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DESIGN OF SINGLE PYLON CABLE STAYED BRIDGE A PROJECT REPORT Submitted by HARISH.R 411711103006 SATHYANARAYANAN.R 411711103031 in partial fulfillment for the award of the degree of BACHELOR OF ENGINEERING in CIVIL ENGINEERING PRINCE SHRI VENKATESHWARA PADMAVATHY ENGINEERING COLLEGE, PONMAR ANNA UNIVERSITY: CHENNAI 600025 OCTOBER 2014

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Page 1: Design of Single Pylon Cable Stay bridge

DESIGN OF SINGLE PYLON CABLE STAYED BRIDGE

A PROJECT REPORT

Submitted by

HARISH.R – 411711103006

SATHYANARAYANAN.R – 411711103031

in partial fulfillment for the award of the degree

of

BACHELOR OF ENGINEERING

in

CIVIL ENGINEERING

PRINCE SHRI VENKATESHWARA PADMAVATHY ENGINEERING

COLLEGE, PONMAR

ANNA UNIVERSITY: CHENNAI 600025

OCTOBER 2014

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ANNA UNIVERSITY: 600 025

BONAFIDE CERTIFICATE

Certified that this project report “DESIGN OF SINGLE PYLON CABLE

STAYED BRIDGE” is the bonafide work of “HARISH.R (411711103006) and

SATHYANARAYANAN.R (411711103031)” who carried out the project work

under my supervision.

Mrs.S. Kavitha Karthikeyan, B.E.,

Assistant Professor

HEAD OF THE DEPARTMENT

Department of Civil Engineering

Prince Shri Venkateshwara

Padmavathy Engineering College,

Ponmar

Chennai: 600 048

Ms. Snekha.G, B.E.,

Assistant Professor

SUPERVISOR

Department of Civil Engineering

Prince Shri Venkateshwara

Padmavathy Engineering College

Ponmar

Chennai: 600 048

Submitted for ANNA UNIVERSITY project viva – voce held on ……………….

INTERNAL EXAMINER EXTERNAL EXAMINER

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ACKNOWLEDGEMENT

We would like to express our sincere thanks to our lovable parents for their

loving support and encouragement.

We gratefully acknowledge our sincere thanks to our honourable Chairman

Dr. K. Vasudevan M.A., M.Phil., Ph.D., for giving his spontaneous and whole

hearted encouragement for completing this project.

We also thank Dr.V.Vishnu Karthik, M.D., Vice-Chairman for his enormous

support and suggestion throughout the period of project.

We are greatly thankful to our honourable principal Dr.T. Sounderrajan

M.Tech., Ph.D., for rendering the technical staffs for successful completion of the

project.

We express our sincere thanks with the sense of gratitude to our respectful Head

of Department Mrs.S.Kavitha Kathikeyan, B.E., for her interest and

encouragement shown in our project.

We sincerely thank our project guide Ms.Snekha.G, B.E., for her valuable

advice, encouragement, suggestions and guidance in technical knowledge for the

successful completion of our project.

We sincerely thank our project co-ordinator Mr.Ramesh.J, B.E., for his valuable

advice, encouragement and suggestions.

We also express our deep gratitude to all other faculty members and lab assistants

in our civil engineering department and all those were directly and indirectly

helpful in the completion of our project.

Last but not least, we thank our ALMIGHTY for enlightening us.

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ABSTRACT

This project focuses on designing a unique, safe, elegant and economical bridge

in India that helps to make a mark in the field of Structural Art. The type of

structure chosen for this project is a Cable Stayed Bridge. The structural cum

artistic factor of the project that qualifies it as Structural Art is that the bridge will

be designed in a way that only one supporting tower will exist to carry the entire

bridge, thus making it a “Single Pylon Cable Stayed Bridge”. Shahpura Pond of

Shahpura Jogger’s Park in Bhopal, Madhya Predesh is chosen as the site location

for this bridge. Bhopal has taken a lot of initiatives to increase the tourism, many

of which are civil related. The bridge is constructed over Shahpura pond with a

fifty metre span. It is constructed as a pedestrian bridge for the joggers and is

elliptical in shape to be supported by a single pylon. The improvement in the

conceptual design is the provision of extended sections of the elliptical deck to

counter balance the weight of the standard deck for maintaining the principle of

Cable Stay. For the structural design, the Guyon – Massonet method was adopted

as it satisfies the differential distribution of loads on a curved bridge deck and

also accounts for torsional moments in its design. With this design being

successful, fellow engineers throughout the country will gain awareness of this

field and India can show the world its engineering and artistic capabilities.

