LOad on Bridge 2

PSZ 19:16 (Pind. 1/07)

UNIVERSITI TEKNOLOGI MALAYSIA

DECLARATION OF THESIS / UNDERGRADUATE PROJECT PAPER AND COPYRIGHT

Author’s full name : __ _ ___________________ ________ __________________GRACE TAN POH YANG Date of birth : __ ________________________ ______________________

05 NOVEMBER 1986 Title : ________________________________________________

__ ________

COMPUTERIZED DESIGN OF REINFORCED

______________________________________CONCRETE BOX GIRDER BRIDGE

________________________________________________ Academic Session : ________________________________________________ I declare that this thesis is classified as : I acknowledged that Universiti Teknologi Malaysia reserves the right as follows:

1. The thesis is the property of Universiti Teknologi Malaysia. 2. The Library of Universiti Teknologi Malaysia has the right to make copies for the purpose

of research only. 3. The Library has the right to make copies of the thesis for academic exchange.

Certified by :

SIGNATURE SIGNATURE OF SUPERVISOR

IR. MOHAMAD SALLEH YASSIN

OPEN ACCESS I agree that my thesis to be published as online open access (full text)

RESTRICTED (Contains restricted information as specified by the organization where research was done)*

CONFIDENTIAL (Contains confidential information under the Official Secret Act 1972)*

√

(NEW IC NO. /PASSPORT NO.) NAME OF SUPERVISOR

Date : Date : 19 APRIL 2010 19 APRIL 2010

861105-23-5768

NOTES : * If the thesis is CONFIDENTAL or RESTRICTED, please attach with the letter from the organization with period and reasons for confidentiality or restriction.

“I/We* hereby declare that I/we* have read this thesis and in my/our*

opinion this thesis is sufficient in terms of scope and quality for the

award of the degree of Bachelor of Civil Engineering”

Signature : ....................................................

Name of Supervisor : IR. MOHAMAD SALLEH YASSIN

Date : 19 APRIL 2010

COMPUTERIZED DESIGN OF REINFORCED CONCRETE BOX GIRDER

BRIDGE

GRACE TAN POH YANG

A report submitted in partial fulfillment of the

requirements for the award of the degree of

Bachelor of Engineering (Civil)

Faculty of Civil Engineering

Universiti Teknologi Malayisia

APRIL, 2010

ii

I declare that this thesis entitled “Computerized Design of Reinforced Concrete Box

Girder Bridge” is the result of my own research except as cited in the references. The

thesis has not been accepted for any degree and is not concurrently submitted in

candidature of any other degree.

Signature : ....................................................

Name : GRACE TAN POH YANG

Date : 19 APRIL 2010

iii

To my beloved father and mother

iv

ACKNOWLEGEDMENT

First of all, I would like to express my greatest and sincere appreciation to my

final year project supervisor, Ir. Mohamad Salleh Yassin for his guidance, critics,

encouragement, and advises throughout the process of this research. I am indebted to

him for his valuable instructions and guidance along the time of the research. I am

truly grateful to him also in the confidence and trust in me from the beginning of the

project until the stage of research accomplishment.

I am very grateful to have my family member with me during the period of

research preparation. Whenever I face any obstacles and problems, they always give

their moral support and encouragement to me throughout the process of research.

Last but not least, I also like to thank to my friends who always accompany

me and give their moral support when I need them especially those involved directly

or indirectly in my preparation of research. Their opinions and views are useful

indeed. May our friendship can last for forever.

v

ABSTRACT

Box girder bridge is the most widely used bridge type nowadays .This study presents

the development for preliminary analysis and design procedures of reinforced

concrete box girder bridge using Microsoft Excel spreadsheet. Branded new software

named “BGB version 1.0” is well developed to assist designers in their works.

Feasibility of choosing number of cell (single, double or triple) for box girder is one

of the advantages of this software. The software focuses on box girder bridge

structural analysis and design. Orthotropic plate theory analysis method is adopted

and bending moments and deflection of longitudinal and transverse beam are the

concerns since the results are needed to prevent the structural failure. Box girder can

be designed according to whole structure or by section depends on the preference of

user. The output data of analysis part can be used to compute the suggestion of

reinforcement required in order to provide a fast, accurate, safe and economic design.

European code of practice EN 1992-1-1 and EN 1992-2 are applied and referred

throughout the analysis and design of the software. The accuracy of the software is

verified through the stress results comparison with LUSAS modeller software in the

analysis part while parametric study method is used in design part of software in

order to identify the relationship among the parameters used.

vi

ABSTRAK

Jambatan galang kekotak merupakan salah satu jenis jambatan yang paling banyak

digunakan kebelakangan ini. Kajian ini membentangkan hasil kerja pembangunan

perisian komputer yang berfungsi untuk menganalisis and mereka bentuk jambatan

galang kekotak konkrit bertelulang. Perisian komputer berjenama “BGB version 1.0”

merupakan aturcara komputer yang boleh mengurangkan kerja-kerja jurutera dari

segi analisis dan rekabentuk. Kebebasan kepada penguna untuk memilih pelbagai

jenis galang merupakan salah satu kebaikan perisian ini. Kaedah analisis yang

digunakan adalah berpandukan “Teori Plat Ototropik” .Focus utama analisis adalah

penentuan pesongan dan momen yang dihasilkan pada anggota jambatan kerana

kecuaian tentang dua aspek tersebut akan menyebabkan kegagalan atau keruntuhan.

Dalam bahagian rekabentuk, pengguna program menentukan dan memilih cara

rekabentuk, iaitu rekabentuk mengikut bahagian kekotak ataupun seluruh struktur.

Keputusan dalam bahagian analisis dapat dimanfaatkan dan digunakan dalam

bahagian rekabentuk supaya menyempurnakan seluruh proses dalam aturcara dan

menghasilkan cadangan rekabentuk yang memenuhi syarat seperti kejituan, selamat,

cepat dan ekonomi. Semua keadah pengiraan untuk analisis dan rekabentuk adalah

berpandukan kod amalan Eropah EN 1992-1-1 dan EN 1992-2. Kejituan program

telah disahkan melalui perbandingan keputusan dengan program yang terdapat dalam

pasaran bernama “LUSAS Modeller”. Kajian parameter dalam bahagian rekebentuk

juga telah dijalankan supaya kejituan pengiraan dapat disahkan.

TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENTS iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES viii

LIST OF FIGURES ix

LIST OF SYMBOLS xiii

LIST OF APPENDICES xv

1 INTRODUCTION 1

1.1 Introduction 1

1.2 Problem Statement 2

1.3 Objective 3

1.4 Scope of Study 3

1.5 Importance of Study 4

2 ANALYSIS OF BOX GIRDER BRIDGE 6

2.1 General 6

2.2 Introduction to Bridges 6

2.3 Types of Concrete Bridge Decks 7

2.3.1 Slab Decks 7

2.3.2 Voided Slab Deck 8

2.3.3 Pseudo Slab 8

2.3.4 Maunsell Top Hat Beam 8

2.3.5 Beam and Slab 9

2.3.6 Box Girders Deck 9

2.4 Box Girder Bridges 10

2.4.1 General 10

2.4.2 Basic Concept of Reinforced Concrete 10

Box Girder Bridge

2.4.3 Components of Reinforced Concrete Box 11

Girder Bridge

2.4.4 Evolution of Box Girder 12

2.4.5 Development of Reinforced Concrete 12

Box Girder

2.4.6 Types of Reinforced Concrete Box Girder 13

2.4.7 Advantages of Reinforced Concrete Box 13

Girder Bridges

2.4.7.1 Relative Shallow Requirement 14

2.4.7.2 Aesthetic Value 14

2.4.7.3 Ideal Space for Utilities 15

2.4.7.4 High Torsional Stiffness 15

2.4.7.5 Cost Saving 15

2.5 Structural Action of Box girder 16

2.5.1 Longitudinal Bending 16

2.5.2 Shear Force 17

2.5.3 Torsion 17

2.5.4 Distortion 19

2.5.5 Shear Lag 20

2.5.6 Transverse Bending 20

2.6 Analysis of Reinforced Concrete Box Girder 21

2.6.1 Concept of Orthotropic Plate Theory 21

2.6.2 Flexural Rigidity of Box Girder 21

Bridge in Orthotropic Plate Analysis

2.6.2.1 Torsional Rigidity 23

2.6.2.2 Equivalent Plate Rigidity 23

2.6.3 Types of Cases in Orthotropic Plate Equation 25

2.6.3.1 Solution of Orthotropic Plate Equations 26

2.6.3.2 Torsionally Stiff and/or Flexural Soft 28

Bridge Deck (

D D

0

2.6.3.3 Isotropic Bridge Decks 28

2.3.6.4 Torsional Soft and/or Flexural Stiff 29

Bridge Decks (H

2.6.3.5 Articulated Bridge Decks ( 29

3 BRIDGE LOADINGS 31

3.1 General 31

3.2 Models of Road Traffic Loads 31

3.3 Loading Classes 32

3.4 Divisions of Carriageway into Notional Lanes 32

3.5 Location and Numbering of Lanes for Design 33

3.6 Traffic Loadings 34

3.6.1 Load Model 1 (LM1) 34




3.7 Load Combinations 37

3.7.1 Design Situation 37

3.7.2 Ultimate Limit States (Loading) 38

3.7.3 Combinations of Actions for Persistent 40

or Transient Design Situations

(Fundamental Combinations)

4 STRUCTURAL DESIGN 41

4.1 General 41

4.2 Ultimate Limit State 41

4.3 General Design Considerations 42

4.3.1 Structural Behavior 42

4.3.2 Minimum Dimensions of Cross Section 43

4.3.3 Fillets 44

4.3.4 Diaphragms 44

4.4 Design Code 44

4.4.1 Introduction to Eurocode 2 45

4.5 Stress-strain Relationship for the Design 45

Sections

4.6 Design Procedures of Reinforced Concrete 47

Box Girder

4.6.1 Flanged Section (Depth of the stress 47

block within the flange)

4.6.2 Flanged Section (Depth of the stress 49

block extends below the flange)

4.6.3 Flanged Section with Compression 51

Reinforcement

4.6.4 Shear Check and Reinforcement Design 53

(Shear reinforcement is not required)

4.6.5 Shear Check and Reinforcement Design 54

(Shear reinforcement is required)

4.6.6 Deflection Check 56

4.6.7 Crack Control 58

4.7 Material Properties 60

4.7.1 Design Compressive Strength of Concrete 60

4.72 Design Tensile Strength 61

4.7.3 Reinforcing Steel 62

5 DEVELOPMENT OF SOFTWARE 63

5.1 Introduction 63

5.2 Application of Microsoft Excel in Design Stages 64

5.3 Flow Chart Establishment 64

5.3.1 Flow Chart of Research 65

5.3.2 Flow Chart of Analysis of Reinforced 66

Concrete Box Girder

5.3.3 Flow Chart of Reinforced Concrete 71

Box Girder Design

6 USER MANUAL 75

6.1 Introduction 75

6.2 Instruments Configuration 75

6.3 Operating Guidelines of Software 77

6.3.1 Operating Guidelines (Part I: Analysis) 77

6.3.2 Operating Guidelines (Part II: Design) 86

7 RESULTS VERIFICATION AND DISCUSSION 92

7.1 General 92

7.2 Verification Tool 92

7.3 Software Verification for Analysis 93

7.3.1 Deflection 94

7.3.1.1 Load Combination 1 94



7.3.2 Bending Moment 97




7.4 Parametric Study 100

7.4.1 Relationship between Amount of 101

Longitudinal Reinforcement Bar Required

Due to Different Values of Bending Moment

Applied

7.4.2 Relationship between Amount of Longitudinal 102

Reinforcement Bar Required Due to Different

Values of Section Width, bf

8 LIMITATIONS, RECOMMENDATIONS 104

AND CONCLUSION

8.1 Limitations of Software 104

8.2 Recommendations 105

8.3 Conclusion 106

REREFENCES 108

APPENDIX I 110

APPENDIX II 117

APPENDIX III 118

viii

LIST OF TABLES

TABLE NO. TITLE PAGE

2.1 Elements of a simple box girder bridge 11

2.2 Typical load functions 27

3.1 Number and width of notional lanes 32

3.2 Characteristic values for load model 1 34

3.3 Classes of special vehicles 36

3.4 Design values of actions (EQU) (Set A) 39

3.5 Design values of actions (STR/GEO) (Set B) 39

3.6 Design values of actions (STR/GEO) (Set C) 40

4.1 Minimum dimension of cross sectional units for box girder 43

4.2 Comparison of stress block idealizations for αcc = 0.85 46

4.3 Recommended value for wmax (mm) 58

4.4 Maximum bar spacing for crack control 59

4.5 Maximum bar size for crack control 59

ix

LIST OF FIGURES

FIGURE NO. TITLE PAGE

2.1 Types of concrete bridge deck: (a) Slab 9

(b) Pseudo slab (c) Beam and slab (d) Cellular

2.2 (a) Construction of single cell box girder bridge 10

(b) Single box girder bridge in Australia

2.3 Section through a typical box girder bridge 11

2.4 Development of the box girder cross section 12

2.5 Single cell box girder 13

2.6 Multi cell box girder 13

2.7 Aesthetic treatment on the side of box girder 14

2.8 Warping of rectangular box subjected to pure torsion 18

2.9 Separation of an eccentrically applied load into two 19

components

2.10 Separation of force couple into torsion and distortion 19

components

2.11 Shear lag with wide flanges (typical variation of stress 20

across top flange)

