Construction Stage Analysis of Cable-Stayed Bridges
by
Marko Justus Grabow Thesis submitted to the Faculty of the Technical University of Hamburg Harburg
in partial fulfilment of the requirements for the degree of Diplom - Ingenieur
in
Civil and Environmental Engineering
June 29th, 2004 Hamburg, Germany
Arbeitsbereich Baustatik und Stahlbau Structures Research Group
Construction Stage Analysis of Cable-Stayed Bridges
Marko Justus GrabowAbstract
Different means and methods exist in the construction industry for the erection of bridges. In the planning and the execution of the complex construction operations, the effects of the chosen erection methods need to be taken into consideration to achieve a safe and economical process. For a defined span range, the cable-stayed structure is a bridge type which offers an aesthetic shape and also a cost-effective solution for crossing rivers and valleys. The Cantilevering Method is a widely used procedure for the construction of the superstructure.
In the structural analysis of this process, changes in the geometry and boundary conditions as well as the material properties and other structural details must be considered. Temporary construction loads and boundary conditions act only during the construction, depending on the method and the sequence of the erection. However, these construction loads can produce considerable stresses in the unfinished structure. Due to its lack of resistance against failure, a detailed investigation prior to the construction is essential.
Not only the influence of individual structural elements, such as the non-linear behaviour of the stay cable, but also the performance of the composed structure in the various stages must be taken into account. Furthermore, time dependent material properties such as creep and shrinkage play a major role, especially in the case of bridges where the main girder is fabricated of cast-in-situ concrete segments or composite sections. The issues and considerations required to develop a save and economical construction sequence are expatiated in this thesis.
An example of a construction stage analysis is provided in detailed for the Second Jindo Bridge. This bridge is a steel cable-stayed bridge with a main span of 344 metres, and is erected with the Cantilever Construction Method. The overall construction process is modelled and analysed.
I
Table of Contents
Acknowledgement... V
List of Figures ... VI List of Tables ...XII List of Symbols and Units... XVI1
General task ... 1
1.1 Introduction ... 1
1.2 Overview ... 3
1.3 Thesis organisation ... 4
2
Cable-Stayed Bridges ... 6
2.1 History of cable-stayed bridges ... 6
2.2 Stay-cables... 13
2.3 Erection of cable-stayed bridges... 15
2.3.1 Static arrangement of cable-stayed bridges ... 15
2.3.2 Erection procedures ... 18
2.3.3 Construction of the pylon ... 23
2.3.4 Erection of the main girder using the cantilever method ... 24
3
General description of a Construction Stage Analysis... 29
3.1 Designed Cable Forces ... 29
3.2 Construction Stage Analysis... 34
3.3 Construction Stage Analysis by MiDAS ... 37
3.3.1 The analysis programme ... 37
3.3.2 Structural Data ... 38
3.3.3 Unknown Load Factor ... 39
3.3.4 Backward Analysis ... 41
3.3.5 Forward Analysis... 43
3.3.6 Forward Method = Backward Method... 45
3.4 Influence matrix... 46
3.4.1 Calculation of influence matrices ... 46
Table of Contents
II
3.5 General considerations and uncertainties... 48
3.5.1 Time dependent effects ... 49
3.5.2 Non-linearity effects ... 61
3.5.3 Temperature ... 74
3.6 Modelling and tuning of cables... 75
3.7 Construction control and monitoring ... 79
3.7.1 Construction Control Systems... 80
3.7.2 Adjustment instruction on site ... 81
3.7.3 Methods of cable-stay adjustment... 82
3.7.4 Control of deck geometry... 83
3.7.5 Computational Systems... 84
4
Example of a Cable-Stayed Bridge including temporary supports...91
4.1 Model data ... 91
4.2 Different restrictions for the Unknown Load Factor... 93
4.2.1 Case I: Use of different connections girder-pylon, restricted displacement ... 93
4.2.2 Case II: Restricted moment distribution ... 95
4.3 Optimisation Method for ideal cable forces by influence matrix... 97
4.3.1 Adjustment of the girder elevation... 98
4.3.2 Adjustment of cable forces... 101
4.3.3 Summary of the adjustment calculation ... 102
4.4 Backward and forward analysis ... 103
4.4.1 Backward analysis... 103
4.4.2 Forward analysis ... 107
4.4.3 Influence of the activation time of the Girder-Pylon connection ... 109
4.5 Construction stage analysis considering creep and shrinkage ... 115
4.5.1 General conditions ... 115
4.5.2 Modelling creep and shrinkage ... 116
4.6 Camber Control... 120
4.6.1 General calculation method... 120
4.6.2 Camber calculation for the Case I example ... 125
4.6.3 Camber calculation for the Case II example ... 129
4.7 Construction Errors ... 130
4.7.1 Error in cable force ... 131
4.7.2 Error in elevation of a segment ... 135
III
5
Model of the Second Jindo Bridge... 150
5.1 Location of the bridge... 150
5.2 Structure... 152
5.3 Erection Options ... 152
5.3.1 Erection of the towers and side spans ... 153
5.3.2 Erection of the main span ... 153
5.4 Modelling of the bridge with MiDAS... 154
5.4.1 Nodes 155 5.4.2 Elements ... 157 5.4.3 Material Properties... 158 5.4.4 Section Properties ... 159 5.4.5 Boundary Conditions ... 161 5.4.6 Loading ... 161
5.5 Initial Cable Forces... 165
5.5.1 Optimised Structural Moments ... 166
5.5.2 Limited Cable Forces... 167
5.5.3 Limited cable forces and restricted bending moment ... 171
5.6 Back- and Forward Analyses of the Second Jindo Bridge ... 173
5.6.1 Construction Stages ... 174
5.6.2 Modified Construction Stage Analysis ... 180
5.6.3 Linear Backward and Forward Analyses ... 182
5.6.4 Differences in the application of cable elements ... 189
5.6.5 Cable elements in forward analysis ... 194
5.7 Comparison with Hyundai and RM Results ... 202
5.8 Minimum and maximum allowable stresses... 205
5.8.1 Tension forces in the cable stays ... 205
5.8.2 Maximal stresses in the girder segments ... 208
5.8.3 Maximum stresses in the pylon... 211
5.9 Fabrication Camber of the Second Jindo Bridge ... 212
5.10 Unstressed cable length L0... 215
5.11 Final comments on the construction stage analysis ... 219
6
Conclusion... 221
6.1 Summary... 221
6.2 Contribution... 228
6.3 Recommendation ... 228
Table of Contents IV
Literature ...231
References... 231 Bibliography ... 232 Internet ... 235Appendix ...237
Appendix A: Creep calculation CEB-FIP 1990 ... 237
Appendix B: Extracts from the correspondence with MiDAS support... 238
Appendix C: Model of the Second Jindo Bridge ... 240
Appendix D: Allowable and existing stresses... 243
Appendix E: Unstressed cable length L0... 249
V
Acknowledgement
I would like to express my gratitude to my teacher Prof. Starossek for his courses and his interest and support of his students. As a main part of this thesis was developed in relation to an internship at the Korea Highway Corporation, I thank him deeply for organizing the unique opportunity to visit Korea and for giving me the time to find the confidence in my decision. I also appreciate his providing advice and support throughout my work on this thesis.
