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OPTIMIZATION OF TRUSS TYPE STEEL
BRIDGES
This thesis was submitted to the Department of Civil Engineering of the University
of Moratuwa in partial fulfilment of the requirements for the Degree of
Master of Science
Submitted by
Karunarathna W.W.N.
Department of Civil Engineering
University of Moratuwa
Sri Lanka
"
January 2011
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iiversity of Moratuwa
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(Author)
DECLARA TION
I hereby, declare, that the work included in this thesis in part or whole,
has not been submitted for any other academic qualification at any
institution.
~
Karunarathna W.W.N.
Certified by
~.~
Dr. Baskaran. K.
Supervisor/ Senior Lecturer
Division of Building & Structural Engineering
Department of Civil Engineering
University ofMoratuwa
Sri Lanka
,-
[iiJ
ABSTRACT
This work aims towards analyzing truss type steel bridges by 3-D finite element modelling
using SAP2000. Details of different truss type steel bridges are discussed together with
gathered information on such bridges found in Sri Lanka. State of the art, regarding design
and assessment of truss type steel bridges were also reviewed. Scale-down model bridges
were tested in the Structural Laboratory (UOM) and the test results were used to validate the
SAP models and observe the overall behaviour. The actual failure loads and failure patterns
were observed and compared with SAP analysis results.
3-D [mite element modelling gives a clear image in modelling of truss type bridges, than 2-D
finite element counterparts due to the facilities available to check the lateral stability of the
bridges. This research contains some methods to improve the lateral stability of truss type
steel bridges too. Failure study and analysis were done for some failed bridges in Sri Lanka
using SAP 2000. Results predicted by SAP 2000 are compared with actual failure modes,
loads and deflections.
Span vs. tonnage graphs were obtained with optimum steel usage, for the selected truss type
steel bridges which include common truss types used in the country and some of other
efficient truss types. It contains span vs. tonnage graphs which were obtained for Modified
Warren, Parker, Inverted Arch, Pratt and Tied Arch bridges which are used for pedestrians
and light vehicles. The weights of the actual existing bridges are presented in the same graph
(if applicable) and the reasons for deviation from the graph are also discussed. Set of span vs.
tonnage curves were plotted for different truss types in same graph, for comparison purpose
which shows tonnage required for each selected truss type, for given range of spans. Finally,
some guidelines for local bridge designers, and some suitable truss types are recommended
by considering minimum steel usage.
[iiiJ
ACKNOWLEDGEMENT
First and foremost I would like to express my gratitude and deep appreciation to my
supervisor Dr. Baskaran. K, Senior Lecturer, Department of Civil Engineering, University of
Moratuwa for his invaluable assistance, advice and guidance throughout this project. This
association has been interesting and rewarding.
Assistance and suggestions provided by Dr. (Mrs.) M.T.P. Hettiarachchi, Senior Lecturer,
Department of Civil Engineering, University of Moratuwa and Prof S.M.A. Nanayakkara,
Professor, Department of Civil Engineering, University ofMoratuwa, were fully appreciated.
I convey my gratitude towards Mr. Rohith Swarna, Director of RDA Engineering Services
Division, Sri Lanka for providing important details on truss bridges in Sri Lanka and Mr.
H.D. Hidallana Gamage, Final year student, Department of Civil Engineering, University of
Moratuwa who has given great help during the entire research.
I also like to thank Prof M.T.R Jayasinghe, Head, Department of Civil Engineering,
University of Moratuwa, for making available all resources and facilities for this research
work. The Senate Research Committee of University ofMoratuwa should also be thanked for
supporting and financing my research.
I appreciate very much invaluable support, encouragement and understanding shown by my
mother, father and all of family members.
Finally, I would like to acknowledge with fraternal love, my colleagues and others who have
assisted me in various ways whose contribution have led to the successful completion of this
project.