2.12 Multi cell box deck 22

2.13 Definition of parameters 27

3.1 Application for load model 1 35

3.2 Load Model 2 35

4.1 Sloped exterior webs of box girder 43

4.2 The Eurocodes 45

4.3 Idealized stress-strain distributions 46

x

4.4 Flanged section with stress block within the flange 47

4.5 Flanged section with stress block below the flange 49

with depth of neutral axis 0.45

4.6 Flanged section with compression reinforcement 51

4.7 Basic span to effective depth ratio 57

4.8 Stress-strain relationships for the design of concrete 61

sections

4.9 Stress-strain diagrams for reinforcing steel 62

5.1 Flow Chart of Research 65

5.2 Flow chart of analysis bridge deck types 66

5.3 Flow chart of torsionally stiff and/or flexural soft 67

bridge decks analysis

5.4 Flow chart of isotropic bridge decks analysis 68

5.5 Flow chart of torsionally soft and/or flexural stiff 69

bridge decks analysis

5.6 Flow chart of articulated decks analysis 70

5.7 Flow chart for box girder design (compression 71

reinforcement is required)

5.8 Flow chart of shear reinforcement design 72

5.9 Flow chart of deflection check 73

5.10 Flow chart of crack control 74

6.1 Front page interface of software with six 77

available command buttons

6.2 Product details 78

6.3 User Manual 78

6.4 Author’s profile 79

6.5 Selection of box girder types in analysis part 79

6.6 Process of input required data 80

6.7 Calculation outputs of bridge loadings 80

6.8 Calculations of flexural rigidities 81

6.9 Determination of types for bridge decks 81

6.10 Computations of parameters and constants 82

6.11 Computations of coefficients, K1 and K2 according 83

to each load case

xi

6.12 Deflection of individual load case 83

6.13 Options for types of load combinations 84

6.14 Selection of design condition for load combination 85

6.15 Results of bending moment for load combination 85

in table form

6.16 Results of bending moment for load combination 86

in graph form

6.17 Interface control button 86

6.18 Selection of box girder types in design part 87

6.19 Selection of design options 87

6.20 Process of insert required data in design 88

6.21 Comparison between maximum bending moment 88

applied and moment of resistance

6.22 Shear check 89

6.23 Deflection check 89

6.24 Cracking control 90

6.25 Detailing diagram of box girder 90

6.26 Interface control button 91

7.1 Bridge model in LUSAS Modeller 93

7.2 Deflection graph of both analysis tools for 95

load combination 1


load combination 2


load combination 3

7.5 Bending moment graph of both analysis tools for 98

load combination 1


load combination 2


load combination 3

7.8 Constants of parametric study 101

7.9 Relationship between amount area of reinforcement 102

bar required and the bending moments applied

xii

7.10 Constants of parametric study 102

7.11 Relationship between amount area of reinforcement 103

bar required and the width of box section, bf

xiii

LIST OF SYMBOLS

2

- Area of enclosed section where

- Area enclosed by mid-line of wall of enclosed

- Reinforcement required in compression part of flange

- Coupling rigidity

- Bending rigidity in x direction

- Bending rigidity in y direction

- Equivalent plate rigidity in x direction

- Equivalent plate rigidity in y direction

- Modulus of rigidity

- Total torsional rigidity in x direction

- Total torsional rigidity in y direction

, - Moments of inertia of the entire cross section about x axes

- Moments of inertia of the entire cross section about y axes

- Bending moment per unit width in x direction

- Bending moment per unit width in y direction

M - Design moment

Mflange - Moment resistance of the concrete

- Torsional moment applied on a section

Z - Lever arm

- Breadth of section

- Depth of enclosed section between mid flange points

- Concrete strength

xiv

, .

ƒ

2

∆

∆

∆

/

- Characteristic axial tensile strength below which 5% of all the

strength test Results would be expected to fall for the specified

concrete

- Normal longitudinal stress in beam bending

ƒyk - Characteristic yield stress

- Thickness of wall of closed portion of the section

- Depth of flange

- Second moments of area of section per unit width in x direction

- Second moments of area of section per unit width in y direction

- Number of cells

- Thickness of end webs

- Thickness of top and bottom flanges ( )

- Thickness of internal web

- Shear flow in St Venant Torsion

- Shear stress in St Venant Torsion

- Total deflection of deck

- Deflection due to shear

- Ultimate design uniform distributed load

- Width of enclosed section

- The change in the longitudinal force in the flange outstand

- Half the distance between the section with zero moment and

where maximum moment occurs

- The change in moment over the distance ∆

- Coefficient taking account of long term effects on the compressive

strength and of unfavorable effects resulting from the way the load is

applied, which the value is recommended to be 0.85 for bridges .

Σ - Summation of the length thickness ratio taken around the line.

- Steel strain which is equal to .

- Strength reduction factor

- Partial safety factor for concrete

s - Partial factor of safety for steel

xv

LIST OF APPENDICES

APPENDIX TITLE PAGE

I Parameters of Orthotropic Plate Theory 110

II Example calculation of bridge deck analysis 117

(single cell box girder)

III Example calculation of reinforced concrete box 118

girder design (single cell box girder – hogging

moment)

1

CHAPTER 1

INTRODUCTION

1.1 Introduction

Bridge is a structure which provides passage over an obstacle without closing

the way beneath. Box girder bridge is one of the most widely used bridge type in

bridge construction especially for highway flyovers and modern elevated structures

of light rail transport. This modern bridge type uses box girders which are made of

concrete reinforced with steel bars.

As we know, computer technology is the most common tool to handle the

tasks which are given by the user in civil engineering field especially in bridge

structures design. However, there are many factors that needed to be taken into the

consideration in the analysis and design stages of reinforced concrete box girders

bridge, especially for the bridge loadings and the quantity of materials used to ensure

the safety of bridge structure for the usage of transportation. Meanwhile, there are a

lot of steps and procedures are involved in order to obtain the final results. In order

to decrease the repeated steps and minimize the work loads, civil engineers are wise

to utilize computer system which comprises of hardware and software during their

works.

2

In addition, with the introduction of Eurocode 2 as the new design standard

and guidelines for the concrete structure, bridge designers or civil engineers require

more time and effort to familiar themselves with the practice code of Eurocode 2.

Therefore, the work of bridges analysis and design will be easier, fast and accurate

with a development of software by using Microsoft Excel based on all of the criteria

that needed in bridge engineering.

1.2 Problem Statement

Reinforced concrete box girders are commonly used in curved bridges,

interchanges, and ramps due to the reason of unique qualities that make them suitable

for such applications. Design of box girder of the bridges are complicated by many

factors including torsional warping, distortional warping, interaction between

different kinds of cross-sectional forces, and the effect of horizontal bridge curvature

on both local and global behavior.

Besides that, the application of available analysis and design software mostly

are seen to be complicated and not user friendly to beginner. There are many input

data are required to be considered before proceeds to the analysis and design stages.

Certainly, a lot of mathematic equations and repeating calculations are involved.

Time consuming will be one of the disadvantages of manual calculations. On the

other hand, work load increment which due to different types of load combination

cases analysis will also become a burden to the designer.

Furthermore, the application of British Standard is no longer relevant in

future design. European code of practice is used to replace the design criteria of

reinforced concrete structure including box girder. Searching or referring processes

3

to guidelines of Eurocode 2 can be reduced in order to compute the results which

comprises of factors in term of time saving, accurate, economic and safety.

1.3 Objective

The objectives of the research are shown as below:

i. To study and quantitatively evaluate the structural properties and behaviors of

reinforced concrete box girder bridge.

ii. To analyze the structural actions of reinforced concrete box girder which are

under fifteen types of individual load cases and three types of load

combinations.

iii. To develop and transform a series procedure of reinforced concrete box

girder analysis and design based on BS EN 1992 Part 2 by using Microsoft

Excel software.

iv. To verify the results of software which comprises of advantages based on

safety, serviceability, reliability and economy in the real world situations.

1.4 Scope of Study

The scopes of the study are defined to achieve the objectives of the research

are shown as below:

4

i. The research focuses on the concept study, analysis and design of

reinforced concrete box girder deck.

ii. Box girder analysis is based on orthotropic plate theory.

iii. Deflection and bending moment are the main concerns of study.

iv. The procedures of reinforced concrete box girder analysis and design are

developed into software by using Microsoft Excel. The input data can be

easily manipulated by user and the design results can be obtained directly

from the software.

v. All of the specifications and procedures of reinforced concrete box girder

analysis and design are based on the latest version of BS EN 1992 Part 2

(Eurocode 2).

1.5 Importance of Study

Generally, software of analysis and design for three typical types of

reinforced concrete box girder in the format of Microsoft Excel is developed in the

end of the study. The software contains several simple input data interfaces which

contribute to the internal calculation processes of the software in order to obtain the

results of the study based on European code of practice (Eurocode 2).

The benefits of this software developing are time saving and ease of use for

the beginners. Certainly, this software can perform well and provide accurate results

in the end of the process to ensure the safety, serviceability, reliability and optimum

sizes of the proposed reinforced concrete box girder design that relate to the real

situation of construction site.

5

Hence, developing of new software by using Microsoft Excel can solve the

problems which mentioned above. It will be more user friendly to the civil engineers

and all the results of analysis and design can be obtained in a meanwhile.

6

CHAPTER 2

ANALYSIS OF BOX GIRDER BRIDGE

2.1 General

Literature review of a research is a critical summary and an assessment of the

current state of knowledge for the research. The aim is to give researcher insights

into aspects of the topic which might be worthy of exploration and future research

based on the information collected. Behaviour and aspects of box girder bridge are

discussed in this chapter.

2.2 Introduction to Bridges

Bridge is a permanent raised structure which allows people or vehicles to

cross an obstacle such as river without blocking the way of traffic passing underneath.

Before a new bridge is built, the planners have to decide on the best location on it.

There are a lot of factors are taken into the considerations of bridge design and

7

construction such as bridge loadings, dimension of carriageway and lanes, amount of

headroom needed by traffic passing underneath and type of bridge deck.

2.3 Types of Concrete Bridge Decks

Basically, there are six types of concrete bridge decks that commonly used in

concrete bridge constructions depending on the location and loadings. According to

Hambly (2003), behaviours of different forms of decks for bridge loading may be

different, which depend on the structural forms and the elements forming the decks.

Hence, a few of them have been well described by him in Figure 2.1 in the following

sub chapter.

2.3.1 Slab Decks

The slab deck behaves like a flat plate, which is a structural continuum for

transferring moments, shears and torsion in all directions in the plane of the plate.

The slab deforms based on the support conditions. Two sides will be supported on

the bearing over the piers in a normal bridge deck and the remaining two sides will

be either free or stiffened by edge beams corresponding to elastic supports.

8

2.3.2 Voided Slab Deck

Voided slab deck is a reinforced concrete slab deck in which voids reduce the

amount of concrete. In order to lighten the structure, void of cylindrical or

rectangular shapes are introduced at the middle height of the cross section and the

slab is not stressed at all.

2.3.3 Pseudo Slab

Pseudo slab are erected by means of standard beams closely packed with

shear connectors. The slabs are analyzed in longitudinal and transverse direction

directly ans separately. In filment of the portion in between the standard beams is

known as shear keys. The main application of this type of slab is for bridge erected

over busy roadways railway.

