Temperature Effect on Prestressed Integral Bridge Beam

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THE EFFECT OF TEMPERATURE ON PRESTRESSED INTEGRAL

BRIDGE BEAM

MUHAMMAD LUTFI BIN OTHMAN

A report submitted in partial fulfillment of the

requirements for the award of the degree of

Master of Engineering (Civil Structure)

Faculty of Civil Engineering

Universiti Teknologi Malaysia

NOVEMBER 2009


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I declare that this report entitled The Effect of Temperature on Prestressed Integral

Bridge Beam is a result of my own research except as cited in the references. The

research has not been accepted for any degree and is not currently concurrently

submitted in candidature of any other degree

Signature :

Name : MUHAMMAD LUTFI BIN OTHMAN

Date :


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Karya ini adalah dedikasi teristimewa buat emak yang

dikasihi, Hamidah Bt Ahmad, abah yang disayangi, Othman Bin Mustaffa serta adik

tercinta, Fatimah Azzahrah Bt Othman yang tidak pernah jemu membekalkan nasihat,

kekuatan dan semangat untukku menghadapi liku-liku hidup seorang mahasiswa.

Tidak lupa juga buat Maktok, Allahyarham Abahtok, Tok Mah,

Tok Mat, sanak saudara serta semua teman-teman

seperjuanganku di Universiti Teknologi Malaysia


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ACKNOWLEDGEMENT

Praise be to Allah S.W.T, after months of hard work and brainstorming, this

masters project entitled The Effect of Temperature on Prestressed Integral Bridge

Beam is finally completed. Thanks to Allah S.W.T as to his guidance and mercy, this

thesis can at last be finished within the allocated time.

In this opportunity, I would like to express my gratitude towards my supervisor

for this project, Dr. Redzuan Bin Abdullah for his advice and kindness in guiding me

and my partner throughout the semester. Only Allah S.W.T can repay your kindness. I

would also like to give my sincerest thanks to Ir. Mohamad Salleh Bin Yassin for his

brilliant ideas, supportive critics, and also for being a huge helping hand in time of

needs. On top of that, I would like to give my special thanks to my partner, Mohd

Fairuz Omar for all the cooperation, help, and unwavering commitment throughout the

development of this study.

Last but not least, thanks to my mother, father, sister, all my family members,

all my friends and all the individuals for the moral support given.


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ABSTRAK

Kebanyakan jambatan di Malaysia ialah jenis konkrit pra-tegasan dan dibina

sebagai rasuk sokong mudah. Struktur jenis ini kebiasaannya terdedah kepada

masalah penyelenggaraan disebabkan kewujudan sambungan dan bering yang mudah

memburuk. Oleh itu, adalah sangat penting untuk tidak menggunakan sambungan

dan bering, atau setidak-tidaknya meminimakan penggunaannya agar kebolehkerjaan

dan jangka hayat struktur jambatan boleh ditingkatkan. Pihak berkuasa tempatan

(Jabatan Kerja Raya) kini telahpun mensyaratkan supaya jambatan dengan panjang

kurang daripada 60m direkabentuk dan dibina sebagai struktur integral.

Walaubagaimanapun, jambatan integral mempunyai ketidaktentuan yang tinggi

selain dipengaruhi oleh kesan suhu. Kesan suhu yang berbeza boleh menyebabkan

lenturan ke atas pada bahagian tengah jambatan. Disebabkan itu, sambungan integral

pada hujung rasuk mempunyai kemungkinan untuk retak. Penyelidikan ini

mensasarkan pembangunan model unsur terhingga untuk jambatan integral dengan

menggunakan perisian LUSAS. Selepas model tersebut berjaya dibangunkan dan

dibuktikan, model tersebut kemudiannya digunakan untuk mengkaji kesan suhu

terhadap daya pra-tegas pada rasuk jambatan integral. Semakin panjang unjuran

rasuk, semakin besar kesan suhu terhadap perubahan daya pra-tegas. Walaupun suhu

hanya berubah antara 22 C hingga 35 C di Malaysia, kesan suhu masih sangat

penting untuk diambilkira dalam merekabentuk jambatan integral.


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TABLE OF CONTENT

CHAP CONTENT PAGE

TITLE i

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENT vii

LIST OF TABLES xi

LIST OF FIGURES xiv

LIST OF NOTATIONS xviii

LIST OF APPENDICES xix

1 INTRODUCTION 1

1.1 Background Study 1

1.2 Problem Statement 2

1.3 Research Objectives 4

1.4 Research Questions 4

1.5 Scope of The Research 4


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CHAP CONTENT PAGE

2 BACKGROUND STUDY OF BRIDGE ANALYSIS

AND INTEGRAL BRIDGE

6

2.1 Bridge 6

2.2 Integral Bridges

2.2.1 Integral Bridge Issues

2.2.2 Integral Bridge Limitations

2.2.3 Integral Bridge Construction

7

8

9

9

2.3 Bridge Deck Analysis 12

2.3.1 Simply Supported Beam/Slab

2.3.2 Series of Simply Supported Beams/Slabs

2.3.3 Continuous Beam/Slab With Full Propping

During Construction

2.3.4 Partially Continuous Beam/Slab

2.3.5 Frame/Box Culvert (Integral Bridge)

13

14

16

16

19

2.4 Articulation 23

2.5 Bridge Loading 26

2.5.1 Dead and Superimposed Dead Loading 28

2.5.2 Imposed Traffic Loading 29

2.5.3 Imposed Loading Due to Road Traffic 29

2.5.4 Thermal Loading 30


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CHAP CONTENT PAGE

3 RESEARCH METHODOLOGY 34

3.1 Introduction 33

3.2 Problem Identification 36

3.3 Data Collection

3.3.1 Previous Research

3.3.2 Adaptation of Real Integral Bridge Design

3.3.2.1 Model Layout

3.3.2.2 Support Connection Details

36

36

38

38

39

3.4 LUSAS Structural Modelling

3.4.1 Assumptions

3.4.2 Geometry Definition

3.4.3 Attributes Definition

3.4.3.1 Meshing Attribute

3.4.3.2 Geometric Attribute

3.4.3.3 Material Attribute

3.4.3.4 Support Attribute

3.4.3.4.1 Example Calculation

For Spring Stiffness

3.4.3.5 Loading Attribute

3.4.4 Prestress Definition to BS5400

40

41

42

42

43

45

49

50

53

54

56

3.5 Prestress Change Determinationby Trial and Error

Method

57

3.6 Comparison of LUSAS and Hand Calculation Trial

and Error Method

59

3.6.1 Example Calculation for Hand Calculation

Method

60

3.7 Analysis and Result Interpretation 64


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CHAP CONTENT PAGE

4 RESULT AND DISCUSSION 65

4.1 Introduction 65

4.2 Analysis Outline 65

4.3 Comparison of Deflection

4.3.1 Case 1: Temperature Gradient (T T>T B)

4.3.2 Case 2: Temperature Gradient (T TT B)

4.4.2 Case 2: Temperature Gradient (T T


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LIST OF TABLES

TABLE NO. TITLE PAGE

3.1 Safety factor calculated according to each bridge

spans Z 1 and Z 2

39

3.2 General details for beam span 20m, 30m and 40m 39

3.3 Section properties for 20m, 30m and 40m integral

bridge span

46

3.4 Material properties 49

3.5

3.6

3.7

3.8

Values of spring stiffness

HA loading details

Trial and error method

Comparison of the reduction percentage between

LUSAS and hand calculation

54

54

59

64

4.1.1

4.1.2

Mid-span deflection comparison for 20m span

integral bridge and simply supported bridge due to

temperature gradient (T T>T B)




