Saif La Ith Khalid m Fka 2009

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COMPARISON BETWEEN GRILLAGE MODEL AND FINITE ELEMENT

MODEL FOR ANALYZING BRIDGE DECK

SAIF LAITH KHALID ALOMAR

A project report submitted in partial fulfilment of the requirement for the award of

the degree of the degree of Master of Engineering (Civil- Structure)

Faculty of Civil Engineering

Universiti Teknologi Malaysia

JUNE 2009


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ACKNOWLEDGEMENTS

Firstly, I would like to thank Dr. Redzuan for his efforts and time. Without

mentioning the help, which I got from him, I feel this work would be incomplete.

Secondly, it was my pleasure to work with him during my study period where

I gained a wonderful opportunity to learn several things from him, which extend

beyond the technical knowledge that definitely will help me to pursue my career.

Finally, I would like to thank my family for their support, patient;encouragement and for the love they gave me to complete this project.


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ABSTRACT

Since its publication in 1976 up to the present day, Edmund Hamblys book

Bridge Deck Behaviors has remained a valuable reference for bridge engineers.

During this period the processing power and storage capacity of computers has

increased by a factor of over 1000 and analysis software has improved greatly in

sophistication and ease of use. In spite of the increases in computing power, bridge

deck analysis methods have not changed to the same extent, and grillage analysis

remains the standard procedure for most bridges deck. In this study analysis bridge

deck using grillage model are compared with the analysis of the same deck using

finite element model. A bridge deck consists of beam and slab is chosen and

modelled as grillage and finite element. Bending moment, Shear force, Torsion and

Reaction force from both models are compared. Effect of skew deck is also studied.

In general for practical skew bridge deck results from finite element model give

lesser value in terms of displacement, reaction, shear force, torsion, bending moment

compare with the results from grillage model. It can be concluded that analysis of

bridge decks by using finite element method may produce more economical design

than grillage analysis. This is due to the fact that the finite element model resembles

the actual structure more closely than the grillage model.


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Abstrak

Semenjak publikasinya dari 1976 ke hari ini, buku Edmund Hambly berjudul

Bridge Deck Behaviors merupakan sumber rujukan paling berguna kepada

jurutera-jurutera jambatan. Semasa tempoh ini kuasa pemprosesan dan kapasiti

penyimpanan komputer-komputer telah bertambah dengan satu faktor melebihi 1000

dan perisian analisis telah banyak meningkat dalam kecanggihan dan

penggunaannya. Meskipun bertambah dari kuasa pengkomputeran, cara-cara

menganalisis geladak jambatan masih dalam takat yang sama, dan kekisi analisiskekal sama untuk kebanyakan jambatan-jambatan bertingkat. Dalam analisis kajian

geladak ini, analisis geladak jambatan menggunakan model kekisi dibandingkan

dengan analisis bagi geladak yang sama menggunakan model unsur terhingga.

Geladak jambatan yang mengandungi rasuk dan papak dipilih dan menjadi model

sebagai kekisi dan unsur terhingga. Momen lentur, Daya Ricih, Kilasan dan Daya

Tindakbalas daripada kedua-dua model adalah dibandingkan. Kesan geladak

pencong adalah juga dikaji. Secara keseluruhannya keputusan analisis daripada

model unsur terhingga memberi nilai yang kurang dalam soal anjakan, tindak balas,

daya ricih, kilasan dan momen lentur berbanding dengan keputusan-keputusan

daripada model kekisi. Di sini dapat disimpulkan bahawa analisis dengan

menggunakan kaedah unsur terhingga mungkin menghasilkan reka bentuk yang lebih

berekonomi daripada kekisi analisis. Ini memandangkan model unsur terhad lebih

menyamai struktur sebenar berbanding model kekisi.


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TABLE OF CONTENTS

CHAPTER TITLE PAGE

REPORT STATUS VALIDATION FORM i

TITLE PAGE ii

SUPERVISOR DECLARATION iii

STUDENT DECLARATION iv

ACKNOWLEDGEMENTS vABSTRACT vi

ABSTRAK vii

TABLE OF CONTENTS viii

1 INTRODUCTION

1.1 Introduction 1

1.2 Problem Statement 2

1.3 Objectives of Study 2

1.4 Scope and Limitations of the Study 3

1.5 Significant of the Study 3

1.6 Methodology 4

2 LITERATURE REVIEW

2.1 Introduction 6

2.2 discussion on neutral axis location in bridge deck 7


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cantilevers

2.3 Up stand finite element analysis of slab bridges 8

2.4 Bending moment distribution at the main structural

elements of skew deck-slab and their implementation

on cost effectiveness

10

2.5 Effect on support reactions of T-beam skew bridge

decks

13

2.6 Types of bridge deck 15

2.6.1 Beam decks 15

2.6.2 Grid deck 16

2.6.3 Slab deck 17

2.6.4 Beam and slab deck 18

2.6.5 Cellular decks 19

2.7 Finite element analysis 21

2.8 Grillage Analysis 23

3 RESEARCH METHODOLOGY

3.1 Introduction 25

3.2 LUSAS Software 26

3.2.1 LUSAS Software Characteristic 27

3.2.2 Procedure Analysis According to LUSAS

Software

27

3.3 Types of Element 28

3.4 Configuration of Bridge Deck 30

3.5 Materials Description 32

3.6 Loadings Description 33

3.6.1 Dead Load 33

3.6.2 Superimposed Dead Load 34

3.6.3 Live loading 35

3.6.3.1 Vehicle Load HA Loading 35

3.6.3.2Vehicle Load HB Loading 36

3.6.4 Loading Combination 38

3.6.4.1 HA loading for all lanes 39


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3.6.4.2 HB loading for lane1 and HA loading

for lane 3&4

40

3.6.4.3 HB loading for lane 2, HA UDL for lane

1, 3 and HA loading for lane 4

40

3.6.4.4 HB loading on lane 1 only 41

3.6.4.5 HB loading on lane 2 only 41

3.6.4.6 Enveloping the basic live load

combinations

41

3.6.4.7 Smart Load Combination 42

3.6.5 Vehicle Loading and Load Combinations 42

3.7 Grillage Modelling 43

3.8 Finite Element Modelling 44

3.9 Layers and Windows 46

3.10 Viewing Results 46

3.11 Bridge Deck Analysis Result & Discussion 47

4 RESULT AND ANALYSIS

4.1 Introduction 48

4.1.1 Displacement Result 49

4.1.2 Reaction Result 52

4.1.3 Shear force Result 57

4.1.4 Torsion Result 60

4.1.5 Moment Result 63

5 CONCLUSION

5.1 Conclusion 69

LIST OF REFERENCES 71


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CHAPTER 1

INTRODUCTION

1.1

Introduction

Even though the finite element method has developed to the maturity and

numerous computer software that use the methods are relatively cheap and easily

available. Engineer still prefer to use grillage method for their analysis of bridge

decks. Hambly (1991) listed out reasons why grillage method is a more popular

choice than finite element method. Firstly the finite element method is much more

complicated and expensive than the grillage method .Though the finite element is

thought to be more accurate, in reality does not produce significant different results

as compared with the grillage. According to Hambly (1991), finite element is

cumbersome to use and the choice of element type can be extremely critical and, if

incorrect, the results can be far more inaccurate than those predicted by simpler

models such as grillage or space frame [Hambly 1991].


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However, perhaps the greatest drawback at present is that while the finite

element technique is developing so rapidly, the job of carrying out finite element

computations is a full time occupation which cannot be carried out at the same time

by the senior engineer responsible for the design. He is unlikely to have time to

understand or verify the appropriateness of the element stiffnesss or to check the

large quantity of computer data. This makes it difficult for him to place his

confidence in the results, especially if the structure is too complicated for him to use

simple physical reasoning to check orders of magnitude [Jenkins, 2004].

1.2

Problem Statement

Grillage method is a fast and simpler approach compared to the finite element

method, and has been used by engineers to analyses bride deck over a long time on

the other hand the finite element method is thought to be better model for the slab

analysis because of its capability to represent the structure more realistically.