Furthermore, I would like to express my sincere thanks to Dr. Park Chan-Min for inviting me to Korea and for his guidance during my internship. I greatly appreciated that I could learn much from his rich experience in the construction field. My life has been enriched by his delightful storytelling. I truly enjoyed the various visits and the trips that we undertook.
I would also like to thank Mr. Choi Gyeong Hag and his family for their far-reaching help and profound hospitality during my stay. The diverse activities gave me great pleasure and an insight into the Korean tradition. I can only hope that they could learn a little about the German culture as well.
I would like to express my sincere appreciation to the whole structural research group and all the people that I have come in contact with during my stay at the Korea Highway Corporation. Thanks for the kindness and open-heartedness. I will keep them in good remembrance.
Finally, and most importantly, I am most grateful for the continuous love and support that my family has always given me, during my work on this thesis and all the time prior.
List of Figures
VI
List of Figures
Figure 2-1: The Albert Bridge across the Thames in London... 6
Figure 2-2: The Strömsund Bridge... 7
Figure 2-3: The Köhlbrand Bridge ... 8
Figure 2-4: The Maracaibo Bridge ... 9
Figure 2-5: The Alex Fraser Bridge during its construction ... 10
Figure 2-6: The Hitsuishijima Bridge ... 11
Figure 2-7: The Sutong Yangtze River Bridge... 12
Figure 2-8: New PWS cable ... 14
Figure 2-9: Fan systems ... 16
Figure 2-10: Multi-cable harp systems with intermediate supports in the side span... 17
Figure 2-11: Erection on temporary supports... 19
Figure 2-12: Erection by free cantilever method... 21
Figure 3-1: Illustration of the pendulum rule ... 30
Figure 3-2: Unit Load Case Method for determining the ideal state... 33
Figure 3-3: Unit Load Case Method for construction stage analysis ... 36
Figure 3-4: Cable-stayed example... 38
Figure 3-5: Flowchart for cable initial prestress calculation ... 39
Figure 3-6: Moment self-weight & unit pretension load [tonf]... 40
Figure 3-7: Results of the Unknown Load Factor calculation ... 40
Figure 3-8: Moment self -weight & initial pretension load [tonf]... 40
Figure 3-9: Sequence for backward analysis... 42
Figure 3-10: Applied cable forces [tonf] ... 44
Figure 3-11: Moment distribution; forward analysis before adding the support [tonfm]... 44
VII
Figure 3-13: Discontinuity between two segments ... 45
Figure 3-14: Influence Matrix of displacement [mm]... 47
Figure 3-15: Time dependent concrete deformation ... 50
Figure 3-16: Creep isochrones ... 55
Figure 3-17: Definition of the Creep-Function J... 55
Figure 3-18: Verification model for creep & shrinkage... 59
Figure 3-19: a) Creep coefficient b) Shrinkage strain... 60
Figure 3-20 Force/deflection curve ... 64
Figure 3-21 Horizontal and inclined stay cable ... 64
Figure 3-22 Deformed and uniformed cable element ... 67
Figure 3-23 Newton-Raphson Method... 69
Figure 3-24 Verification example of non-linear analysis... 70
Figure 3-25: Uniform variation of temperature, a) without supports or with supports but no friction on bearings, b) with supports and fixed bearings ... 74
Figure 3-26: Deflection produced by: a) temperature variation in the deck, b) temperature variation only in the side span... 74
Figure 3-27: Deflections produced by an increase of temperature a) in symmetrical cable-stayed cantilevers b) with side span on supports... 75
Figure 3-28: Stay adjustment definition... 77
Figure 3-29: Deflections produced by construction with final cable forces a) in case of symmetrical cable-stayed cantilever b) in case of bridge with intermediate supports ... 78
Figure 3-30 Theoretical and actual deck profile ... 84
Figure 3-31: Example of camber error... 89
Figure 4-1: Structural system ... 91
Figure 4-2: Moment Distribution under Self Weight [tonfm], Case I... 93
Figure 4-3: Idealised moment distribution after restricted deformation [tonfm], Case I ... 94
Figure 4-4: Deformation dz after restricted deformation [mm], Case I ... 95
Figure 4-5: Moment distribution after restricted deformation [tonfm], Case II... 96
Figure 4-6: Ideal moment distribution after moment restriction [tonfm], Case II ... 96
List of Figures
VIII
Figure 4-8: Moment distribution backward analysis [tonfm], Case I... 103
Figure 4-9: Deformation dz backward analysis [mm], Case I... 104
Figure 4-10: Before removing the cable and activating the support [mm]... 105
Figure 4-11: Addition of support to the deformed (a) and the original structure (b) [mm] ... 106
Figure 4-12: Deformation when first part of the side span is erected [mm] ... 107
Figure 4-13: Moment distribution forward analysis [tonfm], Case I ... 108
Figure 4-14: Deformation dz forward analysis [mm], Case I... 108
Figure 4-15: Different normal forces back- and forward analysis [tonf], Case II ... 108
Figure 4-16: Moment distribution due to considered gap in normal forces in the girder of forward and backward analysis [tonfm]; Case II ... 109
Figure 4-17: Moment distribution forward analysis with changed girder-pylon connection, neglecting normal forces in the key segment [tonfm], Case II... 110
Figure 4-18: Changed backward analysis a) normal force, b) horizontal displacement, Case II ... 111
Figure 4-19: Changed forward analysis a) horizontal displacement, b) normal force, Case II ... 111
Figure 4-20: Moment distribution changed forward analysis, applying a horizontal displacement [tonfm], Case II ... 112
Figure 4-21: Horizontal displacement changed forward analysis, applying a horizontal displacement [mm], Case II... 112
Figure 4-22: Horizontal displacement changed forward analysis, applying a horizontal displacement, Case II ... 113
Figure 4-23: Bending moment in the girder [tonfm] a) 1 day after applying additional load, b) 10 days after applying additional load, c) after 5000 days... 118
Figure 4-24: Vertical displacement of the main girder [mm]... 119
Figure 4-25: Camber and deformation ... 120
Figure 4-26: Cantilever ... 121
Figure 4-27: a) Current displacement b) Construction camber ... 121
Figure 4-28: Erection of a cantilever... 122
Figure 4-29: Erection of a cantilever, current displacement value... 123
Figure 4-30: Fabrication camber, real displacement [mm] ... 124
IX
Figure 4-32: Fabrication camber [mm] (Case I model) ... 128
Figure 4-33: Fabrication camber [mm] (Case II model) ... 129
Figure 4-34: Construction camber [mm] (Case II model)... 130
Figure 4-35: Vertical displacement considering cable tension error... 131
Figure 4-36: Final moment distribution due to changed pre-stressing in cable 4 [tonfm] ... 132
Figure 4-37: Final moment distribution after restressing of cable 1 to 5 [tonfm]... 135
Figure 4-38: Final moment distribution after elevation adjustment [tonfm]... 138
Figure 4-39: Elastic link in order to model an error in the girder elevation... 139
Figure 4-40: Vertical displacement original system and system including error in girder elevation ... 140
Figure 4-41: Fabrication camber [mm] ... 141
Figure 4-42: Structural system of harp type cable stayed bridge (dimensions in [m]) ... 142
Figure 4-43: Non-linear analysis of a single cable (cable 6 in the model Figure 4-42) [m] and [kN] ... 144
Figure 4-44: Deflected shape of the girder due to non-linear analysis and different initial tension [m] ... 145
