COMPARISON OF BRIDGE DESIGN IN MALAYSIA BETWEEN AMERICAN
CODES AND BRITISH CODES
WAN IKRAM WAJDEE B. WAN AHMAD KAMAL
A thesis submitted as a fulfillment of requirements
for the award of the degree of Master of Engineering (Structure)
Faculty of Civil Engineering
Universiti Teknologi Malaysia
MAC , 2005
PSZ 19:16 (Pind. 1/97)
UNIVERSITI TEKNOLOGI MALAYSIA
BORANG PENGESAHAN STATUS TESIS
JUDUL :
COMPARISON OF MALAYSIA BRIDGE DESIGN BETWEEN
AMERICAN CODE AND BRITISH CODE
SESI PENGAJIAN : 2004/2005
WAN IKRAM WAJDEE B.WAN AHMAD KAMAL
Saya
(HURUF BESAR)
mengaku membenarkan tesis (PSM/Sarjana/Doktor Falsafah)* ini disimpan di Perpustakaan
Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut:
1. Tesis adalah hakmilik Universiti Teknologi Malaysia.
2. Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan
pengajian sahaja.
3. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara
institusi pengajian tinggi.
4. **Sila tandakan ( )
SULIT
TERHAD
(Mengandungi maklumat yang berdarjah keselamatan
atau kepentingan Malaysia seperti yang termaktub di
dalam AKTA RAHSIA RASMI 1972)
(Mengandungi maklumat TERHAD yang telah ditentukan
oleh organisasi/badan di mana penyelidikan dijalankan)
TIDAK TERHAD
Disahkan oleh
(TANDATANGAN PENULIS)
Alamat Tetap:
NO. 29, JALAN MELAKA BARU 21,
TAMAN MELAKA BARU,
75350 BATU BERENDAM MELAKA.
Tarikh:
CATATAN:
18 March 2005
*
**
(TANDATANGAN PENYELIA)
ASSC.PROF.DR.HJ. AZLAN B.ADNAN
Nama Penyelia
Tarikh:
18 March 2005
Potong yang tidak berkenaan.
Jika tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak
berkuasa/organisasi berkenaan dengan menyatakan sekali sebab dan tempoh tesis ini perlu
dikelaskan sebagai SULIT atau TERHAD.
Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah dan Sarjana secara
penyelidikan, atau disertasi bagi pengajian secara kerja kursus dan penyelidkana , atau
Laporan Projek Sarjana Muda (PSM).
“We certified that the work undertaken by the candidate has been carried out under
our supervision”.
Signature
:
…………………….
Name of Supervisor :
Assc.Prof.Dr.Hj.Azlan B.Adnan
Tarikh
18 Mac 2005
:
ii
“ I declare that this thesis is the result of my research except as cited in references.
The thesis has not been accepted for any degree is not concurrently submitted in
candidature of any degree.”
Signature
:
………………….
Name of Candidate
:
Wan Ikram Wajdee b. Wan Ahmad Kamal
Date
:
17 MAC 2005
iii
For Abah ,Ma ,Adik-adikku,Saudara-mara,Kawankawan,Awek2ku,
May God Bless You All…
iii
iv
ACKNOWLEDGEMENTS
First of all, I would like to thank my greatest supervisor, Associate Prof. Dr. Haji
Azlan Adnan for his advice and moral support for this research. Also to Structural
Earthquake Engineering Research (SEER) group members for giving their support.
I would like to thank Mr. Azizul from Nik Jai Assc. for his cooperation and
contribution in my research. Also not forget Hendriawan, Hafifi, Miji, Mat Nan, Xsel,Lobey, and others.
Finally, my thanks are also due to my parent (Abah & Ma), my girlfriend Syikin,
and all my friends for understanding and encouragement while doing this research.May
god bless you all.
I LOVE U ALL
v
ABSTRACT
The design of a highway bridge, like most any other civil engineering
project, is dependant on certain standards and criteria. Naturally, the critical
importance of highway bridges in a modern transportation system would imply a
set of rigorous design specifications to ensure the safety and overall quality of the
constructed project.
By general specifications, we imply an overall design code covering the
majority of structures in a given transportation system.In the United States bridge
engineers use AASHTO’s standard Specification for Highway Bridges and, in
similar fashion or trends, German bridge engineer utilize the DIN standard and
British and Malaysia designers the BS 5400 code. In general, countries like
German and United Kingdom which have developed and maintained major
highway systems for a great many years possess their own national bridge
standards. The AASHTO Standard Specification, however, have been accepted by
many countries as the general code by which bridges should be designed.
In this research study, investigation and comparisons using codes of
practices for bridge design in Malaysia is done . American codes has been
choosen as an alternative to British codes in design of bridge, followed by
comparison in term of structure component performance due to seismic loading.
The purpose is to investigate the performance of existing bridge in Malaysia due
to seismic resistant.Thus, the bridge performance over the safety condition and
structure integrity while using both codes of practices, American and British
Codes is identified.
