modelling analysis and design of self anchored suspension bridge
TRANSCRIPT
PROJECT REPORT on
MODELLING, ANALYSIS AND DESIGN OF
SELF-ANCHORED SUSPENSION BRIDGE
Submitted in partial fulfillment for the award of the degree
of
BACHELOR OF TECHNOLOGY
in
CIVIL ENGINEERING
by
GRANDHI VENKATA ROHIT 1011010072
GURU KESAV KUMAR K 1011010075
JHASTHI SATHISH RAO 1011010084
MIRZA ABDUL BASIT BEIGH 1011010112
Under the guidance of
Mrs. B. VELVIZHI Assistant Professor (O.G)
DEPARTMENT OF CIVIL ENGINEERING
FACULTY OF ENGINEERING AND TECHNOLOGY
SRM UNIVERSITY (Under section 3 of UGC Act, 1956)
SRM Nagar, Kattankulathur- 603203
Kancheepuram District
APRIL 2014
ii
PROJECT REPORT on
MODELLING, ANALYSIS AND DESIGN OF
SELF-ANCHORED SUSPENSION BRIDGE
Submitted in partial fulfillment for the award of the degree
of
BACHELOR OF TECHNOLOGY
in
CIVIL ENGINEERING
by
GRANDHI VENKATA ROHIT 1011010072
GURU KESAV KUMAR K 1011010075
JHASTHI SATHISH RAO 1011010084
MIRZA ABDUL BASIT BEIGH 1011010112
Under the guidance of
Mrs. B. VELVIZHI Assistant Professor (O.G)
DEPARTMENT OF CIVIL ENGINEERING
FACULTY OF ENGINEERING AND TECHNOLOGY
SRM UNIVERSITY (Under section 3 of UGC Act, 1956)
SRM Nagar, Kattankulathur- 603203
Kancheepuram District
APRIL 2014
iii
BONAFIDE CERTIFICATE
Certified that this project report titled “MODELLING,
ANALYSIS AND DESIGN OF SELF-ANCHORED SUSPENSION
BRIDGE” is the bonafide work of GRANDHI VENKATA ROHIT
(1011010072), GURU KESAV KUMAR K (1011010075), JHASTHI
SATHISH RAO (1011010084), and MIRZA ABDUL BASIT BEIGH
(1011010112) who carried out the project under my supervision. Certified
further, that to the best of my knowledge the work reported herein does not
form part of any other project report or dissertation on the basis of which a
degree or award was conferred on an earlier occasion or any other
candidate.
Signature of the Guide Signature of the HOD
Mrs. B. VELVIZHI Dr. R. ANNADURAI
Assistant Professor (O.G) Professor & Head
Department of Civil Engineering Department of Civil
Engineering SRM University SRM University
Kattankulathur- 603203 Kattankulathur- 603203
INTERNAL EXAMINER EXTERNAL EXAMINER
DATE:
iv
ABSTRACT
The objective of this study is to Model, Analyze and Design an
optimized Self Anchored Suspension Bridge with sustainable features. With
regard to this the whole process of study would be to design the basic
elements conforming to the most sustainable and optimized design
procedure and that it would be analyzed and modeled to fulfill this criterion.
With regard to Model fabrication (Prototype), the materials used are the
plywood sheets, Aluminium C sections and Aluminium L sections, plastic
wires, nuts, bolts etc.
Genuine focus has been given to the realistic design constraints
which are of a very great significance. These include economic, safety and
political constraints.
After the introduction, the scope, objectives and necessity follow
up and they are succeeded by the literature review and results and
discussion chapter. The results and discussion chapter gives the complete
modeling, analysis and design of the project. The Sag and Span ratio in the
Result and discussion will decide the stability of this structure. The study
includes extensive design of the deck slab, girder, cables which form the
most fundamental elements of this study. A suitable conclusion giving a
synopsis of work concludes the work.
v
ACKNOWLEDGEMENT
We would like to place on record, our greatly thanks Dr. T. P. GANESAN,
Pro-Vice Chancellor (P&D) for providing facilities and help in carrying out this project.
We also thank Dr. C. MUTHAMIZHCHELVAN, Director (Engineering and
Technology), for the stimulus provided.
We wish to express our sincere thanks and gratitude to Dr. R. ANNADURAI,
Professor and Head of Department, Department of Civil Engineering, for his valuable
encouragement for completion of this project work.
We express our sincere thanks to the Coordinator Dr. K.GUNASEKARAN,
Professor, for his guidance and the positive comments during the conduct of review
sessions, which helped us to proceed in right direction in the project.
We hereby acknowledges with deep sense of gratitude the valuable guidance,
encouragement and suggestions given by our Guide, Mrs. B.VELVIZHI, Assistant
Professor (O.G), Department of Civil Engineering, who has been a constant source of
inspiration throughout this project.
Also, we would like to take this opportunity to thank all teaching and non-
teaching staff members in the Department of Civil Engineering, for their direct and
indirect help in completing the project and beyond all ALMIGHTY GOD for blessings.
We also thank the staff of SRM DTP section for their efforts in producing
this project. We record our sincere thanks to our parents for the support and motivation.
We kindly acknowledge the help provided by our friends for successful completion of
project work.
GRANDHI VENKATA ROHIT
GURU KESAV KUMAR K
JHASTHI SATHISH RAO
MIRZA ABDUL BASIT BEIGH
vi
TABLE OF CONTENTS
CHAPTER TITLE PAGE
ABSTRACT iv
ACKNOWLEDGEMENT v
LIST OF TABLES ix
LIST OF FIGURES x
ABBREVATIONS xii
1 OVERVIEW 1
1.1 OBJECTIVE 1
1.2 NECESSITY 1
1.3 SCOPE 1
1.4 METHODOLOGY 1
1.5 MAJOR DESIGN EXPERIENCE 3
1.6 REALISTIC DESIGN CONSTRAINTS 3
1.7 REFERENCE TO CODES AND STANDARS 3
1.8 APPLICATION OF EARLIER COURSE WORKS 4
1.9 MULTIDISCIPLINARY AND TEAM WORK 5
1.10 SOFTWARES / EQUIPMENTS USED 6
2 INTRODUCTION 7
2.1 GENERAL 7
2.1.1 Structural Components 7
2.2 LITERATURE REVIEW 9
2.2.1 Self Anchored Bridges 9
2.2.2 Suspension Bridges 10
2.2.3 Suspension Bridges and Static Behavior 11
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2.3 SUMMARY OF LITERATURE REVIEW 12
3 OBJECTIVES AND SCOPE 13
3.1 OBJECTIVES 13
3.2 SCOPE 13
3.3 MATERIALS AND METHODOLOGY 14
4 RESULTS AND DISCUSSIONS 15
4.1 MODELLING 15
4.1.1 Deck 16
4.1.2 Pylon 16
4.1.3 Suspenders 17
4.1.4 Angle between Main Cable and Pylon 17
4.1.5 Longitudinal Elevation 18
4.1.6 Specifications of the Model 18
4.2 ANALYSIS OF STRUCTURE 19
4.2.1 Analysis of Loads 19
4.2.1.1 Dead Load 19
4.2.1.2 Live Load 19
4.2.1.3 Dynamic Loading 22
4.2.1.4 Longitudinal forces 23
4.2.1.5 Wind Load 23
4.2.1.6 Forces due to Curvature 24
4.2.2 Estimation of Loads 24
4.2.2.1 Calculation of live load 24
4.2.3 Analysis of Cable properties 25
4.2.3.1 Sag in the Main Cable 26
4.2.3.2 Cable Tension 27
4.2.3.3 Length of the Cable 28
4.3 DESIGN 29
4.3.1 Design of Deck 29
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4.3.1.1 Design of interior slab panel 30
4.3.1.2 Design of Slab 36
4.3.2 Design of Main Cables 38
4.3.3 Design of Hangers 43
4.3.4 Design of Longitudinal Girder 45
4.3.4.1 Dead Load of Main Girder 46
4.3.4.2- Dead Load Bending Moment and 47
Shear of Main Girder
4.3.4.3 Live Load Bending Moment 47
4.3.4.4 Sectional properties of Girder 48
4.3.4.5 Check for Adequacy 49
4.3.4.6 Sections 49
4.3.4.7 Permissible Tender Zone 50
At Support Section
4.3.4.8 Check for Stress 51
4.3.4.9 Check for Ultimate Flexural 52
Strength of Beam
4.3.4.10 Check for Ultimate Shear 53
Strength of the Beam
4.3.4.11 Design of Supplementary Reinforcement 55
4.3.4.12 Design of End Blocks 56
5 CONCLUSION 57
5.1 CONCLUSION 57
5.2 FUTURE SCOPE 57
REFERENCES 58
ix
LIST OF TABLES
TABLE TITLE PAGE
1.1 Codes and standards 4
1.2 Application of earlier course work 5
4.1 Modulus of Elasticity of Road and Strands 39
as per IS 9282:2002
x
LIST OF FIGURES
FIGURE TITLE PAGE
1.1 Methodology of the project 2
2.1 Suspension bridge components 8
2.2 Deformations and forces of a suspension bridge 11
4.1 Photograph of scale reduced model in a 15
self-anchored suspension bridge
4.2 3D Model of the deck 16