2.3.4 Maunsell Top Hat Beam

Maunsell top hat beam is referred to small hollow rectangular beams with

flanges extended on one side could be packed to form deck with a screed layers of

concrete on the top forming a cellular deck. The behaviour of this type of deck will

be very similar to the pseudo slabs.

http://en.wikipedia.org/wiki/Reinforced_concrete

9

2.3.5 Beam and Slab

Basically, a beam and slab deck consists of number of longitudinal beams

connected at the top with continuous structural slab. These beams could also be

transversely connected by a diaphragm or cross girder to give transverse stiffness for

the deck. These deck systems could be easily be adopted for bridge span up to 25m.

2.3.6 Box Girders Deck

Box girders deck system is referred to the bottom of the beam and slab deck

are to be tied together at the bottom to keep the geometry. It is structurally a more

efficient cross section for bridge spans with wide decks up to 150 m depending on

the type of construction methods. Normally prestressed box girder is resorted for

long spans bridge. Reinforced concrete box girders will be more suitable in term of

constructability for bridge which is in curved plan.

.

Figure 2.1 Types of concrete bridge deck: (a) Slab (b) Pseudo slab (c) Beam and

slab (d) Cellular

10

2.4 Box Girder Bridges

2.4.1 General

Since the construction of the first reinforced concrete bridge in the United

State in 1937, the popularity of concrete box girder bridges has steadily increased

generally in the western states and particularly in California, where nearly 90 percent

of all bridges were built on the state highway system are concrete box girder.

Nowadays, reinforced concrete box girder bridges are widely used in Malaysia

especially for highway interchange structures.

2.4.2 Basic Concept of Reinforced Concrete Box Girder Bridge

Box girder bridges are commonly used for highway flyovers and modern

elevated structures of light rail transport. Main beams of box girder bridge comprise

girders in the shape of hollow and typically rectangular or trapezoidal in cross

section.

(a) (b)

Figure 2.2 (a) Construction of single cell box girder bridge (b) Single box girder

bridge in Australia

11

2.4.3 Components of Reinforced Concrete Box Girder Bridge

The main elements of a typical simple box girder bridge are the

superstructure, substructure and foundation. These main components are shown in

Figure 2.3 and classified Table 2.1.

Figure 2.3 Section through a typical box girder bridge

Table 2.1 Elements of a simple box girder bridge

Foundation Substructure Superstructure

1 Plate

2 Pile Plate

3 Bored Piles

4 Driven Piles

5 Box Abutment

6 Spill-through Abutment

7 Column, Piers

8 Breast Wall

9 Wing Wall

10 Back Wall

11 Edge Beam

12 End Diaphragm

13 Bridge Seat

14 Support Walls

15 Bridge Seat Beam

16 Access Chamber

17 Bearing

18 Expansion Joint

19 Transverse Diaphragm

20 Box Girder Web

21 Top Slab (Area Between Webs)

22 Top Slabs

23 Bottom Slab

24 Fascia Beam

25 Guard Rail

26 Railing

27 Sealing Membrane

28 Wearing Surface

29 Drain Inlet

30 Cross Drain

31 Longitudinal Drain

12

2.4.4 Evolution of Box Girder

The number of longitudinal beam are increased which leading to a reduction

of stiffness in the transverse direction and relatively high transverse curvature as the

width of the deck is increased. The webs of the beams get opened out spreading

from the top slab. At this critical stage, they could not further be in their original

position under the high transverse bending. In order to keep the webs in their

original position, the bottom bulbs of the webs are to be tied together and this lead to

the evolution of box girder.

2.4.5 Development of Reinforced Concrete Box Girder

The first box girder cross section possessed decks slabs that cantilevered out

only slightly from the box portion (Figure 2.4, a-e). The high formwork costs caused

a reduction in the number of cells (Figure 2.4, f-g). In order to reduce the

construction loads to the minimum possible or to require only one longitudinal girder

in the working state even with multiple traffic lanes, the one cell built up cross

section constructed in modular fashion emerged as the last development (Figure

2.4h).

Figure 2.4 Development of the box girder cross section

13

2.4.6 Types of Reinforced Concrete Box Girder

Generally, there are two types of reinforced concrete box girder which are

single cell box girder and multi cells box girder. Each type of the box girder has its

own advantages and disadvantages during the construction stages.

Figure 2.5 Single cell box girder

Figure 2.6 Multi cell box girder

2.4.7 Advantages of Reinforced Concrete Box Girder Bridges

Reinforced concrete box girder bridges have several advantages over other

types of bridges and this led to its popularity in bridge constructions. The following

sub chapter will cover the advantages of reinforced box girder bridge.

14

2.4.7.1 Relative Shallow Requirement

The relative shallow depth requirement of a box girder bridge is a definite

advantage where headroom is limited which is a condition frequently encountered in

urban areas.

2.4.7.2 Aesthetic Value

Monolithic construction of the superstructure and the substructure offers

structural advantages as well as enhanced aesthetics. In the case of continuous box

girder, the piers caps can be placed within the box and facilitate rigid connection to

the pier shaft to develop continuity. Box girder structures also lend themselves to

easy aesthetic treatment through smooth finishing of the soffit and the side as shown

in Figure 2.7.

Figure 2.7 Aesthetic treatment on the side of box girder

15

2.4.7.3 Ideal Space for Utilities

“Reinforced concrete box girders provide ideal space for utilities such as gas

and water pipelines, power, telephone, cable ducts, storm drains and sewers. All of

the utilities can be easily and safely placed inside the large cells and completely

hidden from view (Degenkolb and Elliot, 1977).” Normally, the cells of box girder

haven been used as culvert to carry large amounts of drainage. If necessary, the

spacing of webs can be easily adjusted to facilitate the placement of these utilities at

desired locations.

2.4.7.4 High Torsional Stiffness

A significantly important characteristic of box girder is their high torsional

stiffness which makes them ideally suited for bridges on curved alignments. This is

especially important for interchanges on freeways where the ramp structures

typically require sharp curved alignment. In state such as California, about 70 to 80

percent of all bridges are multi-cell concrete box girder bridges. Their high torsional

stiffness also makes it possible to design them as a unit rather than as individual

girders.

2.4.7.5 Cost Saving

“Box girder structures lend themselves to easy aesthetic treatment through

smooth finishing of the soffit and the sides (Degenkolb and Elliot, 1977).” Special

treated forms for the outer surfaces of the box girder have been used to obtain a

16

smooth high grade surface that does not require additional finishing. In box girders,

only the soffits and the faces of the exterior girders or webs need to be given a high

quality finish. Thus, a great savings result from the reduced costs of finishing can be

obtained.

2.5 Structural Action of Box girder

The structural action of the box girder bridge deck is complicated. Hence,

analysis of a box girder should take stresses into consideration due to:

i. Longitudinal bending

ii. Shear force

iii. Torsion

iv. Distortion

v. Shear-lag

vi. Transverse bending

2.5.1 Longitudinal Bending

Simple beam action in the longitudinal direction causes the longitudinal

bending. If Mx and My are bending moments acting on the section, the normal stress

in longitudinal bending of a thin walled beam whose cross section had a vertical axis

of symmetry is given by:

17

ƒ . . 2.1

ƒ

, is moments of inertia of the entire cross section about x and y axes

respectively

oint on the middle line of cross section.

.5.2 Shear Force

Shear force causes an internal force in a member which acts in the plane of

the sec

.5.3 Torsion

For St Venant Torsion of thin walled of closed section Koll Brunner and

Basler

where

is normal longitudinal stress in beam bending

, is coordinates of the p

2

tion. The shear stress is referenced according to the particular plane in which

it acts. In a wide flange girder, vertical shear occurs in the box girder cross section if

the box is loaded vertically. Horizontal shear acts along the length of the girder if the

member is loaded longitudinally. In a bridge, the greatest danger for shear occurs at

supports where a load combined with the beam reaction can result in high stresses.

Vertical shear would be computed as the load divided by the girder web area.

2

have given the formula:

18

2.2

where

is shear stress in St Venant Torsion

is thickness of wall of closed portion of the section

closed

The pure torsion of a thin walled section also produces a warping of the

ross-section unless there is sufficient symmetry in the section. This is illustrated in

Figure

Figure 2.8 Warping of rectangular box subjected to pure torsion

is shear flow in St Venant Torsion

is torsional moment applied on a section

is area enclosed by mid-line of wall of en

c

2.8 for a rectangular section that is free to warp at its ends. However, in

practice boxes are not subject to pure torsion. Wherever there is a change of torque

at a point of application of load or at a torsional restraint, there is restraint to warping

because the 'free' warping displacements due to the different torques would be

different. Such restraint gives rise to longitudinal warping stresses and associated

shear stresses in each wall of the box.

19

2.5.4 Distortion

The general case of an eccentric load applied to a box girder is in effect a

ombination of three components which are bending, torsion and distortion. As a

first st

Figure 2.9 Separation of an eccentrically applied load into two components

Figure 2.10 Separation of force couple into torsion and distortion components

c

ep, the force can be separated into two components, a pair of symmetric

vertical loads and a force couple, as shown in Figure 2.9. However, torsion is in fact

resisted in a box section by a shear flow around the whole perimeter and the couple

should in turn be separated into two parts which represent pure torsion and distortion,

as shown in Figure 2.10. The first two components, vertical bending loads and a

torsional shear flow are externally applied forces and they must be resisted in turn at

the supports or bearings. The third component, distortional forces, comprises an

internal set of forces, statically in equilibrium, which do not give rise to any external

reaction. Distortional effects depend on the behaviour of the structure between the

point of application and the nearest positions where the box section is restrained

against distortion.

20

2.5.5 Shear Lag

In very wide flanges shear lag effects must be taken into account. When the

xial load is fed into a wide flange by shear from the webs the flange distorts in its

plane,

Figure 2.11 Shear lag with wide flanges (typical variation of stress across top

flange)

.5.6 Transverse Bending

The transverse bending stresses are generated due to transverse bending

oment caused by the symmetric loading on the deck at any particular individual

a

plane sections do not remain plane in Figure 2.11. The resulting stress

distribution in the flange is not uniform in very wide flanges. Thus, shear lag effects

have to be taken into account for the verification of stresses, especially for short

spans since it causes the longitudinal stress at a flange or web intersection to exceed

the mean stress in the flange.

2

m

cross section. The transverse bending moment is also affected by the longitudinal

flexural action since all the cross sections are connected with flexural rigidity on the

longitudinal direction.

21

2.6 Analysis of Reinforced Concrete Box Girder

The analysis of single and multiple cell of box girder for deflection and

nt will be discussed in this research. Those structural actions are

portant in determine the required reinforcement in the box girder to ensure its

.6.1 Concept of Orthotropic Plate Theory

dge deck as an equivalent plate for

e purpose of determining the distribution of stresses is well established. Cusens

nd Rama (1975) stated that an orthotropic plate is defined as one which has

.6.2 Flexural Rigidity of Box Girder Bridge in Orthotropic Plate Analysis

of

e section expressed per unit width multipled by the modulus of elasticity E as

llowing.

2.3

bending mome

im

safety. The orthotropic plate analysis method is adopted in this research.

2

The concept of considering an actual bri

th

a

different specified elastic properties in two orthogonal directions. There are two

forms of orthotropic may be identified which are material orthotropic and shape

orthotropic. Most of the bridge decks are orthotropic because of shape orthotropic.

More rarely there exists a combination of material and shape orthotropic.

2

The flexural rigidity and are taken as the second moments of area

th

fo

22

2.4

where

is flexural rigidity in x direction

E is modulus of elasticity

is second moments of area of section per unit width in x direction

y direction

bridges are constructed without transverse

dia hra may be found by neglecting the second

moment of area of the flanges about their own centroids, which is shown in Figure

n as below.

4

is flextural rigidity in y direction

is second moments of area of section per unit width in

For the multi cell box girder

p gms, an approximate value of

2.12. This leads to the expressio

2.5

here

is thickness of internal web

is depth of enclosed section between mid flange points

2.12 Multi cell box deck

w

is thickness of bottom flange

is thickness of upper flange

is thickness of end webs

Figure

23

2. .2.1

ear flows around the section are taken into consideration in evaluation

for torsional rigidity of multi cell sections (Cusens and Rama, 1975).” For a structure

consisting of several cells where the webs and flanges are small compared to the

overall dimensions of the section, Wittrick (1963) has shown that the torsional

rigidity GJ may be written as follows.