66

67


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TABLE NO

4.1.3

4.2.1

4.2.2

4.2.3

4.3.1

4.3.2

4.3.3

4.4.1

4.4.2

4.4.3

TITLE






temperature gradient (T T


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TABLE NO

4.5.1

4.5.2

4.5.3

4.6.1

4.6.2

4.6.3

4.7.1

4.7.2

4.7.3

4.8.1

4.8.2

4.8.3

TITLE

Prestress decrement percentage due to temperature

gradient (T T>TB) for 20m span integral bridge






gradient (T T


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LIST OF FIGURES

FIGURE NO. TITLE PAGE

2.1 Typical design of integral bridge 7

2.2 (a) Precast beams made integral over the interior

support

(b) deck continuous over interior support and

integral with abutments

(c) deck integral with abutments and pier

10

10

10

2.3 (a) geometry of integral bridge

(b) deformed shape if bases are restrained against

sliding

(c) bending moment diagram if bases are

restrained against sliding

(d) deformed shape if bases are partially restrained

against sliding

11

11

11

11

2.4 Portion of bridge illustrating bridge engineering

terms

13

2.5 Simply supported beam or slab 14

2.6 Series of simply supported beam/slabs 14

2.7 Continuous beam or slab 15

2.8 Bending moment diagrams due to uniform loading

of intensity

15


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2.9 (a) Elevation view of partially continuous bridge

with full-depth diaphragm at intermediate supports

(b) Plan view from below of partially continuous

bridge with full-depth diaphragm at intermediate

supports

16

17

2.10 Partially continuous bridge with continuity

provided only by the slab at intermediate supports

17

2.11 Joint detail at intermediate support of partially-

continuous bridge of the type illustrated in figure

2.10

18

2.12 (a) Bending moment due to selfweight

(b) Bending moment due to loading applied after

bridge has been made continuous

18

18

2.13 Box culvert 19

2.14 Three-span frame 19

2.15 Typical distributions of bending moment 20

2.16 Effect of thermal contraction of deck in frame

bridge

21

2.17 Sliding support and run-on slab in frame bridge 21

2.18 Composite precast and in-situ concrete frame

bridge

22

2.19 Plan views showing articulation of typical bridges 24

2.20 Uplift of bearings due to traffic loading 25

2.21 Uplift of bearing due to transverse loading caused

by differential thermal effects

25

2.22 (a) Beam on sliding bearing

(b) Beam fixed at both ends

31

31

3.1 Methodology flow chart 35

3.2 Overall elevation of the Charles D. Newhouse

research test setup

37

3.3 Diaphragm details 37


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3.4 Longitudinal integral beam 38

3.5 Integral beam-to abutment connection 39

3.6 Integral beam-to abutment connection detail 40

3.7 Integral bridge beam line 42

3.8 Tendon profile line 42

3.9 Line mesh assignment interface 44

3.10 Active mesh applied to beam and abutments 44

3.11 Arbitrary Section Property Calculator Interface 45

3.12 20m integral bridge span cross-section 46



3.15

3.16

3.17

3.18

3.19

3.20

3.21

3.22

4.1

4.2

4.3

4.4

Material assignment interface

Structural support setting for roller

Structural support setting for spring stiffness

Visual of roller support and spring stiffness

support in LUSAS

Four conditions of temperature effects

Single tendon prestress assignment interface

according to BS5400

Visual of assigned prestress at tendon

Estimation of the effects of unequal extreme fibre

temperatures by the flexibility method

Temperature gradient (T T>T B) case for deflection

comparison

Graph of mid span deflection versus temperature

gradient (T T>TB) for IB and SSB

Temperature gradient (T T


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FIGURE NO.

4.5

4.6

4.7

4.8

4.9

4.10

4.11

4.12

4.13

4.14

4.15

4.16

TITLE

Uniform temperature increment case for deflection

comparison

Graph of mid span deflection versus uniform

temperature increment for IB and SSB

Uniform temperature decrement case for

deflection comparison

Graph of mid span deflection versus uniform

temperature decrement for IB and SSB

Temperature gradient (T T>T B) case for prestress

change analysis

Graph of prestress decrement percentage versus


Temperature gradient (T T


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LIST OF NOTATIONS

LUSAS - London University Stress Analysis System

(engineering software)

d - Dry density of the backfill

- Coefficient of thermal expansion

Gs - Specific gravity

T - Increased temperature

p - Horizontal stress

h - Section depth

emax - Eccentricity at mid-span

emin - Eccentricity at support

A - Area

I - Moment of Inertia

M - Moment

TT - Temperature at extreme top of fibre

TB - Temperature at extreme bottom of fibre

Ec - Modulus of Elasticity

f cu - Characteristic strength

Es - Modulus of Elasticity

- Concrete creep coefficient

- Curvature

Coef. - Coefficient

Temp. - Temperature

IB - Integral bridge

SSB - Simply supported bridge


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LIST OF APPENDICES

APPENDIC NO. TITLE PAGE

A Design Example of Beam Section and Prestressing

Force by Microsoft Excel

87


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CHAPTER I

INTRODUCTION

1.1 Background Study

One of the most important structures is bridge. In Malaysia, most of the existing

bridges were design as simple spans. In simple span construction, joints and bearings are parts

of the bridge structure. It is indeed easier for the engineers to design and easier for the

contractors to build simple span bridge but on the other hand, because of the joints between

the spans of the bridge, it will not be able to provide a smooth riding surface to the public and

furthermore a leaking joint will most certainly cause corrosion. The maintenance is also costly

as the bearing needed to be replaced after every few years.

Today, integral bridges have been constructed all over the world instead of the

conventional simple spans bridges. The advantages of integral bridge have been realized as

early as the 60s. The use of integral deck eliminates the need for deck expansion joints and

bearings. More significantly, maintenance costs are also reduced since deck joints, which

allow water to leak onto substructures elements and accelerate deterioration, are totally

eliminated. In addition, future widening or bridge replacement becomes easier, since the

simple design of the integral abutment lends itself to simple structural modification.


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1.2 Problem Statement

In recent years, it has been established that a significant portion of the world's bridges

are not performing as they should. In some cases, bridges are carrying significantly more

traffic load than originally intended. However, in many others, the problem is one of

durability. This is often associated with joints that are leaking or with details that have

resulted in chloride-contaminated water dripping onto substructures. Problems have also been

reported with post-tensioned concrete bridges in which inadequate grouting of the ducts has

lead to corrosion of the tendons.

The new awareness of the need to design durable bridges has led to dramatic changes

of attitude towards bridge design. There is now a significant move away from bridges that are

easy to design towards bridges that will require little maintenance. The bridges that were easy

to design were usually determinate, e.g. simply supported spans and cantilevers. However,

such structural forms have many joints which are prone to leakage and also have many

bearings which require replacement many times over the lifetime of the bridge.

The move now is towards bridges which are highly indeterminate and which have few

joints or bearings. The structural forms of bridges are closely interlinked with the methods of

construction. The methods of construction in turn are often dictated by the particular

conditions on site. For example, when a bridge is to be located over an inaccessible place,

such as a railway yard or a deep valley, the construction must be carried out without support

from below. This immediately limits the structural forms to those that can be constructed in

this way. The method of construction also influences the distributions of moment and force in

a bridge. For example, in some bridges, steel beams carry the self weight of the deck while

composite steel and in-situ concrete carry the imposed traffic loading.

Integral bridge is advantageous in term of maintenance and long term planning if

compared to the conventional bridge. This type of bridge can also be seen as the future bridge

as it is stiffer and has been observed that the deflection and moments can be greatly reduced

as in case of integral bridge. The elimination or minimizing of bearings and joints is important

as they are fragile elements and represent the weakest links in bridge structures. Joints areexpensive to buy, install, maintain and repair. Sometimes repair costs can run as high as


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replacement costs. Successive paving will ultimately require that joints be replaced or raised.

Even waterproof joints will leak over time, allowing water salt-laden or otherwise, to pour

through the joints accelerating corrosion damage to girder ends bearings and supporting

reinforced concrete substructures. Accumulated dirt, rocks and trash fill Elastomeric glands

leading to failure.

Bearings are also expensive to buy and install and more costly to replace. Over time,

steel bearings may tip over and seize up due to loss of lubrication or buildup of corrosion.