4.3 Model of pylon frame 16
4.4 Modelling of suspenders for the prototype 17
4.5 Angle specification 17
4.6 Longitudinal section of 18
self-anchored suspension bridge
4.7 Traffic load over full length 20
4.8 Traffic load on the main span 20
4.9 Traffic load on the side span 20
4.10 One side full length loading of deck 21
4.11 Alternate side loading of the deck 21
4.12 One side main span loading 22
4.13 Impact percentage curve 22
4.14 IRC class AA loading 25
4.15 Dimensions of each slab panel 31
4.16 Pigeaud’s curve moment coefficients for slab 31
4.17 Pigeaud’s curve for moment coefficients 32
M1 for K= 0.5
xi
4.18 Pigeaud’s curve for moment coefficients 33
M2 for K = 0.5
4.19 Representation of dispersion of load on deck slab 35
4.20 Graph between Δσ, η to find allowable cable stress 41
4.21 Arrangement of class AA loads for maximum 45
eccentricity on deck
4.22 Dimensions of main girder 46
4.23 ILD for live load bending moment over deck 47
4.24 Placement of cables at center span section 50
4.25 Arrangement of cables at support section 51
xii
LIST OF SYMBOLS AND ABBREVIATIONS
Ast – Area of tensile reinforcement
Ast, min – Minimum area of tensile reinforcement
fck – Characteristic compressive strength of concrete
fy – Characteristic yield strength of steel
I.S - Indian Standard
Mu – Ultimate moment
Mu,lim – Limiting moment of resistance
Mu, max – Ultimate maximum moment
Mux – Design moment about x-x axis
Muy – Design moment about y-y axis
pt – Percentage of tension reinforcement
Pu – Design axial load for limit state design
τc – Shear stress in concrete
τv – Nominal shear stress
Vu – Shear force due to factored loads
Vu, max – Ultimate maximum shear force
Xu,max – Maximum depth of neutral axis in
limit state of design
υr
– Diameter of bar
1
CHAPTER 1
OVERVIEW
1.1 OBJECTIVE
The objective of the project is to achieve the most optimised model of a
Self-Anchored Suspension Bridge using steel-concrete composites.
1.2 NECESSITY
The basic necessity of this type of bridge is to deal with the traffic
congestion on the NH-45 due to SRM University, B.S.Abdur Rahman University and
Vandalur Zoo. It would help to regulate the traffic flow which would be very helpful
in reduction of the congestion during the peak hours.
1.3 SCOPE
The scope of this project includes Modelling (Prototype and Virtual –
reduced scale), Analysis and Design of various components of Self-Anchored
Suspension Bridge structure like girder, deck, main cables, suspenders etc.
1.4 METHODOLOGY
The Methodology followed in working of this project has been very
comprehensive. After formation of the objective and site selection literature
survey was carried out. Literature survey included referring the earlier such work
done in journals, conferences and books. Thereafter the Indian Standard Codes
which were used during the work were taken into consideration so that a clear
view about the whole project could be available.
The analytical work was preceded by modelling of a prototype which was
scale reduced and it was instrumental in understanding the intricacies behind the
2
practical work Thus it provided the project with a unique experience of having
exposed to practical domain of understanding. The modelling was also done using
software packages and then analysed to get an optimised model which was
later on judiciously designed.
The flow chart for the methodology followed is shown in Figure 1.1
Fig 1.1 Methodology of the project
REFERENCE
BOOKS
SITE SELECTION/STUDY AREA
(NEAR SRM UNIVERSITY)
FORMATION OF OBJECTIVE
MODELLING OF THE
STRUCTURE
LITERATURE
SURVEY
IS CODE BOOKS
ANALYSIS OF VARIOUS LOADS ACTING
ON THE STRUCTURE (DEAD LOAD, LIVE
LOAD, MOVING LOAD, COMBINED LOAD)
DESIGN OF STRUCTURAL
ELEMENTS AND
ASSEMBLING
OUTCOME
3
1.5 MAJOR DESIGN EXPERIENCE
Analysis and design of suspension bridge (prototype) components.
Deck
Girder
Main cable
Suspenders
1.6 REALISTIC DESIGN CONSTRAINTS
1. Social constraints: Since the construction activities are going to be over
a National Highway during construction, traffic congestion may be
expected. This constraint has been overcome by ensuring alternate route
at the site of work so that the normal traffic can commence regularly and
the work also progresses as planned.
2. Political constraints: This project will have to seek permission from the
Ministry of Road and Transportation. It also requires complete
cooperation from Central and State governments and Local Political
Leaders. This constraint has been overcome by timely action of seeking
help from the concerned authorities for the smooth functioning of the
project during the given duration of the work.
3. Economic constraints: The project involves huge financial cost and
utilization of huge resources including man power hence economic
viability has to be considered. This has been overcome by timely
involving the concerned government authorities so that the flow of
inventory and stock is consistent and the scarcity should not let the work
be delayed
1.7 REFERENCE TO CODES AND STANDARDS
As far as the codes and standards are concerned, for the design of some
components such as slabs, girder and deck, the Indian Standard (IS) codes have been
used. These codes and standards haven been very much instrumental in working on
the project by providing genuine assumptions, and easy methods and ways of
4
construction techniques. The codes and standards used in this project are shown in
Table 1.1.
Table 1.1 Codes and Standards
CODES/STANDARDS CONTEXT
IRC 5:1998 Standard Specifications and Code of Practice for
Road Bridges (Section-1: General Features of
Design).
IRC 6:2010 Standard Specifications and Code of Practice for
Road Bridges (Section-2: Loads and Stresses).
IRC 18: 2000 Code of Practice for Composition of Bridge
Specifications and Standards.
IRC 21:2000 Code of Practice for Road Bridges (Section-III:
Cement Concrete).
IRC 22:1986 Standard Specifications and Code of Practice for
Road Bridge (Section-6: Composite Construction).
IS 456 :2000 Code of Practice for Plain and Reinforced Concrete.
IS 9282: 2002 Specification for Wire Ropes and Strands for
Suspension Bridges.
IS 875: 1987 (Part III) Code of Practice for Design Wind Loads for
buildings.
1.8 APPLICATION OF EARLIER COURSE WORK
This project is a multidisciplinary project. Hence the work done in this
project is a combination of courses taken in various subjects.
Therefore the application of earlier course works in this project work
regulates the flow, understanding and application of knowledge in a gradual way.
The knowledge gained from some of the earlier courses is used in this project and are
listed in Table 1.2.
5
Table 1.2 Application of earlier course work
SUBJECT
CODE
SUBJECT TITLE CONTEXT
CE 0201 Mechanics of Solids Evaluation of bending moment and
shear forces
CE 0202 Strength of Materials Evaluation of deflection
CE 0301 Structural Analysis-I Influence line and rolling loads
CE 0302 Structural Analysis-II Indeterminate Analysis
CE0104- Computer aided building
drawing
Plan, section, elevation of structure
CE0403- Transportation engineering Roadway design
CE0204- Structural Design - I Truss and pylons steel design
CE 0303- Structural Design-II Design of RCC structures
CE
ECN2-
Advanced Construction
Techniques
Study on general features of
Suspension Bridge
CE 0304 Structural Design III Pre stressing of the deck
1.9 MULTI DISCIPLINARY COMPONENTS
This project involves the interaction with various private and government
agencies. There has to be a genuine interaction with the State Road Transport
Corporation authorities, National Highway authority (NHA).