6 Torsional Rigidity

“The sh

11

1 1 12

2.6

2 /

= 1 √2

where

2 is width of enclosed section (see Figure 2.12)

is area of enclosed section where 2

is number of cells

is thickness of top and bottom flanges ( )

is modulus of rigidity

r

= /

2.6.2.2 Equivalent Plate Rigidity

e, its torsional rigidities

will come from the twist in two orthogonal directions. Each of the equivalent plate

ri idity may be taken as one half of the total torsional rigidity

If the deck is treated as an equivalent orthotropic plat

g in torsion, and

24

as given by Equation 2.7 and Equation 2.8 which each divided by the total width or

span of the deck respectively.

12 2.7

12 2.8

here

ty in

is total torsional rigidity in y direction

For box sections consisting of five or more cells, the torsional rigidity may be

approximated by considering the enclosed section as a single box and the total

torsional rigidity may be obtained from Bredt’s formula for a single closed section.

This can be applied if the thickness and are very small compared to the

dimensions, 2 of the cell.

4∑ /

w

is equivalent plate rigidity in x direction

is equivalent plate rigidity in y direction

is total torsional rigidi x direction

2.9

41 4

∑ / 2.10

(2.11)

Σ

2

2 2 2.12

Σ2 2

2.13

25

44 22 2 2.14

where

is area of the section enclosed by the median line

/ is summation of the length thickness ratio taken around the line.

For a box section deck with end diaphragms, it may be assumed that a section

along a longitudinal line is also a single cell b

2 21

2

Σ

ox which is given by Equation 2.15.

4∑ / 2.15

For there are no end diaphragms, Essa (1972) has found that the following

equation may be used provided that the span width ratio is greater than 1.0. For

ratios less than 1.0, torsional rigidity appears to drop below the value given by

Equation 2.16.

21

44

∑ / 2.16

.6.3

There are four cases will be discussed in this study which is categorized as

follow. The roots have to be examined in order to identify the cases of the solution

of orthotropic equations.

2 Types of Cases in Orthotropic Plate Equation

26

i. Case 1: Torsionally stiff and/or flexural soft bridge decks (

iii. Case 3: Torsional soft and/or flexural stiff bridge decks (

iv. Case 4: Articulated bridge decks ( 0

.6.3.1 Solution of Orthotropic Plate Equations

For all the cases except case 4, the deflection and bending moments may be

ases.

i. Def

2

ii. Case 2: Isotropic Bridge Decks (

2

expressed in the form of Equation 2.17 and equation 2.18 respectively. Figure 2.13

illustrates the definition of parameters and the typical load functions are shown in

Table 2.2 for all types of c

lection

2.17

ii. Bending Moments

2

2.18

2 2.19

27

Figure 2.13 Definition of parameters

2.2 Typical load functions

2

Table

4

2

4

8

28

2.6.3.2 Torsionally Stiff and/or Flexural Soft Bridge Deck (

Bridge decks in this category may be considered as torsionally stiff and/or

flexurally soft due to the square of half the total torsional rigidity exceeds the product

of the flexural rigidity in the two orthogonal directions. The constants of integration,

K1 and K2 are shown as following equations. Other parameters are stated in

Appendix I.

2.20

2.21

.6.3.3 Isotropic Bridge Decks

An isotropic deck refers to the flexural rigidities in the two orthogonal

2

2

directions and half the total torsional rigidity is all equal. The coupling rigidities are

also equal. The constants of integration are shown as following equations. Other

parameters are stated in Appendix I.

1 2.22

29

2

12

2 2.23

2.3.6.4 Torsional Soft and/or Flexural Stiff Bridge Decks (

Bridge decks in this category are classified as torsional soft and/or flexural

stiff bridge decks. The constants of integration are shown as following equations.

pendix I.

Other parameters are stated in Ap

2 2.24

2

2222

2.25

2.6.3.5 Articulated Bridge Decks (

n this case. This has

ractical applications with bridge deck of low transverse flexural rigidity which may

The transverse flexural rigidity approaches zero i

p

30

be idealized as articulated plates. The longitudinal beams are thought of as being

i. Deflection

2

jointed together by a series of longitudinal hinges which permit rotation but no

relative displacement between the beams.

2.26

ii. Bending moments

2 2.27

0=yM

The coefficients K1 and K2 are defined as follows:

2.28

31

R 3

BRIDGE LOADINGS

3.1 General

In this chapter, bridge and traffic loadings are discussed according to

different types of situations respectively.

3.2 Models of Road Traffic Loads

Loads due to the road traffic, consisting of cars, lorries and special give rise

to vertical and horizontal, static and dynamic forces. However, only vertical loads

will be considered in this study.

CHAPTE

32

3.3 Loading Classes

The actual loads on road bridges result from various categories of vehicles

and from pedestrians. Vehicle traffic ma differ between bridges depending on its

composition, density, conditio ights of vehicles, axle loads,

and if relevant the influence of road sign rrying capacity also. These

ifferences should be taken into account through the use of load models suited to the

cation of a bridge.

4

The carriageway width, w, should be measured between kerbs or between the

ner limits of vehicle restraint systems. It should not include the distance between

xed vehicle restraint systems or kerbs of a central reservation nor the widths of

th l w of notional lanes on a carriageway and

e greatest possible whole (integer) number l n of such lanes on this carriageway are

efined in Table 3.1.

umber and width of notional lanes

y

ns, the extreme likely we

s restricting ca

d

lo

3. Divisions of Carriageway into Notional Lanes

in

fi

these vehicle restraint systems. The wid

th

d

Table 3.1 N

33

Where the carriageway on a bridge deck is physically divided into two parts

separated by a central reservation, each part including all hard shoulders or strips

should be separately divided into notional lanes if the parts are separated by a

permanent road restraint system. Otherwise, the whole carriageway should be

ivided into notional lanes if the parts are separated by a temporary road restraint

ystem.

.5 Location and Numbering of Lanes for Design

i. The locations of notional lanes should not be necessarily related to their

numbering.

ii. For each individual verification, the number of lanes to be taken into

account as loaded, their location on the carriageway and their numbering

should be so chosen that the effects from the load models are the most

adverse.

iii. For fatigue representative values and models, the location and the

numbering of the lanes should be selected depending on the traffic to be

expected in normal conditions. The lane giving the most unfavourable

only one numbering should be used for the whole carriageway.

d

s

3

The location and numbering of the lanes should be determined in accordance

with the following rules:

effect is numbered Lane Number 1, the lane giving the second most

unfavourable effect is numbered Lane Number 2 and so on.

iv. Where the carriageway consists of two separate parts on the same deck,

34

3.6 Traffic Loadings

The vertical loads from traffic loading will be considered and discussed in

is chapter based on Eurocode 2. Load models defined in this section should be

sed for the design and analysis of road bridges with loaded lengths less than 200 m.

odels

r vertical load which represent different traffic effects. Those effects are discussed

the following sub chapter.

loa

sh

pa h are double-axle concentrated loads (tandem system, TS) and

lso uniformly distributed loads (UDL system).

th

u

The width of carriageway also should not exceed 42 m. There are four load m

fo

in

3.6.1 Load Model 1 (LM1)

Load model 1 (LM1) consists the concentrated and uniformly distributed

ds, which cover most of the effects of the traffic of lorry and cars. This model

ould be used for general and local verifications. This load model consists of two

rtial systems, whic

a

Table 3.2 Characteristic values for load model 1

35

Figure 3.1 Application for load model 1

load applied on specific tyre contact

reas which covers the dynamic effects of the nominal traffic on short structural

embers. As an order of magnitude, load model 2 can be predominant in the range

of loaded lengths up to 3 m to xle load βQQak

with Qak equal to 400kN and βQ is the adjustment factors.

Figure 3.2 Load Model 2


Load model 2 is referred to a single axle

a

m

7 m. This model consists of a single a

36


Load model 3 is a set of assemblies of axle loads representing special

vehicles such as industrial transport, which can travel on routes permitted for

abnormal loads. The classes of special vehicles are shown in Table 3.3 as following.

Table 3.3 Classes of special vehicles

Total weight Notation Composition

600 kN 4 axle es of 150 kN 600/150 -lin

900 kN 6 axle es of 150 kN 900/150 -lin

1200 kN 8 axle ines of 150 kN 1200/150 -l

or 6 ax -lines of200 kN 1200/150 le

1500 kN

10 axle-lines of 150 kN 1500/150

or 7 axle-lines of 200 kN 1500/200

+ 1 axle line of 100 kN

1800 12 axle-lines of 150 kN 1800/150


2400 kN


or 10 axle-lines of 240 kN or 2400/240

6 axle-lines of 200 kN (spacing 12m) 2400/200/200

+ 6 axle-lines of 200 kN

3000 kN

3000/200 15 axle-lines of 200 kN


+ 1 axle-line of 120 kN or


+ 7 axle-lines of 200 kN

3600 kN


or 15 axle-lines of 240 kN or 3600/240


+9 axle-lines of 200 kN

37


some transient design situations.

3.7 Loa inations

Stresses for design should be calculated ost sever com ns of

loads and forces. Load combina considered im t for

checking for adequacy of the bridge.

3.7.1 Design Situation

The relevant design s ing i the

circumstances under which the stru ulfill its function. Design

situations shall be classified as follo

i. Persistent design situations which refer to the conditions of normal use.

ii. Transient design situations which refer to temporary conditions applicable

to the structure (e.g. during execution or repair).

Load model 4 is referred to a crowd loading that intended for general

verifications. This crowd is particularly relevant for bridges located in or near towns

if its effects are not covered by load model 1. Load model 4 should be used only for

d Comb

for the m binatio

tions are generally portan

ituations shall be selected tak nto account

cture is required to f

ws:

38

ii . Accidental design i situations which refer to exceptional conditions

applicable to the structure or to its exposure to fire, explosion, impact or

the consequences of localized failure.

.7.2 Ultimate Limit States (Loading)

The following ultimate limit states shall be verified as relevant according to

differen

i. EQU: Loss of static equilibrium of the structure or any part of it

considered as a rigid body, where minor variations in the value or the

spatial distribution of actions from a single source are significant, and the

strengths of construction materials or ground are generally not governing.

ii. STR: Internal failure or excessive deformation of the structure or

structural members, including footings, piles, basement walls and others

formation of the ground where the strengths

of soil or rock are significant in providing resistance.

iv. Seismic design situations which refer to conditions applicable to the

structure when subjected to seismic events.

3

t situations:

where the strength of construction materials of the structure governs.

iii. GEO: Failure or excessive de

iv. FAT: Fatigue failure of the structure or structural members.

39

Table 3.4 Design values of actions (EQU) (Set A)

Table 3.5 Design values of actions (STR/GEO) (Set B)

40

Ta De )

3.7.3 Combinations of Actions for Persistent or Transient Design Situations

(Fundamental Combinations)

In this study, only combination of actions for persistent or transient design

situations is considered as a part of analysis. The combination of effects of actions to

be considered should be based on the design value of the leading variable action and

the design combination values of accompanying variable actions.

Ed = E{γΣG, j Gk, j + γPP + γQ,1Qk,1 + γQ,i ψ 0,i Qk,i} (3.1)

ble 3.6 sign values of actions (STR/GEO) (Set C

41

CHAPTER 4

STRUCTURAL DESIGN

.1 General

In this chapter, general design considerations, application of European of

discuss

osley (2007) stated that ultimate limit state is required, which the structure

must be able to with with an adequate facto of f failure.

The purpose of designing the ultimate li it state i to nsure of the

tructure occupants or the safety of the structure itself. This sub chapter discusses

ltimate limit states of reinforced concrete box girder which is similar with

inforced concrete flange beam. The following assumptions are made when

nalyzing a cross section to determine the ultimate moment of resistance.

4

practice code and design procedures of reinforced concrete box girder bridge are

ed in detail.

4.2 Ultimate Limit State

M

stand the loads r sa ety against

m s e the safety

s

u

re

a

42

i. Plane sections remain plane.

ii. Strain in bonded reinforcement, whether in tension or compression, is the

same as the strain in the concrete at the same level.

iii. Tensile strength of the concrete is ignored.

iv. The stresses in the concrete in compression are given by the design stress-

strain relationship.

v. The stresses in the reinforcing steel are given by the design stress-strain

relationship.