As such there is a need to conduct a though comparison between the two

models to gain better idea on which model may produce more economical design.

1.3 Objectives of Study

The objectives of this study are as follows:

To compare the performance between grillage and finite element model

for analysing bridge deck.

To conduct analysis of bridge deck using grillage and finite element

model using LUSAS software.


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To study the effect of deck skew on the analysis result for both models.

To propose which model can provide more conservative design.

1.4 Scope and Limitations of the Study

In this study, LUSAS software will be used to model and analyse the

bridge deck. Only grillage and finite element using 3D beam and shell elements areconsidered. Bending moment, Shear force, Torsion and Reaction force will be

compared.

1.5

Significant of the Study

Grillage method consists of members lying in one plane only while the finite

element method lying in 3D plane. Both of these planar methods of analysis are used

to model a range of bridge forms. Planar methods are among the most popular

methods currently available for the analysis of slab bridges. They can, with

adaptation, be applied to many different types of slab as will be demonstrated.Further, their basis is well understood and results are considered to be of acceptable

accuracy for most bridges.

However, grillage model and finite element model can also be considerably

more complex and can take much longer to set up. For this reason, planar grillage

and finite element models are at present the method of choice of a great many bridge

designer for most bridge slabs [O'Brien, 1999].


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The research significance to be obtained from this study will be the results

and analysis of the behaviour of bridge deck. It is necessary to compare between two

models to see which model gives more economical result.

1.6 Methodology

a)

The steps adopted in this study are Identify problem and scope of study, obtain realistic bridge deck plan.

Literature review of the grillage and finite element model. (Books,

Previous studies, Journal, Case studies)

b) In order to achieve the second objective we have to

Choose a realistic a bridge deck section with a different skews.

Analyze the bridge deck section properties using each of grillage and

finite element models for each skews in LUSAS software.

Application of load cases and vehicles loading.

Analysis and result processing.

Graphical and report output.

c)

Compare between the two models (Grillage and Finite element) by using

the results of first and second objectives.

d) Recommendation & Conclusion.


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The methodology that will be used for this study is shown in Figure 1.1.

Figure 1.1: methodology


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CHAPTER 2

LITERATURE REVIEW

2.1

Introduction

Grillage has been around for some time and the method is practical for use

with and without computer. Although computational power has increased many-fold

since 1960s, and other models method such as finite element is within reach, the

grillage method is still widely used for bridge deck analysis. One of the benefits that

have been quoted for the grillage analysis is that it is inexpensive and easy to use and

comprehend. This benefit has made it more preferable than method of finite-element

analysis. Nowadays the environment is inexpensive, high-powered computers

coupled with elaborate analysis programs and user-friendly graphical interfaces are

available, so the finite element method has begun to replace the grillage method in

many instances, even for more straightforward bridge decks [O'Brien, 1999].


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2.2 A discussion on neutral axis location in bridge deck cantilevers

Many bridge decks include transverse cantilevers at their edges. If the edge

cantilevers are long and slender the edge cantilevers tend to bend (in the bridge

longitudinal direction) about their own centroids.

The variation in the neutral axis of a bridge with edge cantilevers is

essentially the same phenomenon as the well known concept of shear lag. In the

design of bridge decks, a two-dimensional analysis is often used which takes account

of shear lag through the use of an effective flange width.

A number of three-dimensional modelling techniques have been used which

allow for variations in neutral axis location. In continuous beams the effective flange

width is dependent on the ratio of actual flange width to the length between points of

zero moment and also dependent on the form of applied loading.

A single span simply supported slab bridge deck with edge cantilevers was

analysed by (O'Brien, 1998) and it was found that the neutral axis location was

dependent on the nature of the applied load. This finding verifies a previous study

reported by Green (1975).

It was used two-span bridge deck to demonstrate the degree to which the

neutral axis may vary from its commonly assumed position. A two-span slab bridge

deck with wide edge cantilevers was analysed by (O'Brien, 1998) and it was found

that the neutral axis location varied in the longitudinal direction as well as the

transverse direction.

The implications of this variation in neutral axis location were determined by

comparison of the prediction of longitudinal stresses at the top of the bridge deck

from the NIKE3D analysis with those from a two-dimensional grillage analysis.


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It was found that the two-dimensional grillage analysis was not capable of

accurately predicting the stresses in the edge cantilever. The greatest discrepancy

was found to exist above the central support towards the edge of the cantilever.

The concept of effective flange width is clearly unsuitable for accurate

structural analysis as there is no simple effective flange width or neutral axis location

that can be used throughout a bridge for all load cases. Hence if greater accuracy is

required than that provided by the two-dimensional grillage analogy, it is necessary

to use an alternative approach. The Up stand Finite Element analogy has been found

by (O'Brien, 1998) to be simple to use and to give excellent results [O'Brien, Keogh,

1998].

2.3 Up stand finite element analysis of slab bridges

The plane grillage analogy is a popular method among bridge designers of

modelling slab bridge decks in two dimensions. Finite element analysis (FEA) is

used extensively by bridge designers, but is most often limited to planar analysis

using plate bending elements, which, like the plane grillage method, assumes a

constant neutral axis depth. It has been reported (O'Brien 1998) that the neutral axis

depth may also vary in the longitudinal direction in some cases, such as close to

concentrated loads or adjacent to intermediate supports in multi span decks.

Variability of neutral axis depth, when significant, results in the incorrect

representation by a planar analysis of the behaviour of the bridge deck. The problem

can be overcome by the use of a three-dimensional model. Such methods do not

require all members or elements representing parts of the deck to be located in the

one plane. Consequently this approach does not require a pre-assumed neutral axis

position, and allows for a rational handling of cases in which the neutral axis depthvaries.


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The up stand FEA method is simple enough to be used in design offices for

everyday design and is significantly more accurate than plane grillage or plane finite

element analysis, particularly for bridge slabs with wide edge cantilevers.

O'Brien (1998) used Single- and two-span bridge decks with solid and voided

sections are considered for longitudinal bending stresses.

For a single-span bridge deck with wide edge cantilevers, both the plane

grillage and the up stand grillage methods are shown to be inaccurate in predicting

longitudinal bending stresses when compared to a 3D FEA method. Up stand finite

element method gives excellent agreement.

The differences in accuracy are attributed to the inability to model both

variations in the depth of the neutral axis and associated in-plane distortions. Similar

results are reported for longitudinal stresses in a two-span bridge deck.

Up stand FEA and the 3D FEA analyses predicted a similar maximum

transverse stress and a similar distribution across the width of the deck. Both

Predictions of transverse stresses were found to compare reasonably well. However,

a discrepancy was noted in the location of the point of maximum transverse stress.

A voided slab bridge deck with wide edge cantilevers was analysed using the

up stand FEA technique. The presence of the voids complicated the modelling and,

for the software used, required the addition of extra beams in order to maintain both

the correct area and second moment of area of the voided sections.

Isotropic finite elements were used as the void depth was less than 60% of the

slab depth. The up stand finite element model was analysed under the action of self-

weight and a 3D FEA was carried out for comparison. The predictions of top

longitudinal stress from the up stand FEA compared very well with those from the

3D FEA [O'Brien, Keogh, 1998].


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2.4 Bending moment distribution at the main structural elements of skew

...........deck-slab and their implementation on cost effectiveness

Many methods used in analyzing such as grillage and finite element method.

Generally, grillage analysis is the most common method used in bridge analysis. In

this method the deck is represented by an equivalent grillage of beams. The finer

grillage mesh, provide more accurate results. It was found that the results obtained

from grillage analysis compared with experiments and more rigorous methods are

accurate enough for design purposes. If the load is concentrated on an area which is

much smaller than the grillage mesh, the concentration of moments and torquecannot be given by this method and the influence charts described in Puncher can be

used. The orientation of the longitudinal members should be always parallel to the

free edges while the orientation of transverse members can be either parallel to the

supports or orthogonal to the longitudinal beams. According to CCA the orthogonal

mesh is cumbersome in input data but the output moments results Mx, My and Mxy

can be used directly in the Wood- Armer equations as in Hambly to calculate the

steel required in any direction [Kakish, 2007].