Figure 4-45: Comparison of deflected shapes,... 146
Figure 4-46: Cable installation in the linear truss model [kN]... 148
Figure 4-47: Cable installation in the Ernst truss model [kN] ... 148
Figure 5-1 Location of Second Jindo Bridge ... 151
Figure 5-2: Girder elevation in the side and main span [m]... 156
Figure 5-3: Working points at the pylon ... 157
Figure 5-4: Working points at the girder... 157
Figure 5-5: Cable-girder connection and tied down condition using elastic links ... 157
Figure 5-6 Element numbers... 158
Figure 5-7: Material numbers... 160
Figure 5-8: Traffic load Korean Standard ... 165
Figure 5-9: Moment distribution restricted displacement [tonfm]... 166
List of Figures
X
Figure 5-11: Displacement dz restricted cable forces [mm]... 169
Figure 5-12: Moment distribution restricted cable forces & bending moments in the girder [tonfm]... 172
Figure 5-13: Construction stages 1-39 ... 179
Figure 5-14: Bending moment before opening the bridge [tonfm] (Case A) ... 181
Figure 5-15: Moment forward and backward analysis Case A [tonfm] ... 184
Figure 5-16: Moment forward analysis, considering the tension forces due to the Self-Weight function Case A [tonfm] ... 186
Figure 5-17: CS 4-Installation of cable 6, considering an effective stiffness in forward and backward analysis [tonf] ... 190
Figure 5-18: CS 16 installation of cable 10, considering an effective stiffness in forward and backward analysis [tonf]... 190
Figure 5-19: Final moment distribution using cable elements, considering the effect of ... 191
Figure 5-20: CS 16 installation of cable 10, cables stressed in 5 steps [tonf] ... 192
Figure 5-21: Pylon and side span before the installation of the first cable[tonfm] ... 193
Figure 5-22: Moment distribution in the main girder using cable elements, considering and neglecting the effect of the Self-Weight function [tonfm] ... 194
Figure 5-23: Vertical displacement neglecting the effect of the Self-Weight function [mm], Case B ... 197
Figure 5-24: Vertical displacement at the tip of the cantilever for each construction step [mm] ... 198
Figure 5-25: Maximum and minimum moments from forward analysis using cable elements and Case B values given in Table 5-15 [tonfm]... 201
Figure 5-26: Final moment [tonfm], Hyundai initial tension, same loading and construction sequence ... 203
Figure 5-27: Final moment [tonfm], RM initial tension, changed self weight, same construction sequence... 203
Figure 5-28: Vertical displacement dz due to changed initial cable forces [mm] ... 204
Figure 5-29: Moment envelope due to traffic load [tonfm] (no dead weight considered) ... 209
Figure 5-30: Load distribution for the maximum bending moment in the centre of the main span... 210
Figure 5-31: Maximum moment at the top of the pylon during the erection of cable 1 [tonfm]... 211
XI
Figure 5-33: Cable ... 216 Figure A-1: Cable element with the length ds... 249
List of Tables
XII
List of Tables
Table 2-1: The 18 longest cable-stayed bridges ... 12
Table 3-1: Input data ... 39
Table 3-2 Flowchart for backward analysis ... 41
Table 3-3: Cable forces [tomf] ... 43
Table 3-4: Input data verification example creep & shrinkage ... 59
Table 3-5: Creep and shrinkage data verification example ... 60
Table 3-6: Result table static verification example for creep ... 61
Table 3-7: Structural classification and calculation procedure ... 62
Table 3-8: Verification table non-linear analysis ... 70
Table 3-9: Compared permanent loads for different bridge types, the bridges are about 20 metre wide ... 77
Table 4-1: Modified input data... 92
Table 4-2: Ideal cable forces for different elastic link types ... 94
Table 4-3: Construction stage analysis data of the backward calculation ... 104
Table 4-4: Calculation of detension force [tonf] ... 105
Table 4-5: Initial cable forces obtained from backward analysis (Case I model) [tonf] ... 106
Table 4-6: New construction stage data for backward analysis ... 110
Table 4-7: Cable forces obtained from backward analysis (Case II model), changed construction sequence [tonf] ... 110
Table 4-8: Horizontal displacement after installing the first cable (Case II b model) [mm]... 114
Table 4-9: Horizontal displacement after applying the additional load (Case II b model) [mm] ... 114
Table 4-10: Input data CEB-FIP code ... 116
Table 4-11: Construction time schedule... 117
Table 4-12: Real displacement table [mm] ... 123
XIII
Table 4-14: Calculation table of the current displacement (Case I model)... 126
Table 4-15: Calculation table for real and net displacement (Case I model) ... 126
Table 4-16: Calculation table for construction camber (Case I model) ... 127
Table 4-17: Construction camber table (Case I model) ... 127
Table 4-18: Fabrication camber table (Case I model)... 128
Table 4-19: Cable forces due to changed pre-stressing in cable 4 ... 131
Table 4-20: Cable forces due to elevation adjustment ... 138
Table 4-21: Required rotational stiffness obtained from MiDAS ... 140
Table 4-22: Fabrication camber data [mm]... 141
Table 4-23: Property table for harp system... 142
Table 4-24: Initial pretension according to the sag to span ratio [kN]... 145
Table 4-25: Tension forces in cable 3 & 4 due to adapted stiffness ... 149
Table 5-1: Main Geometric Data Second Jindo Bridge ... 152
Table 5-2: Material property table ... 159
Table 5-3: Cross section table ... 160
Table 5-4: Boundary table... 161
Table 5-5: Segment load table... 163
Table 5-6: Calculated distributed load ... 163
Table 5-7: Unknown Load Factor restrictions ... 166
Table 5-8: Theoretical ideal cable forces ... 167
Table 5-9: Allowable tension forces in [tonf] ... 167
Table 5-10: Additional Unknown Load Factor restrictions ... 168
Table 5-11: Summary table of ideal cable forces... 169
Table 5-12: Unknown Load Factor restrictions including limited moments in the main girder ... 171
Table 5-13: Summary table of ideal cable forces including moment restriction ... 173
Table 5-14: Sequence of cable erection ... 180
List of Tables
XIV
Table 5-16: Difference in cable tensions between forward - and backward analysis ... 183
Table 5-17: Changed initial cable forces considering the tension due to the self-weight of the cables ... 185
Table 5-18: Results of forward - and backward analysis ... 188
Table 5-19: Initial cable forces from backward analysis [tonf]... 189
Table 5-20: Difference in cable tension forward - and backward analysis considering an effective stiffness [tonf]... 191
Table 5-21: Comparison of cable forces obtained from different calculations ... 195
Table 5-22: Final cable forces truss and cable elements (forward analysis) ... 196
Table 5-23: Vertical displacement at the tip of the cantilever [mm]... 197
Table 5-24: Cable forces back- and forward analysis using truss elements and Case B values given in Table 5-15 ... 199
Table 5-25: Comparison of cable forces using truss and cable elements in forward analysis for Case B values given in Table 5-15 ... 200
Table 5-26: Comparison of cable forces obtained from different calculations ... 202
Table 5-27: Control maximum cable forces during construction... 206
Table 5-28: Calculation of angle and cable force due to concentrated load... 207
Table 5-29: Control maximum cable due to live load ... 207
Table 5-30: Allowable stresses for SM400-steel... 208
Table 5-31: Load cases to consider the maximum load cases for traffic load... 210
