra Singh Bisht, to the Indian Institute of Technology, New Delhi,for the award the Degree of "DOCTOR IN PHILOSOPHY.- in Civil Engineering is a reco

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of the bon

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de research work carried out

by

him under our supervision and guidance. He has fulfilled the requirements for submission of this thesis, which to the best of our knowledge, has reached the requisite standard.

The material contained in this thesis has not been submitted in part or full to any other University or Institute for the award of any degree or diploma.

(Dr. A.K.Jain) Associate Professor Civi!Engineering Deptt.

Indian Institute Of Technology New Delhi 一 110016, INDIA

A4

(Prof. T.K.Datta) P rof essor Civil Engineering Deptt.

Indian Institute Of Technology New Delhi-110016, INDIA

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ACKNOWLEDGEMENTS

It 15 my great pleasure to express my pro加und sense of gratitude to my research guides Dr A K Jamn and Prof T K Datta for their v&uable guidance, inspiration and encouragement during the course of this study. This work would not have been completed without their keen interest and sincere help.

My sincere thanks are also to all my well wishers and friends particularly Mayank Tiwari,Most厨a J証eri, Sameer Mathur, Dr Rajendra Singh Adhikari,Dr Rajeev Srivastava (Khadda), Bharat Suneja, Manoj Bhatt Manoj Kuisherata, Nayak, Anadi Dubey and Vandana Gyandhar for their continuous moral support and encouragement.

My thanks are also due to my cute little special friends Akhil Anshut, Ankita, Jayati and Rishi, for their lovely companionship. I would also like to thank Ms Rachana Jamn, Dr S Karunes, Dr Geetam Tiwari, Dr

Ajai Mathur and Dr C V R Murthy for their silent moral support.

Finally, I would like to thank my wife Mitra, mゾ parents and my sister Neha, for their patience and continued support, and to someone who is yet to come in this world,who has inspired me to complete this thesis.

(Risheendra Singh Bisht)

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ABSTRACT

Present study deals with the investIgation of the dynamic response of idealised Exxon Guyed Tower under regular and random sea waves in the presence of steady current, wind and earthquake. The responses are obtained both in time and frequency domains 化r regular waves. Both approaches duly consider the system non-linearities such as nonlinear force -excursion relationship of guylines, nonlinear hydrodynamic drag force and variable added mass.

In the time domain analysis, Newmark's time integration scheme is used to integrate the equation with iteration employed at each time step to tackle the nonlinearities. A two cycle interpolation technique is used to obtain faster convergence to steady state response.

In the iterative frequency domain technique, the equations of motion are written in the frequency domain. The system nonlinearities are handled using the Newton一Raphson method 化r simultaneous equations.

Stnce the use of exact Newton一Raphson iteration scheme becomes compulationally very expensive, the Jacobian In the New ton -Rap hson Sc十seme is evaluated approximateiy without iosing the exactness of the results. Further, the solutions are obtained i n normal co-ordinates. Thess make the iter・ative procedure computatlonaJIy very efficient. The iteraじivc frequency domain analysis provides same results as those of the tlm。4

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domain analys,s in much less computational time. For random wave loading, which is simulated 化r a given sea surface elevation spectrum, iterative frequency domain method is used to obtain the response. For both regular and random sea states, a parametric study is conducted to investigate the effects of current velocity, initial guy cable tension, number of higher modes, fixity of the base and hysteretic behaviour of the 旬rce-excursion relation 可 the guy cables on the response. Due to the dynamic motion of the tower, the tension in the cable continuously fluctuates and hence, it is highly prone to fatigue damage. Therefore, the fatigue life estimate of the cable is also investig吐ed using the Palmgren-Miner Cumulative Fatigue law and S-N curve approach for sea states idealized by regular waves.