vi
TABLE OF CONTENTS
CHAPTER
TITLE
PAGE
DEDCLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
ABSTRACTS
v
TABLE OF CONTENTS
vi
LIST OF TABLES
xi
LIST OF FIGURES
xiii
LIST OF SYMBOLS
xvii
LIST OF APPENDIXES
xix
CHAPTER I
INTRODUCTION
1.1
General
1
1.2
General Specification
2
1.3
Problem Statement
2
1.4
Objectives
4
1.5
Scope of Study
4
1.6
Organization of Thesis
5
1.7
Unit Conversion
5
vii
CHAPTER II
LITERATURE REVIEW
2.1
Introduction
6
2.2
History of Bridge Construction
7
2.2.1 Ancient Structure
7
2.2.1.1 Ancient Structural Principles
8
2.2.1.2 Trial and Error
9
2.2.1.3 The Earliest Beginnings
9
2.2.1.4
12
Timber Bridges
2.2.1.5 Stone Bridges
13
2.2.1.6 Aqueducts and Viaducts
14
2.2.1.7 Religious Symbolism
17
2.2.1.8 Vitruvius’ De Architectura
18
2.2.1.9 Contributions of Ancient Bridge 19
Building
2.3
The Middle Ages
20
2.3.1
Preservation of Roman Knowledge
20
2.3.2
Bridges in the Middle East and Asia
21
2.3.3
Revival of European Bridge Building
21
2.3.4
Construction and History of Old
22
London Bridge
2.3.5
The Era of Concrete Bridges and Beyond 25
2.3.6
Concrete Characteristics
25
2.3.6.1
Early Concrete Structures
26
2.3.6.2
Concrete Arch Bridges
27
2.3.6.3
Prestressed Concrete Bridges
28
viii
2.4
Concrete Bridges after the Second
29
World War
2.4.1 Cable-Stayed Bridges
30
2.5
Recent Bridge Projects
37
2.6
Contributions of Modern
38
Concrete Bridge Construction
CHAPTER III
THEORITICAL BACKGROUND
3.1
Choice of Abutment
3.1.1 Design Consideration
Choice Of Bearing
3.2
40
41
42
3.2.1 Preliminary Design
44
3.2.2
Constraint
45
Selection of Bridge Type
46
3.3
3.3.1 Preliminary Design Consideration
47
3.3.2 Design Standard for preliminary design
48
3.4
Reinforced Concrete Deck
49
3.4.1 Analysis of Deck
49
3.4.2 Design Standard for Concrete
50
3.4.3 Prestressed Concrete Deck
51
3.4.4 Pre-Tension Bridge Deck
52
3.5
Composite Deck
54
ix
3.5.1 Construction Method
3.6
Steel Box Girder
55
3.6.1 Steel Deck Truss
56
3.6.2 Choice of Truss
57
Cable Stay Deck
58
3.7
3.8
Suspension Bridges
3.8.1 Design Consideration
3.9
Choice of Pier
3.9.1 Design Consideration
3.10
CHAPTER IV
54
59
61
62
63
Choice Of Wingwalls
64
3.10.1 Design Consideration
65
METHODOLOGY
4.1
Introduction
66
4.2
Design Flowchart
67
4.2.1 BS 5400 and AASHTO-Seismic
67
Design Flowchart
4.3
Result and Analysis
80
4.3
Discussion and Conclusion
93
CHAPTER V
CONCLUSION AND SUGGESTION
5.0
Introduction
5.1 Future Research
94
95
x
5.1.1 Future Challenges in
95
Bridge Engineering
5.2
Improvements in Design, Construction,
96
Maintenance, and Rehabilitation
5.2.1 Improvements in Design
96
5.2.2 Improvements in Construction
97
5.2.3 Improvements in Maintenance
98
and Rehabilitation
5.3
Conclusion
100
REFERENCES
101
APPENDIXES
104
xi
LIST OF TABLES
NO.
TITLE
PAGE
2.1
Stay Cable Arrangements
32
2.2
Recent Major Bridge Projects
37
3.1
Selection of bridge type for various span length
46
3.2
The Design Manual for Roads and Bridges
60
BD 52/93 Specifies a Group Designation
4.1
Steel area for different code of practices.Consider
80
for seismic reading 0.15 g
4.2
Cost of steel area for different code.Consider
80
for seismic reading 0.15 g
4.3
Steel Area for different code of practice.Consider
81
for seismic reading 0.075 g
4.4
Cost of steel area for different code.Consider
for seismic reading 0.075g
81
4.5
Time History Analysis due to End Member of Force
by using British code analysis (Staad-Pro)
84
4.6
Time History Analysis due to End Member of Force
by using American code analysis (Staad-Pro)
84
4.7
Time History Analysis due to joint displacement
by using American code analysis (Staad-Pro)
85
xii
4.8
Time History Analysis due to joint displacement
by using British code analysis (Staad-Pro)
86
4.9
Time History Analysis due to support reaction
by using American code analysis (Staad-Pro)
87
4.10
Time History Analysis due to support reaction
by using British code analysis (Staad-Pro)
88
xiii
LIST OF FIGURES
NO.
TITLE
PAGE
2.1
Corbelled Arch and Voussoir Arch
14
2.2
The Pont du Gard, Nîmes, France
15
(taken from Brown 1993, p18)
2.3
The Puente de Alcántara, Caceres, Spain
16
(taken from Brown 1993, p25)
2.4
The Ponte Sant’Angelo, Rome, Italy
17
(taken from Leonhardt 1984, p69)
2.5
Old London Bridge, London, Great Britain
23
(taken from Steinman and Watson 1941, p69)
2.6
The Plougastel Bridge under Construction
28
(taken from Brown 1993, p122)
2.7
Stay Cable Arrangements
31
2.8
The Oberkassel Rhine Bridge, Düsseldorf,
33
Germany (taken from Leonhardt 1984, p260)
2.9
The Lake Maracaibo Bridge, Venezuela
33
(taken from Leonhardt 1984, p271)
2.10
The Pont de Brotonne, France
34
(taken from Leonhardt 1984, p270)
2.11
The Akashi Kaikyo Bridge, Japan
38
(taken from Honshu-Shikoku Bridge Authority 1998, p1)
xiv
3.1
Open Side Span
40
3.2
Solid Side Span
41
3.3:
Elastomeric Bearing
43
3.4
Plane Sliding Bearing
43
3.5
Multiple Roller Bearing
43
3.6
Typical Bearing Layout
44
3.7
Various of Deck Slab
49
3.8
Aspect Ratio vs Skew angle graf
50
3.9
Type of Girder
52
3.10
Types of Beam-Slab
53
3.11
Typical Composite Deck
54
3.12
Cross section of Steel Box Girder
55
3.13
Type of truss
56
3.14
Bridge Truss
57
3.15
Simple Cable Stay Bridge
58
3.16
Suspension Bridge
59
3.17
Types of Parapet
60
3.18
Different Pier Shape
63
3.19
Load acting on Retaining Wall
64
3.20
Distribution Surcharge Load
64
4.1
AASHTO–LRFD seismic design flowchart
69
4.2
BS 5400 design flowchart
71
4.3
Design Flowchart of I Girder Bridge
according to AASHTO
Design flowchart of I-Girder Bridge
according to BS 5400
Design Flowchart of Column Bent Pier
according to AASHTO
Design Flowchart of Column Bent Pier
according to BS 5400
73
4.4
4.5
4.6
4.7
Design Flowchart of Stub Abutment
according to AASHTO
75
76
77
78
xv
4.8
Design Flowchart of Column Bent Pier
79
according to BS 5400
4.9
Steel Area for different code of practice.Consider
82
for seismic reading 0.15 g
4.10
Steel Area for different code of practice.Consider
82
for seismic reading 0.075 g
4.11
Cost of steel area for different code.Consider
83
seismic reading 0.15 g
4.12
Cost of steel area for different code.Consider
83
seismic reading 0.075g
4.13 a Mode Shape of bridge structure during
89
earthquake event for American code design
4.13 b Mode Shape of bridge structure during
90
earthquake event for American code design
4.13.c Natural Frequency vs Participation graph
90
4.13.d
91
Time History Analysis graph for
American code design
4.14. a Mode Shape of bridge structure during
91
earthquake event for British code design by
using Lusas Software
4.14. b Mode Shape of bridge structure during
earthquake event for British code design by
using Lusas Software
92
xvi
4.14.c.