Thank you
Karunarathna W.W.N
[iv]
CONTENTS
Declaration ii
Abstract iii
Acknowledgement iv
List of Figures x
List of Tables xviii
CHAPTERl
Introduction
1.1 Background 1
1.2 Objectives of the Study 3
1.3 Methodology 4
1.4 Outline of the Thesis 6
CHAPTER 2
State of the Art
2.1 Introduction 7
2.2 Classification of Truss Type Bridges 9
2.2.1 Warren Truss 9
2.2.2 Pratt Truss 13
[v)
2.2.3 Howe Truss 14
2.2.4 Parker Truss 14
2.2.5 Baltimore Truss 15
2.2.6 Pennsylvania Truss 16
2.2.7 Truss Type Arch Bridges 17
2.2.8 Lenticular Truss 18
2.2.9 K Truss Bridge 19
2.2.10 Vierendeel Truss Bridge 20
2.2.11 Other Truss Types 21
2.2.12 Sumarry 23
2.3 Previous Studies on Optimization of Truss Bridges 26
2.4 Failure Experiences 26
2.4.1 Global Truss Bridge Failures 28
2.4.2 State of the Art of Truss Bridges in Sri Lanka 29
2.4.2.1 Ehelakanda Bridge Failure 30
2.4.2.2 Failure of Para gas tot a Bridge 31
2.4.2.3 Past Investigations of Truss Bridges in Sri Lanka 32
CHAPTER 3
Laboratory Testing of Model Bridges
3.1 Scaled-Down Modelling 34
3.2 First Stage of the Laborotoy Testing ( First Four Tests ) 35
3.2.1 Scaled-down Parameters 35
3.2.2 Details of the Physical Models 36
[vi]
3.2.4.1 Analysis of the Model 1 39
3.2.3 Material Properties of the Aluminium used 37
3.2.4 Finite Element Analysis of Model Bridges 39
3.2.4.2 Prediction of Failure Load based on Sap Analysis 41
3.2.4.3 Sap Predicted Deflection at Failure Point 44
3.2.5 Experimental Testing of Model Bridges 44
3.2.5.1 Preparation of Model Bridges 44
3.2.5.2 Support Conditions 45
3.2.5.3 Preparation of Models for Vertical Loading 46
3.2.5.4 Monitoring the Deflection of the Bridges 48
3.2.5.5 Vertical Loading 48
3.2.5.6. Lateral Loading 49
3.2.5.7 With Portal and Without Portal Models 50
3.2.5.8 Geometric Nonlinear Behaviour 51
3.2.5.9 Failure Mode of the Physical Models 52
3.3 Modelling of a Variable Height Truss Bridge 54
3.3.1 Scale Used 54
3.3.2 Material Properties 54
3.3.3 Sections Used 55
3.3.4 Finite Element Modelling 56
3.3.5 Preparation ofthe Bridge Model., 58
"
3.3.6 Load Testing : 59
3.4 Laboratory Testing Results 61
[vii]
4.2.2.6 Design Check 85
CHAPTER 4
3-D Finite Element Analysis of Truss Bridges
4.1 Introduction 64
4.2 Failure Analysis of Truss Type Bridges in Sri Lanka 65
4.2.1 Ehelakanda Bridge Failure 65
4.2.1.1 Details of the Bridge 65
4.2.1.2 Material Properties 66
4.2.1.3. Member Sections 67
4.2.1.4 Finite Element Modelling of the Bridge 68
4.2.1.4. Finite Element Analysis Results 69
4.2.1.5. Design Check of the Structure 69
4.2.1.6 Analysis for Dead + Deck Slab Weight 72
4.2.1.7 Importance of Orientation of the Members 74
4.2.1.8 Modified Ehelakanda Bridge 74
4.2.2 Failure of Para gas tot a Bridge 75
4.2.2.1 Details of the Bridge 75
4.2.2.2 Material Properties 77
"
4.2.2.3 Loading : 78
4.2.2.4 Modelling of the Bridge by Sap2000 80
4.2.2.5 Analysis of the Bridge By Sap2000 83
4.2.2.8 Comparison of Analysis Result with Actual Failure 88
[viii]
4.3 Lateral Stability Analysis of Truss Type Steel Bridges 89
4.3.1 'With Portal' and 'Without Portal' Analysis 90
4.3.1.1 Truss Dimensions and Details 90
4.3.1.2 Loading 91
4.3.1.3 Finite Element Modelling 94
4.3.1.4 Maximum Lateral Deflections 96
4.3.2 Analysis for Suitable Lateral Bracing Systems 96
4.4 Span vs. Tonnage Curves for Truss Type Steel Bridges 99
4.4.1 Introduction 99
4.4.2 Material Properties 102
4.4.3 Loading 102
4.4.4 Development of Span vs. Tonnage Curves 106
CHAPTERS
Conclusions and Recommendations
5.1 Conclusions 110
5.2 Recommendations for Future Work 111
5.2 Guidelines for Local Bridge Designers 112
References 116
APPENDIXES
Annex A xx
Annex B xxxii
Annex C xxxviii
Annex D xlviii
fix]