Table 5-32: Camber data [mm] ... 212
Table 5-33: Control calculation for construction camber data ... 213
Table 5-34: Real horizontal displacement final state [mm] ... 213
Table 5-35: Longitudinal deformation of each segment [mm]... 213
Table 5-36: Construction camber data ... 214
Table A-1: Node coordinates ... 240
Table A-2: Element table ... 241
Table A-3: Elastic link table... 242
Table A-4: Control of allowable stresses of the girder segments during construction... 244
XV
Table A-6: Control of allowable stresses of the pylon due to construction loads... 247 Table A-7: Control of allowable stresses of the pylon under live load condition... 248
List of Symbols
XVI
List of Symbols and Units
Scala, Vectors and Matrices c chord length of a cable E modulus of elasticity Er allowable error range F general force
l horizontal projected length of a cable L cable length M bending moment N normal force S cable force q distributed load t time u displacement
w weight per unit length ε strain
σ stress
α error factor or angle
A adjustment vector E adjustment error vector I ideal state vector S cable force vector
Z superposed error mode vector
M vector of shim thickness at each cable
δ deflection or displacement vector Rf field measurements of member
forces and displacements
B relation between strain and nodal displacement
D influence matrix of
displacement or elastic matrix representing the relationship between the stress and strain F error influence matrix
K stiffness matrix ρ weighting matrix
R sum of internal and external generalized forces
T influence matrix for tension forces in the cables
XVII Indices A target value c concrete C cable Co construction cr creep eff effective el elastic er error fac factor fi final state G girder L large displacement Mi MiDAS result N net P permanent load Py pylon R real sag sag sec secant sh shrinkage T temperature tan tangential (or T) tot total
0 initial condition
Mathematic operations d( ) simple differentiation d( )/dt differentiation after time
∂( ) partial differentiation
T transformation of a matrix or vector
Units N/mm² kN/mm² kN/m² MN/m² tonf/mm² tonf/m² 1 N/mm² 1 10-3 103 1 1.02*10-4 1.02*102 kN/mm² 103 1 106 103 1.02*10-1 1.02*105 kN/m² 10-3 10-6 1 10-3 1.02*10-7 1.02*10-1 MN/m² 1 10-3 103 1 1.02*10-4 1.02*102 tonf/mm² 9.807*103 9.807 9.807*106 9.907*103 1 10-6 tonf/m² 9.807*10-3 9.807*10-6 9.807 9.807*10-3 10-6 1
1
General task
This first chapter gives the necessary information on the topics of the study to enable the reader to place these into the right context. On the other hand, the main subjects relating to the investigations performed in this study are describes. An overview of the general considerations in the analyses of construction stages will be given in this part as well. A brief summary of each chapter of this thesis is then provided as a reference for the reader.
1.1
Introduction
The construction of bridge superstructures is a highly complex process due to the interrelationships between the applied erection methods and the manifold internal and external effects concerning loads and material behaviour, and also to the environmental influences. When planning to build a bridge, engineers are required to come up with the most feasible way of erecting the structure in a safe and economic manner. Finding the optimum solution is based on comparing alternative techniques of erecting the bridge, along with the consideration of the different means and methods that can be employed and the implications on schedule and budget. An analysis of these methods always has to consider the bridge itself, as well as the characteristics of the site at which it is to be erected.
This study deals with the constructability and the modelling of the construction stages of cable-stayed brides erected with the cantilevering method.
Cable-stayed bridges are structural systems which are effectively composed of cables, the main girder and towers. This bridge form has a fine-looking appearance and fits in with most surrounding environments. The structural systems can be varied by changing the tower shapes and the cable arrangements. Up to a span length of 1000 metres, the cable stayed system is considered as an economical solution.
In addition to the static analysis of dead and live load, the dynamic analysis and that of wind loads, a detailed investigation of the construction sequence is essential. The interrelationship
Chapter 1: General task 2
between the growing, yet unfinished structure, and the various kinds of loads that affect the construction is a major issue in the actual field operation.
The main objective of this study is to compile and review related topics that are of concern in the analysis and the modelling of the construction process. The focus of interest is on the Cantilever Construction Method and the accompanying issues. This thesis is supposed to serve as an understandable introduction to the broad topic of how to analyse, plan and deal with the complex construction process.
While the Cantilevering Construction is with certainty the main erection method preferred in the construction of cable-stayed bridges, other methods exist as well and may be in some cases, depending on the characteristics of the actual bridge project, even more feasible. However, this study only mentions certain constructability aspects of other erection methods in brief.
Two major sources of information are used in the first part of this thesis. Literature on the history of bridge construction is utilised to outline the development and the different types of construction methods. Following sections on the construction stage analysis and the related concerns are based on professional literature on the state-of-the-art of cable-stayed bridge engineering.
In the second part of this thesis, the concept and the problems relating to a construction stage analysis are illustrated by simple structural systems. Besides the complex erection process, the difficulties which occur when modelling these step-by-step conditions are also explained. The case study of the Second Jindo Bridge, that is located at the south coast of South Korea, is provided as a real-life construction example in order to complement the theoretical part of this study. This concrete example helps to gain a better understanding of the construction stage analysis of cable-stayed bridges.
The computer programme MiDAS is used to model and analyse the examples. In order to give other users a guideline on the application, the programme and its features are described.
1.2
Overview
Due to the high degree of indeterminacy of cable-stayed structures, an extensive degree of understanding for both design and construction is required. In comparison to other types of conventional bridges, cable-stayed bridges demand sophisticated structural analyses and design techniques.
With an optimized adjustment of the cable forces, it is possible to achieve an “ideal state”, at which the girder and the pylon are compressed with little bending only. The “ideal state” of a cable-stayed bridge is associated with the minimized total bending energy accumulated along the girder. This results in a possible design of slender decks. The materials for the deck and the pylons can be efficiently utilized. Moreover, in case of concrete decks, it has dominant influence on the creeping behaviour.