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TABLE OF CONTENTS

CHAPTER TITLE PG NO

List Of Tables i

List Of Figures ii

List Of Symbols iii

List Of Charts iv

1. Introduction 1

1.1. Structural Art 1

1.2. Bridges 1

1.3. Suspension Bridge 2

1.4. Cable Stayed Bridge 5

1.5. Single Pylon Cable Stayed Bridge 7

1.6. Site Location 8

2. Literature Review 10

3. Methodology 13

4. Conceptual Design 14

4.1. Dimensions 14

4.2. Counter Weight Concept 15

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5 Structural Design 18

5.1. Guyon – Massonet Method 18

5.2. Loading 18

5.2.1. Dead Load 18

5.2.2. Live Load 19

5.2.3. Wind Load 19

5.2.4. Earthquake Load 19

5.3. Currents 20

5.4. Effective Length 20

5.5. Design Of Bridge Deck 21

5.5.1. Data 21

5.5.2. Permissible Stresses 22

5.5.3. Cross Section Of Deck 22

5.5.4. Moment Of Inertia And

Sectional Moduli 23

5.5.4.1. Main Girder 23

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5.5.4.2. Cross Girder 26

5.5.5. Torsional Inertia 27

5.5.5.1. Main Girder 27

5.5.5.2. Cross Girder 28

5.5.6. Longitudinal Moment 29

5.5.6.1. Torsional Parameter 29

5.5.6.2. Weighing Factor 31

5.5.6.3. Dead Load 32

5.5.6.4. Live Load 34

5.5.7. Transverse Moment 35

5.5.7.1. Flexural Parameter 35

5.6. Reinforcement 39

5.6.1. Slab 39

5.6.2. Main Girder 40

5.6.3. Cross Girder 41

5.7. Design Of Extended Slabs 41

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5.7.1. Loads 42

5.7.2. Depth 43

5.8. Beam 43

5.9. Design Of Column 43

5.9.1. Loading Plate 43

5.9.2. Data 44

5.9.3. Main Reinforcement

5.9.4. Helical Reinforcement

5.10. Design Of Pile Foundation

5.10.1. Data

5.10.2. Dimensions

5.10.3. Longitudinal Reinforcement

5.11. Design Of Cables

6 Results And Conclusion 48

7 References 50

Appendix 51

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LIST OF TABLES

Table 1: Values For Ko 30

Table 2: Values For K1 31

Table 3: Distribution Coefficients 32

Table 4: 0 Values 36

Table 5: 1 Values 36

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LIST OF FIGURES

Fig 1 Distribution Of Load In An Arch Bridge

Fig 2 Forces Developed In A Suspension Bridge

Fig 3 Forces Developed In A Cable Stay Bridge

Fig 4 Types Of Cable Stayed Connections

Fig 5 The Langkawi Sky Bridge

Fig 6 Site Map

Fig 7 Initial Concept Design

Fig 8 Final Concept Design

Fig 9 Zones Of Earthquake

Fig 10 Arc Length Of An Ellipse

Fig 11 Cross Section Of Main Girder

Fig 12 Cross Section Of Cross Girder

Fig 13 Reference Station And Position Of Loads

Fig 14 Dead And Live Load Positions

Fig 15 Reinforcements Of Slab

Fig 16 Reinforcements Of Main Girder

Fig 17 View Of Extended Slabs

Fig 18 Reinforcements In Column

Fig 19 Reinforcements In Pile

Fig 20 Cross Section Of Cable

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LIST OF SYMBOLS AND ABBREVIATIONS

SYMBOLS ABBREVIATIONS

x X Coordinate

y Y Coordinate

L Effective Length

b Effective Width

P Live Load

tw Thickness Of Wearing Coat

fck Grade Of Concrete

fy Grade Of Steel

cbc Permissible Stress In Concrete In Bending Compression

st Permissible Stress In Steel In Tension

m Modular Ratio

j Lever Arm Coefficient

CG Centre Of Gravity

I,J Moment Of Inertia

i,j Moment Of Inertia Per Unit Length

Zt,Zb Sectional Modulus

a Effective Span

Io,Jo Torsional Moment Of Inertia

io,jo Torsional Moment Of Inertia Per Unit Length

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R Torsional Coefficient

K Total Distribution Coefficient For Longitudinal Moment

Torsional Parameter

Flexural Parameter

Ko Distribution Coefficient For Longitudinal Moment 1

K1 Distribution Coefficient For Longitudinal Moment 2

Weighing Factor

DKw Total Distribution Coefficient For Longitudinal Moment

Mdead Moment Due To Dead Load

Mlive Moment Due To Live Load

Mmean Mean Moment Per Unit Length

0 Distribution Coefficient For Transverse Moment 1

1 Distribution Coefficient For Transverse Moment 2

Distribution Coefficient For Different Values Of

My

Transverse Bending Moment

c Length Of Application Of Live Load

w Factored Load

l Effective Span Of Slab

d Effective Depth Of Slab

Ast Area Of Steel In Tension

Astd Area Of Distribution Steel In Tension

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Pu Axial Factored Load On Compression Member

Asc Area Of Steel In Compression

Ac Area Of Core Of Column

sp Diameter Of Helical Reinforcement

Dc Diameter Of Core

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LIST OF CHARTS

Chart No: 1 Influence Curves For Transverse Moment 37

Annexure B Transverse Moment Coefficients 52

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CHAPTER-1

INTRODUCTION

1.1. STRUCTURAL ART

Civil Engineering and Architecture are one of the oldest known subjects.

From the pyramids in Egypt to Venice in Italy, these two fields have dominated

throughout history and still continue to strive. In recent times these two have

merged to form “Structural Art”. A building can be classified as structural art

when it attains excellence in the areas of efficiency and elegance. The aim of

structural art is to create aesthetically pleasing, imaginative, and elegant

structures, while meeting the safety and serviceability requirements. Many

countries have started establishing their achievements in this field where as India

is yet to initiate the process, which is the idea behind this project. But before that,

a quick overview of the evolution of bridges shall be done.

1.2. BRIDGES

Bridges are one of the oldest types of structures ever to be built in the

world. The idea of the bridge was invented when man wanted to reach points

which were deemed inaccessible due to the presence of a physical obstacle.

The first ever bridges built can be traced back to early civilizations where people

used simple natural materials such as the log of a tree or a cluster of stones to get

over a small stream or river. From there bridges have been under constant

improvement to increase the efficiency. There are various types of bridges,

usually classified according to the shape of the bridge or the material used.

The bridge that dominated the initial years of history was the arch bridge.

Its design was simple and very efficient in connecting short spans. The arch

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bridge consisted of a set of heavy stones laid from one end to the other in the

shape of an arc of a circle. From a civil point of view, this meant that the entire

load that can act on the bridge is immediately transferred to the adjacent stone

and hence to the earth. Heavy stones were used as this system would work only if

the shape of the bridge was rigid.

FIG 1: DISTRIBUTION OF LOAD IN AN ARCH BRIDGE

But the arch bridge had some disadvantages. It could only cover short

spans and the cost of construction was high. Also, it was impossible in high rise

places to construct an arch. To overcome all these negatives, the concept of the

suspension bridge was invented.

1.3. SUSPENSION BIRDGE

The earliest traces of a suspension bridge dates back to before the 16

century. They were built with ropes tied between two points with a series of

wooden planks as the deck. This was the simplest form of a suspension bridge.

The suspension bridges that exist now are much more evolved.

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The idea of a suspension bridge evolved when it was impossible to

construct a normal arch bridge. In a normal bridge the supports are directly

beneath the bridge deck, spaced at equal intervals, so as to transfer the load from

the deck to the earth. It has to be understood that for this type of bridge to be

built, the soil below the bridge had to be strong in bearing and stable enough to

withstand the forces. When it so happened that the soil that takes the load was not

strong enough or was too aggressive to construct a series of supports, a new

technique had to be established. Thus the concept was reducing the number of

direct supports underneath the bridge and transferring the load to a limited

number of supports by means of an indirect support present above the bridge

deck. These indirect supports were steel cables. This breakthrough led to the

construction of various suspension bridges, the most famous one being The

Golden Gate Bridge in San Francisco, California or the The Akashi Kaikyō

Bridge in Japan which the world’s longest suspension bridge.