Elastomeric bearings can split and rupture due to unanticipated movements or ratchet out of

position. Teflon sliding surfaces are fragile for bridge applications and can fail prematurely

due to excessive wear from dirt and other contaminants, or due to poor fabrication and

construction tolerances. Pot bearings also suffer frequent damage due to poor fabrication and

construction techniques.

Integral bridges are characterized by monolithic connection between the deck and the

substructure. Such bridges are the answer for small and medium length bridges where

bearings and joints are either eliminated or reduced to minimum. The integral bridge concept

is an excellent option to incorporating reduced inspection and maintenance features in the

bridge structures. However, it is more complicated to design and the secondary restraint

moments can develop at the connection due to creep, shrinkage, and thermal effects.

In Malaysia, this type of bridge is still not widely used because of its complexity and

the lack of knowledge and experience within Malaysian construction industry.

The purpose of experimental study presented in this paper was to compare the restraint

moments that developed during the early ages of continuity to the predicted restraint moments

using finite element program, LUSAS. It is important to be able to accurately predict the

restraint moment because:

i. Underprediction leads to unconservative designs and the potential for damage

to cracking at the continuity connection

ii. Overprediction may force the designer to use simple span design instead of

continuous design


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1.3 Research Objectives

The objectives of this research are:

1. To study the effect of temperature gradient on the prestressing force in prestressed

integral bridge beam

2. To study the effect of uniform temperature change on the prestressing force in

prestressed integral bridge beam

3. To determine whether temperature effects can be neglected in integral bridge design

considering Malaysian condition

1.4 Research Questions

By the end of this research, it is aimed that the following questions will be answered

1. How integral bridge response to temperature effect?

2. How does the prestress force reacts to temperature loadings?

3. Is it true that integral bridge beam is better than simply supported beam?

4. Can the temperature effects be neglected at certain span of the integral bridge?

1.5 Scope of The Research

In order to finish this research within the limited time, the following scopes are being

considered:

a. The simulation of the integral bridge will be developed using LUSAS programand will be verified by consulting superior LUSAS users


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b. The temperature gradient is fixed between 0 C to 40 C and the span length

between 20m to 40m

c. Typical design of integral bridge consists of the beams, piers and abutments is

used

d. The temperature effect studied only consider Malaysian condition


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CHAPTER II

BACKGROUND STUDY OF BRIDGE ANALYSIS AND INTEGRAL

BRIDGE

2.1 Bridge

According to Heinz Kurth in his book, Bridge, a bridge is a permanent raised

structure which allows people or vehicles to cross obstacles such as a river without blocking

the way of traffic passing underneath. In other words, a bridge is a structure built to span a

gorge, valley, road, railroad track, river, body of water, or any other physical obstacle.

Designs of bridges vary depending on the function of the bridge and the nature of the terrain

where the bridge is to be constructed. There are six main types of bridges:

i. Beam bridges

ii. Cantilever bridges

iii. Arch bridges

iv. Suspension bridges

v. Cable-stayed bridges

vi. Truss bridges.


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2.2.1 Integral Bridge Issues

One of the aims of a designer of concrete bridges should be to reduce maintenance by

minimising the number and sophistication of mechanical engineering devices required for its

operation. Thus, wherever possible, piers should be built into the deck. Where this is not

possible, the next best option is to adopt concrete hinges, then rubber bearings, then fixed

mechanical bearings, and last of all, sliding bearings.

However, the greatest single item of maintenance expenditure on highway bridges is

the expansion joint. Not only do such joints need regular repair and renewal, but they also

allow salt-laden water to attack and corrode the substructure. Most attempts at creating

waterproof joints fail after a number of years of service. Expansion joints also need to be

inspected from beneath, which greatly increases the cost and complexity of abutments.

Integral bridges take the philosophy of mechanical simplicity to its logical conclusion

by either pinning the deck to the abutment or building it in. This eliminates the expansion

joint and greatly simplifies the abutment structure that becomes more like a pier. The

consequence of this type of design is that the abutment either rocks or slides back and forth as

the bridge expands and contracts, causing settlement of the backfill behind the abutment, and

disrupting the road surface. This is overcome either by regular maintenance of the road

surface, or by bridging the disrupted area with a short transition slab. The slab is attached to

the abutment, and so follows its movement, sliding on the substrate. Consequently, a flexible

mastic type joint is required in the blacktop at the end of the transition slab. Some authorities

adopt transition slabs, while others prefer to maintain the road immediately behind the

abutment.

A very economical form of abutment is achieved by separating the functions of soil

retention and support of the deck. The soil is retained by a reinforced earth wall, while the

deck is carried on piles that are allowed to rock within the fill. The piles may be concrete or

steel, and may be encased in pipes to give them the freedom to rock. It needs to be

demonstrated that steel piles would be adequately protected from corrosion; they would

appear to be more at risk than similar piles driven into the embankment. (Benaim et al., 2008)


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2.2.2 Integral Bridge Limitations

There are limitations on the use of integral bridges. These involve the following factors:

i. Length of structure. Limitations on length are concerned with passive pressure effects,

stresses in the piles, and the movement capacity of the joints between the approach

slab and the approach pavement. Many state departments of transportation limit the

lengths to 300 ft for steel superstructures and 600 ft for prestressed concrete

superstructures. A few states , like Tennessee, have successfully used longer lengths.

ii. Structure geometry. Only six states have reported application of integral construction

to curved bridges. Skew angles have generally been below 40 deg. However,

Tennessee has used this method of construction extensively and effectively for curved

bridges as well as bridges with skew angles up to 70 deg.

iii. Foundations. Integral brtdges require that abutment piles be flexible. Therefore, they

should not be used with pile foundation where rock is closer than 10 ft from the

bottom of the abutment beam unless pre-augered holes for piles are employed . The

New York Department of Transportation specifies a minimum pile penetration of 20 ft

into acceptable soils to ensure adequate flexibility and to provide for scour protection.

The minimum depth is also meant to provide sufficient lateral support for the pile.

particularly when conditions dictate that the top portion of the pile is pre-augered and

back-filled with granular material.

Usually. integral bridges are founded on piles However, there are instances where they

have been supported by spread footings that are founded on rock. They can also be supported

on spread footings on soil if the soil is well compacted and the possibility of settlement of the

foundation is considered in the design. (Precast/Prestressed Concrete Institute, 2001)

2.2.3 Integral Bridge Construction

There are many variations on the basic integral bridge. In figure 2.2 (a), the deck iscomposed of separate precast beams in each span. While in the past such a deck might have


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had a joint over the central support, a more durable form of construction is to make it

continuous over the support using in-situ concrete, as illustrated. In figure 2.2 (b), the deck of

the bridge is continuous over the internal support and integral with the abutments at the ends.

Another type is shown in figure 2.2 (c), this bridge is integral with both the abutments and the

intermediate pier.

Figure 2.2 (a): precast beams made integral over the interior support (OBrien et al., 1999)

Figure 2.2 (b): deck continuous over interior support and integral with abutments

(OBrien et al., 1999)

Figure 2.2 (c): deck integral with abutments and pier (OBrien et al., 1999)

While there are considerable durability advantages in removing joints and bearings,

their removal does affect the bridge behaviour. Specifically, expansion and contraction of the

deck is restrained with the result that additional stresses are induced which must be resisted by

the bridge structure. The most obvious cause of expansion or contraction in bridges of all

forms is temperature change but other causes exist, such as shrinkage in concrete bridges. In

prestressed concrete decks, elastic shortening and creep also occur.

A simple integral bridge is illustrated in figure 2.3(a). If the bases of the abutments are

not free to slide, deck contraction induces the deformed shape illustrated in figure 2.3(b) and

the bending moment diagram of figure 2.3(c). Partial sliding restraint at the bases of the


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abutments results in the deformed shape of figure 2.3(d) and a bending moment diagram

which is similar in shape to that of figure 2.3(c), but of a different magnitude.