Chennai Metro Development Authority (CMDA) is the main body which
has to be consulted to seek permission regarding the new constructions over the
roads and anywhere over the new lands or even use the land for activities of
construction.
The State Road Transport Corporation officials provided majority of the
assistance required by providing data, experience and an overall idea of the
methodology in which the design of the bridge has to be conducted.
6
The National Highway Authority (NHA) provides assistance by giving
the schematic maps, rules and regulations regarding the highway bridges
construction and the other necessary supplements for the construction. These play a
key role in the planning of the highway bridge construction.
The other Multidisciplinary components of the project work are given
below:
1. Modelling – Finite Element Concept
2. Analysis & Design – Structural Engineering
3. Deck Design and Moving Loads- Transportation Engineering.
4. Scale Reduction for prototype modelling.
These components have been used in this project. These form the
fundamental concepts of this project. Hence the work has been in accordance to set
standards so as to reach a sustainable outcome.
1.10 SOFTWARE/EQUIPMENT USED
The software has been used for modelling and analysis. Modelling has
also done by fabricating a model of a scale reduced prototype. The AutoCAD 2010 is
used for drawing the plan and sectional drawings.
The Software/Equipment to be used for the project is given as under:
1. AutoCAD 2010 : used for plan and sectional drawing.
2. ABAQUS- FEM-12 Software : used for modelling and analysis.
3. Prototype modelling : using scale reduction concept.
The software and equipments form a substantial part of this project work
and the main work of concern is modelling, analysis and design. These features are
instrumental in deciding these operations of the project work.
7
CHAPTER 2
INTRODUCTION
2.1 GENERAL
Self-anchored suspension bridges differ from conventional suspension
bridges because they do not require massive end anchorages. Instead, the main cables
are secured to each end of the bridge deck, or stiffening girder, which carries the
horizontal component of cable tension. Therefore, the end support resists only the
vertical component of tension an advantage where the site cannot easily
accommodate external anchorages. Self-anchored main cables are fixed to the
stiffening girders instead of the anchorage; the axial compression is carried into the
girders (Ref.1).
Ochsendorf, J. et al (1999), have studied about self-anchored suspension
bridges and mentioned that the compression being equal to the horizontal component
and tension equal to the vertical , and it is balanced from the road decks own weight.
The effect of the design shows that suspension bridges do not apply any horizontal
forces towards the ground level (Ref. 1). This has been studied in course CE ECN2
Advanced Construction Techniques
2.1.1 Structural Components
The basic structural components of a suspension bridge system
are shown in Figure 2.1.
1. Stiffening girders/trusses: Longitudinal structures which support and
distribute moving vehicle loads, act as chords for the lateral system.
2. Main cables: A group of parallel wires bundled cables which support the
stiffening girders/trusses by hanger ropes and transfer loads to towers.
3. Main towers: Intermediate vertical structures which support main cables
and transfer the bridge loads gradually to the foundations.
8
4. Self-Anchorages: Concrete blocks which anchor main cables and act as
end supports of a bridge.
Fig 2.1 Suspension bridge components
The success of the self-anchored suspension bridge is due to three main
aspects of its design.
1. The method of erection.
2. The use of suspending anchors.
3. The use of composite girders.
The second successful design aspect was the suspenders pre-tensioned to
avoid slackening under any load condition.
Because the stiffening girder supports the cable tension, the girder must be
placed before the main cable can be erected.
The analysis should include influence of the large axial force in the deck.
The force in stiffening girder is equal to horizontal component of main
cable tension.
The Sag of the main cable can be increased in order to reduce the value of
axial compression in the stiffening girder.
9
In general, the SAG: SPAN ratio is 1:5 to 1:8 for self-anchored suspension
bridge, considerably greater than typical suspension bridges which have
around 1:10 (Ref.1).
2.2 LITERATURE REVIEW
Various journals and publications were referred to complete the literature
review of this study. The details of the sources referred to have been given in the
reference section. The gist of the concepts taken for the in depth understanding of the
analysis and design of the Self-Anchored Suspension Bridge has been summarised as
under.
2.2.1 Self Anchored Bridges
Summarizing the beginning, analysis, and future of self-anchored
suspension bridges, examines the development of this unique bridge form, its uses
over the past century, and its advantages and disadvantages. The Konohana Bridge in
Osaka, Japan, illustrates this type and provides a case study to compare conventional
suspension bridge theory with the results of a finite-element model. The final portion
of the paper evaluates the potential for self-anchored suspension bridge design, and
provides recommendations for design engineers. The goal here is to describe the
structural behaviour of self-anchored bridges in general and of the Konohana Bridge in
particular.
Classical Theories for Analysis:
Two theories govern the analysis of self-anchored suspension bridge. The
elastic theory and the deflection theory are in-plane analyses for the global suspension
bridge system. In the theories, the entire suspension bridge is assumed a continuous
body and the hanger ropes are closely spaced. Both of these analytical methods
assume:
The stiffening girder is horizontal and straight. The geometric moment of
inertia is constant.
The dead load of the stiffening girder and the cables is uniform. The
coordinates of the cable are parabolic.
10
The cable is completely flexible and all dead loads are taken into the
cables.
Elastic Theory
Elastic theory gives the moment at any point on deck girder determined by
the Equation (2.1),
M = M’- h × y (2.1)
Where,
M’ live load moment of unsuspended girder
h horizontal component of cable tension produced by live load
y ordinate of main span cable curve
The elastic theory did not account for stiffening effect for the main cable
under tension, thus gave higher moments in the stiffening girder, thus the live load
moment produced in girder is reduced by the horizontal component of live load
tension in the cable. The economy of construction offered by deflection theory made
this theory absolute (Ref.1).
2.2.2 Suspension Bridges
Deflection Theory
The deflection theory is an extension of elastic theory. The bending
moment, M(x), of the stiffening girder after the loading the live load is shown in
Equation (2.2).
M(x) = M’(x) – Hp × y(x) – (Hw + Hp) n(x) (2.2)
Where,
M’(x) bending moment resulting from the live load applied to a simple
beam of the same span length as the stiffening girder
y(x) longitudinal position of the cable
n(x) deflection of the cable and the stiffening girder due to live load
Hw, Hp cable horizontal tension due to dead load and live load
11
The deflection accounted for the second order effects of cable stiffness and
correctly reduced the moment carried by the stiffening girder. The difference between
the two theories is whether cable deflections resulting from live load is considered.
Figure 2.2 shows forces and deflections due to load in a suspension bridge (Ref.2).
Fig 2.2 Deformations and forces of suspension bridge
2.2.3 Suspension Bridge and Static Behaviour
This study is done to develop a set of consistent design guidelines for self-
anchored suspension bridges and on current knowledge is done to be filled in order to
enable the formation of a consistent set of design recommendations. This research
indicated discusses static behaviour as well as feasibility study of long span self-
anchored bridges. In order to accomplish this goal, a thorough investigation of
important parameters to determine behaviour of self-anchored suspension bridge and
identify any gaps that a well-chosen ratio between the bending stiffness of deck and
axial stiffness of cable influences the maximum bending moments and the deflections
in the girder. The ratio of sag to span is also investigated to reduce the normal force in
the deck and the maximum bending moment in the deck. A study to the static strength,
stiffness, frequency behaviour and the buckling stability of the box girder, revealed
that a deck slenderness of the box girder of λ =0.01 and even more slender is very well
feasible. The paper also discusses possibilities of increasing main span length and tries
to find a certain span limit for the self-anchored suspension bridges. Increasing the
span length of the bridge will cause several effects on static strength and stiffness.
Several effects are monitored like stresses in cable, girder and pylon, deformations and
12
reaction forces. Based on results of this study, a span length of 500 metres is very well
possible (Ref.3).
2.3 SUMMARY OF LITERATURE REVIEW
The Literature Review for this project work has been comprehensive in
nature. So following is the summary of the literature review. Referring to the journals
following summary can be proposed.