.3.1 Structural Behavior

A reinforced concrete box girder is essentially a T-beam with a transverse

flange sim sulting in a closed and torsionally stiff

nfiguration. The top deck, supported on web which is also referred to as

two basic functions similar to a T-beam bridge. It supported the

r moments.

Consequently, they are usually thinner than the webs of T-beams. This is because in

4.3 General Design Considerations

4

bottom ilar to the top flange, re

multi cell co

girders, perform

variable actions on the bridge, and it acts as the top flange of the longitudinal girders.

Thus, the deck is subjected to simultaneous bending both transversely as well as

longitudinally. However, for the simultaneous effects of maximum stresses

occurring in concrete in both directions.

The interior webs resist shear and often only small portion of girde

43

the case of continuous T-beam spans, the webs must resist the negative girder

moments, as well as the entire shear, and contain all the reinforcement for positive

inc ior webs are inclined,

their slope should preferably be 1:2 which is shown in Figure 4.1 (Caltrans, 1993c).

Figure 4.1 Sloped exterior webs of box girder

.3.2 Minimum Dimensions of Cross Section

The minimum dimensions of the cross sectional units for box girder are

shown

moments. While the interior webs are all vertical, the exterior webs may be vertical,

lined or curved, often to improve aesthetics. When the exter

4

in Table 4.1 as follow:

Table 4.1 Minimum dimension of cross sectional units for box girder

Element Dimension

Top Deck Slab

- Middle

- At cantilever end

200mm

- t junction of the web and slab

200mm

300mm A

Bottom Slab 150mm

Web 300mm (200mm + two duct ofdimension)

44

4.3.3 Fillets

Longitudinal fillets evolved to provide the smooth flow of stresses around

these corners which may develop when an arrangement of live loads on the structure

causes differential deflections between adjacent girders (Degenkolb, 1977).

roviding of fillets between the soffit slab and the webs is based on personal

experience and preference.

4.3.4 Diaphragms

Diaphragms help prevent excessive distortions of the cross section, facilitate

wheel load distribution, and distribute tran s are not required

for box girder unless the box girders are sharply curved.

civil

engineering due to the effects of current British Standard rocedures are

n in 2010. Hence, all of the design procedures and process of

ete box girder will be discussed based on Eurocode 2 in this research.

P

sverse load. Diaphragm

4.4 Design Code

The applications of Eurocode in design are more significant in field of

s for design p

due to be withdraw

reinforced concr

45

4.4.1 Introduction to Eurocode 2

their own Eurocodes. In this research EN 1992-1-1 and

N 1992-2 are referred in the box girder design.

Figure 4.2 The Eurocodes

.5 Stress-strain Relationship for the Design Sections

y the reinforcement (Mosley et al, 2007).” For cross section design, there are three

lternative stress-strain diagrams, which are parabolic rectangular, bilinear and

implified rectangular, as illustrated in Figure 2.8. They are for ultimate limit state

esign only and not for serviceability limit state. The stress-strain diagrams have

een constructed in Figure 4.3.

Eurocode 2 is one of ten Eurocodes that will form into a uniform process of

design in concrete structures. Eurocode 2 will apply to the design of building and

civil engineering structures in plain, reinforced and prestressed concrete. Each part

of them deals with design alone. Hence, the basis of design, loads, materials and

workmanship are covered in

E

4

“The theory of bending for reinforced concrete assumes that the concrete will

crack in the regions of tensile strain and that, after cracking, all the tension is carried

b

a

s

d

b

46

Figure 4.3 Idealized stress-strain distributions

Table 4.2 Comparison of stress block idealizations for αcc = 0.85

The comparison of three idealizations in term of average stress over a

ctangular compression zone which is from extreme compression fiber to neutral

ssion face of the section

the centre of compression. It is produced for αcc = 0.85 and this table can be used

r flexural design calculations. The rectangular block generally gives the greater

flexura

re

axis is shown in Table 4.2 and the distance from the compre

to

fo

l resistance, which is obvious because the depth of the stress block required to

provide a given force is smaller than for the other two alternatives.

47

4.6 Design Procedures of Reinforced Concrete Box Girder

The design of reinforced concrete box girder is similar to the design of

flanged section of beam. The following sub chapter will discuss the general

procedure to obtain the reinforcement bar size of a flange section. It is not possible

to derive equations for all possible situations. A suitable iterative approach for the

calculation of the nf tion can be used

based on its analysis maximum bending m ment.

4.6.1 Flanged Section (Depth of the stress block within the flange)

The design procedures of flanged section where the depth of stress block lies

within the flange are discussed as follows. Figure 4.4 shows the flanged section and

its stress block.

Figure 4.4 Flanged section with stress block within the flange

required rei orcement in the box girder of any sec

o

Fst

Fcc

bf 0.567fck

hf

d

As

Neutral axiss = 0.8xx

bw

s/2

z

Section Stress Block

48

i.

0.567 . . 0.8 0.4 4.1

. 2

Calculate the ultimate moment resistance of flange.

For this case, 0.8 is equal to therefore

0.567 . 4.2

ii. Determine the location of neutral axis. The neutral axis is within the

flange and only tension reinforcement is required when

M < Mflange

iii. Calculate the following expressions.

4.3

where the value of <0.167

0.5 √ 0.25 1.134 4.4

0.87 4.5

49

4.6.2 Flanged Section (Depth of the stress block extends below the flange)

There is a safe but conservative design for a flanged section with can

be achieved by setting the depth of neutral axis to 0.45 , the maximum depth

allowed in

Flanged section with stress block below the flange with depth of

0.45

i. Determine the requirement of compression reinforcement. Calculate the

maximum resistance moment of concrete, by taking moments

about . Compression reinforcement is not required when

= 0.167 0.567 /2 4.6

ii. Determine the depth of stress block, .

the code.

Figure 4.5

neutral axis

12 2

Fst

bf 0.567fck

hf

d

As

Neutral axis

s = 0.8x

bwSection Stress Block

x = 0.45 d

Fcc2Fcc1

z2z1

50

0.8 0.8 0.45 0.36 4.7

iii. Divide the flange section within the depth of stress block into area 1 and 2

as shown in Figure 4.5.

2

iv. Calculate the compression forces developed by these areas.

0.567 0.36 0.2 4.8

0.567 4.9

v. Taking moment about at the centroid of the flange.

/2 2

1 0.36

2

0.87 /20.2 0.36

2 4.10

vi. Calculate the required reinforcement where 0.36

0.1 0.36

0.87 2

4.11

51

4.6.3 Flanged Section with Compression Reinforcement

with compression reinforcement are

discussed as follows. Figure 4.6 shows the flanged section and its stress block.

Figure 4.6 Flanged section with compression reinforcement

Calculate the

maximum resistance moment of concrete, by taking moments

about . Compression reinforcement is required when

0.167 0.567

The design procedures of flanged section

Fst

bf

hf

d

As

Neu

0.567fck

i. Determine the requirement of compression reinforcement.

4.12

ii. Check the yielding of steel.

0.0035

tral axis

s = 0.8x

bwSection Stress Block

x = 0.45 dFcc2Fcc1

z1

12 2

d' FscAs'

z2 z3

52

1 0.0035

with 0.45

1 0.0035

iii. Determine the steel stress, .

iv. The area of compression steel can be calculated from the below

expression.

0.87

200000 4.13

0.87 4.14

vii. Divide the flange section within the depth of stress block into area 1 and 2

as shown in Figure 4.6.

1 0.36

v. Consider the equilibrium of forces on the section.

2

53

0.567 0.36 0.2 4.15

0.567 4.16

0.87 4.17

0.87 4.18

vi. Calculate the area of tension reinforcement.

0.2 0.5670.87

0.87 4.19

4.6.4 Shear Check and Reinforcement Design (Shear reinforcement is not

required)

i. at the web-flange interface.

∆∆

Calculate the design shear

4.20

∆∆

/2/2

4.21

32

∆3

4.22

54

ii. Check for the expression. No shear reinforcement is required if

0.27

um amount of transverse steel required in the

ange.

0.26

iii. Calculate the minim

fl

0.0013 /

Or

0.13100 4.23

4.6.5 Shear Check and Reinforcement Design (Shear reinforcement is

required)

i. Calculate the design shear at the web-flange interface.

∆

∆

4.24

∆∆

/2/2

4.25

∆3

32

4.26

55

ii. Check for the expression. Shear reinforcement is required if

iii. Check the shear stresses in the inclined strut. The angle for the

and upper

alue.

26.5 45 ie. 2.0 cot 1.0 for flanges in compression

38.6 45 ie. 1.25 cot 1.0 for flanges in tension

To prevent crushing of the concrete in the compressive strut the longitudinal

hear stress is limited to

1.5

0.27

inclination of the concrete strut is restricted to a lower

v

s

4.27

0.6 1 250 4.28

0.50.2 1 250

45 4.29

se reinforcement per unit length, / may be calculated

from the equation below.

iv. Calculate the transverse shear reinforcement required. The required

transver

0.87 4.30

56

v. Calculate the minimum amount of transverse steel required in the

flange.

0.260.0013 /

Or

0.13100 4.31

4.6.6 Deflection Check

The appearance and function of a reinforced box girder may be impaired if

e deflection under serviceability loading is excessive. It is more usual to control

deflections by placing a limit on the ratio of the span to the effective depth ratios.

The span to the effective ratio should be limited to span/250 and the basic l/d and K

re determined from Figure 2.26 with additional notes which stated the following.

i. This graph assumes that K=1.0 for simply supported span, K=1.5 for

=0.4 for

cantilevers.

ii. Com ression reinforcement, have been taken as zero.

iii. Curves based on following expressions:

th

a

interior span condition, K=1.3 for end span condition and K

p

11 1.5 3.2 1 4.32

57

where

111 1.5 12 4.33

where

4.34

4.35

100 4.36

Figure 4.7 Basic span to effective depth ratio

58

4.6.7 Crack Control

Cracking shall be limited to an extent that will not impair the proper

the structure or cause its appearance to be unacceptable.

racking is normal in reinforced concrete structures subject to bending, shear,

rsion or tension resulting from either direct loading or restraint or imposed

eform

Table 4.3 Recommended value for wmax (mm)

If crack control is required, a minimum amount of bonded reinforcement is

quired to control cracking in areas where tension is expected. The amount may be

estimated from rium between the tensile force in concrete just before cracking

and the tensile force in reinforcement at yielding or at a lower stress if necessary to

mit the crack width. Unless a more rigorous calculation shows lesser areas to be

adequate, the required minimum areas of reinforcement may be calculated as follows.

In profiled cross sections like box girders, minimum reinforcement should be

determined for the individual parts of the section (webs, flanges). As,min is given by

xpression as follows.

functioning or durability of

C

to

d ations. A limiting calculated crack width, wmax, taking into account the

proposed function and nature of the structure and the costs of limiting cracking

should be established. In this study, control of cracking without direct calculation

method is used.

re

equilib

li

e

59

As,minσs = kc k fct,eff Act

Cracking due to the loading is minimized by ensuring the maximu

spacing between longitudinal reinforcing bars in beam is limited to that give

Table 4.4. The spacing depends on the tress in the reinforcement which should be

n as the stress under the action of the quasi-permanent loadings. The quasi-

4.37

m clear

n in

ke

permanent loading is taken as the permanent load, Gk plus a proportion of the

variable load, Qk which depends on the structure type. The calculation of steel stress

level can be expressed as follows. When consider load induced, cracking bar

iameter may be restricted as indicated in Table 4.5.

1.15

ta

d

0.31.35 1.5

1 4.38

Table 4.4 Maximum bar spacing for crack control

Table 4.5 Maximum bar size for crack control

60

4.7 Material Properties

4.7.1 Design Compressive Strength of Concrete

for materials wit ract ive strength for

concrete is defined as follows:

Design strengths of concrete are obtained by combining partial safety factors

h their cha eristic values. The design compress

4.39

where

is the partial safety factor for concrete

is a coefficient taking account of long term effects on the compressive

strength and of unfavorable effects resulting from the way the load is applied,

which the value is recommended to be 0.85 for bridges .

(a) Parabolic-rectangular distribution (b) Bilinear distribution

The factor contributes to preventing flexural resistances from being

overestimated by neglect of the drop off in stress towards the failure strain due to its

part be a correcting factor between the true stress-strain behaviour. The stress-strain

relationship for the design for concrete sections is shown in Figure 4.8 (a-c).