The other method used in modelling the bridges is the finite element method.

The finite element method is a well known tool for the solution of complicated

structural engineering problems, as it is capable of accommodating many

complexities in the solution. In this method, the actual continuum is replaced by an

equivalent idealized structure composed of discrete elements, referred to as finite

elements, connected together at a number of nodes.

The finite elements method was first applied to problems of plane stress,

using triangular and rectangular element. The method has since been extended and

we can now use triangular and rectangular elements in plate bending, tetrahedron and

hexahedron in three-dimensional stress analysis, and curved elements in singly or

doubly curved shell problems. Thus the finite element method may be seen to be

very general in application and it is sometimes the only valid analysis for difficultdeck problems. The finite element method is a numerical method with powerful


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technique for solution of complicated structural engineering problems. It most

accurately predicted the bridge behaviour under the truck axle loading.

The finite element method involves subdividing the actual structure into asuitable number of sub-regions that are called finite elements. These elements can be

in the form of line elements, two dimensional elements and three-dimensional

elements to represent the structure. The intersections between the elements are called

nodal points in one dimensional problem where in two and three-dimensional

problems are called nodal line and nodal planes respectively.

At the nodes, degrees of freedom (which are usually in the form of the nodal

displacement and or their derivatives, stresses, or combinations of these) are

assigned. Models which use displacements are called displacement models and some

models use stresses defined at the nodal points as unknown. Models based on

stresses are called force or equilibrium models, while those based on combinations of

both displacements and stresses are termed mixed models or hybrid models.

Displacements are the most commonly used nodal variable, with most general

purpose programs limiting their nodal degree of freedom to just displacements. A

number of displacement functions such as polynomials and trigonometric series can

be assumed, especially polynomials because of the ease and simplification they

provide in the finite element formulation.

Finite element needs more time and efforts in modelling than the grillage.

The results obtained from the finite element method depend on the mesh size but by

using optimization of the mesh the results of this method are considered more

accurate than grillage. The finite element method is a well-known tool for the

solution of complicated structural engineering problems, as it is capable of

accommodating many complexities in the solution. In this method, the actual

continuum is replaced by an equivalent idealized structure composed of discrete

elements, referred to as finite elements, connected together at a number of nodes.


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The finite element method was first applied to problem of plane stress, using

triangular and rectangular elements. The method has since been extended and we can

now use triangular and rectangular elements in plate bending, tetrahedron and

hexahedron in three-dimensional stress analysis, and curved elements in singly or

doubly curved shell problems. Thus the finite element method may be seen to be

very general in application and it is sometimes the only valid analysis for difficult

deck problems.

Tiedman shows the finite element method is a numerical method with

powerful technique for solution of complicated structural engineering problems. It

most accurately predicted the bridge behaviour under the truck axle loading.

Qaqish presents the effect of skew angle on distribution of bending moments

in bridge slabs. Qaqish presents comparison between finite element method and

AASHTO specification for the design of T-beam Bridge. The bridge is analyzed by

using the finite element method.

In conclusion the design of bridge deck slab should be carried out in a

structural computer model where the longitudinal beams subjected to vertical wheel

loadings should be designed on the bending moments and shearing force these

girders are subjected to. While the girders which they are not subjected to these truck

loadings should be designed for the actual loadings they are applied on these girders.

This method will achieve economy especially in places where the deck slab is

extended over big area. The vertical displacements are varied from one longitudinal

girder to the other and even these displacements are related to the actual bendingmoments these girders are subjected to. So chambering is also different from one

longitudinal beam to the other which makes the constructions cheaper as some of

these longitudinal beams do not need such chambering due to small vertical

displacement [Kakish, 2007].


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2.5 Effect on support reactions of T-beam skew bridge decks

In order to cater to high speeds and more safety requirements of the traffic,

modern highways are to be straight as far as possible and this has required the

provision of increasing number of skew bridges.

T-beam Bridge is a common choice among the designers for small and

medium span bridges. For the T-beam bridges with small skew angle, it is frequently

considered safe to ignore the angle of skew and analyze the bridge as a right bridge

with a span equal to the skew span. However, T-beam bridges with large angle of

skew can have a considerable effect on the behaviour of the bridge especially in the

short to medium range of spans.

In this study the behaviour of T-beam skew bridges with respect to support

reactions under standard IRC-70R wheeled loading is presented and the study was

based on the analytical modelling of T-beam bridges by Grillage Analogy method.

Effects of support reactions for different spans have been studied. The analysis

provides the useful information about the variation of support reactions with respect

to change in skew. The negative reactions were observed with increase in the span

and skew angles.

The advent of digital computers, computer-aided methods like Finite

Element, Finite Difference and Finite Strip have been developed and are in use to

analysis intricate forms of skew shape of bridges having usual support conditions and

cross-sections. But these methods are highly numerical and always carry a heavy

cost-penalty. Grillage analogy is one of the most popular computer-aided methods

for analysing bridge decks. The method consists of representing the actual decking

system of the bridge by an equivalent grillage of beams. The dispersed bending and

torsional stiffness of the decking system are assumed, for the purpose of analysis, to

be concentrated in these beams. The stiffness of the beams is chosen so that the

prototype bridge deck and the equivalent grillage of beams are subjected to identical

deformations under loading. The method is applicable to bridge decks with simple as


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well as complex configurations with almost the same ease and confidence. The

method is easy to comprehend and use. The analysis is relatively inexpensive and has

been proved to be reliably accurate for a wide variety of bridges. The grillage

representation helps in giving a feel of the structural behaviour of the bridge and the

manner in which the loading is distributed and eventually taken to the supports.

The grillage analogy method is suitable in cases where bridge exhibits

complicating features such as heavy skew, edge stiffening and isolated supports. The

method is versatile in nature and the contribution of kerb beams and the effect of

differential sinking of girder ends over yielding bearings (such as neoprene bearing)

can also be taken into account and large variety of bridge decks can be analysed with

sufficient practical accuracy.

The method consists of converting the bridge deck structure into a network

of rigidly connected beams at discrete nodes i.e. idealizing the bridge by an

equivalent grillage. The deformations at the two ends of a beam element are related

to the bending and torsional moments through their bending and torsional stiffness.

The method of grillage analysis involves the idealization of the bridge deck

as a plane grillage of discrete inter-connected beams. It is difficult to make precise

general rules for choosing a grillage mesh and much depends upon the nature of the

deck to be analysed, its support conditions, accuracy required, quantum of computing

facility available etc. and only a set of guidelines can be suggested for setting grid

lines. It may be noted that such idealization of the deck is not without pitfalls and the

grid lines adopted in once case may not be efficient in another similar case and theexperience and judgment of the designer will always play a major role.

On the basis of analysis it was found that grillage analogy method, based on

stiffness matrix approach, is a reliably accurate method for a wide range of bridge

decks. The method is versatile, easy for engineers to visualize and prepare the data

for a grillage. It has been found that in skew T-beams bridges, the high positive and

negative reactions develop close to each other. The reaction on the obtuse corner

close to load is very high and increases with increasing skew angles 400. With the


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increasing in the span the negative reaction increases at smaller angles [Gupta,

Misra, 2007].

2.6 Types of bridge deck

The types of bridge deck are divided into beam, slab, beam-slab and cellular,

to differentiate their individual geometric and behavioural characteristics. Inevitably

many decks fall into more than one category, but they can usually be analysed by

using a judicious combination of the methods applicable to the different types

[Hambly, 1991].

2.6.1 Beam decks

A bridge deck can be considered to behave as a beam when its length exceed

its width by such an amount that when loads cause it to bend and twist along its

length, its cross-sections displace bodily and do not change shape. Many long-span

bridges behave as a beam because the dominant load is concentric so that the

direction of the cross-section under eccentric loads has relatively little influence on

the principle bending stresses [Edmund, 1991].