Summarizing the beginnings, analysis, and future of self-anchored
suspension bridges, examines the development of this unique bridge form, its uses
over the past century, and its advantages and disadvantages. The Konohana Bridge in
Osaka, Japan, illustrates this type and provides a case study to compare conventional
suspension bridge theory with the results of a finite-element model (Ref.1).
One more important theory is the deflection theory which is an extension
of elastic theory. The deflection theory (exact theory) accounted for the second order
effects of cable stiffness and correctly reduced the moment carried by the stiffening
girder (Ref.2).
Finally the last journal discusses static behaviour as well as feasibility
study of long span self-anchored bridges. In order to accomplish this goal, a thorough
investigation of important parameters to determine behaviour of self-anchored
suspension bridge and identify any gaps that a well-chosen ratio between the bending
stiffness of deck and axial stiffness of cable influences the maximum bending
moments and the deflections in the girder. The ratio of sag to span is also investigated
to reduce the normal force in the deck and the maximum bending moment in the deck
(Ref.3). These basic concepts derived from the Literature Review have been
instrumental in completing this work.
13
CHAPTER 3
OBJECTIVE AND SCOPE
3.1 OBJECTIVES
The objective of this study is to Model, Analyse and Design an
optimised Self Anchored Suspension Bridge with sustainable features.
With regard to this the whole process of study would be to design the basic
elements conforming to the most sustainable and optimised design
procedure and that it would be analysed and modelled to fulfil this criteria.
Since this is the first of its kind in India so the work has been rigorously
referred from journals globally and where ever needed suitable assumptions
do form a part of this project work.
3.2 SCOPE
This project has an extra ordinary scope due to its nature of self-
anchoring.This project includes
Modelling (Prototype and Virtual – reduced scale)
Analysis and
Design
of girder, deck, main cables, suspenders for a Self-Anchored Suspension
Bridge structure.
With respect to common suspension bridges, the self-anchored
suspension bridge takes the lead when it comes to the problem of providing
heavy and massive anchorages which are not possible in every situation
Therefore, the Self Anchored Suspension Bridge eliminates this short
coming and plays a very significant role of being able to establish itself in
any sort of the terrain and surface topography over the amazing long spans.
14
However the design has to be suitably optimized due to the fact
that if there is a slight mistake in the procedure of designing or execution
then it can lead to catastrophes.
3.3 MATERIALS AND METHODOLOGY
As far as the material used in this project are concerned, in the execution
work materials used would be the concrete, steel, cables, bitumen, railings etc. But
all such things are not a subject of study in this work
With regard to model fabrication; the materials used are the plywood sheets,
aluminium C sections and Aluminium L sections, plastic wires, nuts, bolts etc. The
methodology of this report is a very comprehensive.
All these concepts have been studied in the course CE 0201 Mechanics of Solids.
The initial phase was the planning of the work. It was the most daunting
task of the project. Finally the site for the project was finalised. Following this the
model fabrication formed an integral part of the methodology because the model was
a scale reduced model and all calculations are similar to the real design of Self
Anchored Suspension Bridge.
Later on the IS codes of design, reference books and literature survey
followed on to gather a data base of useful information and know-how of the design,
analysis and modelling work. Software packages like AutoCAD and ABAQUS were
used to enhance the analytical abilities.
After modelling the structure the analysis of various loads and the
behaviour of the bridge formed a part of the methodology.
15
CHAPTER 4
RESULTS AND DISCUSSIONS
4.1 MODELLING
Auto CAD 3D was used to model the deck of the Self-Anchored
Suspension Bridge, and then the model was loaded with various possible patterns of
loading. The models were loaded with such patterns in ABAQUS software.
Adjacently a scaled down model of the proposed model was made using cardboard,
aluminium channels and nylon wires. The picture of the prototype model has been
attached below which is reduced to a ratio of 1:1000 Figure 4.1.
Fig 4.1 Photograph of scale reduced model in self-anchored suspension bridge
The deck modelling, elevation and section drawings have been done
using AutoCAD which has been studied in the course CE 0104 Computer aided
building drawing. The Figure 4.1 gives a practical exposure of various realistic
constraints even though it was in perspectives of small scale.
16
4.1.1 Deck
The 3D model of the deck is modelled using the AutoCAD 2010 and it is
shown in Figure 4.2.
Fig 4.2 3D Model of the deck
4.1.2 Pylon
The model of the pylon of the prototype which is modelled has been
given in Figure 4.3.
Fig 4.3 Model of pylon frame
17
4.1.3 Suspenders
The length of Suspenders for prototype has been modelled using Auto
CAD 2010 and is shown in Figure 4.4.
Fig 4.4 Modelling of suspenders for the prototype
4.1.4 Angle between Main Cable and Pylon
The angle between main cable and pylon was calculated to be equal to
56.550 and angle between side cable and pylon was calculated as 75.22
0 and is shown
in Figure 4.5.
Fig 4.5 Angle specification
18
4.1.5 Longitudinal Elevation:
The AutoCAD 2010 drawing of the longitudinal elevation is given below
with specifications given in the Figure 4.6.
Fig 4.6 Longitudinal section of self-anchored suspension bridge
4.1.6 SPECIFICATIONS OF THE MODEL
1. Total span = 1000 mm
2. Length of main span = 545 mm
3. Length of side span = 227.5 mm
4. Sag in main cable = 86 mm
5. Sag in side cable = 15 mm
6. Clearance of deck = 200 mm
7. Height of pylon from deck = 90 mm
8. Angle between pylon and side span cable (α) = 75.22°
9. Angle between pylon and side span cable (ß) = 56.55°
10. Total number of suspenders with spacing of 30.2775 mm = 33
11. Length of the main cable = 581.18
12. Length of the side span cable = 23
19
4.2 ANALYSIS OF STRUCTURE
The Analysis of the Structure is the main feature of study of the project
before designing the bridge components.
4.2.1 Analysis of Loads
The bridge is designed by analysing the forces and loads on the bridge
elements manually. Various types are listed below.
Dead Load
Live load
Impact load
Longitudinal force
Thermal force
Wind load
Forces due to curvature
4.2.1.1 Dead Load
The dead load is the weight of the structure and any permanent load fixed
thereon. The dead load is initially assumed and checked after design is completed.
4.2.1.2 Live Load
Bridge design standards specify the design loads, which are meant to
reflect the worst loading that can be caused on the bridge by traffic, permitted and
expected to pass over it. In this study, tank loading of IRC Class A (Ref.5) has been
used for analysis.
In India, highway bridges are designed in accordance with IRC bridge
code.
IRC: 6: 2010 - Section II gives the specifications for the types of standard
loadings for which the bridges are designed (Ref.6). The various cases of
loading of live loads as per the codes mentioned above have been given
The following work of analysing various types of loadings has been
studied in the course CE 0302 Structural Analysis-II.
20
The following conditions discuss the various possibilities of bridge
loadings and they have been described as below.
Case 1: Full length traffic loading of the bridge deck has been is shown
in Figure 4.7.
Fig 4.7 Traffic load over full length
Case 2: Mid span traffic loading of the bridge deck has been is shown in
Figure 4.8.
Fig 4.8 Traffic load on the main span
Case 3: Side span traffic loading of the bridge deck on both ends is
shown in Figure 4.9.
Fig 4.9 Traffic load on the side span
21
Case 4: Only one side full length traffic loading of the complete bridge
deck has been shown in Figure 4.10. This is the most critical type of loading over
suspension bridge deck.
Fig 4.10 One side full length loading of deck
Case 5: The traffic loading is kept on two side spans and the main span in
an alternate way and it has been shown in Figure 4.11.
Fig 4.11 Alternate side loading of the deck
All these cases of the various loadings are discussed to derive the case
which is the most critical condition of loading so that if such a condition is ensured
to be safe then all the other cases are in the safe mode.
22
Case 6: Only one side traffic loading of the main span has been done and
it has been shown in Figure 4.12.
Fig 4.12 One side mid span loaded
4.2.1.3 Dynamic Loading
The dynamic effect caused due to vertical oscillation and periodical
shifting of the live load from one wheel to another when the locomotive is moving is
known as impact load. The impact load is determined as a product of impact factor, I
and the live load. The impact curve is shown in Figure 4.13.