LIST OF FIGURES
Figure 1.1 - Relocating a variable height truss bridge 1
Figure 1.2 - Old Ulapane Bridge 2
Figure 1.3 - Gampola Bridge 2
Figure 2.1 -Transformation of materials used in truss bridges 8
Figure 2.2 - Connections used in truss bridges 8
Figure 2.3 - Classification of truss bridges according to position of the carriage way 9
Figure 2.4 - Warren truss configuration 9
Figure 2.5 - Modified Warren truss 10
Figure 2.6 - Weralugastotupala Bridge 10
Figure 2.7 - Porupanawa Bridge 10
Figure 2.8 - Truss configuration of the Double Warren truss 11
Figure 2.9 - Truss configuration of a variable height Warren truss 11
Figure 2.10 - Kithulgala Bridge 12
Figure 2.11- Muwagama Bridge 12
Figure 2.12 - Mawanana Pedestrian bridge (A Modified variable height Warren bridge) 12
Figure 2.13 - Basic Pratt truss configuration 13
Figure 2.14 - Gampola Bridge 13
Figure 2.15 - Howe truss 14
Figure 2.16 - Parker truss configuration 14
Figure 2.17 - North Saginaw Road Bridge in US 15
Figure 2.18 - Baltimore truss configuration 15
Figure 2.19 - Blissfield Railroad Bridge in USA 16
Figure 2.20 - Pennsylvania truss 16
Figure 2.21 - Johnstown Incline bridge in US 17
Figure 2.22 - Truss type arch bridges ,.-l{r~
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Figure 2.23 - Naththupana bridge 18
Figure 2.24 - Hiniduma bridge '18
Figure 2.25 - 2-D view of Lenticular truss 18
Figure 2.26 - Ouaquaga bridge in USA 19
Figure 2.27 - K-Truss configuration 19
Figure 2.28 - Banning Railroad Bridge at USA 20
Figure 2.29 - 2-D configuration ofYierendeel Bridge 20
Figure 2.30 - Vierendeel truss bridge at Grammene, Belgium 21
Figure 2.31 - Other truss types 22
Figure 2.32 - Distribution of bridge collapse causes apart from the force majeure for bridges of all
kind of Materials 27
Figure 2.33 - Collapse of Quebec Bridge 29
Figure 2.34 -Ludendorff Bridge failure 29
Figure 2.35 - Second Narrows Bridge collapse 29
Figure 2.36 - Failure ofI-35W Bridge 29
Figure 2.37 - Buckled Ehelakanda Bridge 30
Figure 2.38 - Paragastota steel truss bridge 31
Figure 2.39 - Repairing the timber deck 31
Figure 2.40 - Cross section of the RCC deck 32
Figure 2.41 - View of the collapsed bridge 32
Figure 3.1 - Cross sectional details of the sections 36
Figure 3.2 - 3-D view of the Mod~ls 36
Figure 3.3 - Side view of the truss 36
Figure 3.4 - Plan view of the truss 36
Figure 3.5 - A tensile test specimen 38
Figure 3.6 - During tensile testing 38
Figure 3.7 - Stress strain relationship for Aluminum used in Test 2 38
[xi]
Figure 3.8 - 3-D finite element model of the bridge .40
Figure 3.9 - Model with moment releases onjoints 40
Figure 3.10 - Side view of the finite element model 41
Figure 3.11 - Plan view of the finite element model... .41
Figure 3.12 - 2-D view at top chord level 41
Figure 3.13 - 2-D view after application of unit nodal loads 42
Figure 3.14 - Demand over capacity ratio for unit nodal loads .42
Figure 3.15 - Final scale factors used in load cases for prediction of failure load .43
Figure 3.16 - Demand over capacity relevant to SAP predicted failure load .43
Figure 3.17 - A trial bolted joint 44
Figure 3.18 - View of the Modell 45
Figure 3.19 - Inside view of the Model 1 45
Figure 3.20 - pin supported end 46
Figure 3.21 - Roller supported end 46
Figure 3.22 - Cage 46
Figure 3.23 - A trial nodal load 46
Figure 3.24 - Loading sequence within a stage .47
Figure 3.25 - Overview of the loading satges .47
Figure 3 .26 -Measuring vertical deflection 48
Figure 3.27 - Measuring lateral deflection .48
Figure 3.28 - View after fixing the loading cages ."•........ .49
Figure 3.29 - View ofloading from one side .49
Figure 3.30- View ofloading from the other side .49