Natural Frequency vs Participation graph
92
4.14.d.
Time History Analysis graph for British
93
code design
xvii
LIST OF SIMBOLS
S
-
Distance Between Flanges
MDL
-
Dead Load Moment
MLL
-
Moment Due to Live Load
MLL + I
-
Moment Due to Live Load + Impact
MB
-
Total Bending Moment
MSDL
-
Moment Super Imposed Dead Load
Es
-
Modulus of Elasticity for Steel
Ec
-
Modulus of Elasticity for Concrete
n
-
modular ratio
r
-
stress ratio
k&j
-
coefficient
b
-
Unit width of slab
d
-
minimum depth required
As
-
Required Area Steel Bar
D
-
Distribution Steel
Beff
-
Effective Width
DF
-
Distribution Factor
I
-
Impact Moment
MMax
-
Maximun Moment
R
-
Reaction of Support
V
-
Shear Force
PAE
-
Active Earth Pressure
KAE
-
Seismic Active Earth Pressure Coefficient
ĭ
-
Angle of Friction Soil
A
-
Acceleration Coefficient
į
-
Angle of Friction Between Soil and Abutment
xviii
ȕ
-
Slope of Soil face
Kh
-
Horizontal Acceleration Coefficient
Kv
-
Vertical Acceleration Coefficient
F’T
-
Equivalent Pressure
W
-
Abutment Load
ĮȕȖ
-
Single Mode Factors
S
-
Site coefficient
VY
-
Force Acting on Abutment
Pe
-
Equivalent Static Earthquake Loading
FA
-
Axial Force
r
-
Radius of Gyration
fC
-
Concrete Strength
fS
-
Grade Reinforcement
MU
-
Ultimate Moment
k
-
Stiffness
vS
-
Static Displacement
xix
LIST OF APPENDIXES
APPENDIX
TITLE
A
Design Sheet Calculation
B
Bridge Structure Drawing
C
El –Centro Data
CHAPTER I
INTRODUCTION
1.1
General
Currently, in Malaysia we have not practice in design of bridge for
earthquake situation is not practices. Currently in our code of practice BS 5400, it
did not have allocation or rules in earthquake design consideration for bridge
structure.Eventhough our country does not have earthquake event occurred very
frequently, we must aware that our neighbouring countries such as Indonesia and
Philippines is an active earthquake region. Therefore we must take into attention
and consideration when we start to design bridge so that the effect of earthquake
damage from earthquake event in our neighbouring countries can be minimized to
our structures especially bridge.
Eventhough our bridge structure might just get small vibration due to
earthquake from our near region country, it may also contribute to some side
effect in long term period if it happened for many times. This situation might
cause cracking and collapse to our bridge. So ,in solving this problem we need a
code of practice that considered earthquake loading in design process. In this
research , we try to compare two codes of practice AASHTO-ACI and BS 5400
for bridge design resist of seismic loading. The design of a highway bridge, like
most other civil engineering project, is dependent on certain standards and
criteria. Naturally, the critical importance of highway bridges in a modern
2
transportation system would imply a set of rigorous design specification to ensure
the safety and overall quality of the constructed project.
1.2
General Specifications
In general specifications, we imply an overall design code covering the
majority of structures in a given transportation system. In the United States bridge
engineers use Ashton’s standard Specification for Highway Bridges and, in
similar fashion or trends, German bridge engineer utilize the DIN standard and
British and Malaysia designers the BS 5400 code. In general, countries like
German and United Kingdom which have developed and maintained major
highway systems for a great many years possess their own national bridge
standards. The AASHTO Standard Specification, however, have been accepted by
many countries as the general code by which bridges should be designed.
This does not mean that the AASHTO code is accepted in its entirety by
all transportation agencies. Indeed, even within the United States itself, state
transportation departments regularly issue amendments to the AASHTO code.
These amendments can offer additional requirements to certain design criteria or
even outright exceptions.
