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31295017957605.Pdf NONLINEAR DYNAMIC INTERACTION BETWEEN CABLES AND MAST OF GUYED-TOWER SYSTEMS SUBJECTED TO WIND-INDUCED FORCES by TAREK HASSEN KEWAISY, B.S.C.E., M.S.C.E. A DISSERTATION IN CIVIL ENGINEERING Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Approved Chairperson of the Committee Accepted Dean of the Graduate School August, 2001 ACKNOWLEDGEMENTS During the preparation of this dissertation, the author became indebted to many people to whom he wishes to express his appreciation. Firstly, I would like to express my sincere appreciation to Dr. C.V.Girija Vallabhan, Chairman of the committee, for giving me the opportunity to benefit from his exceptionally valuable expertise in the field of civil engineering. His invaluable advice, encouragement, and objective supervision inspired me to excel in my research work. His dedication and commitment to produce high quality research work helped me greatly to raise my standards of excellence. I would like to thank Dr. James R. McDonald for his continuous guidance, constructive comments, and great support I received from him since the first day I joined TTU and throughout the course of my study. The time and efforts he spent to thoroughly revise this work is highly commendable. I wish to thank Dr. William P. Vann for the great efforts and time he spent to review this work. His constructive criticism and thorough examination of my work helped me to a great extent to produce a better dissertation. The encouragement, and valuable advice he provided during the course of this research is greatly appreciated. I also would like to extend my appreciation to Dr. Kishor C. Mehta for providing me with his valuable comments and for sharing his professional expertise in wind engineering related subjects. I wish to dedicate this work to my mother and to the soul of my father; the reason for my being and to whom I owe everything. I would also like to express my wholehearted appreciation to my family for their continuous encouragement and love, and to my fiancee for the sincere love and passionate encouragement she gave me, and finally to my close fiiends for their support. 11 TABLE OF CONTENTS ACKNOWLEDGMENTS 11 ABSTRACT viii LIST OF TABLES x LIST OF FIGURES xi CHAPTER 1. INTRODUCTION 1 1.1 Introductory Background 1 1.1.1 Structural Cables in Civil Engineering 1 1.1.2 Guyed Towers 3 1.2 Objectives and Scope 3 1.2.1 Research Objectives 3 1.2.2 Research Goals 3 1.3 Plan of Development 5 2. LITERATURE REVIEW 7 2.1 Static Analysis of Cables 7 2.2 Dynamics of Cables 9 2.2.1 Review 9 2.2.2 Solution Methods 10 2.2.3 Free Vibrations 12 2.2.4 Forced Vibrations 16 2.2.5 Equivalent Dynamic Stiffriess 17 2.2.6 Damping of Cables 18 2.2.7 Vibration Measurements 19 2.2.8 Low-Tension Cables 20 2.3 Wind-Induced Vibrations of Cables and Guyed Towers 22 2.4 Static and Dynamic Analysis of Guyed Towers 22 111 3. STATIC ANALYSIS OF CABLES UNDER GENERAL LOADING 27 3.1 Introduction 27 3.2 Development of the Governing Equilibrium Equations 27 3.2.1 Main Assumptions 29 3.2.2 Static Equilibrium Equations 29 3.3 Finite Difference Model for the Nonlinear Partial Differential Equations of Equilibrium 31 3.4 Computational Procedure for the Solution of Equilibrium Equations 32 3.4.1 hiitial Cable Self-weight Profile 32 3.4.2 Cable Response due to General Static Loading 33 3.5 Inclusion ofPrescribed Displacements of Cable Ends 36 4. DYNAMIC ANALYSIS OF CABLES UNDER GENERAL LOADING 37 4.1 Introduction 37 4.2 Development ofthe Governing Equations of Motion 38 4.2.1 Main Assumptions 38 4.2.2 Equations of Motion 38 4.2.3 Normalization ofthe Equations 40 4.3 Direct Time-Integration 43 4.3.1 Classificationof Different Time-Integration Methods 43 4.3.2 Time-Integration Using Newmark-P Method 44 4.4 Finite Difference Model for the Nonlinear Partial Differential Equations of Motion 47 4.5 Computational Procedure for Solution ofthe Equations of Motion 51 4.5.1 hiitial Cable Self-Weight Profile 51 4.5.2 Cable Response due to General Dynamic Loading 51 4.6 Numerical Study 54 4.6.1 Typical Problem Information 54 4.6.2 Parametric Study Information 55 4.6.3 Discussion of Typical Problem Results 57 4.6.4 Discussionof Parametric Problem Results 60 IV 5. NUMERICAL STABILITY ANALYSIS FOR NONLINEAR CABLE VIBRATIONS 68 5.1 Infroduction 68 5.1.1 Spatial Discretization 68 5.1.2 Temporal Discretization 68 5.1.3 The Role of Time-Step in Direct Time-Integration 68 5.2 Properties of Numerical Approximations 69 5.2.1 Convergence 69 5.2.2 Consistency 70 5.2.3 Stability 70 5.2.4 Solution Errors 71 5.3 StabiUty ofthe Nonlinear