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Figure 2.1: Beam deck bending and twisting without change of cross-section shape

(Bridge Deck Behaviour, 1991)

2.6.2

Grid deck

The primary structural member of grid deck is a grid of two or more

longitudinal beams with transverse beams (or diaphragms) supporting the running

slab. Loads are distributed between the main longitudinal beams by the bending and

twisting of the transverse beams. Grid decks are most conveniently analysed with the

conventional computer grillage analysis .The analysis in effect sets out a set ofsimultaneous slop-deflection equations for the moment and torsions in the beams at

each joint and then solves the equation for the load case required [Edmund, 1991].


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Figure 2.2: Load distribution in grid deck by bending and torsion of beam members

(Bridge Deck Behaviour, 1991)

2.6.3 Slab deck

A slab deck behaves like a flat plate which is structurally continuous for the

transfer of moments and torsions in all directions within the plane of the plate. When

a load placed on part of a slab, the slab deflects locally in a 'dish' causing a two

dimensional system of moments and torsions which transfer and share the load to

neighbouring pans of the deck which are less severely loaded.

A slab is 'isotropic' when its stiffnesss are the same in all directions in the

plane of the slab. It is 'orthotropic' when the stiffnesss are different in two directions

at right angle.

The beams of precast concrete or steel have a greater stiffness longitudinally

than the in situ concrete bas transversely; thus the deck is orthotropic.


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If the depth and width of the voids are less than 60% of the overall structural

depth, their effect on the stiffness is small and the deck behaves effectively as a plate.

Voided slab decks are frequently constructed of concrete cast in situ with permanent

void formers, or of precast pre stressed concrete box beams post-tensioned

transversely to ensure transverse continuity. If the void size exceeds 6O% of the

depth, the deck is generally considered to be of cellular construction with a different

behaviour [Edmund, 1991].

Figure 2.3: Load distribution by bending and torsion of slab in two directions (Bridge

Deck Behaviour, 1991)

2.6.4 Beam and slab deck

A beam and slab deck consists of a number of longitudinal beams connected

across their tops by a thin continuous structural slab. In transfer of the load

longitudinally to the supports, the slab acts in concert with the beams as their top

flanges. At the same time the greater deflection of the most heavily loaded beams


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bends the slab transversely so that it transfers and shares out the load to the neigh

boring beams. Sometimes this transverse distribution of load is assisted by a number

of transverse diaphragms at points along the span, so that deck behaviour is more

similar to that of a grid deck. Beam and slab construction has the advantage over slab

that it is very much lighter while retaining the necessary longitudinal stiffness.

Consequently it is suitable for a much wider range of spans, and it lends itself to

precast and prefabricated construction. Occasionally, the transverse flexibility can be

advantageous; it can help a deck on skew supports to deflect and twist comfortably

under load without excessively loading the nearest supports to the load or lifting off

those further away.

Beam and slab decks are most conveniently analyzed with the aid of

conventional computer grillage programs [Edmund, 1991].

Figure 2.4: Contiguous beam and slab deck and slab of contiguous beam and slab

deck (Bridge Deck Behaviour, 1991)

2.6.5

Cellular decks

The cross-section of a Cellular or box deck is made up of a number of thin

slabs and thin or thick webs which totally enclose a number of cells. Thesecomplicated structural forms and increasingly used in preference to beam-and-slab


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decks for spans in excess of 30m (100ft) because in addition to the low material

content, low weight and high longitudinal bending stiffness they have high tensional

stiffnesss which give them better stability and load distribution characteristics. To

describe the behaviour of cellular decks it is convenient to divide them into multi

cellular slabs and box-girders.

When a load is placed on one pan of such a deck, the high torsional stiffness

and transverse bending stiffness of the deck transfer and share out the load over a

wide area. The distribution is not as effective as that of a slab since the thin top and

bottom slabs flex independently when transferring vertical shear forces between

webs, and the cross-section. Such distortion can be reduced by incorporating

transverse diaphragms at various points along the deck but, as with beam and slab

decks, their use is becoming less popular except at support where it is necessary to

transfer the vertical shear forces between webs and bearings [Edmund, 1991].

9

Figure 2.5: Box girder deck (Bridge Deck Behaviour, 1991)


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Finite Element Analysis

The availability of sophisticated computers over the last three decades has

enabled engineers to take up challenging tasks and solve intractable problems of

earlier years. Nowadays rapid decrease in hardware cost has enabled every

engineering firm to use a desk top computer or micro processor. Moreover they are

ideal for engineering design because they easily provide an immediate access and do

not have the system jargon associated with large computer system. It is to be

expected that software to be sold or leased and the hardware supplied with software.

The development of structural analysis up to its present position can be characterised

by four different eras as shown in Table 1.1. After the initial phase, where onlyprinciples of gravity and statics were enunciated resulting in ambiguity in applying to

structural problem, Mathematicians took over from around 1400 A. D. and presented

a variety of formulations and solutions. Purely, as exercise in basic science, around

1700A.D. these formulations and solutions found practical significance in

applications to structures with proper approximations and adaptations. New methods

exclusive for structural analysis were evolved like slope deflection, moment

distribution and relaxation.

Later part of this period witnessed the emergence of superfast calculation and

later computers. Thus started the era of computers wherein the developments in

structural analysis and design were and are still complementary to those in

computers. A reorientation to the developments and formulation proposed in the

earlier eras took place mainly to use the advantageous features of computers like

high speed arithmetic, large information storage and limited logic, bringing in matrixmethods of analysis and later finite element and boundary integral element methods.

In recent years, the increasing availability of high speed computers have

caused civil engineers to embrace finite element analysis as a feasible method to

solve complex engineering problems. It is common for personal computers for home

use today are more powerful than supercomputer previous years. Therefore, the

increasing popularity of Finite Element Analysis can be attributed to theadvancement of computer technology.


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Finite element method is a numerical method with powerful technique for

solution of complicated structural engineering problems. It most accurately predicted

the bridge behaviour under the truck axle loading.

The finite element method involves subdividing the actual structure into a

suitable number of sub-regions that are called finite elements. These elements can be

in the form of line elements, two dimensional elements and three-dimensional

elements to represent the structure. The intersection between the elements is called

nodal points in one dimensional problem where in two and three-dimensional

problems are called nodal line and nodal planes respectively. At the nodes, degrees

of freedom (which are usually in the form of the nodal displacement and/ or their

derivatives, stresses, or combinations of these) are assigned. Models which use

displacements are called displacement models and some models use stresses defined

at the nodal points as unknown. Models based on stresses are called force or

equilibrium models, while those based on combinations of both displacements and

stresses are termed mixed models or hybrid models.

Many shapes of elements are available. Thus this method may seem to bevery general in application. Triangular or quadrilateral plate elements can be adopted

to represent a bridge deck as an elastic continuum. The actual choice will depend on

the geometry of the structure, on the importance of local features such as stress

concentrations and also, upon the convergence properties of the bridge deck

[Nicholas M. Baran, 1988].


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Table 2.1: development in structural analysis (The Finite Element Method 2003)

2.7 Grillage Analysis

The grillage numerical method is known in the static and dynamic analysis of

plate structures. By making use of a grillage discretization, the flexural and torsional

rigidities are determined to closely approximate a plate. The accuracy, simplicity and

speed of the grillage analog make it the most suitable model for bridge analysis

[Zeng, Kuehn, Sun, Stalford, 2000].

The bridge motion is composed of many modes, which cannot be predicted by

either simple bending or torsion theory. Therefore, a torsion beam element is

developed as a grillage member. Such a torsion beam element is subjected to a

transverse force distribution and a torsional moment distribution. The nodes undergo


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not only planar translational and rotational displacements, but also torsional

displacements. Correspondingly, there are transverse joint forces, bending moments

and torsional moments at each node.