At the time of construction, the deck segments are connected with cables so that each cable (or a pair of cables in the case of two cable planes) approximately takes the weight of one segment, with the length corresponding with the longitudinal distance between two cables. In the final state, the effect of other dead loads, such as pavement, curbs, fence, etc., as well as the traffic loads must be taken into account.
There are different methods of determining the cable forces. Two simple ones can be assumed:
• a simple supported beam
• a continuous supported beam
Furthermore, simple formulas which consider the self-weight of the cable and the stiffness of the girder and the pylon are developed. Analytic programmes often use an optimisation method. In this method, to minimize the material used in the girder and the pylon, bending moments and the deflection of the deck and the pylon are limited to prescribed tolerances with the purpose of determining the required tension forces in the stay cables.
For the determination of the cable prestress forces that are induced at the time of the cable installation, the initial equilibrium state for dead load at the final stage must be determined first. Then, using backward and forward analyses, the construction stage analysis can be performed according to the construction sequence.
Chapter 1: General task 4
During the construction of cable-stayed bridges, there are mainly two kinds of errors that frequently occur:
• Tension force error in the cables
• Geometric error in controlling the elevation of the deck
Discrepancies of parameter values between design and reality, such as the modules of elasticity, the mass density of the concrete or the weight of the girder segments, are unavoidable, but possible irregularities may influence the structural performance. Accumulations of these errors must be avoided to ensure a safe design. Therefore, during the construction period, the structure must be continuously monitored so that the most suitable adjustment can be obtained whenever corrections become necessary.
In general, there are two possible adjustment procedures:
• Adjustment of the cable forces
• Adjustment of the girder elevation
The first case may change both, the internal forces and the configuration of the structure. The latter adjustment only changes the length of the cable and does not induce any change in the internal forces of the structure.
In the service stage of concrete bridges, the cable force may need to be adjusted to recover an optimal structural state because of concrete creep effects.
This short introduction demonstrated the complexity of the erection of cable-stayed bridges. In the following chapters, the mentioned topics will be described and discussed in detail.
1.3
Thesis organisation
Chapter 1 of this thesis contains introductory information. It provides the reader with an overview of construction stage analyses and a brief description of each chapter.
Chapter2 covers the historical background of cable-stayed bridge constructions, outlining the developments of this type of bridge in the last decades and gives the salient examples for each era. Different erection procedures are also outlined.
Chapter 3 deals with the general description of construction stage analyses using the cantilevering method for the erection of cable-stayed bridges. By analysing a simple structural system, the procedure using the analysis programme MiDAS is illustrated. The general purpose of using influence matrices is presented. The special functions offered by MiDAS are described and the matrix is evaluated for the given example. Specific considerations and uncertainties, which should be taken into account in the construction process, are clarified to contribute to the reader’s overall understanding. The modelling approaches to cable-stays and the philosophy of tuning sequences during the erection and in the final state of the bridge are also described. Finally, the construction control and the monitoring systems are mentioned.
Chapter 4 concerns itself with the construction stage analysis of a more complex example including temporary supports. The important issues and the considerations necessary for a reliable construction stage analysis are presented in more detail. The optimisation method is used to determine the cable forces to achieve an ideal state. Using back- and forward analyses, the initial cable forces are evaluated for the time of erecting the stay-cables. As creep and shrinkage are important factors to be included in the analysis, the method of considering these effects is illustrated. To ensure a successful erection process, the camber control is a main issue in the construction stage analysis. Moreover, the camber calculation is demonstrated in this chapter and the functions offered by MiDAS are introduced and controlled. Various construction errors are assumed to be incorporated in the already built structure. The errors are modelled and possible solutions are given to adjust the discrepancies. Finally, the influence of non-linearity due to cable elements is investigated. The accuracy of the cable elements is then proved.
Chapter 5 encompasses the case study, the Second Jindo Bridge in the south of the Republic of Korea. Different erection methods are discussed. The generation of the model for the construction stage analysis is illustrated in detail, including the change of boundary conditions and variations in loading. The ideal cable forces are established and a construction stage analysis is performed. In order to rate the modelled system and the obtained initial cable forces, the results are compared with other calculations. The minimum and maximum stresses are proved to be in the allowable limits.
Chapter 6 recapitulates the contributions made in this thesis and calls attention to further related areas of research that may be worth exploring.
Chapter 2: Cable-Stayed Bridges 6
2
Cable-Stayed Bridges
In this chapter, a general overview of cable-stayed bridges and their different erection options are given. The development in the field of cable-stayed bridges is shown by means of a historical outline first. Then, after introducing the importance of static arrangements, the erection methods are explained with the focus on the cantilevering method.
2.1
History of cable-stayed bridges
The principle of supporting a bridge deck with inclined tension members leading to the towers on either side of the span has been known for centuries. Already in 1823, the French engineer Navier published the results of a study on bridges with the deck stiffened by wrought iron chains taking both, a fan shaped and a harp shaped system, into consideration. However, due to the imperfections during the fabrication and the erection in early stayed bridges, it was very difficult to arrive at an even distribution of the loads between all stays. Furthermore, without the reliable tensile strength of steel wires, cable-stayed bridges did not become an interesting option, whereas systems in which the suspension system was combined with the stayed system, was used in major bridges in the second half of the 19th century. The Albert Bridge from 1873 across the Thames in London or the Brooklyn Bridge designed by Roebling are examples of this period.
Figure 2-1: The Albert Bridge across the Thames in London [70]
The first modern cables-stayed bridge was the Strömsund Bridge in Sweden, designed by Dischinger. The bridge is of a three span range and has a main span of 182.6 m with two side
spans of 74.7 m. The stays are arranged according to a pure fan system with two pairs of stays radiating from each pylon top. The steel pylons are of the portal type, supporting the two vertical cable systems arranged on either side of the bridge deck.
Figure 2-2: The Strömsund Bridge [8]
In the following years, numerous innovative cable-stayed bridges were constructed in Germany. The Theodor Heuss Bridge across the Rhine was opened to traffic in 1957. With a main span of 260 m, the bridge introduced the harp-shaped cable system with parallel stays and a free-standing pylon. The Severins Bridge, erected in 1959, was the first application of an A-Shaped pylon combined with transversally inclined cable planes. It was also the first to be constructed as an asymmetrical two span bridge with a single pylon positioned at one side of the river banks. The first cable-stayed bridge with a central cable plane, with the pylon and the stay cables positioned in the centre of the motorway, was the Norderelbe Bridge in Hamburg. In the following years, this system became the preferred solution for the majority of cable-stayed bridges constructed in Germany, e.g. the Leverkusen Bridge and the Maxau Bridge across the Rhine. These bridges have the same centrally arranged cable plane but the cable system is of a harp configuration.
The development of cable-stayed bridges also required improvements in the techniques of structural analysis, allowing the calculation of cable forces throughout the erection period. The efficient use of all cables in the final state, as well as a favourable distribution of dead load moments had to be ensured.