1.3
Problem Statement
According to the latest information we get, most bridge engineers in
Malaysia are using BS 5400 code for guideline in design bridge project. This is
because our bridge engineer got their basic knowledge or tertiary education from
European countries like United Kingdom , New Zealand , and others countries
that practices BS 5400 as a code of practice. That is they use BS 5400 code as a
common practice in our country.Eventhough they already knew that BS 5400
does not have seismic consideration in their practice calculation design, they just
ignored this case because in their opinion our country is outside seismic activity
3
area.They forgot our country is near to our country neighbour such as Sumatera
(Indonesia) and Philiphinnes that still have an active earthquake location
center.However, we received vibration due to earthquake measuring 4.3 Richter
scale in Penang Island , Kelantan , Perak and Kedah.This event was occurred
caused by earthquake in Acheh (Indonesia).Some of our building structure like
column , wall and slab are cracking due to this vibration from Acheh
earthquake.Based on Malaysia Meteorological Services statement and other
source, a reading value of earthquake for peninsular Malaysia as 0.075 g (75 gal)
and for Sabah is 0.15 g (150 gal).These value is considered low vibration by some
engineer and is not concern for a safety of bridge structure but for others person
that concern of it this value can caused collapsed to our building or bridge if it
happened frequently.
Therefore , a need to review our practice design code and also our
construction method especially in design of bridge is much needed so as to protect
bridge structure from the undesired damaging effect due to this natural
disaster.The aim of this research is to compare our currently code of practice (BS
5400) with AASHTO-Seismic Design Code in term of efficiency in design a
bridge in Malaysia.It also investigate which two code much applicable is to be
applied in our country.The way to compare these two codes are by trying to
redesign our existing bridge structure by using the different code of practices.In
our case , we use American code of practice in redesigning our bridge
structure.After that, we analyze and determine which code is much better for our
country in design.
4
1.4
Objectives
The aims of this research are as follow :
a) To investigate codes of practices suitable for our bridge structure
design.
b) To determine whether current codes of practice in Malaysia ( BS
5400) is still practical for now or instead.
c) To determine the existing capacity of bridges in resisting low
intensity seismic loading due to near earthquake source.
d) To compute the cost of using the different codes of practices.
e) To determine the Time History Analysis Response(Timeacceleration) due to earthquake event using both codes of
practices.
1.5
Scope of study
The scope of the research are limited to certain things as follow :
a) Bridge component of structure ; Deck , Girder , Pier and
Abutment.
b) In Malaysia high risk seismic location.( e.g : Sabah and Penang
Island)
c) Compare in term of size of components and cost .(e.g : Volume of
concrete and amount of steel that will be required)
5
1.6
Organization of Thesis
Extensive literature reviews are available in Chapter 2.Background theory
and Principal of bridge engineering are described in Chapter 3.
1.7
Unit Conversion
Both SI Metric and Imperial Units are use throughout this thesis.
CHAPTER II
LITERATURE REVIEW
2.1
Introduction
The following chapter shall introduce the reader to past, present,
and future in bridge engineering. The history of engineering is as old as
mankind itself, and it is without doubt that technical progress and the rise
of human society are deeply interwoven. Bridges have often played an
essential role in technical advancement within Civil Engineering.
The development of important types of bridges and the changing
use of materials and techniques of construction throughout history will be
dealt with in the first part of this chapter. Notably,manifold legends and
anecdotes are connected with the bridges of former eras. Studying the
history of a bridge from its construction throughout its life will always
also reveal a fascinating picture of the particular historical and cultural
background.The second part of this chapter introduces the main
challenges that the current generation of bridge engineers and following
generations will face. Three important areas of interest are identified.
These are improvements in design, construction, maintenance, and
rehabilitation of a bridge, application of high-performance materials, and
creative structural concepts. As technology advances, many new ways of
innovation thus open for the bridge engineer.
7
2.2
History of Bridge Construction
The bridges described in the following sections are examples of
their kind. A vast amount of literally thousands of bridges built requires
choosing a few exemplary ones to show the main developments in bridge
construction throughout the centuries. Any book examining bridges in a
historical context will make its own choice, and studying these works can
be of great value for understanding of the legacy of bridge engineering.
The subdivision into certain periods in time shall provide a framework for
the reader’s orientation in the continuous process of history as it unfolds.
2.2.1 Ancient Structures
It will never be known who built the first actual bridge structure.
Our knowledge of past days fades the further we look back into time. We
can but assume that man, in his search for food and shelter from the
elements and with his given curiosity, began exploring his natural
environment.Crossing creeks and crevices with technical means thus was
a matter of survival and progress,and bridges belong to the oldest
structures ever built. The earliest bridges will have consisted of the
natural materials available, namely wood and stone, and simple
handmade ropes. In fact,there is only a handful of surviving structures
8
that might even be considered prehistoric, e.g. the so-called Clapper
bridges in the southern part of England, as Brown (1993) notes.
2.2.1.1
Ancient Structural Principles
The earliest cultures already used a variety of structural principles.
The simplest form of a bridge,a beam supported at its two ends, may have
been the predecessor of any other kind of bridges; perhaps turned into
reality through use of a tree that was cut down or some flat stone plates
used as lintels. Arches and cantilevers can be constructed of smaller
pieces of material, held together by the compressive force of their own
gravity or by ropes. These developments made larger spans possible as
the superstructure would not have to be transported to the site in one
complete piece anymore.
Probably the oldest stone arch bridge can be found crossing the
River Meles with a single span at Smyrna in Turkey and dates back to the
ninth century BC (Barker and Puckett 1997). Even suspension bridges are
no new inventions of modern times but have already been in use for
hundreds of years. Early examples are mentioned from many different
places, such as India and the Himalaya, China, and from an expedition to
Belgian Congo in the early years of this century (Brown 1993). Native
tribes in Mexico, Peru, and other parts of South America, as Troitsky
(1994) reports, also used them. He also mentions that cantilevering
bridges were in use in China and also in ancient Greece as early as 1100
BC.
Podolny and Muller (1982) give information on cantilevering bridges
in Asia and mention that reports on wooden cantilevers from as early as
the fourth century AD have survived.
9
2.2.1.2
Trial and Error
In some cases, authors of books or book chapters on the history of
bridges use terms such as primitive, probably as opposed to the modern
state-of-the-art engineering achievements. It is spoken of a lack of proper
understanding, and of empirical methods. From today’s point of view it is
easy to come to such a judgement, but one should be careful not to
diminish the outstanding achievements of the early builders. In our
technical
age
with
a
well-developed
infrastructure,computer
communication, and heavy equipment readily available it is easy to forget
about the real circumstances under which these structures were built.