Grillage analysis is the most popular computer aided method for analyzing bridge

decks. It is easy to comprehend and use, and most important, it has been proved to be

reliably accurate for a wide variety of bridge types, It can be used in cases where the

bridges exhibits complicating features such as a heavy skew, edge stiffening and

deep hunches over supports,

The grillage representation is conductive to giving the designer an idea about the

structure behaviour of the bridge and the manner in which bridge loading is

distributed and eventually taken to the supports.

This method is to represent the deck by an equivalent grillage of beams. The

dispersed bending and torsion stiffnesss in every region of the slab are assumed for

purpose of analysis to be concentrated in the nearest equivalent grillage beam. The

slabs longitudinal and transverse stiffnesss are concentrated in the longitudinal and

transverse beams respectively. Ideally, the beam stiffnesss should be such that when

prototype slab and equivalent grillage are subjected to identical loads, the two

structures will deflect identically [Jaeger, LG, Bakht, 1982].


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CHAPTER 3

RESEARCH METHODOLOGY

3.1

Introduction

This project is concerned essentially with the analysis of the bridge deck. A

bridge deck is structurally continuous in the two dimensions of the plane of the slab

so that an applied load is supported two dimensional distributions of shear forces,

moments, reaction, deflection and torques. Normally, an approximate method is

much used to analyze the slab deck behaviour as rigorous solution of the basic

equations for a real deck is seldom possible. In this project, two different analysis

methods are being considered i.e. grillage model and finite element model. Grillage

analysis is a method in which, the deck is represented and analyzed by a two-

dimensional grillage of beams. As for finite element analysis, the deck is notionally

subdivided into a large number of small elements for each of which approximate

plate bending equations can be written. In short, grillage analysis is a stiffness

method; meanwhile, finite element is plate method. All these analysis are aided with


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finite element analysis computer software, LUSAS Modeller version 14.1. The

required outputs from the analysis are:

a)

A deformed shape plot showing the largest displacement value and itslocation.

b) The envelopes of bending moment, shear force and torsional moment in the

Pre-stressed beams for the design load combinations.

c)

Maximum and minimum reaction forces at the support.

3.2 LUSAS Software

LUSAS is finite element analysis software it was first developed in 1970 at

London University as a research tool of finite element technology. Since then,

LUSAS has become a powerful tool for the solution of various types of linear and

nonlinear problems.

LUSAS can analyze and organise complex structure problems and shapes

including 3 dimensional structures and can be used in dynamic structural analyses

with temperature changes LUSAS software can solve problems up to 5000 number

of elements.

LUSAS is an associative feature based Modeller. This means the model

geometry is entered in terms of features which are then sub-divided into finite

elements in order to perform the analysis. Increasing the number of elements usually

increase the accuracy of the analysis but the time for the analysis to be done will also

increase. The features in LUSAS form a hierarchy, whereby Points can be joined


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together to form Lines and then Lines form a Surface and Surfaces in turn can form a

Volume [Lusas Theory Manual, Version 14.1].

3.2.1 LUSAS Software Characteristic

LUSAS software can analysis and organise complex structure problems and

shapes including 3 dimensional structures. This software also can be used in dynamic

structural analyses with temperature changes. LUSAS software can solve problems

up to 5000 number of elements [LUSAS Version 14.1 Software].

3.2.2 Procedure Analysis According to LUSAS Software

There are 3 steps in the finite element analysis using the LUSAS software,

which are as follows:

a) Pre-processing phase

Pre-processing involves creating a geometric representation of the structure,

then assigning properties, then outputting the information as a formatted data

file (dat.) suitable for processing by LUSAS.

b) Finite Element Solver

Sets of linear or nonlinear algebra equations are solved simultaneously to

obtain nodal results, such as displacement values at different nodes or

temperature values at different nodes in heat transfer problems.


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c)

Result-Processing

In this process, the results can be processed to show the contour of

displacements, stresses, strains, reactions and other important information.

Graphs as well as the deformed shapes of a model can be plotted.

In order to perform a full analysis, the LUSAS finite element system consists

of two parts. The two parts are.

i. LUSAS Modeller - a fully interactive pre-processing and post-processing

graphical user interface.

ii.

LUSAS Solver - performs the finite element analysis.

3.3 Types of Element

The elements used in this study are expected to provide acceptable good

analytical results compared to the experimental results. Since the analysis carried out

in this research consists of 3D analysis, therefore all elements used were in the group

of 3D as it could produce more detail output due to the complex behaviour of the

structure. Table 3.1, below shows the summary of the element types used in this

research.

Three types of nonlinear analysis may be modelled using LUSAS. They are:

a) Geometric Nonlinearity e.g. large deflection or rotation, large strain, non -

conservative loading.

b)

Boundary Nonlinearity e.g. lift-off supports, general contact, compressional load

transfer, dynamic impact.

c) Material Nonlinearity e.g. plasticity, fracture/cracking, damage, creep, volumetric

crushing, rubber material.


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Table 3.1: Summary of the element types used in this research

Section Element typeDescription of

elementShape

HX8M

Three dimensional

solid hexahedral

elements

comprising 8 nodes

each with 3 degrees

of freedom

TTS3 and QTS4

Three dimensional

flat facet thick shell

elements

comprising either 3

or 4 nodes each

with 5 degrees of

freedom

BRS2

Three dimensional

bar elements

comprising 2 nodes

each with 3 degrees

of freedom

JNT4

Non-linear contact

gap joint elements

and are used to

model the interface

between the end

plate and the

column flange


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3.4 Configuration of Bridge Deck

The bridge deck of this project consisted cast-in-situ slabs on top of pre-

stressed wide T beams. Each beam is supported on a bearing at each end and the

deck has a single span of 30 meter, giving width of deck of 11.9 meter, the deck

skew are varied skewed (0o- 40o). The parapet walls are not part of the structure but

to be considered as dead loads in these models. The beams were supported on single

bearings, and were longitudinally fixed at one end and sliding at the other. All the

working unit is KN (force), m (dimension), s (time) and t (mass).

Typical cross section of the bridge deck and T beams are as shown in Figure

3.1, and Figure 3.2 respectively.

Figure 3.1: Typical Cross Section of the Bridge Deck and T beams


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Figure 3.2: Cross section of Pre-stressed Beam

Figure 3.3: Longitudinal Section of Grillage Model

Figure 3.4: Breadth Dimension - Actual versus Model


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Figure 3.5: End diaphragm Cross Section

3.5 Materials Description

The following data are to be assumed for the analysis of the entire bridge

deck:

a) Concrete grade C40 for the slab and end diaphragm beams i.e. E slab = 31

x 106 KN/m2.

b) Concrete grade C50 for the pre-stressed beams i.e. E beam = 34 x 106

KN/m2

c) Poisson ratio = 0.2

d) Concrete density = 2.4 t/m3

e)

Surfacing 0.05m thick tarmac with density = 2.0 t/m3


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3.6 Loadings Description

All loading is proportioned to the members and joints (nodes) before the

moments, shears and torsions are calculated. Many programs have the facility for

applying patch loads and point loads which do not necessarily coincide with joints or

members. The program will distribute these loads to the members before calculating

the moments, shears and torsion effects. The bridge is subjected to self-weight,

superimposed dead load and vehicles loading according to BD 37/01.

3.6.1

Dead Load

The Dead load is made up of self-weight of the structure and any permanent

load fixed thereon, which is defined as acceleration due to gravity. The dead load is

initially assumed and checked after design is completed. The load intensity is:

DL (KN/m) = m (t/m3) * g (m/s2) * A (m2)

Dead load is applied to the main longitudinal members. Some programs will

automatically generate dead load by applying a density to the cross-sectional area of

the member. Care is needed to avoid double accounting for the weight of the deck

slab.


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3.6.2 Superimposed Dead Load

Superimposed dead load (carriageway surfacing, footpath fill and surfacing

and parapets) are input as uniformly distributed loads along the length of the

longitudinal members. Some programs have the facility of applying patch loads

which can be used for the surfacing providing it is of constant thickness. The load

intensity for the tarmac is as shown: w = (2.0) t/m3* (9.81) m/s2* 0.05 m = 0.981

KN/m2

This load is applied through discrete load type where the load intensities at

four corners are specified. Figure 3.6 of loading application is as shown.