Fig 4.13 Impact percentage curve with span (in metres) on x-axis and impact
factor (in percentage) on y-axis
23
4.2.1.4 Longitudinal forces
Longitudinal forces are set up between vehicles and bridge deck when the
former accelerate or brake. The magnitude of the force F is given by Equation (4.1),
F =
(4.1)
Where,
G - acceleration due to gravity
δV - change in velocity in time
W - weight of the vehicle
This topic was a part of study in the course CE 0403-Transportation
Engineering.
4.2.1.5 Wind load
Wind load on a bridge may act
1. Horizontally, transverse to the direction of span
2. Horizontally, along the direction of span
3. Vertically upwards, causing uplift
4. Wind load on vehicles
5. For the purpose of the design, wind loadings are adopted from the maps
and tables given in IS: 875 -Part III.
6. A wind load of 2.40
is adopted for the unloaded span of the highway
and footbridges (Ref.4).
The wind load is a part of the dynamic load which is a part of study under
structure dynamics and it includes the earthquake design and the ductile detailing of
the structure. The study of dynamics is not in the scope of this project so the concept
of wind load has been given as for purpose of information.
24
4.2.1.6 Forces due to curvature
When a track or traffic lane on a bridge is curved allowance for
centrifugal action of the moving load should be made in designing the members of
the bridge. All the tracks and lanes on the structure being considered are assumed as
occupied by the moving load.
This force due to curvature is given by the following Equation (4.2),
C =
(4.2)
Where,
C - - centrifugal force
W - equivalent distributed live load
V - maximum speed in km per hour
R - radius of curvature in metres
This topic was a part of study in the course CE 0403-Transportation
Engineering.
4.2.2 Estimation of Loads
Load estimation for the deck slab is calculated by referring the code as
per IRC: 6: 2010 (Ref.6).
4.2.2.1 Calculation of live load
Class AA loading scheme is adopted in estimation of live load.
For 2 lane road Carriage width is 5.3 m to 9.6 m.
Two lanes for class A or One lane of class 70 R.
The width is 7.5 m for 2 lane carriage way as per IRC: 5 (Ref.5), and the
impact load factor is 112 % the actual acting load and for class 70 R Steel, 10%
impact factor is added. The estimation of loads is so significant that without this step
the design of the bridge is not possible.
This topic was a part of course in CE 0403-Transportation Engineering.
25
The Maximum tyre pressure = 24.6
The Class AA loading scheme is represented in Figure 4.14.
Fig 4.14 IRC class AA loading
C= Clearance = 1.3m as per IRC 6:2010
• The tank load is 70 ton acts on lane as shown above. So, the axle load
acting on lane is 700 kN.
• The Impact Factor of live load is 30% for steel bridge and for span length
less than 10m (Ref.5-6).
• Width of each lane is 2.9 m. Clearance of 1.2 m shall be provided
between any 2 lanes in multi-lane highway as per IRC: 6: 2010 (Ref.6).
The following concepts have been covered in CE 0302 Structural
Analysis-II-Indeterminate Analysis.
The rolling loads which are distributed over the deck slab for analysis of
the deck are converted into the equivalent uniformly distributed loads (EUDL) The
EUDL gives an approximate and nearly an exact estimate of the load conversion
from rolling load into a uniformly distributed load.
26
The EUDL (Equivalent uniformly distributed load) for a UDL (Uniformly
distributed load shorter than span) is calculated by using Equation (4.3),
(
) (4.3)
Where,
- EUDL
A - length of UDL.
L - length of span.
W - total live load.
We obtain the value of EUDL by substituting values in Equation (4.3),
W’ =
EUDL = 2395.42
4.2.3 Analysis of cable properties
The following analysis of elements of a Suspension Bridge has been
covered in CE 0302 Structural Analysis-II Indeterminate Analysis (Ref.7).
1. Sag in the main cable
2. Tension in the cable
3. Length of the cable
4.2.3.1 Sag in the main cable
=
So, sag in the main cable is 85 m.
The Sag in the main cable is a very important feature for designing the
cable. The sag to span ratio is a very important aspect of calculation in suspension
bridges.
27
4.2.3.2 Cable tension:
Cable Tension is a very important factor in analysis of this structure
because this structure takes the load through the tension in the main cable which it
transfers to the main pylon. The tension in the main cable is obtained by calculating
using Equation (4.4),
T= √VA2+H
2 (4.4)
Where,
VA - Vertical force component
H - Horizontal force component
The Horizontal force component, is calculated using Equation (4.5),
H =
(4.5)
Where,
p - equivalent load
d - sag in the main cable
L - length of mid span
H=
= 1034.15 × 10
3 kN
The Vertical force component is calculated using Equation (4.6),
VA = VB =
(4.6)
Where,
VA - vertical force at end A
VB - vertical force at end B
P - equivalent load
L - length of mid span
28
By substituting the obtained values in Equation (4.6) we get,
VA = VB =
= 652.75 × 10
3 kN
Vertical component VA= VB= 652.75 × 103
kN
By substituting required values, we obtain cable tension from Equation (4.4),
T= √ (652.75 × 103)2
+ (1034.15 × 103)2
T= 1222 × 106 kN
4.2.3.3 Length of the cable
The total length of cable required is determined by Equation (4.7),
S = L + (
) (4.7)
Where,
S - length of the cable
L - length of main span
d - sag in the main cable
By substituting the calculated values in Equation (4.7) we get,
S = 545 +
= 581 m
So, Length of the main cable is 581 m.
Hence these parameters are the analytical output of this section of study
of the project work (Ref.7). All the parameters have been considered and the
standard SI units have been maintained uniformly.
Thus the optimised values of the parameters such as the sag to span ratio,
cable tension and the length of the cable to be used for the self-anchored suspension
bridge construction. All these parameters are used to design the safest possible
design of the bridge structure elements.
29
4.3 DESIGN
The design of suspension bridge includes the design of following major
components which have been studied in the course CE 0303 Structural Design II and
CE 0304 Structural Design III.
1. Deck
2. Main cable
3. Suspenders
4. Girder
4.3.1 Design of Deck
1. The primary function of a bridge deck is to support the vehicular vertical
loads and distribute these loads to the steel superstructure.
2. The deck is typically continuous along the span of the bridge and
continuous across the width of the span. The deck will also act as a
horizontal diaphragm that is capable of transferring lateral loads, such as
wind or seismic loads, to the supports.
3. The deck system in self-anchored suspension bridges acts as a continuous
girder over the interior piers, but with additional intermediate elastic, but
relatively stiff, supports at the anchoring points of the stay cables (Ref.8).
For the design of post tensioned pre-stressed concrete bridge deck the
following design parameters were considered (Ref.9).
Effective span of slab = 40 m (assume)
Clear width of road = 10 m
Thickness of wearing = 40 mm asphalt layer
Spacing of cross girders = spacing between hangers = 6 mm c/c
Live load = IRC class AA loading
Material M40 concrete for deck slab
30
fci = 40
= Compressing strength of concrete at transfer
fck = 50
Permissible Stresses and Design Constraints as per IRC: 18: 2000 (Ref.12).
1. fck < 0.5 fci .
fck < 0.5 (40) = 20
.
fck = Permissible compressive stress in concrete at transfer and working
loads.
2. Loss ratio =
3. Permissible compressive stress is concrete under service load (fck) = 0.13
(fck) = 0.33 x 50 = 16.5
4. Allowable tensile stress in concrete at initial pressure transfer (ftt) = 0
5. Allowable tensile shear is concrete load = 0
For M40 concrete, Fe415 steel as per IRC: 21:2000 (Ref.13), following
coefficients were assumed.
n = 0.4
j = 1 -
= 1 -
= 0.866
Q =
=
4.3.1.1 Design of interior slab panel
Step 1: Dead load bending moment and shear force
Since slab is pre stressed the thickness may be reduced and could be
termed as 50mm per meter span of slab.
Hence the dead load bending moment and shear force is used to design
the panels of slab such that the design is safe enough to respond to the worst
condition.
31
Dead weight of slab = 1 × 1 × 50 mm × 5 × 24
= 6
Wearing coat = 0.04 × 0.22 = 0.88
Total design load = 7
Each panel slab = 5 × 2.5 × 7
= 87.5 kN
The dimensions of the slab panel have been shown in Figure 4.15.