Figure 2.3(a): geometry of integral bridge (OBrien et al., 1999)

Figure 2.3 (b): deformed shape if bases are restrained against sliding (OBrien et al., 1999)

Figure 2.3 (c): bending moment diagram if bases are restrained against sliding


Figure 2.3 (d): deformed shape if bases are partially restrained against sliding

(OBrien et al., 199 9)

Time-dependent contractions in concrete bridge decks induce bending moments in

integral bridges. While the magnitude of creep contraction is time dependent, creep also has

the effect of relieving the induced bending moments overtime. The net effect of this is that

moments induced by creep contraction are small. Shrinkage strain increases with time but the

resulting moments are also reduced by creep.


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Elastic shortening occurs in post-tensioned prestressed concrete decks during the

application of prestress. If the deck is integral with the supports at the time of stressing,

bending moments are induced. On the other hand, many integral bridges are constructed from

precast pretensioned beams and the bridge is not made integral until after the pretensioning

process is complete. In such cases, no bending moments are induced by the elastic shortening.

Temperature changes are another major source of deck expansion and contraction.

Temperature can be viewed as having a seasonal and hence long-term component as well as a

daily or short-term component. The resistance of an integral bridge to movement of any type

depends largely on the form of construction of the substructures. Three alternative forms are

illustrated in Fig. 4.3. In each case , a run-on slab is shown behind the abutment.

These are commonly placed over the transition zone between the bridge and the

adjacent soil which generally consists of granular backfill material. Figures 4.3(a) and (b)

show two bridges which are integral with high supporting abutments and piled foundations. In

such a case , a reduction in lateral restraint can be achieved by using driven H-section piles

with their weaker axes orientated appropriately. An alternative form of integral construction is

one in which abutments sit on strip foundations like the small bank seat abutment illustrated

in Fig. 4.3 (c). Minimising the sliding resistance at the base of these foundations helps to

reduce the lateral restraint. Care should be taken in the design to ensure that bank seats have

sufficient weight to avoid uplift from applied loads in other spans. (OBrien et al., 1999)

2.3 Bridge Deck Analysis

According to Bridge Deck Analysis by Eugene J. OBrien and Damien L. Keogh, t he

main body of the bridge superstructure is known as the deck and can consist of a main part

and cantilevers. The deck spans longitudinally, which is the direction of span, and

transversely, which is perpendicular to it. There may be upstands or downstands at the ends of

the cantilever for aesthetic purposes and to support the parapet which is built to retain the

vehicles on the bridge.


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It is also said that bridge decks are frequently supported on bearings which transmit the

loads to abutments at the ends or to piers or walls elsewhere. Joints may be present to

facilitate expansion or contraction of the deck at the ends or in the interior. Illustration which

shows the bridge engineering terms is shown in figure 2.4.

Figure 2.4: Portion of bridge illustrating bridge engineering terms


2.3.1 Simply Supported Beam/Slab

The simplest form of bridge is the single-span beam or slab which is simply supported

at its ends. This form is widely used when the bridge crosses a minor road or small river. In

such cases, the span is relatively small and multiple spans are infeasible and/ or unnecessary.

The simply supported bridge is relatively simple to analyse and to construct but is

disadvantaged by having bearings and joints at both ends. The cross-section is often solid

rectangular but can also be voided rectangular, T-section or box-sections. (OBrien et al.,

1999)


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Figure 2.5: Simply supported beam or slab (OBrien et al., 1999)

2.3.2 Series of Simply Supported Beams/Slabs

When a bridge crossing is too wide for an economical single span, it is possible toconstruct what is in effect a series of simply supported bridges, one after the other, as

illustrated in figure 2.6 below:

Figure 2.6 : Series of simply supported beam/slabs (OBrien et al., 1999)

Like single-span bridges, this form is relatively simple to analyse and construct. (It is

particularly favoured on poor soils where differential settlements of supports are anticipated.

It also has the advantage that, if constructed using in-situ concrete, the concrete pours aremoderately sized. In addition, there is less disruption to any traffic that may be below as only

one span needs to be closed at any time . However, there are many joints and bearings with

the result that a series of simply supported beams/ slabs is no longer favoured in practice.

Continuous beams/ slabs, as illustrated in figure 2.7, have significantly fewer joints and

bearings.


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Figure 2.7: Continuous beam or slab (OBrien et al., 1999)

A further disadvantage of simply supported beam/ slabs in comparison to continuous

ones is that the maximum bending moment in the former is significantly greater than that in

the latter. For example, the bending moment diagrams due to a uniformly distributed loading

of intensity w (kN/m) are illustrated in figure 2.8. It can be seen that the maximum moment in

the simply supported case is significantly greater (about 25%) than that in the continuous

case. The implication of this is that the bridge deck needs to be correspondingly deeper.


Figure 2.8: Bending moment diagrams due to uniform loading of intensity, w: (a) 3

simply supported spans of length, l; (b) One 3-span continuous beam with span lengths, l


(a)

(b)


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2.3.3 Continuous Beam/Slab with Full Propping During Construction

Continuous beam/slab construction has significant advantages over simply supported

spans in that there are fewer joints and bearings and the applied bending moments are less.

For bridges of moderate total length, the concrete can be poured in-situ in one pour. This

completely removes the need for any joints. However, as the total bridge length becomes

large, the amount of concrete that needs to be cast in one pour can become excessive. This

tends to increase cost as the construction becomes more of a batch process than a continuous

one. (OBrien et al., 1999)

2.3.4 Partially Continuous Beam/Slab

When support from below during construction is expensive or infeasible, it is possible

to use precast concrete or steel beams to construct a partially continuous bridge. Precast

concrete or steel beams are placed initially in a series of simply supported spans. In-situ

concrete is then used to make the finished bridge continuous over intermediate joints. Two

forms of partially continuous bridge are possible. In the form illustrated in figure 2.9, the in-

situ concrete is cast to the full depth of the bridge overall supports to form what is known as a

diaphragm beam. (OBrien et al., 1999)

Figure 2.9 (a): Elevation view of partially continuous bridge with full-depth diaphragm

at intermediate supports (OBrien et al., 1999)


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Figure 2.9 (b): Plan view from below of partially continuous bridge with full-depth

diaphragm at intermediate supports (OBrien et al., 1999)

In the alternative form of partially continuous bridge, illustrated in figure 2.10,

continuity over intermediate supports is provided only by the slab. Thus the in-situ slab alone

is required to resist the complete hogging moment at the intermediate supports. This is

possible due to the fact that members of low structural stiffness (second moment of area) tend

to attract low bending moment. The slab at the support in this form of construction is

particularly flexible and tends to attract a relatively low bending moment. There is concern

among some designers about the integrity of such a joint as it must undergo significant

rotation during the service life of the bridge.

Figure 2.10: Partially continuous bridge with continuity provided only by the slab at

intermediate supports (OBrien et al., 1999)


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Further, as the main bridge beams rotate at their ends, the joint must move

longitudinally to accommodate this rotation as illustrated in figure 2.11.

Figure 2.11: Joint detail at intermediate support of partially-continuous bridge of the

type illustrated in figure 2.10 (OBrien et al., 19 99)

In partially continuous bridges, the precast concrete or steel beams carry all the self

weight of the bridge which generates a bending moment diagram such as that illustrated in

figure 2.12 (a) for a two-span bridge.

Figure 2.12 (a): Bending moment due to selfweight (OBrien et al., 1999)

By the time the imposed traffic loading is applied, the bridge is continuous and the

resulting bending moment diagram is as illustrated in figure 2.12 (b).

Fig. 2.12 (b): Bending moment due to loading applied after bridge has been made

continuous (OBrien et al., 1999)


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The total bending moment diagram will be a combination of that due to self weight and

other loading. Unfortunately, due to creep, self weight continues to cause deformation in the

bridge after it has been made continuous. At this stage it is resisted by a continuous rather

than a simply supported beam/ slab and it generates a distribution of bending moment more

like that of figure 2.12(b) than figure 2.12(a). This introduces a complexity into the analysis

compounded by a great difficulty in making accurate predictions of creep effects. (OBrien et

al., 1999)

2.3.5 Frame/Box Culvert (Integral Bridge)

Frame or box bridges, such as illustrated in figure 2.13 and 2.14, are more effective at

resisting applied vertical loading than simply supported or continuous beams/slabs.