61

(c) Alternative concrete design stress blocks for fck 50MPa

Figure 4.8 Stress-strain relationships for the design of concrete sections

4.72 Design Tensile Strength

The design tensile strength of concrete is defined as:

, .

4.40

where

is the partial safety factor for concrete

is a coefficient taking account of long term effects on the tensile strength

and of unfavourable effects, resulting from the way the load is applied and

the value is recommended to be 0.85 for bridges

l tensile strength below which 5% of all the strength

test results would be expected to fall for the specified concrete , . is the characteristic axia

62

4.7.3 Reinforcing Steel

The behaviour of the steel is identical in tension and compression which is

being linear in the elastic range up to the design yield stress of ƒyk/γs. The

representative short term design stress strain curve for reinforcement is given in

igure 4.9.

Within the elastic range, the relationship between the stress and strain is as following.

Stress = Elastic Modulus × Strain

4.41

So that the design yield strain is

F

Figure 4.9 Stress-strain diagrams for reinforcing steel

4.42

where

ƒyk is the characteristic yield stress

�s is the partial factor of safety

63

CHAPTER 5

ill be carried out in this

search as well as the analysis and design procedures of reinforced concrete box

irder by using software of Microsoft Excel. The processes of preparation for the

research also will be covered in this chapter in order to achieve the objectives which

have been stated in chapter one of research.

have been identified in conducting

thi h

from the beginning until the end product of the research. In order to simplify or let

reader ha

illustrate sub chapter.

DEVELOPMENT OF SOFTWARE

5.1 Introduction

Generally, this chapter will discuss the methods that w

re

g

There are three important stages which

s research which covered the aspects of information that needed in this researc

ve a clearer pictures about this research, three important stages will be

d in types of flow chart as shown in the following

64

5.2 Application of Microsoft Excel in Design Stages

Microsoft Excel is an electronic software program that can be used for storing,

rganizing and manipulating data. Nowadays, it is a very user friendly program in

applyin

and helpful wizards to guide new users through the more complicated

processes. The arrangement of the required functions or equation due to different

situations by the users are easy if compare to other software. Calculations of

repeated equations can be done in a short time by entering the required input data.

Every changes of the input for the software will produce results immediately in the

interface.

5.3 Flow Chart Establishment

In this sub chapter, flow charts of the processes of preparation for the

Microsoft Excel, the general procedures a d formulas involved will be shown in the

related flow charts. Three which are:

i. Flow chart of research

ii. Flow chart of analysis of reinforced concrete box girder

concrete box girder design

o

g, analysis and presenting the scientific calculations which involves different

kind of mathematic functions. Excel is also widely considered to be one of the most

easily accessible software programs, with instinctive design, simple point-and-click

functionality

research are constructed. For ease of understanding and application of software of

n

flow charts have been constructed

iii. Flow chart of reinforced

65

5.3.1 Flow Chart of Research

The flow chart of the research is

ensuring

manner and appropriate to the scope of rese

shown in Figure 5.1.

Figure 5.1 Flow Chart of Research

a very important part of the research

the research is conducted in the right

arch. The flow chart of research is

methodology due to its function of

Start

Preliminary Study of

Exploration of Topic of Research Identify the Problem

Statement of Research

Iden e Scope of Research

tify th Determine the Objectives of the

Research

Literature Review

Yes

Program Development (Software by using Microsoft excel)

Adequate and Accuracy of Result

Result and Discussion Final Report

Presentation of Final

Year Project

Submission of Final

Year Project

NoFlow chart of design

procedures

66

5.3.2 Flow Chart of Analysis of Reinforced Concrete Box Girder

Due to the complication of analysis of box girder which involves many

rmulas, the flow chart of analysis is required to simplify the procedures. The flow

harts of analysis for deflection and bending of box girder are illustrated in Figure

Figure 5.2 Flow chart of analysis bridge deck types

fo

c

5.2 to 5.6.

Start

Yes

Calculate flexural rigidities , and torsional rigidity ,

2

Calculate load function:

0

Yes4 Articulated Bridge

Deck

No

Yes

2

No

1

Yes Isotropic Bridge Deck

Yes Torsionally stiff and/or flexural soft

bridge decks Yes

4 Torsional soft and/or flexural stiff bridge decks

3

67

igure 5.3 of torsionally stiff and/or flexur ks

nalysis

1

Input data:

Bridge dimension, L, b; Load position, c; Longitudinal section, x; Edge beam rigidities, EI, GJ; Load eccentricities, EE; Transverse

stations, yb = -1 to 1

Calculate parameters: r , r , β , β 1 2 1 2

Calculate constants: a1, b1, c1, d1

a3, b3, c3, d3 S , S

F Flow chart al soft bridge dec

a

1 2, S , S3 4

Calculate constants: A, B, C, D

Calculate coefficients:

K1, K2

Calculate:

, M w, Mx y

End

68

Figure 5.4 Flow chart of isotropic bri

dge decks analysis

Input data:

Bridge dimension, L, b; Load position, c;

Longitudinal section, x; Edge beam rigidities,

EI, GJ; Load eccentricities, EE; Transverse

Calculate parameters:

βn

Calculate constants: a1, b1, c1, d1 a3, b3, c3, d3 S1, S2, S3, S4

Calculate constants:

A, B, C, D


K1, K2

Calculate: w, Mx, My

2

End

69

3

igure 5.5 Flow chart of torsionally soft and/or flexural stiff bridge decks

nalysis

Input data:

B

Longitudinal sectio ; Edge beam rigidities,


ridge dimension, L, b; Load position, c;

n, x

Calculate parameters:

r3, r4, β3, β4


a1, b1, c1, d1 a3, b3, c3, d3

S1, S2, S3, S4 E1, E2, E3, E4, E5, E6, E7


A, B, C, D


K1, K2

Calculate: w, Mx, My

End

F

a

70

Figure 5.6 Flow chart of articulated decks analysis

Input data:

Bridge dimension, L, b; Load position, c;

Longitudinal section, x; Edge beam rigidities,


Calcu rameters:

ro, βo

late pa

Calculate constants: a1, b1, a2, b2

S1, S2

Calculate constants: A, B

Calculate:

w, Mx, My

4

Calculate coefficients: Kl, K2

End

71

5.3.3 Flow Chart of Reinforced Concrete Box Girder Design

igure 5.7 Flow chart for box girder design (compression reinforcement is

quired)

Start

, , , ,

,Data input:

F

re

0.567 . . /2 Calculate t n flange: he moment i

M < Mflange

Dept block below the flange (

h of the stress)

C t is re

ompression reinforcemenquired

Calculate shear reinforcement (A)

1 0.0035

C steel: heck the yielding of

200000

Determin eel stress, . e the st

Calculate the required compression and tension reinforcement:

. . ;

. .

. .

72

Start (A)

Figure 5.8 Flow chart of shear reinforcement design

∆∆

Calculate the design shear at the web-flange interface.

0.27

Shear reinforcemis not require

ent d

She

Yes No

ar reinforcement is required

0.6 1 250

0.50.2 1 250

0.260.0013 /

Calculate the minim amount of transverse steel required in the flange.

um

45

1.5

Calculate the following parameters:

0.87

Calculate required transverse reinforcement per unit length, / :

Def tion check lec

B

73

B

Determine l/d basic and K

Figure 5.9 on check Flow chart of deflecti

1.0

1.0

Increase Asprov

No

Yes

Deflection checking passed

C

74

Figure 5.10 Flow chart of crack control

C

Determine crack width,

Wmax

1.150.3

1.51.351

Calculate steel stress

Crack control passed

Increase Asprov

Determination of maximum allowable clear bar spacing

No

Allowacle spacing > actual

spacing

Yes

End

75

CHAPTER 6

During the process of developing and application of software, the

is very important which may affects the duration

y the output data of analysis and d r will

ation of instruments and application guidelines of the

ed “BGB version 1

6.2 Instruments

The main instrument to be used in software operating is a computer with

Windows” operating system. Microsoft Excel software is needed to complete the

order to prevent the delays of computer

USER MANUAL

6.1 Introduction

configuration of computer system

and accurac esign of software. This chapte

explain the required configur

software nam .0” in detail.

Configuration

“

analysis and design of the software. In

76

system, the computer system must fulfill the minimum requirement and

onfiguration as below:

i. Processor

• Pentium 133 MHz or above

ii. Memory (RAM)

The required memory of computer depends on the operating system used.

• Windows 98 atau

• Windows ME atau Windows NT® - 32MB

• Windows 2000 Professional - 64MB

• Windows XP Professional atau Windows XP Home Edition

128MB

• Windows Vista - 32MB

• Windows Vista – 64MB

• Windows Seven– 32MB

• Windows Seven

iii. Capacity of hard disk

• 1.2 GB or above

iv. Display Card

• Super VGA (800 × 600) with 256 colours or above

v. Others

• CD-ROM

• Optical Mouse

• Keyboard

• Printer

c

Windows 98 SE - 24MB

– 64MB

77

6.3 Operating Guidelines of Software

The software is created according to the flow chart and procedures discussed

previous chapter. The analysis procedures have been simplified to avoid confusion

of user. The software guidelines of “BGB version 1.0” in both analysis and design

part will be discussed step by step in this sub chapter in order to give a clear

overview of program to the user.

6.3.1 Operating Guidelines (Part I: An lysis)

In analysis part of the software, several procedures and steps have to be

followed in order to obtain the fin

i. Click on the software in format of “Microsoft Office Excel Macro-

Enabled Worksheet (.xlsm)”. The front page interface of the program is

are six command buttons available in the interface (About,

User Manual, Author, Analysis, Design and Exit).

ftware with six available command buttons

a

al output data.

loaded. There

Figure 6.1 Front page interface of so

78

ii. After the front page interface of the program is loaded, user is advised to

view the product details by clicking on the “About” button.

iii. use the software. The

anual of the program.

Figure 6.3 User Manual

Figure 6.2 Product details

“User Manual” button guide the user how to

procedures to operate this software will be eased by following the

instructions and m

79

iv. Creator of the program can be viewed by user also by clicking on “Author”

Figure 6.4 Author’s profile

v. Select ‘Analysis’ button from the command button bar to enter second

box girder.

Figure 6.5 Selection of box girder types in analysis part

button.

interface for selection of box girder type. Box girder types included

single cell, double cells and triple cells

80

vi. of bridge deck and box girder cross

ess of surfacing and deck, dimension

of parapet and m box girder in the blue box only.

Click “Next” button afte

Figure 6.6 Process of input required data

vii. The values of all data inserted in step 7 are used to complete the

calculation part of bridge loadings and others. Live load of the deck is

selected automatically in this section according to Eurocode 2.

Figure 6.7 Calculation outputs of bridge loadings

Input required data such as geometry

section, type of road system, thickn

aterial properties of

r completed all data inputs.

Insert required data into the blue boxes.

View the calculation result

of bridge loadings.

81

viii. This interface shows the flexural rigidities which are calculated based on

the data inputs from step 7.

Calculations of flexural rigidities

ix. Calculations for bridge deck type determination will be done. The

software will show the result of bridge case to user before proceed to the

calculation of parameters part. In this example, torsionallt soft and/or

flexurally stiff bridge deck is selected.

Figure 6.9 Determination of types for bridge decks

Figure 6.8

View the calculation result flexural rigidities

Determination of types for bridge

decks

82

x. User can view the values of parameters, which are required in the

computation of coefficients, K1 and K2 in the following interface.

xi. The coefficients, K1 and K2 are obtained in order to calculate the

deflections and bending moments of each individual load case. Fifteen

types of load cases are prepared in this software in order to give user

more options during load combination part. Figure 6.11 shows an

example of load cases. The load cases included are deck and prem

weight, structural self weight, superimposed dead lo el 1

(Tandem system) at Lane No.1, 2 and 3, load m form

distributed load system) at lane no.1, 2 and 3, load model 2 (9 kN/m2) at

lane no.1, load model 2 (2.5 kN/m2) at lane no.2, 3 and remaining area

and load model 3 (special vehicle) at lane no.1.

Figure 6.10 Computations of parameters and constants

Computations of parameters and

constants

ix self

ad, load mod

odel 1 (Uni

83

Figure 6.11 Computations of coefficients, K1 and K2 according to each load case

xii. The deflection, bending moment, Mx and My of each stations will be

computed automatically. User can obtain the concern location of the box

girde y s the division of

transverse and longitudinal sections of the deck. However, the values

lained in step following. Figure 6.12 shows

the example of deflection results.

