E-book

# Beam Theory for Subsea Pipelines: Analysis and Practical Applications

ISBN: 978-1-119-11766-7
320 pages
August 2015

## Description

Introducing a new practical approach within the field of applied mechanics developed to solve beam strength and bending problems using classical beam theory and beam modeling, this outstanding new volume offers the engineer, scientist, or student a revolutionary new approach to subsea pipeline design. Integrating use of the Mathematica program into these models and designs, the engineer can utilize this unique approach to build stronger, more efficient and less costly subsea pipelines, a very important phase of the world's energy infrastructure.

Significant advances have been achieved in implementation of the applied beam theory in various engineering design technologies over the last few decades, and the implementation of this theory also takes an important place within the practical area of re-qualification and reassessment for onshore and offshore pipeline engineering. A general strategy of applying beam theory into the design procedure of subsea pipelines has been developed and already incorporated into the ISO guidelines for reliability-based limit state design of pipelines. This work is founded on these significant advances.

The intention of the book is to provide the theory, research, and practical applications that can be used for educational purposes by personnel working in offshore pipeline integrity and engineering students. A must-have for the veteran engineer and student alike, this volume is an important new advancement in the energy industry, a strong link in the chain of the world's energy production.

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List of Figures xiii

Abstract xvii

Preface xix

List of Symbols xxiii

Acronyms xxv

PART I CLASSICAL BEAM THEORY: PROBLEMSET AND TRADITIONAL METHOD OF SOLUTION

1 Euler's beam approach: Linear theory of Beam Bending 3

1.1 Objective to the part I 3

1.2 Scope for part I 3

1.3 Theory of Euler’s beam: How to utilize general beam theory for solving the problems in question? 4

1.3.1 Short history of beam theory 4

1.3.2 General Euler – Bernoulli method: Traditional approach 5

1.3.3 Loading considerations (from Wikipedia). Symbolic solutions 8

PART II STATICALLY INDETERMINATE BEAMS: CLASSICAL APPROACH

2 Beam in classical evaluations 13

2.1 Fixed both edges beam 13

2.1.1 Problem set and traditional method of solution: Unknown reactions 13

2.1.2 The equations of beam equilibrium 15

2.1.3 Differential equation of beam bending 16

2.1.4 The boundary conditions for a beam 16

2.1.5 The solution for forces and moments 17

2.1.6 Visualizations of solutions 17

2.1.7 Well-known results from "black box" program 20

2.2 Fixed beam with a leg in the middle part 20

2.2.1 Problem set 20

2.2.2 Static equations 22

2.2.3 Differential equations for the deflections of the spans 23

2.2.4 Transmission and boundary conditions 24

2.2.5 Reactions 24

2.2.6 Visualizations of the symbolic solutions 24

PART III NEW METHOD OF SYMBOLIC EVALUATIONS IN THE BEAMTHEORY

3 New method for solving beam static equations 33

3.1 Objective 33

3.2 Problem set 34

3.3 Boundary conditions 37

3.4 New practical application for Classical Beam Theory: Uniform load 38

3.4.1 Elementary Problems: Rectangular Load Distributions. Hinge and roller supporters of beam 38

3.5 Statically indeterminate beams 46

3.5.1 Objective 46

3.5.2 Problem b): Rectangular load distribution 47

3.5.3 Problem c): Pointed force 50

3.5.4 Problem d): Moment at the point 57

3.5.5 Problem set: Beam with hinge at the edge 61

3.5.6 Problem set: Beam with weak stiff ness at edge 65

3.6 Statically indeterminate beams with a leg 68

3.6.1 Problem bb): Two spans 68