A typical suspension bridge consists of two towers or supports located at

the 1/3rd and 2/3rdpoints of the span. The main cable, which is bigger in diameter,

spans between the ends going over the two supports. From this main cable, the

secondary cables drop vertically down and are tied to the bridge deck. This

mechanism transfers the entire load from the deck to the towers via the steel

cables.

FIG 2: FORCES DEVELOPED IN A SUSPENSION BRIDGE

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Given all this, suspension bridges still have a few disadvantages and

inefficiencies;

i. The amount of steel and concrete used in the construction of a suspension

bridge is very high. Concrete is meant for compression and steel for

tension, since bending cannot be naturally overcome by the material, the

design has to be altered to make the towers carry both the direct and

bending forces and this decreases the efficiency of the bridge.

ii. The cost of maintenance is a huge drawback in suspension bridges. Usually

suspension bridges will be in constant exposure to moisture and other harsh

weather conditions. This results in high levels of corrosion in the steel

cables.

iii. The width of a suspension bridge is directly proportional to its span by a

very small ratio, which means that for larger spans, the width of the tower

and the deck automatically increase. This results in a very large centre of

gravity of the bridge and due to this the bridge can easily be damaged in

the occurrence of an earthquake.

iv. The stiffness of the bridge deck is very low in a suspension bridge, which

means that carrying concentrated loads or impact loads is very difficult for

the bridge.

v. The construction process of a suspension bridge is very time consuming,

tedious, and very dangerous as all the components are heavy and need to be

lifted to great heights.

vi. Since a large vertical area of the bridge consists of closely spaced steel

cables, the bridge is prone to vibrations during heavy winds or gusts.

To overcome these inefficiencies, Cable Stayed Bridges were introduced.

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1.4. CABLE – STAYED BRIDGE

The Cable Stayed Bridge is a sub category of Suspension bridges. The

oldest application of the cable stayed bridge concept was found in the 17th century

but the use of this design was prominently seen throughout the 1800s.The earliest

known surviving example of a true cable-stayed bridge in the United States is

E.E. Runyon's largely intact steel bridge in Bluff Dale, Texas (1890).

In a Cable Stayed bridge, the main cable is eliminated and the cables are

connected directly from the deck to the tower. This way, all the steel cables are in

tension and are used to their full efficiency. Due to the direct connection of cables

to the pylon, all forces acting on the members are axial. The steel cable is

stretched straight between the pylon and the deck which means it’s subjected to

axial tension, and the pylon has half of the total load acting on either side of it

which means the resulting force is direct compression.

FIG 3: FORCES DEVELOPED IN A CABLE STAYED BRIDGE

The bending moment in a Cable Stayed bridge is very less, due to the direct

forces. This reduces the amount of steel and concrete required by a large scale,

making the bridge more efficient and more economic than the suspension bridge

by reducing the cost of maintenance. With the reduced bending moments, the

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width of the deck can also be reduced. This gives the bridge a small centre of

gravity and thus automatically makes it safe against earthquakes.

The most common type of cable-stayed bridges is a bridge with two pylons

and three spans. The length of side span is 30-40 % of the mid span. No massive

earth anchoring structures are needed. The number of cable plains on the deck

varies with each bridge, but a bridge with three cable plains and two lanes is the

most efficient, reducing the bending moment to 1/4th of the original value.

There are various types of Cable Stayed bridges, based on the type of connection

of the steel cables. They can be Harp type, Fan type or radial type, Mono or

single cable type, or star type. They are given in the diagram below;

FIG 4: TYPES OF CABLE STAYED BRIDGE CONNECTIONS

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Out of these four types, the fan pattern cable connection is the most efficient for

many reasons;

i. The compressive stresses are not induced at the same point in the pylon but

are distributed vertically.

ii. The horizontal forces that develop in the deck are reduced by a large scale.

iii. The vertical component of the cables increase which makes the forces

acting on the pylon more direct.

iv. The cables extend to the ends of the span which decreases the longitudinal

bending considerably.

One major disadvantage of the fan pattern is that the construction of the anchors

and its design is difficult and must be done carefully.

The most important feature in a Cable Stayed bridge is that the two or three

pylons at the centre of the span are enough to carry the entire load of the bridge.

The ends of the bridge need minimum support and carry minimum load. This

means that using the concept of Cable Stay, bridges can be built with a cantilever

type structure with the pylon at one end of the span, which brings up the topic of

this project; Single Pylon Cable Stayed Suspension Bridge.

1.5. SINGLE PYLON - CABLE STAYED BRIDGE

A single pylon cable stayed suspension bridge comes under the category of

“Structural Art”. These type of bridges are designed for the sole purpose of

marking how far civil engineering has come and how much can be accomplished.

The beauty of this bridge type is that the entire bridge is supported by one pylon

alone.

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This is accomplished by making the shape of the bridge deck curved and

positioning the single pylon at a neutral point within the curve. The shape of the

deck is usually parabolic and the pylon is positioned at the centre of gravity of the

curved deck. The best example for a Single Pylon Cable Stayed bridge is the

Langkawi Sky Bridge, Malaysia. The Sky Bridge is one of the most successful

curved pedestrian cable-stayed bridges in the world. This 125m engineering

marvel is built 700m above sea level to access the famous mountain peak Gunung

Mat Chinchang. It has become a popular tourist attraction ever since its erection

in 2005.

FIG 5: THE LANGKAWI SKY BRIDGE, MALAYSIA

1.6. SITE LOCATION

The city of Bhopal has always had a keen eye on promoting its city. It has a

lot of significant historical places in the city many of which are civil related.

Bhopal created the first ever piped water supply system in the early 1940s. It also

holds the oldest ever man made artificial lake, called the Upper Lake of Bhopal.

This lake was built in the 11th century by King Bhoj. In recent times, the state

government increased the yielding capacity of the lake from 86MLD to 135MLD

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and to promote an aesthetic view to the city, Shahpura Joggers Park was

constructed. An integral part of this park is the artificially created Shahpura Pond,

over which the Single Pylon Bridge is to be designed.

FIG 6: SITE MAP

The Shahpura Park is a very important land mark in the city with people

flocking in and out frequently. The presence of a jogger’s track that goes around

the pond is what makes this the ideal site location for a Single Pylon Stayed

Cable Bridge.