Reference point for assigning load

Figure 3.6: Superimposed Dead Load


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3.6.3 Live loading

Live loading can consist of HA (UDL + KEL) load, HB load, Pedestrian load,

Accidental Wheel load and Wind load. Collision load on parapets is only included if

high containment parapets are required. Horizontal loads such as traction or braking

and skidding are generally not included as the deck is very stiff in resisting these

loads and they will have negligible effect on the results from the grillage analysis.

3.6.3.1

Vehicle Load HA Loading

HA loading represent normal actual vehicles loads on bridges. In this project,

UK vehicle loading code BD 37/01 is referred. The HA loading consists of UDL

(equivalent uniform dead load) and KEL (knife edge loading).

Table 3.2: Vehicle load HA Loading

Loaded length 30m

Width of carriageway 11.5m

Number of notional lane (Clause

3.2.9.3.1)4

Notional lane width 11.5m /4 = 2.875m

HA UDL per linear meter of loaded

length

34.4kN/m

(Table 13)

HA KEL (Clause 6.2.2) 120kN / notional lane

The HA loading is being assigned to each notional lane in the centre

coordinate as shown in Figure 3.7. To obtain maximum shear and reaction force,

separate HA KEL should be applied at location near the support.


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Figure 3.7: Notional Lanes & Center Coordinates

3.6.3.2

Vehicle Load HB Loading

The HB vehicle consists of 4 axles. One unit of HB loading is taken as 10kN.

6m axle spacing with 45 units of HB load per axle is selected for this project.

Static vehicle, lane, and knife edge loading types are provided for many

regional codes of practice. These currently include: AASHTO LFD & LRFD (USA),

BD21/97 (UK), 21/01 (UK), BD37/88 (UK), 37/01 (UK), BRO94 and BRO2002

Vehicle and Classification loads and BRO Train loading (Sweden), Korean,

Israel, Norway, and HK (Hong Kong), Australia, China, Eurocode vehicle and train

loading, Finland, India, New Zealand and Poland. Additional loading types are being

added all the time.

Table 3.3: Vehicle loadHB Loading

HB loading for one axle of 45 units 45 x 10kN/ unit = 450kN

Point load for each wheel 450/4 = 112.5kN

Notional lane 2

Notional lane 3

Notional lane 4

Notional lane 1


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Figure 3.8: Dimension of HB Load

Figure 3.9: HB at lane 1

Figure 3.10: HB at lane 2

Notional lane 2

Notional lane 1

Notional lane 4

Notional lane 1

Notional lane 2

Notional lane 3

2.55

3.5

2.55

3.5

2.25


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3.6.4 Loading Combination

A key feature of LUSAS Bridge is the Basic, Smart and Code-specific load

combination facilities which allow manual or fully automated assembly of design

load combinations. From these, envelopes, contour and deflected shape plots, and

results graphs can be readily obtained for any load case under consideration.

Basic load combinations allow for manual definition of load cases and load

factors. The Smart Combinations facility, unique to LUSAS Bridge, automatically

generates maximum and minimum load combinations from the applied loadings to

take account of adverse and relieving effects. This enables the number of

combinations and envelopes required to model a bridge to be substantially reduced.

Absolute maximum envelopes are included.

Load Combination Wizards use predefined bridge load cases for country-specific

design codes and help automate the definition of load combinations for bridges.

When used in conjunction with a design code template, combinations of load

combinations are automatically created to give the resultant maximum and minimum

ULS or SLS load cases. The loading combination made including of:


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3.6.4.1HA loading for all lanes

Table 3.4: HA loading for all lanes

Load case nameAdverse factor Lane factor

(Table 14)

Factors to be

appliedf1 f3

HA + KEL lane 1ULS 1.5

1.10 1 = 0.891.47

SLS 1.2 1.17


1.10 1 = 0.891.47

SLS 1.2 1.17


1.10 3 = 0.600.99

SLS 1.2 0.79


1.10 n = 0.540.89

SLS 1.2 0.71

3.6.4.2

HB loading for lane1 and HA loading for lane 3&4

The HA load is not required on lane 2 because the clear space of lane 2 is

2.25m which is less than 2.5m.

Table 3.5: HB loading for lane1 and HA loading for lane 3&4

Load case name

Adverse

factorLane factor

(Table 14)

Factors to be

applied

f1 f3

HB lane 1ULS 1.3

1.10

1.43

SLS 1.1 1.21

HA lane 2


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1.10 1 = 0.891.27

SLS 1.1 1.08


1.10 2 = 0.890.27

SLS 1.1 1.08

3.6.4.3HB loading for lane 2, HA UDL for lane 1, 3 and HA loading for lane 4

Table 3.6: HB loading for lane 2, HA UDL for lane 1, 3 and HA loading for lane 4


(Table 14)

Factors to be

appliedf1 f3

HB lane 1ULS 1.3

1.10 bL=2.5 = 0.841.20

SLS 1.1 1.02

HA lane 2ULS 1.3

1.10 1.43

SLS 1.1 1.21

HA lane 3ULS 1.3

1.10 bL=2.5 = 0.841.20

SLS 1.1 1.02


1.10 2 = 0.891.27

SLS 1.1 1.08


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3.6.4.4HB loading on lane 1 only

Table 3.7: HB loading on lane 1 only


(Table 14)

Factors to be

appliedf1 f3

HB lane 1ULS 1.3

1.10 1.43

SLS 1.1 1.21

3.6.4.5HB loading on lane 2 only

Table 3.8: HB loading on lane 2 only


(Table 14)

Factors to be

appliedf1 f3

HB lane 2ULS 1.3

1.10 1.43

SLS 1.1 1.21

3.6.4.6

Enveloping the basic live load combinations

Enveloping is used to perform results processing on maximum and minimum

values of results of load cases. LUSAS modeller does this by creating two load

cases, one for the maximum values and one for the minimum of the specified

load cases.


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3.6.4.7Smart Load Combination

Smart load combinations take account of adverse and relieving effects for the

load cases being considered. The Self-weight, Superimposed Dead Load, and the

Live Load Envelope will all be combined using the Smart Load Combination

facility to give the design combination.

Table 3.9: Smart Load Combination

Load case

name

Variable factor Load

factor

Permanent

factor

Factors to be

appliedf1 f3

Dead loadULS 1.15

1.201.38

1.00.38

SLS 1.0 1.20 0.2

Super dead

load

ULS 1.751.20

2.11.0

1.1

SLS 1.0 1.2 0.2

Live load

envelope

(max)

1.0 1.0 1.0 0 1.0

Live load

envelope

(min)

1.0 1.0 1.0 0 1.0

3.6.5

Vehicle Loading and Load Combinations

LUSAS Bridge provides static vehicle loading options for many worldwide

bridge design codes. These loadings can be used either on their own or with a

moving load generator.

Moving vehicle/train load generators can be used to automatically generate the

required loadcases for a vehicle as it tracks across a bridge.


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For special heavy vehicles, an Abnormal Indivisible Load generator is

included which can generate the load pattern for all possible combinations of

vehicles/axle load/axle spacing.

An optional Vehicle Load Optimisation facility allows an optimised load

pattern to be generated in accordance with the chosen code of practice.

3.7 Grillage Modelling

Longitudinal beam is placed at the pre-stressed beam position, i.e. at 1.9 m

c/c, while the transverse beam representing the slab stiffness in the transverse

direction is placed at 2m c/c. The slab can act as a flange to the end diaphragm beam.

The recommended length of the flange is 0.3*beam spacing = 0.57 m. Dummy beam

is used in the model for assigning parapet wall load. 1 meter wide solid diaphragm

beams are provided at each end and no additional transverse beams are provided

within the span. The parapet walls are not part of the structure but to be considered asdead loads in the model.