Fig 4.15 Dimensions of each slab panel
The Pigeaud’s Curve given in Figure 4.16 is used to find out the moment
coefficients of a completely loaded slab with uniform distributed load.
Fig 4.16 Pigeaud’s Curve-moment coefficients for slab completely loaded
with uniformly distributed load
32
Ratios
= 1,
= 1
K =
=
= 0.5 and
= 2
By Pigeaud’s Curve, given in the Figure 4.17 and Figure 4.18 we get,
For, k = 0.5, M1= 0.047 and
= 3.0, M2 = 0.01
M1, M2 = Moment coefficients in dead load bending moment in short, long span
directions respectively are found using Figure 4.17 and Figure 4.18.
Fig 4.17 Pigeaud’s Curve for Moment coefficients M1 for K=0.5
33
Fig 4.18 Pigeaud’s Curve for Moment coefficients M2 for K=0.5
The dead load bending moments along long, short span directions are
obtained by referring the Equation (4.8) and Equation (4.9).
MBD = W [M1 + μ M2] (4.8)
MCD = W [M2 + μ M1] (4.9)
Where,
MBD - dead load bending moment along long span
MCD - dead load bending moment along short span
W - dead load of slab
M1, M2 - moment coefficients in dead load bending moment
along long span, short span respectively
μ - Poisson’s Ratio
34
By substituting the obtained values in Equations (4.8), (4.9) we get,
MBD = 87.5 (0.047 + 0.15 (0.01)) = 4.24 kN-m
MCD = 87.5 (0.01 + 0.15 (0.047)) = 1.5 kN-m
Dead load shear force = k × dead load × Q = 8.05 kN
Step 2: Live load bending moment and shear force:
In order to generate the maximum live load and the bending moment the
IRC class AA attached wheel (single) is placed on panel of slab. This has been
studied in the course CE0403-Transportation Engineering and (Ref.9).
Dispersion length of wheel = U = (0.85 + 2 × 0.04) = 0.93 m
Dispersion width of wheel = V = (3.6 + 2 × 0.04) = 3.68 m
Ratios,
K =
Referring to Pigeaud’s Curve K = 0.5,
Moment coefficient for short and long coefficient of slab
M1 = 0.1; M2 = 0.02
The short span and long span live load and bending moment are obtained by using
equation (4.8), (4.9).
MBL = 350 [0.1 + 0.15 × 0.02] = 35.35 kN-m
MLL = 350 [0.02 + 0.15 × 0.1] = 12.2 kN-m
As slab is continuous, design live load, bending moment an 80% of the actual and
considering impact factor of 25%
35
MBL = 1.25 × 0.8 × 35.45 = 35.35 kN-m
MLL = 1.25 × 0.8 12.2 = 12.2 kN-m
Step 3: Live Load Shear Force:
It can be calculated by approximation. Maximum shear can be obtained
by placing the wheel such that dispersion is present within the interior panel of slab.
Span wise dispersion length of wheel load = 0.85 + 2 × (0.04 + 0.25) = 1.45 m
Fig 4.19 Representation of dispersion of load on deck slab
This has been studied in course CE 0403 Transportation Engineering.
Clear length of panel = 5 – 0.2 = 4.8 m
=
From IRC: 21:2000 (Ref.13) for
= 2.08; K = 2.6 for continuous slab.
Effective width of slab = 2.6 × 0.774 × (1 -
) + (3.6 + 2 × 0.04) = 5.1 m
Live load per meter width of slab =
=
Shear force per meter width of slab =
Shear force considering impact = 1.2 × 45 = 56.5 kN
36
4.3.1.2 Design of slab:
This has been studied in the course CE 0303 Structural Design-II RCC
Structures (Ref.11).
Total moment acting along length, breadth of slab is,
MB = 35.5 (live load) + 4.24 (dead load) = 39.6 kN-m
ML = 12.2 (live load) + 1.5 (dead load) = 137 kN-m
Effective depth of slab is calculated using Equation (4.10),
d = √
(4.10)
Where,
d - Effective depth of slab.
M - Moment along width of slab.
Q - Coefficient as per IRC-21:2000
B - Width of slab.
d = √
= 131.16 mm
Adopt effective depth is 200 mm
The slab bridge deck comprising longitudinal and cross girders with the
deck slab may be considered as rigid grid structure for the purpose of analysis under
the concentrated live loads. Concentrated wheel load on the deck is shared between
the longitudinal girders depending upon the position of load, the number of girders
and their spacing (Ref. 6).
The bending moment calculated due to dead load and live load is used to
find out the moment co-efficient used in Pigeaud’s curve for the design.
37
Reinforcement:
1. Area of the steel in longer direction (Ast) is calculated by using the
Equation (4.11),
Ast =
(4.11)
Where,
Ast - area of steel in longer direction
M - effective moment along longer direction
- principal stress
j - co-efficient as per IRC: 21: 2000
d - depth of slab
By substituting obtained values in Equation (4.11) we obtain area of steel
required,
Ast =
= 1150 mm
2
Use 14 mm bars at 130 mm c/c, Area of steel provided = Ast = 1184 mm2
Effective depth available along long span using 10 mm diameter bars = 100 mm
2. Area of steel in transverse direction (Asd),
Asd =
= 423.6 mm
2
Use 10 mm bars are placed at 140 mm c/c
The area of the reinforcement in longer direction gives the area of the
steel bars to be used and then the spacing of the bars so that the design can be safe.
Now following this calculation the check for shear stress check has to be done to
ensure complete safety.
38
Check for Shear Stress:
Design shear force = dead load shear + Live load shear = 64.3 kN (Ref.10).
Nominal shear stress is calculated by using Equation (4.12),
Nominal shear stress =
(4.12)
V - Shear force
b - Width of slab panel
d - Depth of slab panel
Nominal shear stress = 0.306
Percentage of steel =
= 0.56
For M40 permissible shear stress = 0.32
And multiplication factor of 1.1 we get actual permissible shear stress
= 1.1 × 0.32 = 0.352
Since 0.306
< 0.352
Therefore, Shear stress in the slab is within permissible limits (Ref.15).
4.3.2 Design of Main Cable:
1. The main cable is modelled with cable elements. These are beam
elements with a very low bending stiffness. Also no shear forces exist for
the cable. The cable element is subjected to its own weight and accounts
for the slackening effects in cables under self-weight load.
2. Due to the relative small center to center distance of the hangers, the
effect of elastic stretch and lengthening due to change of geometry can be
neglected.
39
3. The cable spans a very short distance between each hanger. Various types
of cable systems are shown below and the modulus of elasticity values
before and after pre-stressing as per IS: 9282: 2002 (Ref. 16) are
discussed in table 4.1.
Table 4.1 Modulus of Elasticity of Ropes and Strands as per IS: 9282:2002
S. No High strength
tension components
Manufactured Steel
wires Modulus of
Elasticity(EQ)[
]
After pre stressed
Modulus of
Elasticity[
]
1 Spiral ropes 11.1×103 13.1×10
3
2 Full locked coil
ropes
10.3×103 13.1×10
3
3 Strand ropes 6.9×103 8.6×10
3
The design of main cable shall conform to IS: 9282: 2002 Wire Ropes
and Strands for Suspension Bridges Specification (Ref.16).
The following steps are considered to determine the cable dimensions
1. Analyzing ratio between variable load and self-weight acting on the
structure is found using Equation (4.13),
η =
(4.13)
Where,
η - Ratio between variable load and self-weight.
q - Variable load
g - Self-weight of the structure + permanent loading.
40
2. Assuming the maximum level of Δσ (principal stress).
3. Finding the maximum stress caused by the self-weight + permanent
loading and analyze the cable diameter (Ref.10).
Step by Step Procedure
Step 1: Variable Load q = 0.3 × traffic load
Traffic load = Equivalent Uniformly Distributed Load (EUDL)
= 147.9
Variable load = 0.3×147.9 = 44.37
Self-weight g = 115
girder (assume)
Cable weight = 5
diameter (d = 300mm)
Deck slab =30
asphalt layer of 40mm
Ratio between variable load and self-weight (η) =
= 0.3
Step 2: Assume maximum level of Δσ = 200
Step 3: Total permanent load Gd = Factor of Safety (1.35) × Self weight (g)
= 1.35× (150
) = 202.5
The Main Cable has both horizontal and vertical components of force.