Since mathematics and the natural sciences had yet even begun being
developed it is not astonishing that no engineering calculations and
material testing as adhering to our modern understanding were
performed. But a feeling for structures and materials was present in the
minds of these ancient master builders.With this and much trial and error
they built beautiful structures so solid and well engineered that many
have survived the centuries until our days.
2.2.1.3
The Earliest Beginnings
Earliest cultures to use bridges according to our current
knowledge were the Sumarians in Mesopotamia and the Egyptians, who
used corbelled stone arches for the vaults of tombs (Brown 1993).
In the fifth century
BC
the Greek historian Herodotus, who lived
from about 490 to 425 BC (Brown 1993), wrote the history of the ancient
world. His report on the city of Babylon includes a description of the
10
achievements of Queen Nitocris, who had embankments and a bridge
with stone masonry piers and a timber deck built at the River Euphrates.
This bridge is believed to have been built in about 780 BC (Troitsky 1994)
and was built as described in the following (Greene 1987, p118).
“… and as near as possible to the middle of the city she built a bridge
with the stones she had dug, binding the stones together with iron and
lead. On this bridge she stretched, each morning, square hewn planks on
which the people of Babylon could cross. By night the planks were
withdrawn, so that the inhabitants might not keep crossing at night and
steal from one another.”
Herodotus’ report does not tell about the construction of this bridge and
leaves much room for imagination on how the bridge might actually have
looked like. His second report on a bridge,however, gives a more detailed
view. A floating pontoon bridge was used by Persian King Xerxes to
cross the Hellespont with his large army in the year 480
BC
(Brown
1993). Herodotus describes the bridge in detail (Greene 1987, pp482f):
“It is seven stades (a stade was about 660 feet) from Abydos to the land
opposite.[…] This is how they built the bridge: they set together both
penteconters and triremes, three hundred and sixty to bear the bridge on
the side nearest the Euxine and three hundred and fourteen for the other
bridge, all at an oblique angle to the Pontus but parallel with the current
of the Hellespont. This was done to lighten the strain on the cables. […]
When the strait was bridged, they sawed logs of wood, making them equal
to the width of the floating raft, and set these logs on the stretched cables,
and then, having laid them together alongside, they fastened them
together again at the top. Having done this, they strewed brushwood over
it,and, having laid the brushwood in order, they carried earth on the top
of that; they stamped down the earth and then put up a barrier on either
side…”
11
If one considers Herodotus’ account to be accurate the bridge must have
been a fairly impressive structure and without any equivalent at its time.
Especially the description of how the pontoons were anchored indicates a
well developed understanding of structural principles. Use of bridges for
military needs was not uncommon in ancient times. Gaius Iulius Caesar
(100 - 44 BC) is amongst the authors who left us very clear records of
early bridges. In his De Bello Gallico,written in 51 or 50 BC, he mentions
several bridges that he had his troops build during his conquest, e.g.
across the Saône, and in the fourth book he describes the famous timber
bridge built across the Rhine in 55 BC. This type of bridge was actually
rebuilt a second time later during his conquest. His description of the
structure is to such detail that several attempts were made to reconstruct
it, and it shows the level of knowledge to which the engineering
profession had grown by that time (Wiseman and Wiseman 1990, pp7880):
“Two piles a foot and a half thick, slightly pointed at their lower ends and
of lengths dictated by the varying depth of the river, were fastened
together two feet apart. We used tackle to lower these into the river,
where they were fixed in the bed and driven home by pile drivers, not
vertically, as piles usually are, but
obliquely, leaning in the direction on the current. Opposite these, 40 feet
lower down the river, two more piles were fixed, joined together in the
same way, though this time against the force of the current. These
two pairs were then joined by a beam two feet wide, whose ends fitted
exactly into the spaces between the two piles of each pair. The pairs were
kept apart from each other by means of braces that secured each pile to
the end of the beam. So he piles were kept apart, and held fast in the
opposite direction, the structurebeing so strong and the laws of physics
such that the greater the force of the urrent, the more tightly were the
timbers held in place.A series of these piles and beams was put in
position and connected by lengths of timber set across them, with poles
and bundles of sticks laid on top. The structure was strong, but additional
piles were driven in obliquely on the downstream side of the bridge; these
were joined with the main structure and acted as buttresses to take the
force of the current. Other piles too were fixed a little way upstream from
12
the bridge so that if the natives sent down tree trunks or boats to demolish
it, these barriers would lessen their impact and prevent the bridge being
damaged.Ten days after the collection of the timber was begun, the work
was completed and the army led across.”
Troitsky (1994) reports on an even older Roman timber bridge,
the Pons Sublicius. It is the oldest Roman bridge whose name is known,
named after the Latin word for wooden piles. This bridge was built in
about 620
BC
by King Ancus Marcius and spanned the River Tiber
(Adkins and Adkins 1994).
The brief record of timber bridges given in this section would not be
complete without mentioning Appolodorus’ bridge across the Danube. It
was built in about 104
AD
under Emperor Trajan (O’Connor 1993). Its
magnitude – the length must have been more than a kilometer – and the
unique structure of timber arches makes it special among the Roman
bridges of which we have record.
2.2.1.4
Timber Bridges
Timber bridges and timber superstructures on stone piers will
probably have been prevailing in many parts of the Roman Empire at that
time. Wood was a cheap construction material and abundantly available
on the European continent. Furthermore it can be readily cut to shape and
transported with much less effort than stone. The Romans already knew
nails as means of connecting timber. Even the principle of wooden trusses
was already known, as reliefs on both
the Trajan’s Column in Rome
Aurelius
(AD
(AD
113) and the Column of Marcus
193) clearly show truss-type railings of military bridges
(O’Connor 1993). However, there is no historic evidence that the Romans
13
actually used the truss as a structural element in their bridges. Truss
systems may have actually been used for the wooden falsework that was
used for erection of stone masonry arches.