3.6.2 Exercises 75

3.7 Cantilever Beam: Point Force at the Free Edge 75

3.7.1 Simple cantilever beam 75

3.7.2 Cantilever Beam: Point Force in the middle part of the beam 78

3.8 Point Force in the middle part of the beam: Hinge and Roller 83

3.8.1 Simple beam: Mechanical Problem Set 83

3.8.2 Point Force in the middle part of the beam: Three-point bending 84

3.8.3 Exercise 87

3.8.4 Moment at the edge of beam 91

3.8.5 Fixed beam with the Hinge at the edge of the beam 94

3.9 Multispan beam 101

3.9.1 Symbolic evaluation for multispan beam 101

3.9.2 Example of strength of multispan beam: Symbolic solutions 106

3.9.3 Numerical solutions for a peak like force 111

3.9.4 Numerical and symbolic solutions formultispan beam 115

3.9.5 Fixed edges of multispan beam 121

PART IV BEAMS ON AN ELASTIC BED: APPLICATION OF THE NEWMETHOD

4 Beam installed at the elastic foundation: Rectangular load. Symbolic Evaluations  129

4.1 Beam at elastic bed: Problem set 129

4.2 Finited size beam at the Winkler bed: Fixed edges 130

PART V APPLICATIONS FOR SUBSEA PIPELINES: COMPUTATIONAL EVALUATIONS

5 Fixed beam on elastic bed: Symbolic Solutions for Point Force 141

5.1 Boundary problem: Uncertain constants method 142

5.2 Symbolic solution: Steel Pipeline at seabed 151

5.3 Fixed Pipeline on elastic seabed in Arctic: Iceberg's Dragging Load. Numeric solutions 156

5.3.1 Problem set. Iceberg load 156

5.3.2 Free beam on elastic bed: Narrow rectangular load 156

5.3.3 Free pipeline on elastic bed: Combined loads 164

PART VI INSTALLATION OF THE SUBSEA PIPELINE AT SHALLOWWATER: INSTALLATION MODE IN ARCTIC REGION

6 Linear quadratic control 173

6.1 Objective 173

6.2 Subsea pipeline on elastic seabed in Arctic region: Impact of Iceberg Dragging Force 174

6.3 Strength and stability of the subsea pipeline 178

6.4 Subsea pipeline in current: Subsea Current Dragging Force. Strength and Stability 186

PART VII SUBSEA PIPELINES IN ARCTIC REGION: PERSPECTIVE AND PROJECTS

7 Subsea Pipeline: Installation and Operation Stages 199

7.1 Linear Th eory of Bending of Pipeline 199

7.2 French Method of Installation with Lay Barge: MultiLayers Pipe 206

7.2.1 Theory of bending of multilayers pipe: Timoshenko's beam approximation 206

7.2.2 Subsea Pipeline Installation by S-method 208

7.2.3 Equilibrium of the sagging part of subsea pipeline 208

7.2.4 Symbolic Solutions of the Bending Shape of Subsea Pipeline 211

7.2.5 Bending Shape and Strength of Subsea Pipeline. Case 1 212

7.2.6 Numeric solution for French Installation Project. Case 2 223

7.2.7 Numeric solution for French Lay Barge Project. Case 3 229

PART VIII IMPACT OF ICEBERG ON SUBSEA PIPELINE: INSTALLATION MODE

8 Historical view: Arctic regions 239

8.1 Norway, Barents Sea 239

8.2 Russia: Prirazlomnoye (Off shore) 242

9 Subsea Pipeline in Arctic Region 245

9.1 Problem set 248

9.1.1 Design properties 248

9.1.2 Iceberg load 250

9.1.3 Mechanical model. Symbolic solutions 252

9.2 Strength of the Pipeline under Impact of Iceberg. Numeric solutions 255

Conclusion 267

References 269

Appendix A 275

Index 277

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## Author Information

Alexander N. Papusha, PhD, is the Dean of the Arctic Technology Faculty and the head of the Continuum Mechanics and Offshore Exploration Department at Murmansk State Technical University (MSTU, Russia). He received an M.S. in mechanics from Kiev State University in 1972 and a doctorate in theoretical mechanics in 1979 from the Institute of Mechanics, Ukrainian Academy of Sciences, as well as a Doctor of Sciences from the Institute of Machinery (St. Petersburg), Russian Academy of Sciences in 1999. Since 1983, he has been a full professor at MSTU.

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