The first cable-stayed bridges only had a limited number of cables, which were generally composed of several prefabricated strands. The first multi-cable bridges were designed by Homberg. The Friedrich Ebert Bridge contains a central cable plane with two pylons, each supporting 2x20 stays.
Chapter 2: Cable-Stayed Bridges 8
In multi-cable systems, the girder is supported more continuously. The cable forces, that are to be transmitted at each anchor point, are reduced so that a local strengthening of the girder is not necessary. It also has important advantages during the erection. Shorter deck cantilevers are required to reach from one anchor point to the next. This leads to simpler construction processes and, as it should be realized later, to slender decks.
In 1972, the first parallel-wire strands were used in the Mannheim-Ludwigshafen Bridge across the Rhine. Additionally, the bridge introduced a new design concept. In the main span, the deck girder is entirely made out of steel, while the side span is made out of concrete. With a maximum free side span of 65 m and a main span of 287 m, the higher dead load of the side span reduces the requirements for a vertical anchoring of the girder.
The Köhlbrand Bridge (1974) in the port of Hamburg was the first application of the multi-cable system with double cable planes supported by A-shaped pylons. With a modified fan-system during the construction, no temporary supports or temporary stays were required.
Figure 2-3: The Köhlbrand Bridge [68]
The first twenty years in the evolution of cable-stayed bridges took place, to a large extent, in Germany. Under the large influence of German developments, cable-stayed bridges become more popular in other countries, too. In the UK, the Wye Bridge was completed in 1965. This bridge is quite unique by having only one set of stays leading from the pylons to the deck. Based on a similar design, the Erskine Bridge in Scotland was constructed in 1971 with a main span of 305 m. Because this bridge also has only one stay leading from each of the two pylons to the deck despite its length, the girder has to span more than 100 m without a support from the cable system. During the erection, it was necessary to use temporary stays to reduce the moment in the deck girder when cantilevering in the main span. In France, the Saint Nazaire Bridge (1975) across the Loire River was the first cable-stayed bridge to span more than 400 m.
The beginning of modern cable-stayed bridges was to a large extent dominated by steel bridges with orthotropic decks together with plate or box girders and cellular pylons. In the Maracaibo Bridge (1962) in Venezuela, which was designed by Morandi, the pylon and the deck girder are made of concrete. However, because of the unusual design and abnormal proportions, this stays an exception and hardly a typical example of the bridge type described above. Nevertheless, it was the first multi-span cable-stayed bridge.
Figure 2-4: The Maracaibo Bridge [70]
Another early example for the use of multi-cable systems in a concrete cable-stayed bridge is the Pasco-Kennewick Bridge. The deck is supported by a double cable system in the fan configuration. The stays, which are made of a single parallel-wire strand, are inside a grouted polyethylene tube. The deck girder was erected by the segmental method using heavy prefabricated elements.
After ship collisions with pylons, original bridges were replaced by cable-stayed bridges to increase the open width. This was a further proof of the superiority of cables-stayed systems. To replace the original arch bridge, the Tjörn Bridge was built with a span of 366 m, 86 m longer than the original one, which allowed both pylons to be located on land. The Tjörn Bridge belongs to the group of cable-stayed bridges with different structural materials in the side and the main spans. The side spans are designed as continuous concrete girders with intermediate supports at each cable anchor point, whereas the main span is made of a steel box with an orthotropic steel deck.
Also after a ship collision accident, the new Sunshine Skyway Bridge, a single bridge having a 360 m long cable-stayed main span, was decided to replace the existing two parallel bridges. At its completion in 1986, the Sunshine Skyway Bridge was the longest cable-stayed bridge in the USA. Prior to its construction, two designs were considered, one based on a composite deck and two cable planes, and the other on a concrete box girder and a single central cable plane. In this
Chapter 2: Cable-Stayed Bridges 10
case, the second option was chosen. However, the alternative of the composite girder was subsequently applied in the Alex Fraser Bridge at Vancouver, which became the longest cable-stayed bridge in the time between 1986 and 1991.
Figure 2-5: The Alex Fraser Bridge during its construction [67]
The advantages of composite girders were used during the construction of the Alex Fraser Bridge. The cantilevering from one cable anchor point to the next was easily achieved by the relatively light steel girder. The stay cables had been added before the heavy concrete deck was erected by precast slabs. The concrete slab could be efficiently utilized to transfer the axial compression through the deck, which is induced into the girder by the horizontal components of the stay cable forces. In the following years, after the completion of the Alex Fraser Bridge, the system of composite girders was generally preferred for the majority of cable-stayed bridges in North America.
Major developments of cable-stayed bridges can also be found in the Far East. In 1977, the first double deck cable-stayed bridge – the Rokko Bridge- was completed in Japan. In a much larger scale, the double deck concept was later used for the twin cable-stayed bridges, the Hitsuishijima and Iwagurojima Bridge. Each of the two neighbouring bridges has a span of 185 m – 420 m – 185 m. The traffic runs on a two level truss with a four-lane expressway on the upper deck and a double track railway on the lower deck. The cable systems are of the modified fan configuration with two vertical cable planes positioned directly above the deck trusses. As extensively used in Japan, parallel-wire strands are applied for the stays.
Figure 2-6: The Hitsuishijima Bridge [69]
At present, the Tatara Bridge (1999, Japan) is the world’s longest cable-stayed bridge, measuring 1480 m in total length. With an 890 m centre span, it is 34 m longer than the one in the Normandy Bridge in France. The main tower of this bridge is 220 m high and designed in an inverted Y shape. It has a cross section with corners cut for a higher wind resistance stability. The bridge is very flexible due to not only its length but also to the low girder-depth. The girder-depth to span-length ratio is about 1/300. One side span is 270 m, while the other side span is 320 m. To prevent this large difference in the lengths of the centre and the side spans from causing dead load unbalance problems, PC girders are installed at each end of both side span sections. These function as counterweight girders to resist negative reactions. Steel girders are used in the remaining part of the side span and in the main span. The girder is designed as a slender box girder and contains three cells, each 2.7 m high. The box girders are attached to fairings in order to ensure wind stability. The cables are installed in two-plane multi-fan systems with a maximum cable length of about 460 m. The cables of the bridge have dimpled surfaces, similar to that of a golf ball, to resist vibration caused by both wind and rain.
However, the evolution of cable-stayed bridges continues and in the near future, they will exceed the magical 1000 m length. At 1596 m in length, the Stonecutters Bridge is a part of Hong Kong's plan to develop its infrastructure. The main span will be 1018 m and the side span 2x289 m. The pylons are designed with a height of 289 m. The Sutong Bridge over the Yangtze River will span 1,088 metres making it 70 metres longer than the Stonecutter Bridge. The full length of this bridge is 7600 meters. The height of the central span of 62 meters will enable fourth and fifth generation container ships to pass through in virtually any weather. The bridge is designed on six-lane expressway standards with a maximum vehicle speed of 100 km. The construction has already commenced and is expected to be continued until 2008.