Figure 3.31 - Application of lateral loads 50
Figure 3.32 - View after load stage 7 with constant lateral loads 50
Figure 3.33 - View of the Model Bridge with portal 51
[xii]
Figure 3.34 - View of the Model Bridge without portal 51
Figure 3.35 -Geometric nonlinear behavior 51
Figure 3.36 - Another view of Geometric nonlinear behaviour 51
Figure 3.37 - After 1 ton of loading in Model 1 52
Figure 3.38 - Bubbles in the top chords 52
Figure 3.39 - View of the Model 1 after collapse 53
Figure 3.40 - Failure modes (Model I) 53
Figure 3.41 - Side view of the Model 1 after collapse 53
Figure 3.42 - Failure mode of Model 2 53
Figure 3.43 - Failure mode of Model 3 53
Figure 3.44 - Failure mode of Model 4 53
Figure 3.45 - Sections used for variable height model bridge 55
Figure 3.46 - 3-D finite element mode1... 56
Figure 3.47 - 2-D view of the finite element model.. 56
Figure 3.48 - Plan view of the truss 56
Figure 3.49 - Demand to capacity ratio for unit nodal load 57
Figure 3.50 - Demand to capacity ratio relevant to SAP predicted failure load 57
Figure 3.51 - Scale factors used in to obtain the SAP predicted failure load 58
Figure 3.52- Built main trusses 58
Figure 3.53 - Assembling the model bridge 58
Figure 3.54 - View while preparing lateral bracing ~~ 59
Figure 3.55 - Preparation of modelled bridge 59
Figure 3.56 - Preparing for testing 59
Figure 3.57 - During Testing 59
Figure 3.58 - View of the bridge before loading 60
Figure 3.59 - View of the bridge with buckled top chord 60
[xiii]
Figure 3.60 - Failed Bridge Model. 60
Figure 3.61 - Another view of Failed Bridge Model so
Figure 3.62 - Vertical Load vs. maximum vertical deflection curve for test I 62
Figure 3.63 - Vertical Load vs. maximum lateral deflection curves for test 3 and test 4 63
Figure 4.1- Truss configuration of Ehelakanda Bridge 65
Figure 4.2- Top & bottom chord members 67
Figure 4.3 -Bracings 67
Figure 4.4 - Vertical members 67
Figure 4.5 - 3-D finite element model of Ehelakanda Bridge 68
Figure 4.6 - 2-D view of the Ehelakanda bridge model.. 68
Figure 4.7 - Plan view of the truss 68
Figure 4.8 - Axial force diagram 69
Figure 4.9 - Moment 3-3 69
Figure 4.10 - Moment 2-2 69
Figure 4.11 -Design check of the Model.. 70
Figure 4.12 - Manual check of the slenderness ratio 70
Figure 4.13 - Design check details for member 133 71
Figure 4.14 - Application of slab deck weight.. 72
Figure 4.15 - Stress ratio diagram after applying slab deck weight 72
Figure 4.16 - Design details of member 133 with dead load and super imposed dead load 73
Figure 4.17 - Orientation used for initial design ,•......... 74
Figure 4.18 - Modified Bridge : 74
Figure 4.19 - Components of the truss 75
Figure 4.20 - Section of the top chord 76
Figure 4.21 - Section of the bottom chord 76
Figure 4.22 - Diagonal member type 2 (section A-A) 76
[xiv]
Figure 4.23 - Diagonal member type 1(section B-B) 76
Figure 4.24 - Section of the cross girder 76
Figure 4.25 - Vertical member (section C-C) 76
Figure 4.26 - Support arrangement for bridge deck 77
Figure 4.27 - Side view of the truck 79
Figure 4.28 - Back view of the truck 79
Figure 4.29 - Plan view of the wheel arrangement 79
Figure 4.30 - View of the created top chord section 80
Figure 4.31 - View of the created bottom chord section 80
Figure 4.32 - View of the created diagonal member type 1 80
Figure 4.33 - View of the created diagonal member type 2 80
Figure 4.34 - View of the created vertical member 81
Figure 4.35 - View of the created section of the cross girder 81
Figure 4.36 - View of the created bottom support to the cross girder. 81
Figure 4.37 - 3-D finite element model of the Paragastota Bridge 81