2.2.1.5
Stone Bridges
Apart from timber bridges, stone masonry arch structures are
examples of the outstanding skills of the ancient Romans. The Roman
stone arches where built on wooden falsework or centering which could
be reused for the next arch once one had been completed. The
semicircular spans rested on strong piers on foundations dug deeply into
the riverbed. Brown (1993) points out that due to the width of these piers
between the solid abutments the overall cross section of the river was
reduced, thus increasing the speed of the current. To deal with this
problem the Romans built pointed cutwaters at the piers. A very
comprehensive study on Roman arches can be found in O’Connor (1993).
The arches used were voussoir arches, which are put together of tapered
stones with a keystone that closes the arch. Compressive forces from the
dead load and the weight of traffic on the bridge hold the stones together
even without use of any mortar. Corbelled arches, on the other hand,
consist of stones put on top of each other in a cantilevering manner until
they two halves finally meet in the middle. This principle was already
known prior to Roman times and was used in vaulted tombs throughout
the Old World. Both different arch types are shown in Figure 2-1.
14
Figure 2.1 : Corbelled Arch and Voussoir Arch
2.2.1.6
Aqueducts and Viaducts
The Roman infrastructure system was very well developed. It
served both military and civil uses by providing an extensive network of
roads. Aqueducts and viaducts of the Roman era can still be found
scattered over the former Roman Empire, primarily in Italy, France, and
Spain. Some Roman bridges or their remainders are also located in
England, Africa and Asia Minor (O’Connor 1993).
Probably the best-known Roman aqueduct is the Pont du Gard near
Nîmes in Southern France,which is shown in Figure 2-2. Built by Marcus
Vipsanius Agrippa (64 - 12 BC) in about 19 BC, this structure was part of
an aqueduct carrying water over more than 40 km (Liebenberg 1992).The
crossing of the River Gard has an impressive height of 47.4 m above the
river, consisting of three levels of semicircular arches that support the
covered channel on top. The spans of the two lower levels are up to 22.4
m wide. All of its stone masonry was built without use of mortar except
for the topmost level. A more recent addition to the Pont du Gard built in
1747 provides a walkway next to the bottom arch level that is an exact
15
copy of the Roman architecture (Leonhardt 1982). Another well-known
aqueduct can be found at Segovia in Spain.
Figure 2-2: The Pont du Gard, Nîmes, France (taken from Brown 1993, p18)
Sextus Iulius Frontius (c. 35 - 104 AD) wrote De Aquis Urbis Romae on
the history and technology of the Roman aqueducts (O’Connor 1993).
Aqueducts were used to provide thermae,baths, and public fountains with
water; few residential buildings had an own connection.However though,
the amount of water available for every citizen is estimated to have
equaled or even exceeded today’s standards for water supply systems.
Adkins and Adkins (1994) speak of
half a million to a million cubic meters of water that were provided
through Rome’s aqueducts per day. Located in Spain is a bridge that
attracts interest because of its scale and the magnificent setting.
The Puente de Alcántara crosses the River Tagus at Caceres close to the
border to Portugal with six elegant masonry arches as shown in Figure 2-
16
3. Again, these arches were built without the use of mortar. The name of
the bridge contains some redundancy, since it is derived from an old
Arabic term for ‘bridge’. The two main arches with a gate on the roadway
are higher than the Pont du Gard and remain the longest Roman arches,
both spanning 30 m (Brown 1993). The name of the Roman engineer who
built this masterpiece in 98
AD
under Emperor Trajan is known. Caius
Iulius Lacer’s tomb is found nearby, and the gate with the famous
inscription Pontem perpetui mansuram in saecula mundi (I leave a bridge
forever in the centuries of the world) has survived the centuries (Gies
1963, p16).
Figure 2-3: The Puente de Alcántara, Caceres, Spain (taken from Brown 1993, p25)
Even earlier dates the Pons Augustus or Ponte d’Augusto in Rimini, Italy.
It was begun underEmperor Augustus and finished in 20
AD
under
Emperor Tiberius (O’Connor 1993) and is considered one of the most
beautiful Roman bridges known. Five solid spans of only medium lengths
between 8 and 10.6 m are decorated in an extraordinary way, with niches
framed by pilasters over each pier (Steinman and Watson 1941). Andrea
Palladio, architect of the Renaissance, used this bridge to develop his own
bridges, and thus spread the fame of this bridge across Europe, as Gies
17
(1963) writes. Rome itself still houses ancient bridges built during the
Roman era. Brown (1993) gives information that eight major masonry
bridges are known of in Rome, of which six still exist at the River Tiber.
They are the Ponte Rotto or Pons Aemilius, of which only a single span
remains,initially built in the second century
BC,
the Ponte Mollo (or
Milvio) or Pons Mulvius, built 110 BC; and the Ponte dei Quattro Capi or
Pons Fabricius, built 62
BC.
The Ponte Cestius was built 43
BC
and
altered under subsequent emperors. Considered to be the most beautiful
of Rome’s bridges is the Pons Aelius (now known as Ponte Sant’Angelo),
built
AD
134 under Emperor Hadrian. Giovanni Lorenzo Bernini (1598 -
1680) modified it in 1668 by adding statues of angels and a cast iron
railing. The Ponte Sant’Angelo is shown in Figure 2-4. The Ponte Sisto,
the youngest bridge of this ensemble, was built in AD 370.
Figure 2-4: The Ponte Sant’Angelo, Rome, Italy (taken from Leonhardt 1984, p69)
2.2.1.7
Religious Symbolism
An interesting fact in the context of early bridge building is
religious symbolism. Higher positions in Roman hierarchy often involved
both spiritual and practical tasks, such as control of the markets and
18
storage facilities, or the building activities. O’Connor (1993, p2) tells that
bridge building supervision “was placed in the care of the high priest,
who received the title pontifex,
commonly translated as ‘bridge builder’, from the Latin pons (bridge) and
facere (to make or build).