Response of the Guyed Towers to low frequency second order wave forces in the random ocean environment is determined using a simplified procedure in which hydrodynamic loads are calculated us;ng Morison's equation. The second order drift force is considered to be proportional to the square of the wave elevation and is simulated using a d r i ft 化rce coefficient and the time history of slowly varying wave envelope in random sea. The response due to the second order wave forces

!s o1ンtained incorporating the nonlinear force-excursion behaviour of 工he guy:inp_s. The solutions are obtained using the iterative frequency domain technique. Investigations have been carried cut to r eiiect the reiative importance of response due to second order wave forces wi ti. respe【ン L to the response due to first.order wave forces. The statistにs of the respo:1'ぐ

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due to second order wave

rce alone and due to the combined fIrst order and second order wave forces are also evaluated.

Responses of the Guyed Tower to the combined actions

wind and wave, and wind, wave and current are obtaIned using the iterative frequency domain analysis. Both gustiness of wind and wave are considered to be stationary random process and the two are assumed to be uncorrelated. The time histories of water particle kinematics and wind velocities on the exposed portion of the tower are simulated from their respective power spectral density functions. Davenport's wind velocity spectrum and the Pierson Moskowitz(wind driven)sea surface elevation spectrum are used for this purpose. For generating the time histories of wind velocities, it is assumed that the wind velocities are fully correlated along the height of the tower. For the purpose of duly considering the effect of the structural displacement on the hydrodynamic loading and nonlinear guyline resistance, the mean and fluctuating component of the wind forces are added together and applied onto the structure (i.e.

responses are not separately obtained for mean and fluctuating components of the wind). The responses of the tower are compared between the cases when(1)wave forces are only acting (ii)wave and wind

rces are acting together and,(III)wave, wind and current forces are acting together. The results highlight the conditions when wind induced vibration assume importance.

Finally, the seismic response of the guyed tower is obtained with and without the presence of wave and current. For the analysis, two

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regular waves(10.24 sec/12 m and 5.12 sec/6 m) and N-S component o f the EI Centro Earthquake are used. The responses are obtained in time domain (using Newmark's integration procedure). Time integration technique Is used in order to investigate the effect of initial condition of the tower on the seismic response. Initial condition refers to the steady state osciHation of the tower when the earthquake first hits the tower. The nature and magnitude of the seismic response with and without wave forces acting on the tower are investigated with the help of numerical study.

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ー ・ー -ー × ・:I -ー V ・引 X ~f I X 3 7 9 0 3 J『ー dll 8 2 L4- 2 つ一

CONTENTS

Page 軸匹 CERTIFICATE

ACKNOWLEDGEMENTS

INTRODUCTION AND LITERATURE SURVEY General

2 Guyed Tower Concept

.3 Guyed Tower Analysis:Special Problems 4 Literature Survey

4.1 Guyed Tower Mooring System Analysis 4.2 Guyed Tower Analysis

4.3 Second Order Wave Drift Forces

5 Need for the present work &objectives of the Study 6 Organisation of the Thesis

ABSTRACT CONTENTS

LIST OF FIGURES LIST OF TABLES NOMENCLATURE

CHAPTER 一 I

Vii

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CHAPTER 一 H

2

GUYED TOWER BEHAVIOUR UNDER REGULAR WAVES General

8 8 2 2 29 29 30 2 3 3 3 34 34 5 6 3 3 6 9 3 3 40 4O 43 43 44 「1 5 4 5 1 8 5 5

2.2 The Guyed Tower

2.2.1 The Theoretical Model 2.2.2 The Equation Of Motion

2.3 Comp utation 叶 Natural Frequencies and Mode Shapes

2.4 Uncoupled equations of Motion 2.5 Hydrodynamic Loading

2.5.1 General 2.5.2 Wave Theory

2.5.3 Generation Fluid Loading Vector 2.5.4 Intensity Of Horizontal Fluid Loading 2.5.5 Added Mass Correction

2.6 Solution Of Equation Of Motion 2.6.1 Time Domain Analysis

2.6.2 Time Optimization Technique

2.6.3 Evaluation Of Structural Response 2.6.4 Mode Acceleration Method

2.7 Iterative Frequency Domain Method

2.8 Numerical Study 一 Exxon Prototype Tower 2.8.1 Effect Of Higher Modes

2.8.2 Effect Of Base Rotational Spring Stiffness v"

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i 06 107 i 08 i 09 0 1 1 41- Jl- Jl d叫ー 1