Figure 2.13: Box culvert (OBrien et al., 1999)

Figure 2.14: Three-span frame (OBrien et al., 1999)


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This is because the maximum bending moment tends to be less, as can be seen from the

examples of figure 2.15.

Figure 2.15: Typical distributions of bending moment: (a) simply-supported spans; (b)

continuous beams; (c) frames/ box culverts (OBrien et al., 1999)

However, accommodating movements due to temperature changes or creep/shrinkage

can be a problem and, until recently , it was not considered feasible to design frame bridges of

any great length (about 20 m was considered maximum). The effects of deck shortening

relative to the supports is to induce bending in the whole frame as illustrated in figure 2.16 If

some of this shortening is due to creep or shrinkage, there is the usual complexity and

uncertainty associated with such calculations. A further complexity in the analysis of frame

bridges is that, unless the transverse width is relatively small, the structural behaviour is three-dimensional. Continuous slab bridges on the other hand, can be analysed using two-

dimensional models.

(a)

(b)

(c)


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Figure 2.16: Effect of thermal contraction of deck in frame bridge: (a) deflected shape;

(b) distribution of bending moment (OBrien et al., 1999)

The minimal maintenance requirement of frame/ box culvert bridges is their greatest

advantage. There are no joints or bearings as the deck is integral with the piers and abutments.

Given the great upsurge of interest in maintenance and durability in recent years, this lack of

maintenance has resulted in an explosion in the numbers of bridges of this form. Ever longer

spans are being achieved. It is now considered that bridges of this type of 100 m and longer

are possible.

There are two implications for longer frame-type bridges, both relating to longitudinal

movements. If the supports are fully fixed against translation, deck movements in such

bridges will generate enormous stresses. This problem has been overcome by allowing the

supports to slide as illustrated in figure 2.17.

Figure 2.17: Sliding support and run-on slab in frame bridge (OBrien et al., 1999)

(a)

(b)


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If the bridge is supported on piles, the axes of the piles are orientated so as to provide

minimum resistance to longitudinal movement. The second implication of longer frame

bridges is that the bridge moves relative to the surrounding ground. To overcome this,

engineers specify 'run-on' slabs as illustrated in the figure which span over loose fill that is

intended to allow the abutments to move. The run-on slab can rotate relative to the bridge

deck but there is no relative translation. Thus, at the ends of the run-on slabs, a joint is

required to facilitate translational movements. Such a joint is remote from the main bridge

structure and, if it does leak, will not lead to deterioration of the bridge itself. (OBrien et al.,

1999)

A precast variation of the frame/box culvert bridge has become particularly popular in

recent years. Precast pretensioned concrete beams have a good record of durability and do not

suffer from the problems associated with grouted post tensioning tendons. These can be used

in combination with in-situ concrete to form a frame bridge as illustrated in figure 2.18

Figure 2.18: Composite precast and in-situ concrete frame bridge (OBrien et al., 1999)


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2.4 Articulation

In order to understand more about the importance of not having joints and bearings, it is

essential to have the general idea on the matter. Bridge design is often a compromise between

the maintenance implications of providing joints and bearings and the reduction in stresses

which results from the accommodation of deck movements. While the present trend is to

provide ever fewer joints and bearings, the problems of creep, shrinkage and thermal

movement are still very real and no one form of construction is the best for all situations.

The articulation of a bridge is the scheme for accommodating movements due to creep,

shrinkage and thermal effects while keeping the structure stable. While this clearly does not

apply to bridges without joints or bearings, it is a necessary consideration for those which do.

Horizontal forces are caused by braking and traction of vehicles, wind and accidental impact

forces from errant vehicles. Thus, the bridge must have the capacity to resist some relatively

small forces while accommodating movements.

In-situ concrete bridges are generally supported on a finite number of bearings. The

bearings usually allow free rotation but may or may not allow horizontal translation. They are

generally of one of the following three types :

i. fixed - no horizontal translation allowed ;

ii. free sliding - fully free to move horizontally;

iii. guided sliding - free to move horizontally in one direction only.

In many bridges, a combination of the three types of bearing is provided. Two of the

simplest forms of articulation are illustrated in figures 2.19 (a) and (b) where the arrows

indicate the direction in which movements are allowed. For both bridges, A is a fixed bearing

allowing no horizontal movement. To make the structure stable in the horizontal plane, guided

sliding bearings are provided at C and, in the case of the two-span bridge, also at E. These

bearings are designed to resist horizontal forces such as the impact force due to an excessively

high vehicle attempting to pass under the bridge. At the same time they accommodate

longitudinal movements, such as those due to temperature changes. Free sliding bearings areprovided elsewhere to accommodate transverse movements. When bridges are not very wide


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(less than about 5 m), it may be possible to articulate ignoring transverse movements such as

illustrated in figure 2.19(c).

(a)

Figures 2.19: Plan views showing articulation of typical bridges: (a) simply supported

slab; (b) two-span skewed slab; (c) two-span bridge of small width (OBrien et al., 1999)

When bridges are not straight in plan, the orientation of movements tends to radiate

outwards from the fixed bearing. Bearings are generally incapable of resisting an upward

'uplift' force. Further, if unanticipated net uplift occurs, dust and other contaminants are likely

to get into the bearing, considerably shortening its life. Uplift can occur at the acute corners of

skewed bridges such as Band E in figure 2.19( b). Uplift can also occur due to applied loading

in right bridges if the span lengths are significantly different, as illustrated in figure 2.20

(c)

(b)


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However, even with no skew and typical span lengths, differential thermal effects can

cause transverse bending which can result in uplift as illustrated in figure 2.21.

Figure 2.20: Uplift of bearings due to traffic loading (OBrien et al., 1999)

Figure 2.21: Uplift of bearing due to transverse loading caused by differential thermal

effects (OBrien et al., 1999)

If this occurs, not only is there a risk of deterioration in the central bearing but, as it is

not taking any load, the two outer bearings must be designed to resist all of the load which

renders the central bearing redundant. Such a situation can be prevented by ensuring that the

reaction at the central bearing due to permanent loading exceeds the uplift force due to

temperature. If this is not possible, it is better to provide two bearings only. (O Brien et al.,1999)


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2.5 Bridge Loading

For bridges, it is often necessary to consider phenomena which would normally be

ignored in buildings. For example, effects such as differential settlement of supports

frequently need to be considered by bridge designers while generally being ignored by

designers of building structures. Other types of loading which may occur but which are not

considered here are the effects of shrinkage and creep, exceptional loads (such as snow) and

construction loads.

Another source of loading is earth pressure on substructures. This must be considered

in the context of integral bridges. Three codes of practice can be referred to, namely, the

British Department of Transport standard BD37/ 88 (1988), the draft Eurocode EC1 (1995)

and the American standard AASHTO (1995). Dead and superimposed dead loads consist of

permanent gravity forces due to structural elements and other permanent items such as

parapets and road surfacing. Imposed traffic loads consist of those forces induced by road or

rail vehicles on the bridge. The predominant effect is the vertical gravity loading including the

effect of impact. However, horizontal loading due to braking/traction and centrifugal effects

in curved bridges must also be considered. Where footpaths or cycle tracks have been

provided, the gravity loading due to pedestrians/cyclists can be significant.

Thermal changes can have significant effects, particularly in frame and arch bridges.

Both the British standard and the AASHTO treatments of temperature are somewhat tedious

in that different load 'combinations' must be considered. For example, the AASHTO standard

specifies one combination which includes the effects of temperature, wind and imposed traffic

loading. An alternative, which must also be considered, excludes some thermal and wind

effects but includes a higher traffic loading. The calculation is complicated by the use of

different factors of safety and the specification of different design limits for the different

combinations. For example, the service stresses permitted in prestressed concrete bridges are

higher for the combinations in BD37/88 which include temperature than for combinations

which do not. The draft Eurocode treats temperature in a manner similar to other load types

and applies the same method of combining loads as is used throughout ECl.