Figure 6.12 Deflection of individual load case

r deck easil ince the orthotropic plate theory allows

displayed in this interface only concern about each load case individually.

Load combination will be exp

84

xiii. User can obtain the desired type of load combination by clicking the

command button of the load combination. This software provides three

types of load combination which are:

a) Load combination 1: dead load + superim

LM1(Tandem system) + LM2

b) Load combination 2: dead load + superimposed dead load + LM1(UDL)

+ LM2

c) Load combination 3: dead load + superimposed dead load + LM1(UDL)

+ LM3

Figure 6.13 Options for types of load combinations

xiv. User is required to insert the desired design condition into blue box in

order to complete the computation of load combination.

posed dead load +

Options for typ

load combina

es of

tions

85

Figure 6.14 Selection of design condition for load combination

xv. After insert the desired load combination, the result of deflections and

bending moments can be viewed in the tables or graph according to each

station point. Figure 4.14 shows an example of bending moments in table

while Figure 6.15 show the result in graph.

igure 6.15 Results of bending moment for load combination in table form F

Selection of

design condition

for load

86

Figure 6.16 Results of bending moment for load combination in graph form

Click on

Figure 6.17 Interface control button

6.3.2 Operating Guidelines (Part II: Design)

In design part of the software, several procedures and steps have to be

followed in order to obtain the final output data.

xvi. the “Main Page” button to enter back to the front page of

software for design or others function. Click on the “Back” button if

want to view the previous pages.

87

i. User is required to choose the type of box girder they preferred.

Figure 6.18 Selection of box girder types in design part

ii. ious analysis part

can be used to obtain the most economic reinforcement design for box girder.

However, if user intends to use other value of bending moment, this design

section also provides this feature. User can choose either design the

reinforcement bar for the whole structure nor by section and also hogging or

sagging for section. Figure 6.19 shows the interfaces of those features.

Figure 6.19 Selection of design options

The output values of maximum bending moment in the prev

88

iii. Designation of single box girder by consider whole structure is been chosen

as example in this sub chapter. Firstly, insert required data into the blue

boxes such as characteristics of concrete and steel preferred, dimension of

cross section, proposed reinforcement bar in each layer and other relevant

data.

Figure 6.20 Process of insert required data in design

iv. The result of the maximum moment resistance of box girder cross section is

determined and compare with the ultimate bending moment from previous

analysis.

Figure 6.21 nt

of resistance

Comparison between maximum bending moment applied and mome

Comparison between maximum bending moment applied and

moment of resistance

89

v. Moment of resistance for section must be greater than maximum bending

nt applied. Shea ty of reinforcement

check

ture.

Figure 6.23 Deflection check

mome

provided.

r is provided to ensure the safe

Figure 6.22 Shear

Shear check

vi. Deflection check is provided to control the deflection of the struc

Deflection check

90

vii. Cracking control is provided to prevent the cracking failure of structure.

Figure 6.24 Cracking control

viii. The detailing diagram

concrete box girder is provided in the end of the design procedures.

Figure 6.25 Detailing diagram of box girder

Cracking check

of proposed reinforcement bar size of reinforced

91

ix. Click o a of software

r design or others function. Click on the “Back” button if want to view the

revious pages.

Figure 6.26 Interface control button

n the “Main P ge” button to enter back to the front page

fo

p

92

CHAPTER 7

RESULTS VERIFICATION AND DISCUSSION

portant to ensure its reliability for further usage. Analysis and design results for

rder bridge are discussed in this chapter. Result

comparison method between developed software, BGB version 1.0 and market

available analysis software, LUSAS Modeller is done in order to verify its accuracy

in the analysis part while parametric study method is used in the design part of

reinforced concrete box girder bridge.

7.2 Verification Tool

LUSAS Modeller is chosen for the software verification in analysis part of

this study. LUSAS Modeller is an associative feature-based modeling system that

7.1 General

As we know, the accuracy of result for the new developed software is very

im

reinforced concrete box gi

93

geom betry features are su

orresponding increase in solution time and disk space required.

owever, the results which provided from the LUSAS Modeller analysis are reliable

nd accurate.

7.3 Software Verification for Analysis

Basically, the results for the analysis part of software are verified and

compared with LUSAS Modeller software based on two aspects, which are

deflection and bending moments. In this study, single cell box girder bridge is

chosen as an exam is

results of displacem

n in Ap

the BGB version 1.0, the width and length of span for the bridge deck are

(-b, -3b/4, -b/2, -b/4, 0, b/4, b/2, 3b/4, b) and eleven

stations (0, L/10, 2L/10, 3L/10, 4L/10, 5L/10, 6L/10, 7L/10, 8L/10, 9L/10, L)

respectively. Thus, the same geometry, specifications and loadings applied are

followed during the bridge modeling process in LUSAS Modeller.

Figure 7.1 Bridge model in LUSAS Modeller

-divided into finite elements in order to perform an analysis.

Increasing the density of the mesh will usually result in an increase in accuracy of the

solution, but with a c

H

a

ple to compare with the LUSAS Modeller. The software analys

ent and bending moments of single cell box girder bridge are

show pendix II.

In

divided into nine stations

94

7.3.1 Deflection

In this study, there are three types of load combinations for bridge decks are

stablished. In order to compare both of the analysis tools, the maximum deflection

tation, 0 along the longitudinal span is chosen and compare with the same locations

f the bridge model in LUSAS Modeller.

.3.1.1 Load Combination 1

Load combination 1 includes the combination of dead load, superimposed

ead load, load model 1 (Tandem system) and load model 2. The maximum

deflection of software analysis is 19 mm while the result obtained from LUSAS

analysis is 24 mm. Although there is difference between both analyses tools, the

difference of both deflection values is not significant since the length of span is 30m.

This length of span is considered as a quite long span. Furthermore, the shape of

both graphs produced is similar which support the accuracy factor of the developed

software. The deflection near the support is small and increases steadily until the

mid span of the bridge, where the location that maximum displacement take place.

The deflection values decreases after the distance from the mid span. Figure 7.2

shows the comparison deflection re software and LUSAS Modeller for

load combination 1.

e

s

o

7

d

sults graphs of

95

(a) Deflection graph of software (b) Deflection graph of LUSAS

Figure 7.2 Deflection graph of both analysis tools for load combination 1

.2 2

ly until the mid span of the bridge, where the location that maximum

isplacement takes place and the deflection is values decreases after the distance

om the mid span. Hence, the shape of both graphs produced is similar which

roved that the accuracy of the software in application for preliminary stage of

nalysis. Figure 7.3 shows the comparison deflection results graphs of software and

7.3.1 Load Combination

The combination of load combination 2 includes of dead load, superimposed

dead load, load model 1 (UDL system) and load model 2. The maximum deflection

of software analysis is 18 mm while the result obtained from LUSAS analysis is 29

mm. The condition is similar to the load combination 1. Since the length of span is

30m and the length of span is considered as long span, the difference of both

deflection values is not significant. The deflection near the support is small and

increases steadi

d

fr

p

a

LUSAS Modeller for load combination 2.

96



7.3.1.3 Load Combination 3

For load combination 3, the combination includes of dead load, superimposed

dead load, load m eloped software,

on is 20 mm while the result obtained from LUSAS analysis is

35mm. The condition is similar to the load combination 2 and 3. The deflection

near the support is small and increases steadily until the mid span of the bridge,

where

e, the shape of both graphs produced is

similar which proved that the accuracy of the software. Figure 7.4 shows the

comparison deflection results graphs of software and LUSAS Modeller for load

combination 3.

odel 1 (UDL system) and load model 3. In the dev

the maximum deflecti

the location that maximum displacement takes place and the deflection is

values decreases after the distance from the mid span. Since the length of span is

30m and the length of span is considered as long span, the difference of both

deflection values is not significant. Henc

97



7.3.2 Bending Moment

Similar to the verification process of deflection, there are three types of load

combinations for bridge decks are established and needed to be compared between

both tools. In the process of comparison, the maximum bending moment station, 0

along the longitudinal span is chosen and compare with the same locations of the

bridge model in LUSAS Modeller.



ead load, load model 1 (Tandem system) and load model 2. The maximum bending

momen

7

d

t of software analysis is 1398 kNm while the result obtained from LUSAS

analysis is 1290 kNm. As we know, orthotropic plate theory is adopted in software

while finite element method is used in LUSAS modeller. Furthermore, the Eurocode

98

load model 1 to 3 is preset in the LUSAS Modeller which give more accurate loading

applied to the surface of the deck if compare to the manual formulas and calculation

of software. The bending moment near the support is approximately to zero and

increases steadily until the mid span of the bridge, where the location that maximum

bending moment takes place and decreases after the distance from the mid span.

Moreover, the shape of both graphs produced is similar which support the accuracy

of the software in application for preliminary stage of analysis. Figure 7.5 shows the

comparison bending moment results graphs of software and LUSAS Modeller for

load combination 1.

S

Fig e 1

(a) Bending moment graph of software (b) Bending moment graph of LUSA

ure 7.5 B nding moment graph of both analysis tools for load combination

7.3.2.2 Load Combination 2

For combination of load combination 2, it includes of dead load,

superimposed dead load, load model 1 (UDL system) and load model 2. The

maximum bending moment of software analysis is 1114 kNm while the result

obtained from LUSAS analysis is 1270 kNm. The condition is similar to the load

combination 2. Orthotropic plate theory is adopted in software while finite element

method is used in LUSAS modeller. On the other hand, the Eurocode load model 1

99

to 3 is preset in the LUSAS Modeller. This will give more accurate loading applied

to the surface of the deck if compare to the manual formulas and calculation of

software. At the support, bending moment approximately to zero and increases

steadily until the mid span of the bridge, where the location that maximum bending

moment takes place and decreases after the distance from the mid span. Moreover,

the shape of both graphs produced is similar which proved that the accuracy of the

oftware. Figure 7.6 shows the comparison bending moment results graphs of

oftware and LUSAS Modeller for load combination 2.

(a) Bending moment graph of software (b) Bending moment graph of LUSAS

Bending moment graph of both analysis tools for load combination 2


9 kNm while the result obtained from LUSAS

analysis is 1400 kNm. The condition is similar to the load combination 2 and 3. The

bending moment near the support is approximately to zero and increases steadily

until the mid span of the bridge, where the location that maximum bending moment

takes place and decreases after the distance from the mid span. As we know,

s

s

Figure 7.6

7


dead load, load model 1 (UDL system) and load model 3. The maximum bending

moment of software analysis is 111

100

orthotropic plate theory is adopted in software while finite element method is used in

USAS modeller. Furthermore, the Eurocode load model 1 to 3 is preset in the

USAS Modeller which give more accurate loading applied to the surface of the

deck if

(a) Bending moment graph of software (b) Bending moment graph of LUSAS

Bending moment graph of both analysis tools for load combination 3

7.4 Parametric Study

Parametric study is used to analyze the effect due to the manipulation of

cases of param

f reinforcement bar required and different values of bending moment applied is

tudied for different types of reinforced concrete box girder bridge. Besides that, the

lationship between the amount of reinforcement bar area required and the different

alues of section width is being studied also.

L

L

compare to the manual formulas and calculation of software. Howeover, the

shape of both graphs produced is similar which support the accuracy of the software

in analysis. Figure 7.7 shows the comparison bending moment results graphs of

software and LUSAS Modeller for load combination 3.

Figure 7.7

different parameter in design part of the developed software. In this research, two

etric study will be discussed. The relationship between the amounts

o

s

re

v

101

7.4.1 Relationship between Amount of Longitudinal Reinforcement Bar

equired Due to Different Values of Bending Moment Applied

Figure 7.8 Constants of parametric study

The constants are remained in the software but the bending moments applied

are vary. Figure 7.9 shows the relationship between amount area of reinforcement

bar required and the bending moments applied. The x-axis is the amount area of

reinforced bar required while y-axis showed the different values of bending moments

applied. The graph showed that when the value of applied bending moment is

increased, the amount area of reinforcem bar required is increased as well.

R

A study has been conducted to analyze the effect of bending moment applied

to the reinforcement bar required. The first case being studied is the left or right and

middle section of box girder which is in hogging and sagging situation respectively.