112 113

2.8.3 Effect Of Current and Wave 59

2.8.4 Effect Of Initial Horizontal Tension Of the Guy Cab'es

2.8.5 Effect Of Hysteretic Behaviour of Force- Excursion relationship Of Guy Cables 2.8.6 Linearization Of Cable Stiffness 2.8.7 Linearization Of Drag Linearity 2.8.8 Fatigue Life estimate of Guy Cables

2.8.9 Time Domain Vs Iterative Frequency Domain 2.9 Conclusions

60 41 つ」 3 6 6 6 64 65 66

TABLES

FIGURES

CHAPTER 一 I]:' GUYED TOWER BEHAVIOUR UNDER RANDOM WAVES 106 3 Random Ocean Environment

3.1.i Description Of Sea State

3.1.2 Simulation Of Sea Surface Elevation

3.2 Evaluation of the Time Histories Of Wave Kinematics 3.2.1 Simulation Of Wave Forces

3.3 Response Analysis

3.4 Numerical Study-Exxon Prototype Tower 3.4.1 Effect Of Sea States

3.4.2 Effect Of Higher

ix

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3.&3 Effect Of Base Rotational Spring Stiffness 115 3.4.4 Effect Of Current and Wave 115 3.4.5 Effect Of Hysteretic Behaviour Of Force-

Excursion relationship Of Guy Cables 117

3.5 Conclusions 117

TABLES FIGURES

CHAPTER 一 Iv GUYED TOWER BEHAVIOUR UNDER SECOND ORDER

WAVES 151

Introd uction 151

4.2 Analysis 152

4.2.1 Guyed Tower Model and Equation Of Motion 152 4.2.2 Simulation Of Second Order Wave Forces 153 4.2.3 Determination Of R2 and F(t) 155 4.2.4 Determination Of Drift Force Coefficient 156 4.2.5 Simulation Of F!rst Order Wave Forces i 58

4.3 Response Analysis 159

4.4 Numerical Study 159

4.5 Conclusions i 63

TABLES FIGURES

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cJ 口」 8 8 JI 4ll dd1 彫 別

155 185 i 89

6.1 6.2

3 4

66

CHAPTER-v GUYED TOWER BEHAVIOUR UNDER WIND, WAVE

CURRENT LOADS

Introd uction 5.2 Anatysis

5.2.1Guyed Tower Modet and Equation Of Motion 5.2.2 DeterminatIon Of Wind Loads

5.2.3 Simulation Of Wind Vetocity and Water Particle 5.3 Solution Procedure

5.4 Numerical Example and Results 5.5 Conclusions

TABLES FIGURES

CHAPTER-VI GUYED TOWER BEHAVIOUR UNDER EARTHQUAKE LOADS IntroductIon

AnalysIs

205 206 6.2.1 Guyed Tower Model and EquatIon Of Motion 206

6.2.2 Earthquakes Loads 206

Solution Procedure 207

Numerical Example and Results 208 6.4.1 Response due to Earthquake Only 209 6.4.2 Response due to Earthquake and Current 210 6.4.3 Response due to Earthquake and Waves 21 1

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APPENDIX I APPENDIX APPENDIX

6.4.4 Effect Of Initial Conditions 212

6.5 Conclusions 213

TABLES FIGURES

CHAPTERVII CONCLUSIONS AND RECOMMENDATION FOR FUTURE

WORK 233

Conclusions 233

7.2 Recommendationr Future Work 237

Mooring System and Cable Damping 239 Two Cycle Integration Technique 249 Simulation Of Sea Surface Elevation 253

REFERENCES 259

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References

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