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Differential settlement of supports can induce significant bending in continuous beam

or slab bridges. The draft Eurocode on Geotechnical Design, EC7 (1994), recommends that

the process of soil/structure interaction be taken into consideration for accurate analysis of

problems of this type, i.e. it is recommended that a combined model of the bridge structure

and the supporting soil be used to determine the stresses induced by settlement. No

geotechnical guidance is given in either BD37/88 or AASHTO on how bridges should be

analysed to determine the effect of this phenomenon. The loading due to impact from

collisions with errant vehicles can be quite significant for some bridge elements. The load

specified in the UK has increased dramatically in recent years. Similarly high levels of impact

loading are in use in many European national standards, in AASHTO and in the draft

Eurocode. Vibration is generally only significant in particularly slender bridges. In practice,

this usually only includes pedestrian bridges and long-span road and rail bridges, where the

natural frequency of the bridge is at a level which can be excited by traffic or wind. In

pedestrian bridges, it should be ensured that the natural frequency of the bridge is not close to

that of walking or jogging pedestrians.

In addition to its ability to induce vibration in bridges, wind can induce static

horizontal forces on bridges . The critical load case generally occurs when a train of high

vehicles are present on the bridge resulting in a large vertical projected area. Wind tends not

to be critical for typical road bridges that are relatively wide but can be significant in elevated

railway viaducts when the vertical projected surface area is large relative to the bridge width.

Both the British and the American standards specify a simple conservative design wind

loading intensity which can be safely used in most cases . More accurate (and complex)

methods are also specified for cases where wind has a significant effect.

Prestress is not a load as such but a means by which applied loads are resisted.

However, in indeterminate bridges it is necessary to analyse to determine the effect of

prestress so it is often convenient to treat prestress as a form of loading. The methods used are

very similar to those used to determine the effects of temperature changes. (OBrien et al.,

1999)


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2.5.1 Dead and Superimposed Dead Loading

For general and building structures, dead or permanent loading is the gravity loading

due to the structure and other items permanently attached to it. In BD37/ 88, there is a

subdivision of this into dead loading and superimposed dead loading. The former is the

gravity loading of all structural elements. It is simply calculated as the product of volume and

material density. For prestressed concrete bridges, it is important to remember that an

overestimate of the dead load can result in excessive stresses due to prestress. Thus dead load

should be estimated as accurately as possible rather than simply rounded up. Superimposed

dead load is the gravity load of non-structural parts of the bridge. Such items are long term

but might be changed during the lifetime of the structure. An example of superimposed dead

load is the weight of the parapet.

There is clearly always going to be a parapet so it is a permanent source of loading.

However, it is probable in many cases that the parapet will need to be replaced during the life

of the bridge and the new parapet could easily be heavier than the original one. Because of

such uncertainty, superimposed dead load tends to be assigned higher factors of safety than

dead 1oad. The most suitable item of superimposed dead load is the road pavement or

surfacing. It is not unusual for road pavements to get progressively thicker over a number of

years as each new surfacing is simply laid on top of the one before it. Thus, such

superimposed dead loading is particularly prone to increases during the bridge lifetime. For

this reason, a particularly high load factor is applied to road pavement.

Bridges are unusual among structures in that a high proportion of the total loading is

attributable to dead and superimposed dead load. This is particularly true of long-span

bridges. In such cases, steel or aluminium decks can become economically viable due to their

high strength-to-weight ratio. For shorter spans, concrete or composite steel beams with

concrete slabs are the usual materials. In some cases, lightweight concrete has been

successfully used in order to reduce the dead load.

In addition to its ability to induce vibration in bridges, wind can induce static

horizontal forces on bridges. The critical load case generally occurs when a train of highvehicles are present on the bridge resulting in a large vertical projected area. Wind tends not


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to be critica l for typical road bridges that are relatively wide but can be significant in elevated

railway viaducts when the vertical projected surface area is large relative to the bridge width.

Both the British and the American standards specify a simple conservative design wind

loading intensity which can be safely used in most cases. More accurate (and complex)

methods are also spicified for cases where wind has a significant effect. (OBrien et al., 19 99)

2.5.2 Imposed Traffic Loading

Bridge traffic can be vehicular, rail or pedestrian cycle or indeed any combination of

these. Vehicular and rail traffic are considered in subsections below. While pedestrian/cycle

traffic loading on bridges is not difficult to calculate, its importance should not be

underestimated. Bridge codes commonly specify a basic intensity for pedestrian loading (e.g.

5 kN/m 2 in the draft Eurocode and the British standard and 4 kN/m 2 in the American code).

When a structural element supports both pedestrian and traffic loading, a reduced intensity is

allowed by some codes to reflect the reduced probability of both traffic and pedestrian loading

reaching extreme values simultaneously. Most codes allow a reduction for long footpaths.


2.5.3 Imposed Loading Due to Road Traffic

While some truck-weighing campaigns have been carried out in the past, there has

been a scar city of good unbiased data on road traffic loading until recent years. Bridge traffic

loading is often governed by trucks whose weights are substantially in excess of the legal

maximum. In the past, sampling was carried out by taking trucks from the traffic stream and

weighing them statically on weighbridges. There are two problems with this as a means of

collecting statistics on truck weights. In the first place, the quantity of data collected is

relatively small but, more importantly, there tends to be a bias as drivers of illegally


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overloaded trucks quickly learn that weighing is taking place and take steps to avoid that point

on the road.

In recent years the situation has improved considerably with the advent of weigh-in-

motion (WIM) technology which allows all trucks passing a sensor to be weighed while they

travel at full highway speed. WIM technology has resulted in a great increase in the

availability of truck weight statistics and codes of practice are being revised to reflect the new

data.

Bridge traffic loading is applied to notional lanes which are independent of the actual

lanes delineated on the road. In the Eurocode, the road width is divided into a number of

notional lanes, each 3 m wide. The outstanding road width, between kerbs, after removing

these lanes, is known as the ' remaining area'. (OBrien et al., 1999)

2.5.4 Thermal Loading

As integral bridge is concerned, there are considerable durability advantages in

removing joints and bearings, but their removal does affect the bridge behaviour. Specifically,

expansion and contraction of the deck is restrained with the result that additional stresses are

induced which must be resisted by the bridge structure. The most obvious cause of expansion

or contraction in bridges of all forms is temperature change.

There are two thermal effects which can induce stresses in bridges. The first is a

uniform temperature change which results in an axial expansion or contraction. If restrained,

such as in an arch or a frame bridge, this can generate significant axial force, bending moment

and shear. The second effect is that due to differential changes in temperature. If the top of a

beam heats up relative to the bottom, it tends to bend while if it is restrained from doing so,

bending moment and shear force are generated.

If a beam is on a sliding bearing as illustrated in figure 2.22 (a) and the temperature isreduced by T , it will contract freely. A (negative) strain will occur of magnitude ( T)


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where is the coefficient of thermal expansion (strain per unit change in temperature). The

beam then contracts by ( T) l where l is its length. However, no stresses are generated as no

restraint is offered to the contraction . As there is no stress, there can be no tendency to crack.

If, on the other hand, the beam is fixed at both ends as illustrated in figure 2.22 (b), and its

temperature is reduced by T , then there will be no strain. There cannot be any strain as the

beam is totally restrained against contraction. This total restraint generates a stress of

magnitude E ( T) , where E is the elastic modulus. The stress is manifested in a tendency to

crack.