Since only one element is used to represent the beam and slab which have

different material stiffness, it is important to calculate the equivalent breadth section

by adopting same material stiffness. In this project, the material stiffness of beam is

selected i.e. the stiffness of slab is factor by a modular ratio, m = Es /Eb.

Equivalent breadth of slab, beq = mb = (31/34) x 1.9 = 1.730m


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Figure 3.11: Grillage and Finite element model

3.8

Finite Element Modelling

The finite element model of this project is shown in Figure 3.12; Types of

beams to be used in the model are longitudinal beam, end diaphragm beam and

dummy beam. Longitudinal beam is placed at the pre-stressed beam position, i.e. at

1.9 m c/c. Unlike the grillage model, the original pre-stressed I section shall be

adopted. 1 meter wide solid diaphragm beams are provided at each end. The parapetwalls are not part of the structure but to be considered as dead loads in the model.

Dummy beam is used in the model for assigning parapet wall load.


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Figure 3.12: Finite Element Model

Figure 3.13: Finite Element Model

As shown in Figure 3.13, the span of a skew bridge measured along an

unsupported edge of the bridge in plan is called Skew Span. The directions parallel

and perpendicular to the flow of traffic on the bridge are still called the longitudinal

and transverse directions respectively.

Slab thickness = 0.2m &

6 nos. of Longitudinal I Beam


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3.9 Layers and Windows

Models are formed of layers where the visibility and properties of each layer

can be controlled and accessed via the layer name which is held in the Tree view. As

the model is built up, model features may be grouped together and manipulated to

speed up data preparation or to enable parts of the model to be temporarily hidden.

3.10 Viewing Results

A whole host of facilities and wizards are available to help you evaluate your

results.

Results can be viewed using separate layers for diagram, contour, vector and discrete

value data.

Plot bending moments, shears forces, and deflections.

Contour ranges and vector/diagram scales can be controlled locally in

each window or set globally to apply to all windows.

Load cases are selected on a window basis allowing multiple views of the

model with each window displaying results for different load cases.

Results can be displayed in global or local directions, in element

directions, or at any specified orientation.

Results can be plotted on deformed or undeformed fleshed or unfleshed

beam sections.

Multiple slices may be cut through 3D solid models on arbitrary planes

and made visible or invisible in any window.


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3.11 Bridge Deck Analysis Result & Discussion

It is always a good practice to carry out approximate checks of the output as

the job proceeds. One simple check is to obtain the total reactions for each load case

to see if they agree with an estimate of the total load applied in each load case.

All the results from these two different models shall be discussed in this

chapter for the beam. The beam results are taken only for both models (grillage,

finite element) after removing (making invisible) all of dummy, transverse, end

diaphragm for grillage model; because the grillage analysis is meant to get the result

for rectangular beam while the rest is not that useful in the design. In finite element

model, removing (making invisible) all of shell split divisions y = 3, y = 2 and end

diaphragm for the finite element model. The division (x,y) is same for all skews for

each of the models, When the surface is divided differently, the result is a little bit

different because of the interpolation. Also the loadings in both models with different

skews are same (value, coordinate). Deflection results are illustrated for better

visualization. Also, the summaries of bending moment, shear force, reaction andtorsion are mentioned and tabulated, while the objective of the contents of this thesis

is to court all the case of the modelling by Lusas software.

Figure 3.14: Simple of bridge deck


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CHAPTER 4

RESULT AND ANALYSIS

4.1 Introduction

In recent times research has been carried out into improving vehicle models,

road surface models and numerical models for the bridge-truck dynamic interaction.

It is hoped to advance the knowledge of the dynamic interaction between bridges and

crossing trucks using a finite element approach, whereby different load cases and

simulation of critical load events can be carried out, using complex models [Rattigan,

Obrien, Gonzalez, 2005].

It is important in the design of highway bridges that adequate consideration is

given to the level of bridge excitation resulting from the dynamic components of a

bridge-truck interaction system [Rattigan, Obrien, Gonzalez, 2005].

The presence of skew in a bridge makes the analysis and design of bridge decks

intricate [Gupta, Misra, 2007]


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4.1.1 Displacement Result

Graphs of the largest displacement value and its location for each modelling

are plotted below. According to the result obtained, minimum combination is taken

for displacement because there is no upward movement. The result depends on the

geometry and the position of a point load from (HB) loading, because theres no

interpolation at that point.

The minimum displacement for both models is occurring close to mid span

Figure 4.3. When the skew increases, the load (the position of HB loading varies

with increasing the skew) will move far away from the mid span experiencing a

decrease in displacement value. For instance, in grillage analysis, the result of 0

skew was ( 0.0717 m) while it was ( 0.0687 m) with 40 skew. Whilst in finite

element analysis the minimum value at 0 skew angle was ( 0.043 m) and will

reduce with increasing the skew till ( 0.0407 m) at 40skew. Both analysis models

yield to the same reduction value of the displacement while increasing the skew,

Table 4.2.

From 0onward the maximum displacement for both models (grillage model

and finite element model) decrease approximately linearly till 40skew.

The reason for that is because the displacement value affected by (supports)

and (loads), since the bridge is simply supported for both models, all the beams are

symmetrical in properties (thickness, width, materials, loading ...) and the value of

loading is the same for each model with different skew values. Consequently,

difference in load position (HB loading) and mesh (decreasing mesh by increasing

the skew) result in a difference in the value of displacement between the beams when

the skew is increasing for both models. For both models the position of maximum

displacement was in the right position of bridge span beam 6 because (HB loading)

lies in the right position of the bridge span Figure 4.3.


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In the table (4.2) the value of grillage model result gives almost one and half

times the finite element model result, because finite element model is more precise

than grillage model and possesses more discretization (more accurate). Therefore

finite element gives less response than grillage model.

Table 4.1: Displacement, Dz (m) versus skew

Table 4.2: largest value of displacement, Dz


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Figure 4.1: location of displacement, Dz, Grillage model skew 200

Figure 4.2: location of displacement, Dz, Finite element model skew 200


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Figure 4.3: location of displacement, Dz

4.1.2 Reaction Result

According to the result obtained in Table 4.4, the maximum support reaction

(largest value) in the grillage model at 0was (2130 KN) at the end of girder support

beam 6. However, at 40the maximum reaction (largest value) was (3190 KN) in the

same position beam 6. Meanwhile in finite element model, the maximum support

reaction (largest value) at 0was (1340 KN), (1530 KN) at 40 skew and all in the

same position beam 6, see Figure 4.8. The results for Grillage and finite element

analysis are increasing linearly while incrementing skews.

The minimum support reaction (smallest value) for the grillage model at 0

was (439kN) at the end of girder support to the right position beam 5. However, at

40the minimum reaction (smallest value) was (-139 KN) in the same position (beam

6), grillage model decrease continuously. While in finite element model, the location

happened to be in beam 1 and the minimum support reaction (smallest value) at 0

and 40was (130 KN), (144 KN) respectively.


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The maximum support reaction (largest value) for grillage model is almost

one and half times the finite element at 0and twice in 40, because finite element is

obviously more precise than grillage model.

In both models with different skews, all the beam symmetrical properties

(dimension, materials...), have same value of loading in all cases with only position

difference for (HB loading) because all different skews positions are dependent on

beam 6. The result increases constantly while increasing the skew because the

loading becomes closer to the support (right support); we can say increasing the skew

will increase the value of reaction.

In grillage model case, when the skew becomes larger, the maximum reaction

increases but minimum reaction reduces (can become negative at 40 ) which means

that the reaction behaviour is an upwards movement (moving up). As a conclusion,

finite element model gives less response than grillage model in reaction force.