Figure 4.3 8 - Side view of the bridge mode!.. 82
Figure 4.39 - Plan view of the truss at bottom chord 82
Figure 4.40 - Sectional view of the Paragastota Bridge Model 82
Figure 4.41 - Axial force envelope for a typical truss 83
Figure 4.42 - Axial force envelope for members in middle of the truss 83
Figure 4.43 - Axial force envelope for members near to end of the truss v- 84
Figure 4.44 - Deformed shape when truck is at middle of the truss 84
Figure 4.45 - Stress ratio envelope 85
Figure 4.46 - Stress ratio of bottom chord members at middle of the truss 85
Figure 4.47 - Critical member and distance to front wheel of the truck 86
Figure 4.48 - Axial force variation of the member 48 vs. position of the vehicle on the bridge 88
[xv]
Figure 4.49 - Naththupana Bridge 89
Figure 4.50 - Warren truss configuration :90
Figure 4.51 - Parker truss configuration 90
Figure 4.52 - Plan view of each truss 90
Figure 4.53 - Load patterns on bridge deck 92
Figure 4.54 - With portal model of Parker type bridge 95
Figure 4.55 -Without portal model of Parker type bridge 95
Figure 4.56 - With portal model of Warren type bridge 93
Figure 4.57 - Without portal model of Warren type bridge 95
Figure 4.58 - Different lateral bracing types assigned to top chrods 96
Figure 4.60 - Warren bracing type 1 97
Figure 4.60 - Parker bracing type 1 97
Figure 4.61 - Warren bracing type 2 97
Figure 4.62 - Parker bracing type 2 97
Figure 4.63 - Warren bracing type 3 97
Figure 4.64 - Parker bracing type 3 97
Figure 4.65 - Warren bracing type 4 98
Figure 4.66 - Parker bracing type 4 98
Figure 4.67 - Warren bracing type 5 98
Figure 4.68 - Parker bracing type 5 98
Figure 4.69 - Details of Modified Warren truss Bridge "!, ••••••••• 98
Figure 4.70 - Details of Pratt truss bridge 100
Figure 4.71 - Details of Tied arch bridge 101
Figure 4.72 - Details of the Inverted arch truss bridge 101
Figure 4.73 - Details of the Parker bridge 101
Figure 4.74 - Span tonnage curve for modified Warren bridges 107
[xvi]
Figure 4.75 - Span tonnage curve for Tied arch bridges 108
Figure 4.76 - Comparison of all analyzed truss types 109
[xvii]
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LIST OF TABLES
Table 2.1 - Comparison of different trusses 23
Table 2.2 - Local truss bridge examplesfor different truss types 25
Table 3.1 - Description of the first four tests 35
Table 3.2- Scaled down measurement for model bridges 35
Table 3.3 - Details of the sections used. 36
Table 3.4 - Common properties of the Aluminium for all tests 39
Table 3.5 - Strength properties usedfor Aluminium used in different tests 39
Table 3.6 - SAP predictedfailure loads for model bridges 44
Table 3.7 - Scaled-down parameters of Model 54
Table 3.8 - Material properties 54
Table 3.9 - Section details of variable height model bridge 55
Table 3.10 - Laboratory testing results 61
Table 3.11 -Maximum vertical deflections found for first four tests 62
Table 4.1- Measurements of the Ehelakanda Bridge 65
Table 4.2- Material properties 66
Table 4.3 - Material properties 78
Table 4.4 - Joint deformations 84
Table 4.5 - Member forces of frame element 48 according to movement of the vehicle
(Influence Line * 25 ton) 86
Table 4.6 - Section usedfor different groups in the bridge 91
Table 4.7- Safety factors usedfor the Load combinations 93
[xviii]
Table 4.8 - Load combinations 94
Table 4.9-Maximum lateral nodal deformation 96
Table 4.10 - Maximum lateral deformations for different bracing types 98
Table 4.11 - Material properties of steel.. 102
Table 4.12 - Safety factors usedfor analysis 104
Table 4.13 - Load combinations used for analysis 105
Table 4.14- Different loading values according to span 106
[xix]