Chapter 2: Cable-Stayed Bridges 12
Figure 2-7: The Sutong Yangtze River Bridge [66]
Table 2-1 shows the 18 longest cable-stayed spans. It is remarkable that twelve of the longest cable-stayed bridges already built are located in the Far East.
No. Name Span
[m]
Girder material
main span Traffic Country Year
1 Sutong Bridge 1088 Steel Road China ca. 2008
2 Stonecutters Bridge 1018 Steel Road China ca. 2008
3 Tatara Bridge 890 Steel Road Japan 1999
4 Normandie Bridge 856 Steel/Conc Road France 1995
5 Nanjing Bridge 628 Steel Road China 2001
6 Wuhan Baishazhou 618 Steel Road China 2000
7 Qingzhou Minjiang Br. 605 Composite Road China 1998
8 Yangpu Bridge 602 Composite Road China 1993
9 Meiko Chuo Bridge 590 Steel Road Japan 1997
10 Xupu Bridge 590 Composite Road China 1996
11 Rion-Antirion Bridge 560 Composite Road Greece 2004
12 Skarnsund Bridge 530 Concrete Road Norway 1991
13 Queshi Bridge 518 Composite Road China 1999
14 Tsurumi Tsubasa Bridge 510 Steel Road Japan 1994
15 Jingzhou Bridge 500 - Road China 2002
16 Øresund Bridge 490 Steel Road & rail Denmark/Sweden 2000
17 Ikuchi Bridge 490 Steel Road Japan 1991
18 Higashi-Kobe 485 - Road Japan 1992
Table 2-1: The 18 longest cable-stayed bridges
In the last twenty years, cable-stayed bridges have developed to become dominating in bridge constructions with the span range from 200 m to 500 m. Under specific conditions, the cable-stayed bridges may even be a competition to suspension bridges up to spans more than 1000 m. Table 2-1 also shows that the girder in the main span is dominantly fabricated by steel and, up to a span of 600 m, also by composite sections.
2.2
Stay-cables
The cable-stay is a basic element in all cable-stayed bridges and therefore a short introduction to the different existing cable types will be given. More details on the cable-stay technology with an emphasis on the corrosion protection are given by Ito [31]. Gimsing also describes the basic types and mechanical properties of structural cables in his text book [8], and the recommendations made by Setra [13] provide a fine guideline to all topics relating to cable-stays, too.
The cables require excellent mechanical properties, such as a high tensile strength, a high elastic modulus, a sectional compactness and also ease of handling during the installation. Furthermore, it is important that the cables have a high corrosion resistance and a satisfactory fatigue strength. The first cable-stayed bridges in Germany employed locked-coil cables. The locked coil rope (LCR) is composed of two types of twisted wires, normally of round wires in the core layers and of T- and Z-shaped wires in the outer layers. The LCR has a smooth surface and compact cross sections. Compared to other cable types, these are stiffer to handle. These cables are hardly used nowadays, mainly due to the rather complicated anchorage details and the difficulty of their replacement.
From 1970 to 1985, most cable-stayed bridges applied parallel-wire cables. Some bridges were also built with parallel bars. Then, the Brotonne Bridge in France and later the Sunshine Skyway Bridge in the United States, were the first to use cable-stays made of 7-wire pre-stressing strands.
Bar stay cables consist of round steel bars with a diameter of 26-36 mm and are covered by a steel pipe. To provide protection against corrosion, the inside is filled with cement grout. Since the lengths of the bars cannot be too long, coupling is normally necessary. However, this type of stay member has been scarcely used, particularly not for long cable-stayed bridges.
Parallel wire stay cables (PWS) are composed of a bundle of pre-stressing wires with a diameter of 6-7 mm in a polyethylene or stainless steel pipe filled with cement grout as a corrosion protection. The parallel wires are kept in place by twisting a steel rope around the bundle. A bundle of wires forms a hexagonal cross section, and in some cases, numerous PWSs are formed into one large round cable on site. These parallel wire cables were widely used on both prestressed concrete (PC) and steel cable-stayed bridges. Later on, it became more common to utilize galvanized wires and wax as fillings in the pipes, as this is a non-cracking and ductile
Chapter 2: Cable-Stayed Bridges 14
material. The shop-prefabricated parallel wire strands could be extensively found in Japanese bridges. In the 1980s, these cables were improved to the New PWS system.
In the New PWS cable, the wire bundle is slightly twisted up to 3-4° so that the wire bundle is enabled to reel easily and the strands made self-compacting under axial tension without spoiling the mechanical properties. It is also characteristic of the New PWS cables to have the protecting polyethylene cover extruded directly onto the wire bundle so that no void volume exists between the wires and the surrounding pipe (Figure 2-8). Through the elimination of the spiral rope and the voids for cement grouting, the New PWS cables become more compact than traditional PWS cables.
Figure 2-8: New PWS cable [13]
New PWS cables are fabricated in sizes ranging from 7 No. 7 mm to 421 No. 7 mm wires. The longest stay cable of this type is 460 m long with the outer diameter of 165 mm and is used on the Tatara Bridge.
In the 1980s, the technology of the parallel-strand cables (PSC) evolved towards higher protection of cables and improved fatigue performance of the anchorages by using wedges. However, a method was developed in the 1990s to protect the parallel strands individually by an extruded high density polyethylene sheath.
Parallel-strand and parallel wire cables are similarly composed, with the sole exception of the individual 7 mm wires substituted by seven-wire strands. A parallel-strand cable can be fabricated as a complete unit, such as the parallel-wire cables. Yet, it has become more common to insert and stress the seven-wire strands one by one; a procedure called Isotension Method. Each strand is tensioned with a mono-strand jack and the application of appropriate devices finally ensures that all installed strands have the same tension. This reduces the size of the stressing equipment but increases somewhat the amount of work to be carried out on site.
2.3
Erection of cable-stayed bridges
In order to compare cable-stayed bridges with other bridge types, these must be categorised into medium and long span bridges. For the medium span length, cable-stayed bridges have to compete with conventional structures and they were often built only for aesthetic reasons when technical conditions as the span length did not require them. A serious analysis of construction methods has improved their economical efficiency. In the medium-span range cable-stayed bridges can be built on temporary supports or constructed by rotation. There is also a possible to install the deck by the incremental launching method.
However, cable-stayed bridges have experienced great success during the last twenty years in the field of long span bridges. The cantilever method is an economical and practical solution for the construction of long cable-stayed bridges. In this method each new segment is built or installed and subsequently supported by a new cable (or a pair of cables) which balances its weight.
In addition to the construction of the pylon, the different construction methods for the main structural parts, i.e. the cables and the girder, are mentioned in the following chapters to give a complete overview of the different possible construction procedures. The main focus of this thesis is the cantilever method which is therefore dealt with especial attention.