The bridge, after being constructed, would increase the aesthetic

appearance of the pond, and it will receive acclamation from all over for being

the first ever Single Pylon Bridge in India.

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CHAPTER 2

LITERATURE REVIEW

1. The report, “Seasonal Analysis of Soil Sediment of Shahpura Lake” a part

of the International Journal of Environmental Science and Development, was

done by Anu, et.al.,. In this report, the soil samples of Shahpura Lake were

analyzed due to the increase in garbage dumping near the lake. During the

study period Physico–chemical parameters such as pH, Moisture content, Bulk

Density, Chloride of soil was assessed as per the standard methods.

2. The report “Physicochemical Analysis of Water Quality of Shahpura Lake

Bhopal” was done by Shalini Shivhare, et.all,. This report was done in

reference to Scenedesmus Obliquus and Monoraphidium Minutum Algae. The

main aim of this project was to study the biological life forms of the lake but

for that the water properties like temperature, turbidity, pH, Electrical

Conductivity, Total Suspended Solids, Total Dissolved Solids, etc of the lake

had to be known.

3. The report “Design of Bridges, Cable Stayed Bridge” was done by Jani

Juvani and Olli Lipponen. This report explains the concept of cable stayed

bridges, its basics, history, design, etc. Each component of the bridge is

explained separately with two case studies at the end. From this report, we

learnt the advantage of cable stayed bridges over a normal suspension bridge.

4. The report “Cable – Stayed bridges” was written by Man-Chung Tang of

T.Y Lin International. This report thoroughly explains the configuration to

loading, design and finishing of a cable stayed bridge. From this the general

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layout, the static and dynamic load conditions of a cable stayed bridge were

taken.

5. The project report “Design of a Pedestrian bridge crossing over Coliseum

Boulevard” was done by Renan Constantino, et.all,. The Indian Standard

codes do not have a provision for pedestrian loading and thus the values of

forces developed in a pedestrian bridge were obtained from this report.

6. This book “Design of bridges” was written by Professor N.Krishna Raju. In

this, the concept of suspension bridges, cable stayed bridges and culverts are

given. The design of Tee Beam Deck Slab, Longitudinal girders and Cross

girders were adopted from this book. Also the requirements and permissible

stresses required for the design of Cables were obtained from this book.

7. The book “Design of Reinforced Concrete Elements” was also written by

N.Krishna Raju. The designs of basic RC structural elements such as beam,

slab, column, etc are given in this book. The design of Columns and Pile

groups were obtained from this book and used in the design.

8. The report “Cable-loss analysis and collapse behavior of cable-stayed

bridges” was done by M.Wolff and U. Starossek. In this review, they

analysed present cable stayed bridges for the losses developed in them. This

paper shows the possibilities and limits of such an approach for cable-stayed

bridges.

9. The thesis “Behavior and Analysis of horizontally curved and skewed I-

girder bridge” was written by Ozgur Cagri. This thesis investigates the

strength behavior of a representative highly skewed and horizontally curved

bridge as well as analysis and design procedures for these types of structures.

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10. The report “Cable – Stayed bridge” written by “Partha Pratim Roy” as a

part of International Journal of Science and Advanced Technology explains

the various features and working of a stayed cable bridge. It also clearly states

the advantage that a cable stayed bridge has over a normal suspension bridge.

11. The report "Excreta Matters" by the Centre for Science and Environment is

a profile of the water and sewage situation in 71 Indian cities - including

Bhopal. The history of Bhopal’s water was obtained from this.

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CHAPTER 3

METHODOLOGY

Initial Analysis

Type of Structure

PurposeSite

Location

Data collection

Pond dimension

Water Properties

Soil Properties

Planning Site MapPlan &

ElevationConceptu--al design

Design Stage 1

Loading Deck SlabBeam & Girder

Design Stage 2

Pylon Foundation Cables

Report Review Results Final Draft

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CHAPTER 4

CONCEPTUAL DESIGN

4.1. DIMENSIONS

The bridge has to be designed around a single column and hence the name

Single Pylon. For this to be achieved the shape of the bridge deck cannot be

straight, it has to curved. The Langkawi Sky Bridge has a parabolic shape for the

deck, this was apt for the bridge as the 125metre span did not reveal the sharp

turn of the parabolic shape, but in the case of a smaller span the parabolic curve

will not be suitable and also the sharp turn will be a hindrance to the joggers

using the bridge. Considering all these factors, the shape of the bridge deck was

taken as Elliptical.

The maximum length and width of Shahpura pond is approximately 200m

and 75m respectively. The joggers track goes around the perimeter of the frustum

shaped pond. The ideal start and end points of the bridge was found to be at the

approximate center of the length, parallel to the width of the pond. This position

is at equidistance from the upper and lower widths of the pond, which avoids the

redundancy of two paths being too close to each other. Also, this position

provides the joggers with a similar but relatively shorter path to jog on. Another

advantage of this position is that it restricts the span of the bridge to 50metres,

which is the most optimum option in this case.

To accommodate ample space for two jogging lanes on the bridge, the

width of the deck was taken as 2 metres with a 600 millimeter kerb on either

side. This brings the effective span of the bridge deck to 3.12 metres. The kerbs

are provided to accommodate for steel railings at the edges of the bridge.

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The column has to be placed at the centre of gravity of the elliptical shaped

bridge deck, which is the centre of the ellipse. The distance of the bridge deck

from the centre of the ellipse (the minor axis) was restricted to 7.5 metres as to

maintain the shape of an ellipse and also to make the structure cost efficient. A

bigger minor axis results in a large amount of concrete and steel to be used, to

avoid this it was taken as an optimum 7.5m.

The column is placed at the centre of gravity of the ellipse. The material

used for the column is concrete as the major forces acting on it will be direct

compression. The column will be a cylindrical column but taking into account

that this bridge is for aesthetic appearance, an external plastering for the column

is given making it appear as a Frustum of a Pentagonal Cone. The grade of

concrete used for this is M50 and steel grade is Fe500.

The deck of the bridge needs to be supported by girders. The girder

adopted for this design is T – Beam Girder. This was chosen as it can sustain

tension, compression and also torsion to an extent. Also, according to our Guyon

– Massonet design, T – beam girders are most suitable for bridge decks subjected

to torsion. Apart from the main longitudinal girders, transverse girders or cross

girders are provided at equal intervals. The girders are of concrete and

reinforcements in steel. The grades used are M25 and Fe415.