The applied bending moments are 1000 kNm, 2000 kNm, 3000 kNm, 4000 kNm and

5000 kNm. Other parameters are fixed as constants are shown in Figure 7.8 as

follows.

ent

102

Figure 7.9 Relationship between amount area of reinforcement bar required and

the bending moments applied

7.4.2 Relationship between Amount of Longitudinal Reinforcement Bar

Required Due to Different Values of Section Width, bf

In this case, the target is to study the effect of bending moment applied to the

reinforcement bar required. The width of the section, bf are 0.5 m, 1.0 m, 1.5 m, 2.0

m and 2.5 m respectively. Other parameters are fixed as constants are shown in

Figure 7.10 as follows.

Figure 7.10 Constants of parametric study

103

The constants above are remained in the software but the widths, bf of the box

girder section are varied. Figure 7.11 shows the relationship between amount area of

reinforcement bar required and width of the box section. The x-axis is the amount

area of reinforced bar required while y-axis showed the different values of width of

the box section. The graph showed that when the value of width of the section is

increased, the amount area of reinforcement bar required is decreased. This means

that the greater value for width of box section, the less reinforcement bar area is

quired in order to prevent the structural failure.

Figure 7.11 Relationship between amount area of reinforcement bar required and

the width of box section, bf

re

104

CHAPTER 8

LIMITATIONS, RECOMMENDATIONS AND CONCLUSION

re

BGB version 1.0 is new developed software which specializes in reinforce

oncrete box girder bridge analysis and design. Certainly there must have some

t

i.

e is unable to analyze box girder bridge which consists

continuous span in analysis part.

iii. Number of lanes applied in bridge is limited to three lanes and one

remaining area.

8.1 Limitations of Softwa

c

restric ions and limitations if compare to available software in market. The

limitations are listed as follows.

This software is applicable to single, double or triple cells of box girder

analysis and design only.

ii. This softwar

105

iv. There are only fifteen general types of individual load cases and three

types of load combinations to be manipulated by user in the software.

v. Design of bridge diaphragm is not included in this software.

vi. The dimension of detailing in box girder design part is not subjected to

scale. It r ork.

8.2 Recommendations

Since there are some limitations in this software, several recommendations

are proposed in order to improve the output results of the software are listed as

follows.

i. Number of box girder cell can be increased up to four cells since this type

of box girder also available in market.

ii. Number of notional option can be increased until six lanes which consist

iii. The software should be upgraded to the stage of analysis reinforced box

girder bridge deck with continuous span instead of simply supported only.

can only be a eference for draftsman in their w

vii. User can only utilize this software by using computer with the assistance

of Microsoft Excel software.

viii. This software does not possess the function of output file. This mean all

the data and result are only can be store in the Microsoft excel format.

of two way traffic.

106

iv. The number of load combination cases can be increased to make the

software more practical in real traffic situation.

v. Design of diaphragm is suggested in this software in order to complete

the bridge design.

vi. Detailing produced in the design part should be developed in AutoCAD

format which is subjected to scale.

vii. This software should be developed or upgraded to level which can

function in computer without software of Microsoft Excel.

viii. The function of output file should be developed for ease of application

and reference.

8.3 C

In the end of the research, it can be concluded that the new software, BGB

ersion 1.0 has been developed successfully. This software possesses two major

of reinforced concrete box girder. The benefits of

is software developing are time saving and ease of use for the new beginners.

ed when the research was carried out. A series of

nalysis and design procedures has been transform and developed into software with

ssistance of Microsoft Excel and it can be applied easily. All of the analysis and

str

onclusion

V

functions in analysis and design

th

On the other hand, the objectives of the research are achieved in the end of

the study. Structural properties and behaviours of reinforced concrete box girder

bridge had been study and review

a

a

design procedures are based on the latest version of Eurocode 2 to prevent the

uctural failure of the design.

107

Besides that, this software is able to analyze structural actions of reinforced

typ also had been verified through the

omparison results of both tools in aspects of deflection and bending moment. For

am can be manipulated in the design part of the software.

so ity,

liability and economy in the real world situations. The objectives of the research

ant in to the

designer in the future.

concrete box girder which are under fifteen types of individual load cases and three

es of load combinations. The results

c

the design part, parametric study had been carried in order to obtain the relationship

ong the parameters which

In this research, it can be concluded that the results obtained from the

ftware comprises of the advantages which are based on safety, serviceabil

re

were achieved and hopefully this software can contribute its signific

108

REFERENCES

te Structure: General Rules and

Rules for Building and Structural Fire Design. Thomas Telford Publishing,

3. Bill Mosley, John Bungey, et al. Reinforced Concrete Design to Eurocode 2.

4. C. R. Hendy and D. A. Smith. Designers’ Guide to EN 1992-2 Eurocode 2:

5. Dr. Kim S. Elloitt. The Design of Reinforced and Prestressed concrete

structure. The University of Nottingham. 2009

mien L. Keogh. Bridge Deck Analysis. Department

of Civil Engineering, University College Dublin, Ireland. E & FN SPON.

1999

1. R. Cusens and R. P. Rama. Bridge Deck Analysis. A Wiley – Interscience

Publication.1975

2. W. Beeby and R. S. Narayanan. Designers’ Guide to EN 1992-1-1 and EN

1992-1-2 Eurocode 2: Design of Concre

Thomas Telford Ltd. 2005

Palgrave Macmillan. 2008

Design of Concrete Structure Part 2: Concrete Bridges. Thomas Telford

Publishing, Thomas Telford Ltd. 2007

6. Eugene J. O’Brein and Da

7. BS EN 1991-2: 2003 (Eurocode 2: Actions on Structures Part 2: Traffic

Loads on Bridges). British Standards Institution, London. 2003

109

8. S EN 1992-1-1: 2004 (Eurocode 2: Design of Concrete Structures Part 1-1:

eneral Rules and Rules for Buildings). British Standards Institution, London.

B

G

2004

9. BS EN 1992-2-2: 2005 (Eurocode 2: Design of Concrete Structures Part 2:

Concrete bridges: Design and Detailing Rules). British Standards Institution,

London. 2005

10. N. Rajagopalan. Bridge Superstructure. Alpha Science International Ltd.

2006

110

APPENDIX I

Parameters in Orthotropic Plate Theory

Case 1: Torsionally stiff and/or flexural soft bridge decks (

The constants are defined as follows:

11 rLbnπβ = , 22 r

Lbnπβ = ,

by1

1 =ξ , by0

0 =ξ

)(2)()(

3113

321143

bababSSbSS

A−

+−−=

)(2)()(

3113

143321

babaaSSaSS

B−

−−+=

)(2)()(

3113

321143

dcdcdSSdSS

C−

−−+=

)(2)()(

3113

143321

dcdccSScSS

D−

+−−=

1211 )()(2

2

1

11

ηβηβ αα −− +−+= eGJrueGJ

ruS nn

2221 )()(2

2

1

12

ηβηβ αα −− +−+= eGJrueGJ

ruS nn

1211 )(1)(14

23

13

ηβηβ αα −− +−+= eEIur

eEIur

S nn

2221 )(1)(14

23

14

ηβηβ αα −− +++−= eEIur

eEIur

S nn

111

11111 sinhcosh βαβ rGJua n−=

22221 sinhcosh βαβ rGJub n−=

11111 coshsinh βαβ rGJuc n−=

22221 coshsinh βαβ rGJud n−=

1313 sinhcosh ββα uEIa n −=

2423 sinhcosh ββα uEIb n −=

1313 coshsinh ββα uEIc n −=

2423 coshsinh ββα uEId n −=

22

11 DrDu y −=

22

22 DrDu y −=

)]([ 22

113 yxxyy DDDrDru ++−=

)]([ 22

224 yxxyy DDDrDru ++−=

y

x

yy DD

DH

DHr −+= 2

1 )(

y

x

yy DD

DH

DHr −−= 2

2 )(

Ln

nπα =

112

Case 2: Isotropic Bridge Decks (


11 rLbnπβ = , 22 r

Lbnπβ = ,

by1

1 =ξ , by0

0 =ξ

)(2)()(

1331

321143

adaddSSdSS

A−

−−+=

)(2)()(

1331

321143

bcbccSScSS

B−

+−−=

)(2)()(

1331

143321

bcbcbSSbSS

C−

−−+=

)(2)()(

1331

143321

adadaSSaSS

D−

+−−=

} 1)1()1({ 111ηβηβηβ

αnevv

DGJ

S nnx

n −⎥⎦

⎤⎢⎣

⎡+−−−−=

} 2)1()1({ 222ηβηβηβ

αnevv

DGJ

S nnx

n −⎥⎦

⎤⎢⎣

⎡+−−−−=

{ } { } 1113 1)1(2 ηβηβ

αηβ ne

DEI

vS nx

nn

−⎥⎦

⎤⎢⎣

⎡+−−+=

{ } { } 2224 1)1(2 ηβηβ

αηβ ne

DEI

vS nx

nn

−⎥⎦

⎤⎢⎣

⎡++−+−=

nx

nn D

GJva β

αβ coshsinh)1(1 −−=

nx

nn D

GJvb βα

β sinhcosh)1(1 −−=

)sinhcosh(cosh2sinh)1(1 nnnx

nnnn D

GJvc βββα

βββ +−+−=

113

)coshsinh(sinh2cosh)1(1 nnnx

nnnn D

GJvd βββα

βββ +−+−=

nx

nn D

EIva βα

β sinhcosh)1(3 +−=

nx

nn D

EIvb βα

β coshsinh)1(3 +−=

nnx

nnnn D

EIvvc ββα

βββ sinhsinh)1(cosh)1(3 ++−−=

nnx

nnnn D

EIvvd ββα

βββ coshcosh)1(sinh)1(3 ++−−=

y

x

yy DD

DH

DHr −+= 2

1 )(

y

x

yy DD

DH

DHr −−= 2

2 )(

Lbn

nπβ =

114

Case 3: Torsional soft and/or flexural stiff bridge decks (


)(2)()(

1331

143321

dadadSSdSS

A−

−−+=

)(2)()(

3131

143321

bccbcSScSS

B−

+−−=

)(2)()(

3131

321143

bccbbSSbSS

C−

−−+=

)(2)()(

1331

321143

dadaaSSaSS

D−

+−−=

[ ] 13142141141 sincossin ηβηβηβηβα −−−= eEEGJS n

[ ] 23242241242 sincossin ηβηβηβηβα −−−= eEEGJS n

13)sincos()(

cossin 14314424

23

1441433ηβηβηβ

αηβηβ −

⎥⎦

⎤⎢⎣

⎡+

+−+= err

rrEI

EES n

23)sincos()(

cossin 24324424

23

2442434ηβηβηβ

αηβηβ err

rrEI

EES n⎥⎦

⎤⎢⎣

⎡+

++−−=

)sincoshcossinh(sinsinhcoscosh 4344334344351 ββββαββββ rrGJEEa n −++=

)coscoshsinsinh(cossinhsincosh 4344334344351 ββββαββββ rrGJEEb n ++−=

)sinsinhcoscosh(sincoshcossinh 4344334344351 ββββαββββ rrGJEEc n −++=

)cossinhsincosh(coscoshsinsinh 4344334344351 ββββαββββ rrGJEEd n ++−=

434374363 coscoshsincoshcossinh ββαββββ nEIEEa +−=

434314363 sincoshcoscoshsinsinh ββαββββ nEIEEb ++=

434374363 cossinhsinsinhcoscosh ββαββββ nEIEEc +−=

434374363 sinsinhcossinhsincosh ββαββββ nEIEEd ++=

115

[ ])()(

24

2322

42

3

41 rrDD

rrrE y +++

=

[ ])()(

24

2322

42

3

32 rrDD

rrr

E y +−+

=

)()( 22

32

43 yxxyy DDDrrDE +++−=

434 2 rrDE y=

)( 24

2325 rrDDE y −−=

)3()( 243

33236 rrrDDDDrE yyxxy −−++=

)3()( 234

34247 rrrDDDDrE yyxxy −+++=

33 brnαβ =

44 brnαβ =

yy

x

DH

DDr +=

21

3

yy

x

DH

DDr −=

21

4

Ln

nπα =

116

Case 4: Articulated bridge decks (

ts are defined as follows:

The constan

12

12

2

2

2

2

2

117

APPENDIX II

Example calculation of bridge deck analysis

(single cell box girder)

118

APPENDIX III

Example calculation of reinforced concrete box girder design

(single cell box girder – hogging moment)

LOad on Bridge 2

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