The horizontal and vertical components of force are the most important factors which
will determine the nature of response of the structure towards any stimulus from any
disturbance due to dead loads or even live loads. However, the dynamic loads such
as wind loads and earth quake loads have not been taken into account in this analysis.
The design of main cables is followed by the design of the other important elements
which are described in the sections below. Hence the horizontal components and
41
vertical components have been used to design the deck and the value of the
horizontal component of tension in the cable is given by Equation (4.14),
H =
(4.14)
Where,
qG - uniformly distributed dead load
G - permanent load
Q - variable load
l length of the main span
f1 sag of the cable in main span
H = 91,688 kN.
So, the Horizontal component of Tension acting per cable is 45,844 kN.
The value of allowable cable stress is found by using graph given in Figure 4.20.
Fig 4.20 Graph between Δσ, η to find allowable cable stress
42
Step 4: The largest normal force Ncable is determined by equation (4.15),
N cable = √V2+H
2 (4.15)
Where,
V - vertical component of tension force
H - horizontal component of tension force
α1 - - angle between main cable and deck
H = 45,844 kN
V = 45,844 × tan33045’ = 30,632 kN
N cable = √V2+H
2 = 55,136 kN
The effective cross sectional area of cable required is determined by
Equation (4.16),
A req =
(4.16)
Where,
N - Normal force acting in the cable
σ - Maximum allowable cable stress
The effective cross sectional area of cable required by Equation (4.16),
A req =
=
= 1, 10,272 mm2
The effective cross area of the cable required which is calculated by using
Equation (4.16) is used to find out the diameter of the cable to be used for the bridge
elements and the value of the diameter is calculated as described below.
43
The diameter of cable is calculated by using Equation (4.17),
d = √ (
) (4.17)
Where,
d - diameter of cable
A - cross sectional area of cable
By substituting values in Equation (4.17) we get,
d = √ (
) = √ (
) = 374 mm
Hence a cable of 400 mm is taken for consideration for laying main cable.
4.3.3 Design of Hangers
As per IRC 5 Class AA loading, the axle load under tank load condition is
700 kN (Ref.5).
Under Fatigue load model condition is 0.7 times variable axle loading (Qik).
Variable loading
q = 0.3×150
traffic load (udl)
Q= 0.7×700 kN axle loads
The total Self weight (g) is sum of girder weight (assume), estimated
cable weight and asphalt layer, deck slab unit weight.
Self-Weight (g) = 115 + 5 30 = 150
1. Ratio between variable load and self-weight (η)
=
= 0.3
44
2. Maximum level of Δσ = 200
is assumed
3. Maximum allowable stress caused by self-weight and permanent loading
σ = 350
determined by using the design graph in Figure (4.20)
4. Total permanent load design value
Gd = γG × (115+ 5 +35) = 1.35 × 150 = 202.9
The value of the vertical force in hanger = 202.9
×30 m = 6087 kN for
2 suspenders
So, 3043.5 kN per each hanger
The effective cross sectional area of cable required is calculated by Equation (4.18),
A required =
(4.18)
Where,
- vertical force in hanger
- maximum allowable cable stress
A req - effective cross sectional area of cable
By substituting obtained values in Equation (4.18) we obtain value of area of cable
=
= 5,072.5 mm2
The effective cross sectional area of cable required A req = 5,072.5 mm2
The Diameter of suspenders is calculated by using Equation (4.17). By substituting
values in equation (4.17) we get the value of diameter of suspenders is 80 mm.
45
4.3.4 Design of Longitudinal Girder
This has been studied in the course CE 0304 Structural Design III-Pre
stressing of the deck.
Firstly, it is required to find Carboun’s reaction factor, for IRC class AA
loads which are arranged for maximum eccentricity as shown in Figure 4.21 (Ref.5).
Fig 4.21 Arrangement of class AA loads for maximum eccentricity on deck
Reaction factor for exterior girder (A or D).
RA =
(
) = 0.764 W1
So, Reaction factor for exterior girder (A or D) = RA= 0.764 W1
Reaction factor for interior girder (B or C)
RB =
= 0.588 W1
So, Reaction factor for interior girder (B or C) =RB = 0.588 W1
W = 700 kN; W1 =
RA = 0.764 ×
= 0.382 W = 267.4 kN
RB = 0.588 ×
= 0.294 W = 205.8 kN
46
The following are the dead loads from deck:
1. Load from suspension = 0.8
2. Load from front path = 7.2 kN-m
3. Load from deck slab = 6
Dead load from deck = 14
Total dead load = 2 × 14 + 10 × 6 = 28 × 60= 88 kN
It is shared by 4 girder equals. So, load acting on each girder = 22 kN
4.3.4.1 Dead Load of Main Girder:
Assuming a depth of 40 mm per meter span of the girder as has been shown
in Figure 4.22.
Overall depth of main girder = 40 × 40 = 1600 mm
Self-weight per meter run of girder = 0.5 × 0.45 × 24 + 1.1 × 0.2 × 24 = 10.7
Weight of cross girder (assume depth = 1 m) = 1 × 0.2 × 2 = 4.8
Fig 4.22 Dimensions of main girder
47
4.3.4.2 Dead Load Bending Moment and Shear of Main Girder
Reaction of cross girder as main girder = 4.8 × 2.5 = 12 kN
Reaction from deck slab = 22 kN
Total dead load girder including self-weight = 2.2 + 10.7 =
Maximum shear force = Reaction at support = 0.5 (12 ×7 + 32.7×40) = 696 kN
Maximum bending moment =
So, Maximum bending moment = 4600 kN-m
4.3.4.3 Live load Bending Moment
Fig 4.23 ILD for live load bending moment over deck
This has been studied in the course CE 0302 Structural Analysis-II
Indeterminate Analysis and (Ref.7 - 10) and the ILD is given in Figure 4.23.
Bending moment at centre of girder =
= 5390 kN-m
Bending moment for the outer girder = 1.1 × 0.382 ×5390 = 2268.878 kN-m
Considering impact and reaction factor
Bending moment for inner girder = 1.1×0.294 × 5390 = 1743.126 kN-m
Reaction of W1 on girder B = 63 kN
Reaction of W2 on girder A = 350 kN
So, Total load girder B = (350 + 63) = 413 kN
Maximum Reaction of Shear Force in Girder is calculated as under (Ref. 10).
48
Maximum reaction in girder B =
394.4 kN
Maximum reaction in girder A =
= 274 kN
Design Live Load Shear Force Considering Impact Factor:
Inner girder (B) = 394.4 × 1.1 = 433.84 kN
Outer girder (A) = 274 ×1.1 = 301.4 kN
4.3.4.4 Sectional Properties of Girder
Area of cross section = A
= 69.75 × 104
mm2
Distance of the centroid axis from top = Yt
=
= 615.15 mm
Distance of centroid axis from bottom = Yb
= 1500 – 615.15 = 884.85 mm
Moment of inertia of the section about centroid axis is
I = [
] (MI of top flange)
+ [
] (MI of web)
+ [
]
= 9.66 × 1010
+ 8.76 ×109 + 7.32 × 10
9
I =14.37 × 1010
mm4
Section modulus of bottom section
Zb =
=
2
49
Section modulus of top section
Zt =
= 2.33×10
8 mm
2
4.3.4.5 Check for Adequacy
By using the section property, sectional adequacy is verified (Ref.13).
The various design parameters considered are
fk = 50
; ;
fci = 40
fct = 20
ftw = 16.5
fbr = (η fct – ftw) = (0.85 × 20 - 0) = 17
ftr = (fcw – ηftr) = 16.5
Mq = 2268 kN-m
Mg = 4600 kN-m
Total Md = 6868 kN-m
Required section modulus for the bottom section of beam
Zmin =
= [
] × 10
6 = 1.74 × 10
8 mm
3
Zmin > 1.23 × 108 mm
3
4.3.4.6 Sections
Pre stressing force with maximum cover = 150 mm
Eccentricity is provided for pre stressing force is (884.5 - 150) = 734.5 mm
Pre stressing force P =
=
= 4725 kN.