Figure 2.22 (a): Beam on sliding bearing (OBrien et al., 1999)

Figure 2.22 (b): Beam fixed at both ends (OBrien et al., 1999)

Uniform changes in temperature result from periods of hot or cold weather in which

the entire depth of the deck undergoes an increase or decrease in temperature. Both the draft

Eurocode and the British standard specify contour plots of maximum and minimum ambient

temperature which can be used to determine the range of temperature for a particular bridge

site. The difference between ambient temperature and the effective temperature within a

bridge depends on the thickness of surfacing and on the form of construction (whether solid

slab, beam and slab, etc.). The American approach is much simpler. In 'moderate' climates,

metal bridges must be designed for temperatures in the range - 18C to 49 C and concrete

bridges for temperatures in the range - 12 C to 27 C. Different figures are specified for 'cold'

climates.


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It is important in bridge construction to establish a baseline for the calculation of

uniform temperature effects, i.e. the temperature of the bridge at the time of construction. It is

possible to control this baseline by specifying the permissible range of temperature in the

structure at the time of completion of the structural form. Completion of the structural form

could be the process of setting the bearings or the making of a frame bridge integral. In

concrete bridges, high early temperatures can result from the hydration of cement, particularly

for concrete with high cement contents. Resulting stresses in the period after construction will

tend to be relieved by creep although little reliable guidance is available on how this might be

allowed for in design. Unlike in-situ concrete bridges, those made from precast concrete or

steel will have temperatures closer to ambient during construction. The AASHTO code

specifies a baseline temperature equal to the mean ambient in the day preceding completion of

the bridge. The British Standard and the draft Eurocode specify no baseline.

Integral bridges undergo repeated expansions and contractions due to daily or seasonal

temperature fluctuations. After some time, this causes the backfill behind the abutments to

compact to an equilibrium density. In such cases, the baseline temperature is clearly a mean

temperature which relates to the density of the adjacent soil. In addition to uniform changes in

temperature, bridges are subjected to differential temperature changes on a daily basis, such as

in the morning when the sun shines on the top of the bridge heating it up faster than the

interior. The reverse effect tends to take place in the evening when the deck is warm in the

middle but is cooling down at the top and bottom surfaces. Two distributions of differential

temperature are specified in some codes, one corresponding to the heating-up period and one

corresponding to the cooling-down period. These distributions can be resolved into axial,

bending and residual effects.

As for uniform changes in temperature, the baseline temperature distribution is

important, i.e. that distribution which exists when the structural material first sets. However,

no such distribution is typically specified in codes, the implication being that the distributions

specified represent the differences between the baseline and the expected extremes.

Transverse temperature differences can occur when one face of a superstructure is subjected

to direct sun while the opposite side is in the shade. This effect can be particularly significant

when the depth of the superstructure is great.


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Cracking of reinforced concrete members reduces the effective cross sectional area

and second moment of area. If cracking is ignored, the magnitude of the resulting thermal

stresses can be significantly overestimated. The effects of both uniform and differential

temperature changes can be determined using the method of 'equivalent loads'. A distribution

of stress is calculated corresponding to the specified change in temperature. This is resolved

into axial, bending and residual distributions. The corresponding forces and moments are then

readily calculated. (OBrien et al., 1999)


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CHAPTER 3

RESEARCH METHODOLOGY

3.1 Introduction

Generally, the steps in this study can be divided into five different parts. The first step

is the literature review on how to model integral bridge, the effects of temperature on integral

bridge, and how to use finite element software, LUSAS. After the literature review, the

second step is data collection which consists of the data on the model to be developed,

Malaysian temperature gradient, and also the current status of the usage of integral bridge in

Malaysia. The third step is to develop a model of the integral bridge and to verify the

developed model by consulting with the experts. The verified model will then be manipulated

to study the significance of thermal effects on integral bridge in Malaysian weather and

temperature. With the intention of achieving research objectives, it is important to implement

the right approach in order to address the problems. This chapter will explain the details on

research method that will be adopted along the study. The flow chart of this study is shown in

figure 3.1.


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Figure 3.1: Methodology flow chart

Problem

Identification

DataCollection

Consultation withLUSAS users and

Finite Element

specialists

Development of themodel using LUSAS

Adaptation of realintegral bridge design

Verification of themodel

Verified model is usedto analyze and study

the effect of temperature for various

length of integralbridge

Findings andconclusion

Data from previousresearch


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3.2 Problem Identification

It is understandable that integral bridge offers a great minimization of costs compared

to conventional type of bridge. However, expansion and contraction of the deck is restrained

with the result that additional stresses are induced. This additional stresses must be resisted by

the bridge structure. Temperature is one of the m ost dominant factors in the bridges

expansion and contraction but is it significant in Malaysian condition? Will the thermal

effects only be significant at certain length of the bridge? How much is the changes in the

prestressed force? The questions to these answers are the main objective of this study.

3.3 Data Collection

The data collection sources are mainly from previous research, discussion with

experienced LUSAS users and also adaptation of the real design of integral bridge.

3.3.1 Previous Research

This research is inspired by the previous study conducted by Charles D. Newhouse et

al entitled Modelling Early -Age Bridge Restraint Moments: Creep, Shrinkage, and

Temperature Effects. A lot about the temperature effects is learned from this research. The

research mainly consists of experimental study, monitoring the early age restraint moments

that develop in a two-span continuous system made of full-depth precast concrete bulb tee

girders and comparison of the restraint moments observed to the predicted restraint moments

using the RMCalc program. They also proposed a simplified model to predict the restraint

moments considering the thermal effects. The overall elevation of the test setup is shown in

the following figure 3.2 and figure 3.3;


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Figure 3.3: Diaphragm details (Newhouse C. D. et al., 2008)

There were two tests monitored in order to achieve the purpose of the experimentalstudy; that is to compare the restraint moments that developed during the early ages of

continuity to the predicted restraint moments using RMCalc program. The two tests were

monitored for the development of restraint moments in a continuous system from the time the

deck was cast until the deck reached its design compressive strength. Full-depth specimens

and full-width deck sections were used in the testing to simulate actual conditions. The

changes in end reactions on the two span systems were carefully monitored and recorded

throughout the testing. The restraint moments were determined by multiplying the change in

the end reaction by the span length. Finally, a simplified model was developed to predict the

restraint moments considering early age thermal effects. This model is presented as an

alternate way to predict restraint moments.

Figure 3.2: Overall elevation of the Charles D. Newhouse research test setup (NewhouseC. D. et al., 2008)


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3.3.2 Adaptation of Real Integral Bridge Design

A real integral bridge design of Pantai Timur Second Phase Highway Project

designed by Ir. Mohamed Salleh Yassin is adapted as the basis in developing the integral

bridge model in LUSAS software.

The real design of the integral bridge is then simplified to a much simpler design,

therefore it is easier to be modelled. It is important to emphasize that the main objective of the

development of the model is to study the effect of temperature on the prestressed integral

bridge beam. Hence, a simple design of an integral bridge would suffice but at the same time,

the attributes of a real integral bridge design is needed.

3.3.2.1 Model Layout

The following figure shows a simple sketch of the integral bridge to be modelled.

Assumptions and conditions are applied in the development of the model. In this study, the

analysis is done for integral bridge with spans 20m, 30m and 40m.