2.3.1
Static arrangement of cable-stayed bridges
For cable-stayed bridges the choice of the structural system is an important factor in the design process. The common systems in cables-stayed bridges are the fan and the harp systems. The fan system is mostly applied in the form of a modified fan system in which the cable anchorage points are spread over a certain height at the pylon top. While studying the rigidity offered by the cable system itself and by assuming that the girder and the pylon only provide axial resistance, Gimsing defines the fan-shaped system a system which is stable of the first order [8]. This means that an equilibrium can be achieved without assuming any displacement. All stay cables must be fixed to the pylon top so that the horizontal components of the forces in any of the cables can be transferred to the anchor cable. Thus, the stability of the fan-shaped system depends to a large extent on the anchor cable. It is also required for this cable to be in tension for any loading case.
Chapter 2: Cable-Stayed Bridges 16
In a harp-shaped cable system an equilibrium condition cannot be achieved by the cable system itself. But this does not imply that the total structural system of the bridge is unstable. The bending stiffness of the stiffening girder and the pylons add the stability that lacks in the cable system. A complete stabilization of the harp system can be obtained when intermediate supports are placed in the side spans under the cable anchor points. This can be seen in several large bridges with a harp-shaped system, such as the Oberkasseler Bridge in Düsseldorf. Even small changes in the supporting condition or the addition of a few structural elements often change the structure to a significant extent. Although the cable system forms only one part in the total structural system of the bridge, it highly influences the overall stiffness.
In bridges with one main span several different solutions exist for arranging a fan-shaped cable system, e.g. a single pylon with only one fan system in the main span and a single anchor cable in the side span, or two pylons with fan system on both sides. The adopted solution often depends on the local conditions at the bridge site. In early cable-stayed bridges only few concentrated stay cables were used, as it is the case in the Strömsund Bridge (Figure 2-2). In bridges with few stay cables the fans could often be arranged symmetrically about the pylon as the large bending stiffness of the girder prevented a too large unloading of the anchor cables under traffic load in the side span (a traffic load only in the side span decreases the tension in the anchor cable). In modern cable-stayed bridges with a multi-cable system and a slender stiffening girder, a symmetrical fan is not possible with the top cable in the side span forming the anchor cable. The required minimum tension in the anchor cable cannot be achieved for all loading cases. Consequently, skew fans, - in which the side span is shorter than the main span - , are generally in use. In such a system the anchor cables must have a considerably lager cross-section than the normal cables do.
As mentioned before, in modern cable-stayed bridges with more cables, there is no need for cross sections with large inertia. Walther [14] demonstrates in his work that the longitudinal bending moments increase with the larger bending stiffness without reducing the stresses in the pylon or in the stay cables. In these cases the stiffness of the deck has only a minor contribution to the overall structural stiffness. Thus, there is no need for a high bending stiffness of the girder.
a) Fan system with shorter side span than main span
b) Modified fan system with an anchorage cable composed of several stay cables
The side-to-main span ratio has a very strong influence on the stress ratio of the anchor cable and the deformation of the system. Gimsing [8] shows the effects of different ratios in a parametric study and suggests short side spans to increase the structural stiffness using ratio values from 0.25 to 0.5. The anchor cable is often composed of a number of individual strands, as in the Köhlbrand Bridge where the anchor cable is formed by three individual cables. In this case the chosen side-to-main span ratio is 0.3.
A solution to the application of a symmetrical fan structure in a multi cable-system is the displacement of the end pier from the side span towards the pylon. By this arrangement, it is possible to reduce the side span length to less than half of the main span length. In this case, the side span cables near the support are activated to form the anchor cable. It should be noticed that this can induce a local bending in the stiffening girder near the intermediate pier, which does not appear in systems with a concentrated anchor cable connected to the girder above the end pier. As for the fan system, the first cable-stayed bridges built with a harp system only had few symmetrically arranged stays and a very stiffening girder. Here, the pylon was usually slender. As mentioned before, with intermediate supports in the side span, the global stability of the structural system can be achieved without a bending stiffness of the girder or the pylon. Thus, the girder and the pylon can be designed to be more slender. But in case of few concentrated stays, the local bending in the stiffening girder must be considered.
In modern multi-cable harp bridges the local bending of the girder can be reduced and a very slender girder can therefore be applied if the global stiffness is achieved without the bending stiffness of the girder. A heavy pylon with a considerable stiffness may be advantageous in this case. The harp system may be chosen for aesthetic reasons, but in general, they are less economical.
Figure 2-10: Multi-cable harp systems with intermediate supports in the side span
In contrast to harp systems with all cable stays parallel, the inner stay cables in a modified harp system do not have the same angle at the girder and the pylon. In the Rhine Bridge at Flehe, a bridge with intermediate supports in the side span, the stay cables are arranged in a true harp shape with parallel cables in the sides, whereas the main span cables form a modified harp.
Chapter 2: Cable-Stayed Bridges 18
The construction method is also considerably influenced by the longitudinal configuration of the bridge. To simplify matters, only the bridge type with one main cable-stayed span suspended from two pylons is considered in the following description of construction methods. Bridges with long side spans are divided into two types:
a) Typical three span bridges which can be extended on both sides by a series of non-cable-stayed access spans
b) Bridges where the main span is balanced by access spans on the intermediate supports. As mentioned previously, the existence of intermediate supports has a favourable influence on the structural behaviour, which can be summarized as below:
• The anchor cables are distributed over the side spans and not concentrated on the abutments
• The deformation and deflection of the pylons are reduced when the main span is loaded.
• The bending moment in the pylons is reduced when the main span is loaded
• Bending moments and deflections are small in case of loaded side spans
The existence of intermediate supports has a dominant influence on the chosen erection method. For example, intermediate piers allow the use of the incremental lunching method whenever this is reasonable. When the main span is built by the cantilever method and connected with the side span, the temporary stability of the cantilever increases during the construction.
2.3.2
Erection procedures
The erection method which is applied in the construction of a cable-stayed bridge clearly depends on the size of the structure, the structural system and the conditions found at the intended location. In general, there are four different construction methods possible:
• Construction on temporary supports
• Construction by rotation
• Construction by incremental launching
• Construction by the cantilever method
2.3.2.1
Construction on temporary supports
A straightforward solution is to erect the entire girder on temporary supports before adding the cables. In the four stages illustrated in Figure 2-11, the following main operations are performed:
Figure 2-11: Erection on temporary supports [8]
Stage 1: Erection of the stiffening girder on permanent and temporary supports. Any of the procedures used for the construction of girder bridges can be applied in this stage.
Stage 2: Erection of the pylons from the deck of the completed girder.
Stage 3: Installation of the stay cables. In this stage the cables only need to be tensioned moderately as the final tensioning takes place in the following stage.
Stage 4: After the installation of all cables the temporary supports can be removed. During this process, the load is transferred to the cable system. Since the girder deflects downwards, it is necessary to erect the girder in an elevated position to reach the desired final position.
This erection procedure offers the advantage that the girder can be erected continuously from one end to the other. The procedure leads to an efficient control of the geometry and the cable tension.
The disadvantage is related to the temporary supports that are applied. In many cases, the erection of temporary supports, - often over a large water depth in the main span - , is not economical so that the procedure itself is not feasible.