” This title, pontifex maximus, was passed on to later Roman emperors
and through early Christian bishops even to the present Pope. In this
context O’Connor (1993, p3) offers the explanation that this important
title symbolized the “bridge from God to man…”
2.2.1.8
Vitruvius’ De Architectura
The famous Roman architect and engineer Marcus Vitruvius
Pollio (Morgan 1960) does not specifically mention bridges in his work
De Architectura (The Ten Books on Architecture),which was written in
the first century BC. However, aqueducts are the topic of a whole chapter
in Book Eight, and cofferdams, important for erecting bridge piers in
riverbeds, are described in detail in a section on harbors, breakwaters, and
shipyards. According to him, a double enclosing was constructed of
wooden stakes with ties between them, into which clays was placed and
compacted. Afterwards, the water within the cofferdam was removed
(several different engines to pump water, such as water wheels and mills,
and the water screw are described by him), and work on the pier
foundations could begin. In case the soil was to soft Vitruvius advised to
stake the soil with piles.
Another fact of particular interest for today’s engineers is the
description of concrete that Vitruvius gives. In a comprehensive list of
19
construction materials the origin and use of pozzolana is described, a
volcanic material that performs a cementitious reaction if mixed as a
powder with lime, rubble, and water. This reaction is hydraulic; i.e. the
concrete obtained, called opus caementitium, can harden even under
water. Together with use of brick masonry and natural stone, as well as
with timber and sand, the Romans had an enormous range of flexibility in
constructing their buildings and structures. A truly unique example of
their skills is the Pantheon in Rome, built under Emperor Hadrian around
the year
AD
125. It is topped with a majestic 43.2-m wide dome made of
ring layers of concrete (Harries 1995). Use of lighter aggregates towards
the top, stress-relieving masonry rings, regular voids on the inside and
tapering of the dome to reduce its weight provide the structural stability
that has made the Pantheon withstand all influences until the present day.
2.2.1.9
Contributions of Ancient Bridge Building
In conclusion, the main bridge construction principles were
already known and used to some extent in ancient times. Due to lack of
surviving timber structures one can only rely on historical reports and
depictions of these. Prevailing structures in ancient times were the
semicircular stone arch bridges, many of which have survived until the
present day. Roman builders left a legacy of impressive structures in all
parts of former Roman Empire. Arch structures were intelligently used
both for heavy traffic and elaborate water supply systems; temporary
timber structures also served military purposes. These systems were
developed to the full extent that was technically possible and were not to
be surpassed in mastery until many centuries later.
Engineering knowledge was already documented systematically by
authors such as Vitruvius, whose work influenced the builders of later
20
centuries considerably. Great builders and artists, such as Bramante,
Michelangelo, and Palladio were careful students of his works.
2.3
The Middle Ages
For the historical overview given in this study, the term Middle
Ages refers to the period of time between the fifth and the late fifteenth
century; other authors may set somewhat different limits, e.g. the eleventh
to the sixteenth century (Troitsky 1994). Thus, spanning a time of about a
thousand years in one section of this study can necessarily not cover all
bridges built, but give a
representative selection of the achievements that were made. Their
significance and history will be discussed further in this section.
2.3.1
Preservation of Roman Knowledge
After more than 1,200 years of existence, the once mighty Roman
Empire finally fell apart around the fifth century
AD
(Adkins and Adkins
1994), and a period of anarchy and chaos began.Invasions of the Eternal
City destroyed much of the former grandeur. The major achievements of
the Roman civilization began to be forgotten, and their cities were
deserted. Bridges as large and solid as the Roman bridges were to be built
again only centuries later. Gies (1963) reports that the predominant
community structures in Europe of the eighth and ninth century were
small feudal agricultural states. The knowledge of Roman culture was
kept in monasteries scattered across the old continent. Ancient authors,
21
such as Vitruvius, were copied by hand many times by the monks who
thus preserved these treasures for future generations.
2.3.2
Bridges in the Middle East and Asia
At about the same time another rise of bridge building began. Had
the Romans themselves vanished in Europe, their influence on the Middle
East and even Asia began to prosper. Persian rulers built pointed brick
arches, and the coming blossom of bridge building reached as far as
China, as Gies (1963) reports. The Chinese skillfully built elegant
segmental stone arches with roadways that followed the swinging shape
of the arch, and they also built cantilevers of timber on stone piers.
According to Gies (1963) examples were reported by the thirteenth
century Venetian explorer Marco Polo (c. 1254 - 1324), who traveled
Asia for several decades and contributed much to the European view of
the world. Indian cultures undertook own bridge building under this
influence and further developed the suspension bridges.
2.3.3
Revival of European Bridge Building
Finally, the art of bridge building also began to blossom in Europe
again. Most authors particularly mention the importance of the church in
22
the Middle Ages that contributed to this development. Contacts with the
Middle East were made during the crusades, when the pilgrims and
knights saw evidence of the skills of Arabian cultures.
Importance of the church in these times cannot be exaggerated,
since in many cases the order that in society existed was enforced
primarily by clergymen who held court, regulated merchants’ fairs, and
kept the monasteries as centers of knowledge and spiritual experience. It
has already been mentioned in Section 2.1.1.7 how the ancient title
pontifex maximus of the Roman high priest became to be used by the
Popes.The church had considerable influence on all major medieval
building undertakings. The biggest of these structures, the awe-inspiring
cathedrals and large stone bridges, would not have been built otherwise.
Working on them was considered to be pious work (Gies 1963) and was
thus a very honorable task to be performed. Some religious orders formed
to bring progress to hospices and to build bridges for the travelers’ sake
(Steinman and Watson 1941). Spreading from Italy,where the Fratres
Pontifices originated from, similar brotherhoods also formed in other
countries, e.g. France (Frères Pontiffes) and England (Brothers of the
Bridge).