Table 4.3: Reaction, Fz (m) versus skew


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Table 4.4: largest & smallest value of reaction, Fz

Figure 4.4: location of largest reaction, Fz, Grillage model skew 200


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Figure 4.5: location of smallest reaction, Fz, Grillage model skew 200

Figure 4.6: location of largest reaction, Fz, Finite element model skew 200


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Figure 4.7: location of smallest reaction, Fz, Finite element model skew 200

Figure 4.8: location of largest reaction, Fz


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Figure 4.9: location of smallest reaction, Fz

4.1.3

Shear force Result

Shear element on the deck has been analyzed to affect the entire model in

skewed analysis, where the piers or the abutment has been recorded with the greatest

effect of the shear loading. We will take the magnitude for shear force in the beam,

after that take the largest between them. Therefore, the condition at the two models

has recorded a desirable effect of the loading.

The grillage has been provided in the grillage wizard in such a way that the

model does not need to take special consideration of providing more elements and

nodes for analysis. Finite element analysis has been divided into better small

partitions for more discretization. Grillage and finite element models with different

skews give same position they give in beam 6 Figure 4.12, for example the result in

grillage model at 0 skew was (1680 KN), and value was increasing till 20 skew,

after that it starts to decrease a little bit at 30 skew, whereupon it increases again,


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this also happens with finite element model. Grillage value is one and a half times

the finite element value. Again finite element model gives a less response than

grillage model.

Table 4.5: Shear Force, Fz (m) versus skew

Table 4.6: largest value of Shear Force, Fz


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Figure 4.10: location of Shear Force, Fz, Grillage model skew 200

Figure 4.11: location of Shear Force, Fz, Finite element model skew 200


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Figure 4.12: location of Shear Force, Fz

4.1.4

Torsion Result

As mentioned before, all the results must be taken on the beam because the

grillage analysis is to get the result for rectangular beam only, the others (end

diaphragm ...) is not that useful for design. Torsion is induced when there is a vertical

loading, when bridges are curved or crooked in plane. The analysis result for Finite

element model and grillage model increases gradually when increasing the skew, the

value of grillage model at 0

skew was (401 KN.m) and was continuously increasingtill (561 KN.m) at 40 skew, while in finite element, it was (262 KN.m),(336 KN.m),

at 0, 40 skewsrespectively. See Table 4.8. The difference between them is only the

position. In grillage model, it happened in beam 6, while in finite element model, it

happened in beam 5, Figure 4.15.

The difference is because the position of (HB loading) value increases

whenever the skew increases, because the (HB loading) is moving to the right if


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compared with beam 6 (stable). Since torsion depends on the position of loading, the

position of (HB loading) is closer to the support when skew increases. Again grillage

value is one and half times the finite element value.

Table 4.6: largest value of Shear Force, Fz

Table 4.8: largest value of Torsion, Mx (KN.m)


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Figure 4.13: largest value of torsion, Mx (KN.m), Grillage model skew 200

Figure 4.14: largest value of torsion, Mx (KN.m), Finite element model skew 200


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Figure 4.15: largest value of torsion, Mx (KN.m)

4.1.5 Moment Result

Moment depends on the value of loading and the position of loading. Since it

is different in position because of the variation of skews, therefore we get different

value of moment.

Ultimate bending moment = l2

8

In addition to the longitudinal loading, horizontal loading in bridges can affect the

design of bearings and generate bending moment in substructures and throughout

Frame Bridge [O'Brien, Keogh, Lehane, 1999].

In grillage model (largest value) the 0 skew result was (2220 KN.m). It was

increasing regularly till (2940 KN.m) at 40skew, It also happens in finite element

model in which the result in 0

skew was (948 KN.m), the value increases to (973KN.m) at 20 skew. Suddenly, the amount of value decreases to (957 KN.m) at 30


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skew, the quantity appears to be continuously reducing, the value (941 KN.m)

resulted at 40 skew, see Table 4.10. The position resulting from each of the two

models happened in beam 6. The difference was that in grillage model, the location

was on (right support) position, while in finite element; it was on the left support

Figure 4.20.

Again in both of the models (using smallest value), grillage model behaves

the same with the (largest value) in value but the difference was in position, it was in

the same position for both models and skews in beam 6 Figure 4.21.

Finite element gives the smallest positive and negative because of the

difference in mesh (more discretization), while all the beams are symmetrical in

properties (thickness, width, materials, loading ...) and the value of loading is same

for each model with different skews. Finite element model gives less response than

grillage model.

Table 4.9: moment, My (KN.m) versus skew


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Table 4.10: largest & smallest value of moment, My (KN.m)

Figure 4.16: largest value of moment, My (KN.m), Grillage model skew 200


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Figure 4.17: smallest value of moment, My (KN.m), Grillage model skew 200

Figure 4.18: largest value of moment, My (KN.m), Finite element model skew 200


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Figure 4.19: smallest value of moment, My (KN.m), Finite element model skew 200

Figure 4.20: largest value of moment, My (KN.m)


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Figure 4.21: smallest value of moment, My (KN.m)


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CHAPTER 5

CONCLUSION

5.1 CONCLUSION

The focus of this modelling is to find the reason of the results differences of the

two models (Grillage, Finite Element), while the objective of this thesis is to simulate

the behaviour of bridge structure in terms of (displacement, reaction, shear force,

bending moment, and torsion) by varying the skew angle value. All done by Lusas

software.

In general for practical skew bridge deck result for finite element give lesser

value in terms of displacement, reaction, shear force, torsion, bending moment

compare with grillage model, therefore can be concluded that analysis by using finite

element method made produce more economical design then compare with the

grillage analysis. In grillage model the result got for both the slab and beam, whilst in

finite element (separate) the result only for beam.


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All the characteristic results increase during the increase of skew except the

displacement result (decreasing), the reason for that is because the position of HB

loading becomes near to the support by increasing the skew angle, in addition to the

element (the load distribution) the distribution is transfer throw the element, of

course the mesh is also important, the last reason is the stiffness change due to skew

into the element skew.

In conclusion, Finite Element model is less precise than grillage model and

possesses more discretization (more accurate), so the design base of this response

with the smaller element gives less amount of materials and so on (that is the

economical factor), subsequently finite element model is more economical design

than grillage model.


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REFERENCES

HAMBLY, E.C., 1976 Bridge Deck Behaviour, CHAPMAN & HALL.

Edmund, C. Hambly, 1991 Bridge Deck Behaviour, Taylor & Francis.

Eugene J. O'Brien, Damien L. Keogh, Barry M. Lehane Contributor Damien L.

Keogh, 1999 Bridge Deck Analysis,Taylor & Francis.

Doug Jenkins, 2004 Bridge Deck Behaviour Revisited; BSc MEngSci MIEAust

MICE.

E.J. O'Brien, D.L. Keogh, 1998 A discussion on neutral axis location in bridge deck

cantileversDepartment of Civil Engineering, University College, Dublin, Ireland.

E.J. O'Brien, D.L. Keogh, 1998 Up stand finite element analysis of slabbridgesDepartment of Civil Engineering, University College, Dublin, Ireland.

Lusas Theory Manual, Version 14.1 Software, United Kingdom.

Maher Kakish, 2007 Bending moment distribution at the main structural elements

of skew deck-slab and their implementation on cost effectiveness, College of

Engineering, Al- Balqa Applied University, Salt, Jordan.

Trilok Gupta,Anurag Misra,2007 Effect on support reactions of T-beam skew

bridge decks,India.

Nicholas M. Baran, 1988 Finite Element Analysis on Microcomputers, McGraw-

Hill Book Company.


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Jaeger, L.G., Bakht B., 1982 The Grillage Analogy in Bridge Analysis, Canadian

Journal of Civil Engineering, Vol.9, Part 2, pp.224-235, Canada.

H. Zeng, J. Kuehn, J. Sun, H. Stalford, 2000 An Analysis of Skewed Bridge/VehicleInteraction Using the Grillage Method, University of Oklahoma.

P.H. Rattigan, E.J. OBrien, A. Gonzalez,2005 The Dynamic Amplification on

Highway Bridges due to Traffic Flow, University College Dublin, Earlsfort Terrace,

Dublin 2, Ireland.

BD 37/01, 2001, Highway Bridge Loading, British Standards Institution.

Saif La Ith Khalid m Fka 2009

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