50
Using 7 strands of 15.2mm diameter of cables
Therefore, force in each cables = 7 × 181.45 × 1500 = 1905 kN
Number of cable required =
Therefore, 3 cables are provided.
Area provided by 3 cables = 3 × 7 × 181.45 = 3810 mm2
The arrangement of cables at central section of girder is shown in Figure 4.24.
Fig 4.24 Placement of cables at centre span section
4.3.4.7 Permissible Tender Zone at Support Section
Check for eccentricity to avoid stress concentration at supports, the cables
are placed is such a way to satisfy eccentricity requirement (Ref.13 – 14).
E
= 687.4 mm
E
0 -
= -230 mm
51
The cables are arranged is parabolic profile providing are eccentricity of
150 mm towards top flange of beam at support section as shown in the Figure 4.25.
Fig 4.25 Arrangement of cables at support section
All the pre stressing design has been covered in the course CE 0304
Structural Design III - Pre stressing of the deck.
4.3.4.8 Check for Stress
The stress levels are section of beam located at centre of span (Ref.13).
1.
2.
3.
= 21.3
4.
5.
6.
52
7.
Stresses at transfer of pressure:
In top fibres, σt =
= 6.7 – 14.88 + 19.74 = 11.56
In bottom fibres, σb =
= 6.7 + 21.3 – 28.75 = - 0.75
Stresses at working stage
In top fibre, σt =
= 0.85 (6.7) – 0.85 (14.88) + 19.74 + 9.33 = 47.87
In bottom fibre, σb =
= 0.85 (6.7) + 0.85 (21.3) - 13.97 - 28.7 = -18.97
It is observed that stresses in top, bottom under both conditions is within permissible
limits.
4.3.4.9 Check for Ultimate Flexural Strength of Beam
The ultimate moment to be considered as per IRC: 18:2000 (Ref.12) is
MU = 1.5 Mg + 2.5 Mq = 15 × 4600 + 2.5 × 2268 = 12510 kN-m
Failure condition can occur by yielding of steel that is under reinforcement or by
direct crushing of concrete over reinforcement. The smaller of both values is
considered as ultimate moment of resistance of section for design
Type 1: Failure by yielding of steel is calculated using Equation (4.19),
MU = 0.9× db × AS × fP (4.19)
Where,
AS - area of tensile steel
db - depth of beam from maximum compression edge
fP - ultimate tensile strength for steel
53
By substituting values obtained in Equation (4.19),
MU = 0.9 × 1350 × 3810 × 1860 = 8.61 × 108 N-mm
Since, MU < Mq limit
So, redesign by assuming Ast = 6000 mm2
Mq = 13.5 × 109 N-mm > 1.57 × 10
9
Hence OK.
Type 2: Failure by crushing of concrete:
For T- beam section, the ultimate moment is calculated by Equation (4.20),
MU = 0.176 bdb2 fck +
(
) (4.20)
Where,
B - width of web
Bf - width of flange
T - thickness of flange
MU = 0.176 (200) (1350)2
× 60 +
) × 250 × 60
= 13,800 kN-m
4.3.4.10 Check for Ultimate Shear Strength of the Beam
Ultimate shear force to be considered is calculated using Equation (4.21),
Vu = 1.5 Sg + 2.5 Sq (4.21)
Where,
Sg - dead load shear force
Sq - live load shear force
Vu = 2140 kN
54
According to IRC: 18: 2000 (Ref. 7) the ultimate shear strength of the
section uncracked in flexure, Vw corresponds to the occurrence of a maximum
principal tensile stress, at the centroid axis of section of ft = 0.24 and
fck = 0.24 x 60 = 14.4
In the calculation axis of Vw, the value of pre stress at the centroid axis
has to be taken as 0.8fy.
The ultimate shear strength of the section is then calculated and found by
using Equation (4.22),
Vw = 0.67 bd √ (4.22)
Where,
b - width of the rib
Vw - ultimate shear strength of the section
d - overall depth of the member
ft - maximum principal tensile stress
fy - compression stress at centroid axis due to pre stress
(ft ) Maximum principal tensile stress = 0.24 × √ = 0.24 × √ = 1.859
(fy) Compression stress at Centroid axis due to pre stress =
= 5.75
Eccentricity of cables at the centre span = 734.5 mm
Eccentricity of cables at support = 150 mm
Net eccentricity = 734.5 – 150 = 584.5 mm
Slope of the cable = θ =
=
= 0.093
55
By substituting the values calculated we obtain the value of ultimate shear
strength by using Equation (4.22),
Vw =1069 kN
Ultimate shear resistance considered = 2140 kN
Ultimate shear capacity of the section = 1069 kN
Balance shear = 2140 – 1069 = 1071 kN
Shear reinforcement is to be designed to resist the balance shear
Use 10mm diameter stir ups and the spacing is given by Equation (4.23),
S =
(4.23)
S =
= 77.2 mm
Provide 10 mm diameter stirrups at 100 mm c/c near support and at a
spacing of 200 mm c/c near the centre of the span.
4.3.4.11 Design of Supplementary reinforcement
Longitudinal supplementary reinforcement at 0.15% of gross sectional
area is provided to limit the shrinkage cracks.
Area of steel = Ast = 0.0015 x 69.75 x 104
= 1046.25 mm2
14 mm diameter bars (8 numbers) are placed in the compression flange of the beam.
After this part of part of the design of the project work the last part of the design
work is the design of the end block which anchors the pre stressing cables so as to
increase the pre tensioning capacity.
56
4.3.4.12 Design of End Blocks
End block is designed to distribute the concentrated pre-stressing force
the anchorage. It shall have sufficient area to accommodate anchorages at the jacking
end and shall preferably be as wide as the narrowest flange of the beam (Ref.13).
Length of end block is in no case be less than 600 mm nor less than this
width. Generally, end blocks are provided at supports for a length of 1.5 m.
The bursting force generated during the post tensioning should be
assessed on the basis of the ultimate strength. The bursting force, Fbst existing in an
individual square and block located by symmetrically placed square anchorage or
bearing plate may be derived as follows:
Pk = force in each cable = 1905 kN
2ypo = 225 mm
2yo = 900 mm
Ratio (
) = 0.25
Bursting force = 0.23 x 1905 = 438.15 kN
Area of steel required to resist this tension =
= 1214 mm
2
Provide 12 mm bars at 100 mm c/c in the horizontal and transverse direction.
57
CHAPTER 5
CONCLUSION
5.1 CONCLUSION
The optimised design of the expected Self Anchored Bridge has been
finalized in this project report. The process has been supplemented by prototype
modelling to get a clear idea about realistic design parameters of a structure such as
Self Anchored Suspension Bridge.
The realistic design constraints have been taken into very serious
consideration as they form the basis of working on any project. As a result the
methodology followed has been formulated accordingly.
The results and discussion give the complete modelling, analysis and
design of the project. The work done using various software packages has been
provided in the respective topics of the Result and Discussion Chapter. It also
includes extensive design of the deck slab, girder, cables which form the most
fundamental elements of this study. The pylons and foundation have not been
designed in this project work as they would require more duration of work than
planned so they can be carried on for further study of this work. However certain
aspects such as dynamics of bridge have not been able to be covered in this study due
to the reason that such topics are beyond the scope of this project.
5.2 FUTURE SCOPE
This project has a highly extensive due to its diverse and interdisciplinary
nature. Therefore the future scope of such a project is very diverse .With respect to
finite element modelling and computational fluid dynamics this project would go to
an in depth study as these are the further fields of specialized study. It is
recommended that the same report work can be used to carry out in depth wind
analysis and design using the wind tunnel.
58
REFERENCES
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Suspension Bridges, Journal of Bridge Engineering, Vol. 4, page.
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Suspension Bridge to existing Kaluthara Bridge, Journal of
Structural Engineering, Vol. 2, page 61- 66.
3. Arie Romeijn et al (2008), Parametric Study on Static Behaviour
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4. IS: 875 (1987), Part III - Code of Practice for Design Wind Loads
for buildings.
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Road Bridges, Section-I - General Features of Design.
6. IRC: 6 (2010), Standard specifications and Code of Practice for
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59
12. IRC: 18 (2000), Code of Practice for Composition of Bridge
Specifications and Standards.
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