4.2. COUNTER WEIGHT CONCEPT

To increase the design efficiency of the bridge, the concept of counter

weight was applied to the bridge.

Usually straight span cable stayed bridges work under this concept where

the cables stretching on both sides in the longitudinal direction of the span carry

equal weight and hence produce the same moment on the column but in opposite

directions. These moments, being equal in magnitude, cancel each other out and

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result in only a direct compression force on the column. This same principle

cannot be directly adopted in Single Pylon Cable Stayed Bridge as the deck spans

only on one side of the column.

FIG 7: INITIAL CONCEPT DESIGN

In the above case, the column must be designed to support a cantilever type

load which breaks the cable stayed principle. To rectify this, the elliptical bridge

deck was extended by 1/3rd of its original length on both sides of the column

forming a partially closed ellipse with the middle part of the span missing.

The extended parts of the span are designed to have separate dimensions,

so that the total weight that can act on the right side of the bridge also acts on the

left side. And when these two sides are connected via cables, the moments

developed cancel each other out and results in a direct compressive load of both

weights put together.

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FIG: 8 FINAL CONCEPT DESIGN

The above figure (FIG: 8) shows the final design concept of the bridge.

This way, the same principle of balancing weights is applied but not directly. In

this the principle is applied laterally to the span of the bridge since the column

and the deck are not in the same axis, unlike straight cable stayed bridges.

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CHAPTER 5

STRUCTURAL DESIGN

5.1. GUYON – MASSONET METHOD

The conventional method of design for bridge decks could not be adopted

as they are for straight decks. The Guyon – Massonet method provides a design

that can be adopted for almost any type of bridge as it can cover both extremes of

torsional moments with only a single set of distribution coefficients. Since the

bridge deck in this case is curved, there is a possibility of a large amount of

torsional moments that can develop in the deck slab and girder. Hence this

method was adopted.

5.2. LOADING

Bridges are susceptible to three types of loading; dead load, live load and lateral

load.

5.2.1 DEAD LOAD

The dead load for this bridge includes the self weights of railings, deck slab

and girders. All members of this structure are in concrete so they share a common

unit weight of 25 kN/m2. The load is transferred from the deck slab to the girders

to the column via the cables and then to the foundation. It has to be noted that the

distribution of the dead load among the components of the bridge is not equal.

The extension spans of the bridge are of different dimensions (greater) and are

completely filled with concrete, which means the dead load at that area, is more.

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5.2.2 LIVE LOAD

The main live load of bridges is from dwellers and joggers on the bridge. It is

important to consider the fact that more force is applied per person when he/she is

jogging when compared to walking. Since the provision for pedestrian loads were

not found in Indian Standard Code books, the minimum live load of a pedestrian

was obtained from AASHTO (American Association of State Highway and

Transportation Officials) as 100psf. This value, when converted to SI units equals

5kN/m2. A factor of safety of 1.5 was adopted as per limit state design. In the

design of bridges, the area of impact of a load has to be determined. In case of

vehicular loads, the area of impact is 85cm (which is the average distance

between the tires) and in pedestrian bridges, 50cm was adopted (the area around

one foot).

5.2.3 WIND LOAD

The city of Bhopal falls on the lower side of the range of wind intensities

which means the load of the wind can be negligible. Also the overall height of

the bridge is only 10 metres which is not greatly affected by the wind forces.

5.2.4 EARTHQUAKE LOADS

Bhopal also falls under the lower side of Seismic prone areas, which means

it will not be affected by earthquakes. Apart from this, Cable Stayed Bridges are

safe against earthquakes as they have a low centre of gravity.

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FIG 9: SIESMIC ZONES OF MADHYA PRADESH

5.3. CURRENTS

Usually structures built in water bodies are prone to loads caused by waves,

tides or currents, but since Shahpura pond is an artificial pond under a controlled

environment, there is no effect on the pylon or foundation of the bridge.

5.4. EFFECTIVE LENGTH

The span of the bridge is 50m but since the deck is curved, the effective

length increases. Considering points A,B,O and constructing a circle with AB as

diameter the formula for the arc length of an ellipse is given by;

AB = 2 2( ) ( )

2 1 2 12 2x x y y

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FIG 10: ARC LENGTH OF AN ELLIPSE

The value of half of the arc length was found to be 29.329m. Adding the

extended spans on the other side of the column, the total arc length of the deck

comes to 97.76m. This is obtained by dividing the half arc length by 3 and

obtaining the length of one slab of the bridge which is 19.552m. For design

purposes the length of one slab is rounded off to 20 metres.

5.5. DESIGN OF BRIDGE DECK

5.5.1. DATA

1. Clear width of walkway = 2m

2. Width of kerbs = 0.6 x 2 = 1.2m

3. Span of one deck slab = 19.552 say 20m

4. Live load = 5 kN/m2

5. Thickness of wearing coat = 50mm

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6. Concrete Mix = M25

7. Grade of steel = Fe415

5.5.2. PERMISSIBLE STRESSES

1. Permissible stress in Concrete in Bending Compression: cbc = 8.3 N/mm2

2. Permissible stress in Steel in Tension: st = 200 N/mm2

3. Modular ratio: m = 10

4. Lever Arm coefficient: j = 0.90

5. Q = 1.10

5.5.3. CROSS SECTION OF DECK

The deck is designed as a Tee – Beam deck with longitudinal and lateral

girders.

Two main (longitudinal) girders are provided along the length of the bridge

deck at 600mm centre to centre spacing.

Cross girders are provided perpendicular to the main girders at a 4m

interval, which means that there will be five cross girders for a single span

of slab.

Since the bridge is a pedestrian bridge, thickness of the deck slab is taken

as 150mm.

Width of main girder is taken as a nominal 300 mm.

Depths of main and cross girders are taken equal for easier calculations.

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Depth = 6cm per metre span = 6 x 20m = 120cm D = 1200mm

Subtracting flange thickness, 1200 – 150 = 1050 say d = 1000 mm

5.5.4. MOMENTS OF INERTIA AND SECTION MODULI

The moment of inertia and the section modulus of both the girders are

found in this step. They are needed to access the stability of the assumed

dimensions. The distribution of the load form the deck to the girder is based on

the shape and size of the girders.