Figure 3.4: Longitudinal integral beam

In order to make sure that the results for all spans are not too affected by the

geometrical difference, the beam geometry is designed so that the safety factor for each

integral bridge span is about the same. The safety factors for each bridge span is shown in

table 2;

L


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Table 3.1: Safety factor calculated according to e ach bridge spans Z 1 and Z 2

actual (mm 3) required (mm 3) Safety factor

length z 1 z2 z1 z2 z1(actual) /z1(required) z2(actual) /z2(required)

20 147.05 150.9 123.21 107.13 1.19 1.41

30 293.21 294.48 244.1 212.23 1.20 1.39

40 501.56 504.79 417.84 363.28 1.20 1.39

Table 3.2: General details for beam span 20m, 30m and 40m

Beam span (m) 20 30 40

Prestressing force (kN)

No of strand

No of Tendon

Type of strand

P at each tendon (kN)

6000

48

4

7-wire standard strand

12.9 mm

1500

7200

60

4

7-wire standard

strand 12.9 mm

1800

11200

90

4

7-wire standard

strand 12.9 mm

2800

3.3.2.2 Support Connection Detail

Figure 3.5: Integral beam-to abutment connection (Connal J., 2003)


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Figure 3.6: Integral beam-to abutment connection detail. (Connal J., 2003)

3.4 LUSAS Structural Modelling

LUSAS Modeller is an associative feature -based modelling system. The model

geometry is entered in terms of geometry features which are sub -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 corresponding increase in solution time and

disk space required. The geometry features form a hierarchy, that is volumes which are

enclosed by surfaces, which are made up of lines, which are defined by end points

A LUSAS model is graphically represented by geometry features (points, lines,

surfaces, volumes) which are assigned attributes (materials, thicknesses, loading, supports,

mesh, etc.). In developing the finite element model, the following general guidelines are

followed:

a. Understand the structural behaviour of the problem to be solved which includes

physical behaviour, loading type and magnitude, and boundary conditions


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b. Understand the behaviour and limitations of applicable theory of various

elements available for use. This will help the choosing of proper types of

elements to match as close as possible to the physical behaviour of the problem

c. Understand the programs option and limitations

d. A good practice is to; work with experienced people and search for reference

e. Avoid 3D because most problems can be modelled in 2D: Plane truss, plane

frame, plane stress, plane strain, axis symmetric, plate bending

f. Understand how various elements behave in various situations

g. Understand the physics of the problems well enough to make an intelligent

choice of elements and mesh

h. Start with a simple model and gradually refine them to a more complicated

one.

i. Anticipate the results and know the goal

j. Check the model

k. Check the results and typical post processor results

3.4.1 Assumptions

A few assumptions are considered in this model. They are;

1) The model is built using only line element.

2) The HA load is only consider based on the spacing between the beam, that is, 1900

mm.

3) The height of abutment is fixed to 6000 mm for all models.

4) Beam cross-section is the same along the span

5) The post-tensioned beam is designed for 4 tendons, but only 1 tendon is considered in

the model

6) Only 1 beam is considered in the integral bridge model

7) The abutment is designed for 1m depth


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3.4.2 Geometry Definition

The integral bridge with a prestressed beam basically can be modelled with

combination of lines. The lines are grouped as integral bridge beam and tendon profile. For

the integral bridge line, straight line is used to draw the bridge beam connecting to the bridge

abutment. Meanwhile, spline curve is used to visualise the parabolic tendon profile line.

These lines are easily drawn using the coordinates system in the software. It is shown in the

following figure 3.7 and figure 3.8:

Figure 3.7: Integral bridge beam line

Figure 3.8: Tendon profile line

3.4.3 Attributes Definition

Attributes are used to describe the properties of the model. Attributes are assigned to

geometry features and are not lost when the geometry is edited, or the model is re -meshed.

Attribute assignments are inherited when geometry features are copied and are retained when


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geometry features are moved. The attribute types can be categorized as general attributes and

specific attributes. To study temperature effects, only general attributes is used. The general

attributes are:

i. Mesh : describes the element type and discretisation on the geometry.

ii. Geometric : specifies any relevant geometrical information that is not inherent in

the feature geometry, for example section properties or thickness.

iii. Material : defines the behaviour of the element material, including linear,

plasticity, creep and damage effects.

iv. Support : specifies how the structure is restrained. Applicable to structural, pore

water and thermal analyses.

v. Loading : specifies how the structure is loaded

3.4.3.1 Meshing Attribute

Model for the integral bridge in this study uses beam elements. In LUSAS, beam

elements are used to model plane and space frame structures. LUSAS incorporates a variety

of thin and thick beams in both 2 and 3 -dimensions. In addition, specialised beam elements

for modelling grillage or eccentrically ribbed plate structures are also available. LUSAS beam

elements may be either straight or curved and may model axial force, bending and torsional

behaviour.

In this case, 2 dimensional thick beam structural elements with linear interpolation

order is used. For the prestressed beam, the number of divisions used vary from 20, 30 to 40

depending on the length of the span. The more number of divisions, the more accurate will the

model be. For instance, when analysing 30m span integral bridge, 30 number of elements are

used. At the same time, the number of division for the abutment is fixed at 6 for all three span

lengths. The following figures show the meshing assignment interface in LUSAS and also

active meshing applied to the beam and abutments respectively;


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Figure 3.9: Line mesh assignment interface

Figure 3.10: Active mesh applied to beam and abutments


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3.4.3.2 Geometric Attribute

There are 3 bridge spans to be analyzed. Therefore, there are 3 different beam designs

with different section properties. The section properties for each beam designs are calculated

using LUSAS. After the section properties for specific beam design is calculated, the data

were then stored in the section library database of LUSAS. Geometric assignment for the

specific bridge span length can be done by simply selecting the stored data from the section

library database. Figure below shows the arbitrary section property calculator interface used

in LUSAS to calculate and store the section properties data.

Figure 3.11: Arbitrary Section Property Calculator Interface

Geometric properties which have not been defined by the feature geometry are

assigned using geometric attributes. The properties required are element dependent and are

defined for an element family such as bars, beams or shells etc. In this case, the attribute used

is beam elements and it is then assigned to the required line.

Figure 3.12, figure 3.13 and figure 3.14 shows the cross section and the dimensions

for 20m, 30m and 40m span length respectively. Meanwhile, table 3.3 shows the section

properties of the spans.


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Table 3.3: Section properties for 20m, 30m and 40m integral bridge span

Beam span (m): 20 30 40

Cross-sectional area (mm ) 0.583 x 10 0.74 x 10 0.943 x 10

Centroid (mm):

Y1

Y2

517

504

822

818

1088

1082

Moment Inertia (mm ) 76.04x10 241.02x10 545.94x10

Section Moduli (mm ):

Z1

Z2

147.05 x 10 6

150.90 x 10 6293.21 x 10 6

294.48 x 10 6501.56 x 10 6

504.79 x 10 6

Figure 3.12: 20m integral bridge span cross-section and dimensions


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Figure 3.15: Material assignment interface

3.4.3.4 Support Attribute

Support conditions describe the way in which the model is restrained. A supportattribute contains information about the restraints to be applied to each degree of freedom.

There are three valid support conditions:

i. Free : the degree of freedom is completely free to move. This is the default.

ii. Fixed : the degree of freedom is completely restrained from movement.


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iii. Spring Stiffness : the degree of freedom is subjected to a specified spring stiffness.

Spring stiffness values can be applied uniformly to All nodes meshed on the assigned

feature or their values may vary over a feature by applying a variation. Alternatively,

per unit length or per unit area values can be applied

For this study, the supports used are roller and spring support. For roller support,

translation in y, z and rotation in x are set to be fixed. The rest are set to be free. Figure 3.16

shows the structural support assignment for roller.

Figure 3.16: Structural support setting for roller

Spring support is used to represent the soil pressure behind the abutment. The spring

stiffness is set at translation x with varying values according to the span length analysis while

the spring stiffness distribution is set for stiffness per unit length. Figure 3.17 shows the

structural support assignment for spring stiffness. Figure 3.18 shows the visual of roller

support and spring stiffness support in LUSAS.


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k horz =

=

= 136 482.623 kN/m/m2

Table 3.2 shows the value of spring stiffness for all span length.

Span Length (m) k horz (kN/m/m 2)

20 136 482.623

30 116 048.854

40 103 434.486

3.4.3.5 Loading Attribute

The loading considered in this study are self weight, HA bridge loading and

temperature loading. In LUSAS, self weight can be defined by assigning the linear gravity

acceleration, 9.81 m/s to y-direction.

For HA load, the following is the example data that used in this study;

Loading Code BD37/01

Loaded Length(m) 30

Notional Lane Width (m) 2.88

Skew Angle deg) 0

Table 3.5: Values of spring stiffness.

Table 3.6: HA loading details.


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As stated earlier, there are two types of temperature effects. They are the uniform

temperature change, and differential temperature change. From these two temperature effects,

the cases are then elaborated into four conditions as shown i

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Temperature Effect on Prestressed Integral Bridge Beam

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