Newmark ImpUcit Integrafion (Finite Difference Equations Approach) 71 5.3.1 Eigenproblem Formulation 71 5.3.2 Finite Difference Equations 73 5.3.3 Stability Criterion (Mathematical Model) 76 5.4 Other Stability Criteria 77 5.4.1 Hughes' Stability Criteria for Newmark Method 77 5.4.2 Courant Condition 78 5.5 Numerical Study 78 5.5.1 Typical Problem Information 78 5.5.2 Parametric Study Information 78 5.5.3 Study Layout 79 5.5.4 Discussion of Study Results 80 6. MODELLING OF WIND FORCES ACTING ON GUY CABLES 90 6.1 Infroduction 90 6.2 TimeHistory Simulation of Wind and Wind Loads 91 6.2.1 General 91 6.2.2 Numerical Simulation of a Boundary Layer Flow 91 6.2.3 Dynamic Problem Main Informafion 93 6.2.4 Dynamic Wind Force Computation 94 6.3 Quasi-Static Wind Forces on a Single Cable 102 6.3.1 Quasi-Static Problem Main Information 102 6.3.2 Quasi-Static Wind Forces Computation Procedure 102 6.4 Numerical Study No. 1: Dynamic Wind-Induced Forces on Cables 104 6.4.1 Typical Problem Information 105 6.4.2 Parametric Study Information 105 6.4.3 Discussion of Study Results 107 6.5 Numerical Study No. 2: Quasi-Static Wind-Induced Forces on Cables 118 6.5.1 Typical Problem Informafion 118 6.5.2 Discussion of Study Results 118 ANALYSIS OF GUYED TOWERS SUBJECTED TO WIND LOADING 127 7.1 Infroducfion 127 7.2 Structural Configuration 128 7.3 Analytical Techniques 131 7.4 Static Analysis of Guyed Towers 132 7.4.1 Static Guy Cable Element (FD Formulation) 132 7.4.2 Stafic 3-D Bar Element (FE Formulation) 134 7.4.3 Quasi-Static Nodal Forces 136 7.4.4 Solution Procedure 136 7.5 Dynamic Analysis of Guyed Towers 139 7.5.1 Dynamic Guy Cable Element (FD Formulation) 140 7.5.2 Dynamic 3-D Bar Element (FE Formulation) 142 7.5.3 Dynamic Nodal Forces 143 7.5.4 Solution Procedure 143 7.6 Nvmierical Studies of Analysis of Guyed Towers 147 7.6.1 Typical Problem Information 147 7.6.2 Discussion of Dynamic Analysis Study Results 153 7.6.3 Discussion of Dynamic Versus Static Analysis Study Results 180 7.6.4 Discussion of Dynamic Analysis Study Results (Dynamic Versus Static guy stifftiess) 186 VI 7.6.5 Discussion of Dynamic analysis Study Results (Variable Mean Wind Direction) 193 8. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS 202 8.1 Infroduction 202 8.2 Summary 202 8.2.1 Dynamic Analysis of Cables Under General Loading 202 8.2.2 Stability Analysis ofNonlinear Cable Vibrations Problems 203 8.2.3 Modeling ofWind Forces on Guy Cables 203 8.2.4 Analysis of Guyed Towers Subjected to Wind Loading 204 8.3 Conclusions 204 8.3.1 Dynamic Analysis of Cables Under General Loading 204 8.3.2 Numerical StabiUty Analysis for Nonlinear Cable Vibrations 205 8.3.3 Modeling ofWind Forces on Guy Cables 206 8.3.4 Analysis of Guyed Towers Subjected to Wind Loading 206 8.4 Recommendations 209 REFERENCES 211 vu ABSTRACT Guyed towers are special structures widely used in communication industry as antenna-supporting structures. A guyed tower is a nonlinear structural system in which the mast, consisting of single beam-column or multiple members (trusses) is supported elastically at various points along its height by inclined pretensioned cables with their ends anchored to the ground. As a result of the overall slendemess and flexibility of the system, guyed tower exhibit a high degree of nonlinearity and dynamic sensitivity to turbulent wind excitation. Thus to obtain reliable structural responses of the vibrating tower, a 3-D nonlinear dynamic analysis is mandatory. This research work comprehensively investigates the important subject of dynamic interaction between the mast of a guyed tower and its supporting cables when the tower is excited by turbulent winds. To achieve this objective, a comprehensive set of analytical studies are pursued and relevant mathematical models are obtained. In the following a brief description of each of these studies is given. The first study involves a new and general nondimensional finite difference formulation that considers all the important parameters influencing the vibration characteristics of guy cables. The second study complements the first one by investigating the stability and convergence ofthe Newmark-p; step-by-step integration technique and their dependence on both spatial and temporal discretization parameters. The third study proposes new dynamic and quasi-static computational procedures to model the wind-induced forces on cables and bars. The procedures utilize generation techniques for wind speed records and take into consideration the major characteristics of both the exciting wind and the vibrating cable.
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