5.5.4.1. MAIN GIRDER

FIG 11: CROSS SECTION OF MAIN GIRDER

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Effective width of the main girder is the same value of the centre to centre

distance between the girders which is 600mm.

Centre of Gravity

The standard formula to find the centre of gravity of an unsymmetrical

section is given below;

1 1 2 2

1 2

a y a yCG

a a

The flange portion of the girder is taken as the first area and the web

portion as the second and their respective centre of gravities are measured from

the top of the tee beam.

CG =6

3

(600x150x75) (1000x300x575) 179.25x10459.62

(600x150) (1000x300) 390x10

CG = 460mm

Using the value of Centre of Gravity the difference between the common

centroid and the material centroid is measured for both the flange and the web, to

be used in finding the Moment of Inertia.

Moment of Inertia

Similar to the centre of gravity, to find I, the section is divided into two

parts; web and flange.

3 22 21 1 2 2

1 1 2 2I=12 12

bd b dAh A h

I3 3

2 2300x1000 600x150300x1000x190 600x150x385

12 12

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25

I= 10 45x10 mm

To find the distribution coefficient, the Moment of Inertia per Spacing

between the girders is used. This is done as the distribution is the same between

equal spans amongst girders.

i = I

B =

105x10

600

i = 88.33 x 106 mm4/mm

Section Modulus

The section modulus is found by dividing the Moment of Inertia with the

respective kern distances.

IZt yt

= 105x10

460 = 108.69 x 106 mm3

IZ

b yb

= 105x10

690= 72.463 x 106 mm3

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5.5.4.2. CROSS GIRDER:

Effective flange with of the cross girder is equal to the centre to centre distance

between the girders that is 4000mm.

FIG 12: CROSS SECTION OF CROSS GIRDER

Centre of Gravity

1 1 2 2

1 2

a y a yCG

a a

CG =(4000x150x75) (1000x300x575)

241.67(4000x150) (1000x300)

CG = 242mm

Moment of Inertia

The Moment of Inertia for the cross girder is represented by using J and j,

to differentiate between the two girders.

3 22 21 1 2 2

1 1 2 2J=12 12

bd b dAh A h

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J3 3

2 24000x150 300x10004000x150x92 300x1000x408

12 12

j = J

B =

108.114x10

4000

j = 20.225 x 106 mm4/mm

Section Modulus

The section modulus is found by dividing the Moment of Inertia with the

respective kern distances.

JZt yt

= 108.114x10

242 = 335.287 x 106 mm3

JZ

b yb

= 108.114x10

908

= 89.36 x 106 mm3

5.5.5. TORSIONAL INERTIA

The Torsional Inertia of the girders also has to be found as the girders are

subjected to both moments and torsion.

5.5.5.1. MAIN GIRDER

Torsional Inertia = Io or Jo = Ra3b

Where ‘a’ and ‘b’ are the shorter and longer spans of the section and ‘R’ is a

constant.

Flange

6004.00

150

b

a R = 0.281

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28

Web

10003.33

300

b

a R = 0.269

Io = 3 3(0.281x150 x 600) (0.269x300 x1000)

Io = 0.783 x 1010 mm4

Torsional Moment per width:

io = oI

B =

100.783x10

600

io= 13 x 106 mm4/mm

5.5.5.2. CROSS GIRDER

Flange

400026

150

b

a R = 0.333

Web

1000

3.33300

b

a R = 0.269

Jo = 3 3(0.333x150 x 4000) (0.269x300 x1000)

Jo = 1.175x 1010 mm4

Torsional Moment per width:

jo = oJ

B =

101.175x10

4000

jo = 2.939 x 106 mm4/mm

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29

5.5.6. LONGITUDINAL MOMENT

To calculate the longitudinal moments produced in the deck, the

distribution of the loads from the deck slab to the girder have to be studied. The

distribution coefficient ‘K ’ depends on the torsional parameter and flexural

parameter.

5.5.6.1. TORSIONAL PARAMETER

2

Gi jo o

E

ij

Assume G = 0.4E

0.4 615.9x102

151.69x10

E

E

= 0.278

Using the values of , the values of distribution coefficients for

longitudinal moments 0K and 1K are determined with which the value of K is

calculated.

The values of the distribution coefficients corresponding to =0 and =1

are presented by ROWE for five reference stations. Since the bridge designed in

this project is only for pedestrian roads and not for vehicular loads and also since

the width of the bridge is actively only 2 metres, the number of reference points

were brought down to three.

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30

FIG 13: REFERENCE STATION AND POSITION OF LOADS

The values for 0K and 1K for = 0.20 are given below;

TABLE 1: Values for Ko

Reference

point/Load

point

-b -b/2

0

b/2 b

0 0.94 0.97 1.06 0.97 0.94

b/2 -0.53 0.25 0397 1.72 2.49

b -1.90 -0.53 0.94 2.49 4.00

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TABLE 2: Values for K1

Reference

point/Load

point

-b -b/2 0

b/2

b

0 0.96 1.00 1.03 1.0 0.96

b/2 0.86 0.93 1.00 1.07 1.13

b 0.75 0.86 0.96 1.13 1.35

5.5.6.2. WEIGHING FACTOR

The weighing factor is multiplied with 0K and 1K values for each

reference point and load point are represented in tables 7.5, 7.6 (Design of

Bridges – N.Krishna Raju).

The weighing factors provided are for IRC Class AA vehicular loads. The

values taken from it are modified to be substituted in this pedestrian bridge. The

value of the load is changed but the positions of the loads that create maximum

bending moment are kept the same.

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32

TABLE 3: DISTRIBUTION COEFFICIENTS

Reference Points -b -b/2 0 b/2 B

0K 1.924 2.355 2.896 3.55 1.675

0

2

K 0.962 1.177 1.448 1.775 0.836

1K 2.972 2.942 2.947 3.134 3.325

1

2

K 1.486 1.471 1.473 1.565 1.662

1 0

2 2

K K

0.884 -1.294 0.089 -0.775 0.080

Thus the distribution coefficient for Longitudinal Girders is obtained by,

DKw = 1.020 + 1.537 1.020

x 0.330.78

= 1.238

5.5.6.3. DEAD LOAD

Slab = 0.15 x 24 = 3.60 kN/m2

Wearing course = 0.05 x 22 = 1.10 kN/m2

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33

Slab + Wearing course = 4.70 kN/m2

Kerb = 0.3 x 0.6 x 24 = 4.32 kN/m2

Railing = = 1.50 kN/m2

Kerb + Railing = = 5.82 kN/m2

Main Girder = 0.3 x 1 x 24 = 7.20 kN/m2

Cross Girder = 0.3 x 1 x 24 = 7.20 kN/m2

Reaction of Main Girder due to weight of cross girders = (7.2 x 0.6) = 4.32 kN

Reaction from the deck slab = (4.7 x 0.6) = 2.82 kN

Maximum Bending Moment at centre due to dead load:

Mdead = 22.82x20 4.32x20 4.32x20

8 4 4

Mdead = 184.2 kNm

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34

5.5.6.4. LIVE LOAD

FIG 14: DEAD AND LIVE LOAD POSITION

Mmean = [(75 x 10) - (75 x 0.25)] = 731.75 kNm

Mlive = 1.1x x

3

DK Mw mean

= 1.1x 1.238x 731.75

3

Mlive = 331.93 kNm

Total moment on the Exterior Girder = 516.138 kNm.

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5.5.7. TRANSVERSE MOMENT

The distribution coefficients for transverse bending moment are 0 and 1 .

5.5.7.1. FLEXURAL PARAMETER

0.25

2

b i

a j

2b = Effective width of the deck = 0.6 + 2 + 0.6 = 3.12 m

2a = Effective span of deck = 20 m

0.251.56 3.33

20 20.285

= 0.111 (Very Low)

The minimum value for is 0.20, but the value obtained is 0.111 which

signifies that the bridge deck has very low flexure and is rigid. The values for the

distribution coefficients are found out by plotting an influence curve between

,3 ,5 and the reference points and loading points.

To plot this, the curve Transverse Moment coefficients at reference stations

for various load eccentricities were used. ( Fig 7.3, Design of Bridges, N.Krishna

Raju). The value for the coefficients was dependent on the reference point curve

and the corresponding value in Y axis for the theta value in X axis. This was done

for both 0 and 1 and the values are tabulated in the next page.

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TABLE 4: 0 VALUES

Reference/

0 b/2 b 1 2

4

0x10

0.20 2500 -100 -2500 2500 250 2650

0.60 1800 -250 -2200 1800 -200 950

1.00 1200 -300 -500 1200 -300 1300

TABLE 5: 1 VALUES

Reference/

0 b/2 b 1 2

4

1x10

0.20 2800 750 -1800 2800 800 5350

0.60 1500 150 -500 1500 250 2900

1.00 1000 -20 1000 1000 0 2980

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CHART 1: INFLUENCE CURVES FOR TRANSVERSE MOMENT

-3000

-2000

-1000

0

1000

2000

3000

Reference points

INFLUENCE CURVES

θ0

3θ0

5θ0

θ1

3θ1

5θ1

(1) 2 b/2 b

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From the influence curves the values of 0 and 1 for the different values of

theta are calculated as follows;

= 0.265 + (0.575 – 0.265) x 0.161 = 0.314

3

= 0.895 + (0.290 – 0.075) x 0.161 = 0.126

5

= 0.130 + (0.298 – 0.130) x 0.161 = 0.157

Transverse Bending Moment = My

3 5sin sin sin

3 52 2 24

1 3 5

c c c

a a apbM y

P = 150

0.5 = 300 kN/m c =

0.5

2 = 0.25 m

2b = 3.12 b = 1.56 m

2a = 20 m

0.25 3 0.25 5 0.250.314sin 0.126sin 0.157sin

4x300x1.56 20 20 20

3.14 1 3 5M

y

My = 15.339 kNm

Total Moment on Cross Girder = 61.357 kNm/m.

Page 53: Design of Single Pylon Cable Stay bridge

39

5.6. REINFORCEMENT:

5.6.1. SLAB:

Dead Load = 0.15 x 3.12 x 24 = 11.232 kN/m2

Live Load = 100 psf = 5 kN/m2

16.232 kN/m2

Factored Load = 16.232 x 1.5 = 24.35 kN/m2.

Moment = 2

8

wl =

3 224.35x10 x3.12

8 = 29.629 x 106 Nmm

Ast = st

M

jd =

629.629x10

200x0.9x150 = 1097.37 mm2

Provide 6 numbers of 16mm diameter bars at centre to centre spacing of 150 mm

Distribution reinforcement

Astd = 0.12% x b x D = 0.12

100 x 1000 x 150 = 180 mm2

Provide 10mm diameter bars along the length at a centre to centre spacing

of 300mm

An additional Reinforcement with Fe250 bars for an area of 1030 mm2 is

provided in the slab at 150mm from the soffit of the slab. This is to withstand the

small local vibrations and variations that occur in the slab. Provide 10 numbers of

10 mm diameter bars of Fe250 grade at a centre to centre spacing of 150mm.

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FIG 15: REINFORCEMENT IN SLAB

5.6.2. MAIN GIRDER:

Ast = M

jdst =

6516.138x10

200x0.9x1000 = 2867.40 mm2

Provide 10 numbers of 20 mm diameter bars at a centre to centre spacing of 110

mm. Provide 10 mm diameter 4 legged stirrups at 150 mm c/c throughout the

length of the longitudinal girder.

FIG 16: REINFORCEMENT OF MAIN GIRDER

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41

5.6.3. CROSS GIRDER:

Ast = M

jdst =

661.375x10

200x0.9x1000 = 340 mm2

Minimum Ast to be provided = 0.3% x b x D

Ast = 0.3

100 x 300 x 1000 = 900 mm2

Provide 4 numbers of 16 mm diameter rods at a spacing of 120 mm centre to

centre.

Provide 10 mm diameter 2 legged stirrups at spacing 150 mm centres throughout

the length of the cross girder.

5.7. DESIGN OF EXTENDED SLABS

These two spans of the bridge were designed separately. They had to be

designed in such a way that the total load acting on spans A to C was balanced by

these two spans AE and CD. For this, the total weight was converted into volume

of concrete required and using the volume the dimensions of the spans were

determined.

5.7.1. LOADS:

Slab and Wearing course= 4.7 x 3.12 x 58 = 850.512 kN

Kerb and railing = 5.82 x 58 = 337.560 kN

Main girder = 2 x 7.20 x 58 = 835.200 kN

Cross girder = 14 x 7.20 x 3.12 = 314.496 kN

Live Load: 5 x 3.12 x 58 = 904.800 kN

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Total load =3242.568 kN

5.7.2. DEPTH

Total weight of normal span = 4900 kN

Volume of concrete required = 4900 / 24 = 205 m3

Volume for one span = 205/2 = 102 m3

1 = 20 x 3.12 x 0.150 = 9.36 m3

2 = 1 x 20 x 1 x 3.120 = 62.4 m3

3 = 0.5 x 2 x 20 x x x 1.11 = 22.22x m3

1 + 2 +3 = 102 m3

Solving the equations, we get x = 1.36 m

FIG 17: VIEW OF EXTENDED SLAB

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43

The reinforcements of the girders are extended to these sections as well.

5.8. BEAM:

A horizontal beam is provided for additional support and mainly to prevent

the bridge from horizontal motion caused due to any sudden external forces like

wind, etc. The beam is designed as a PRE FABRICATED CANTILEVER

BEAM subjected to a minimum point load at the free end. The beam is connected

to the column which means that the principle of single pylon bridge is not

violated.

5.9. DESIGN OF COLUMN

5.9.1. LOADING PLATE

A loading plate is provided below the anchorage of the three cables. This is

done to convert the eccentric positions of the cables to axial position. The plate

bears the entire load and transfers it to the column as an axial direct load. The

thickness of the plate is 60 mm.

5.9.2. DATA

Length of column, L = 10m

Diameter of column, D = 3.5m

Grade of concrete = 50 N/mm2

Axial Load = 9800 kN

Slenderness ratio:

L/D = 10000/350 = 28057 (> 12)

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5.9.3. MAIN REINFORCEMENT

0.4 0.67 0.4P f A f f Au g y scck ck

3 29800x10 x350

0.4x50x 0.67x500-0.4501.05 4

Asc

Asc = 23.492 x 103 mm2

Provide 16 numbers of 45 mm diameter bars.

5.9.4. HELICAL REINFORCEMENT

Clear cover is given as 50 mm.

Core diameter = [350 - (2 x 50)] = 250 mm

Area of core = Ac = 0.78 x 2502

Ac = 25 x 103 mm2

Assume diameter of spiral reinforcement as 8 mm.

Pitch:

2 2

11.1 c sp sp y

c ck

D a fp

D D f

Substituting the values the pitch distance comes to 18.67 which is roughly 18 mm

Page 59: Design of Single Pylon Cable Stay bridge

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FIG 18: REINFORCEMENTS IN COLUMN

5.10. DESIGN OF PILE FOUNDATION

The moisture content of the surface soil at the pond is high. The soil is

under constant saturation as the pond is perennial and will always have water.

The pond is artificially built, which implies very less variations in properties of

soil. Since it is a pond, no water currents or waves are present, Pile foundation is

considered to be most suitable for the bridge.

5.10.1. DATA

Factored load on each pile = 9800/4 = 2450 kN

Depth of foundation = 5 m

Grade of Concrete = 50 N/mm2

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Grade of Steel = 500 N/mm2

5.10.2. DIMENSIONS

Length of pile above ground level = 0.6 m

Total Length of pile = 5 + 0.6 = 5.6 m

Cross Section of pile = 200 mm diameter

5.10.3. LONGITUDINAL REINFORCEMENT

0.4 0.67 0.4P f A f f Au g y scck ck

3 22450x10 =0.4x50x0.78x200 + 0.67x500-0.4x50 Asc

Asc = 5796.82 mm2

5.11. DESIGN OF CABLES

According to the plan, a total of 5 cables are provided. The type of cable

used is Freyssinet cable for values from BS 5896: 1980. The ultimate tensile force

for one strand is 265 kN. Dividing the total load by 5 and then by the ultimate

force we get,

Diameter of one strand = 15.70 mm

Type of anchorage: Saddle type

Cable Size: 5H15

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FIG 20: CROSS SECTION OF CABLE

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CHAPTER 6

RESULTS AND CONCLUSION

The result of this attempt to design a Single Pylon cable stayed bridge is as

follows;

The elliptically shaped bridge is proposed to be built across Shahpura

Pond, of Bhopal, Madhya Pradesh.

The span if the bridge is 50 metres and the width is 3.12 metres. It is

present 2 metre above the water level.

The deck slab is a standard simply supported slab of 20 m span and 3.12 m

width. The depth was calculated to be 150mm. It has 6 numbers of 16mm

diameter bars at centre to centre spacing of 150 mm as main reinforcement and

10mm diameter bars along the length at a centre to centre spacing of 300mm as

distribution reinforcement. An additional reinforcement of 10 numbers of 10 mm

diameter bars of Fe250 grade at a centre to centre spacing of 150mm is provided

in the slab.

The deck is a concrete T – beam girder deck designed under Guyon

Massonet method. The two longitudinal girders have 10 numbers of 20 mm

diameter bars at a centre to centre spacing of 110 mm and 10 mm diameter 4

legged stirrups at 150 mm c/c throughout the length of the girder.

The concrete cross girders are placed at 4 metre intervals and have 4

numbers of 16 mm diameter rods at a spacing of 120 mm centre to centre and 10

mm diameter 2 legged stirrups at spacing 150 mm centre to centre throughout the

girder.

Page 63: Design of Single Pylon Cable Stay bridge

49

The extended slabs of the deck are designed separately with varying depths

to counter act the load of the working span. The reinforcements provided in the

main girder are extended to these slabs.

The column is subjected to direct compression and is provided with 16

numbers of 45 mm diameter bars as longitudinal reinforcement and 8mm

diameter rods at a pitch of 18 mm as helical reinforcement.

The pile…

The 5 cables provided are Freyssinet type cables of specifications 5H15

and are anchored saddle like.

Through this a lot was learnt about the complex design of a bridge and the

various stages that have to be crossed while designing it.

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50

CHAPTER 7

REFERENCES

Jani Juvani and Olli Lipponen, “Design of Bridges, Cable Stayed Bridge”.

N.Krishna Raju, “Design of bridges”, fifth edition.

N.Krishna Raju, “Design of Reinforced Concrete Elements”.

Skandinavisk Spændbeton,” Post-tensioning Cables Freyssinet ETA-

06/0226”

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APPENDIX

ANNEXURE A

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ANNEXURE B

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ANNEXURE C

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ANNEXURE D