2.3.4
Construction and History of Old London Bridge
Probably the most colorful and vivid history, unsurpassed by any
other, is related to a bridge located in a city that gained an enormous
growth in the medieval times (Gies 1963, p47). London had been founded
by the Romans, who called it Londinium. Little is known about the
centuries after the Romans had left and about former bridges in London,
23
although there is arguments for an early timber structure that crossed the
Thames in
AD
993 (Gies 1963).Peter of Colechurch, a monk from a
nearby district of the city, was the builder of Old London Bridge, which
was built between 1176 and 1209. He was never to see his bridge
finished, since he died in 1205 and was buried in the chapel that he had
built on the bridge. As can be seen in Figure 2-5, Old London Bridge
altogether consisted of nineteen pointed masonry arches on crude piers
with large cutwaters, none of them equal in shape. A drawbridge was also
included in the structure. Piles were rammed into the soft bed of the river
on which the piers rested. The bridge must have seemed very massive and
inelegant to an observer, and its appearance would change even further
with later centuries. Fortifications on the bridge, namely the two towering
gates were added. It became customs to display the heads of executed
prisoners on top of this gate, and after building a new tower for a decayed
one, it was thereafter called Traitor’s Gate (Gies 1963).As the length of
Old London Bridge was only about 300 m the massive piers of Old
London Bridge took away more than half of the width of the river so that
the speed of the current increased tremendously. Boats with passengers
were said to be “shooting the bridge” when they passed under it, and
records of numerous accidents have been reported (Gies 1963, p40).
Figure 2-5: Old London Bridge, London, Great Britain
(taken from Steinman and Watson 1941, p69)
24
Located in the heart of London, Old London Bridge served the city for
more than six hundredyears, and for most of this time, about five and a
half centuries, it remained the only solid passing of the Thames. In 1740
finally, Westminster Bridge was built, and in 1831 building a new bridge
at the old location was begun.
Over all this long time Old London Bridge continuously changed
its appearance. Apart from the chapel already mentioned, more buildings
were added on top of the superstructure. Except for a few openings where
the river could actually be seen from the roadway, the bridge in its later
days carried literally dozens of houses. These were crammed at both sides
of the roadway, leaving only relatively little space in the middle. Wooden
frames held the houses together over the roadway, and some reportedly
even had basements under the arch spans, leaving even less room for
boats to pass. Even wheels were erected under several spans to power
watermills.Merchandising flourished on the bridge and tolls were
collected for passing it. The ease of water supply and wastewater removal
at the bridge made it a favorite place for the trades of the Londoners, Gies
(1963) lines out.
Many anecdotes and legends are attached to Old London Bridge.
It even once happened that a complete house fell off the bridge into the
Thames. As Steinman and Watson (1941, p64) put it,the “life story of this
six-hundred-year-old bridge would fill many a good-sized volume and
would include exciting accounts of fire, tournaments, battles, fairs, royal
processions, dramas,songs, and dances.” A highly readable description of
these centuries full of history is given in a chapter by Gies (1963).
25
2.3.5
The Era of Concrete Bridges and Beyond
The following sections will introduce the wide range of modern
bridge structures and their development. The main focus is placed on
concrete structures. Historic developments and characteristics of certain
types of concrete bridges will be presented. Certain specialties in bridges
will not be discussed, e.g. moving bridges of all kinds (i.e. bascule
bridges, lift and swing bridges), and highway bridges, many of which are
made of prefabricated concrete beams. The specific problems of skewed
and curved bridges are also excluded from this section.
2.3.6
Concrete Characteristics
Concrete had already been commonly in use in Roman times, as
described in early this section.Simple mortars had already been used
much earlier. Strong and waterproof mortars as the Romans had used,
however, were only rediscovered around the late eighteenth century, as
Brown (1993) notes.Concrete is an artificial stone-like inhomogeneous
material that is produced by mixing specified amounts of cement, water,
and aggregates. The first two ingredients react chemically to a hard
matrix, which acts as a binder. Most of the volume of the concrete is
taken by aggregates, which is the fill material. In modern concrete design
mixtures special mineral additives or chemical admixtures are added to
influence certain properties of the concrete. Strength can be increased
26
through use of special types of cement and a low water-cement ratio;
workability can be improved with retarders and superplasticizers; and
durability depends on the volume of air enclosed within the concrete.
Proportions and chemistry of the ingredients as well as the manner of
placement and curing determine the final concrete properties.Concrete is
the universal construction material of modern times due to several
advantages. It is formable into virtually any shape with formwork, its
ingredients are relatively cheap and can be found ubiquitously, it has a
high compressive strength and, provided good quality of workmanship, is
very durable at little maintenance cost.
Reinforced concrete is a composite material that is composed of
concrete and steel members that are embedded and bonded to it. These
steel bars or mats fulfill the purpose of enhancing the resistance of a
reinforced concrete member to tensile stresses, as concrete alone is strong
in compression but has less resistance to tension that is applied. The
amount and location of the reinforcement needed for a certain structure is
determined during its design. In sound concrete the steel reinforcement is
protected by the natural alkalinity of the concrete that creates a passifying
layer on the steel surface.
2.3.6.1
Early Concrete Structures
Several names are linked with the beginnings of reinforced
concrete. A comprehensive historical review of the developments that led
to application of reinforced concrete in the construction industry is given
by Menn (1990). In 1756 John Smeaton came up with a way of cement
production and in 1824 the mason Joseph Aspdin invented Portland
cement in England.Thaddeus Hyatt (1816 - 1901) examined behavior of
concrete beams as early as 1850 in the U.S.
27
Some years later, in 1867, French engineer Joseph Monier
received a patent on flowerpots whose concrete was reinforced with a
steel mesh. Monier also became first in building a bridge of reinforced
concrete in 1875 (Menn 1990). In the years to come, the first scientific
approaches to the behavior and analysis of reinforced concrete were taken
and opened the way to more and more advanced structures. French
engineer François Hennebique (1842 - 1931) researched T-shaped beams
and received patents on these around 1892, after which a larger number of
bridges was built in European countries in the following years. While
construction of reinforced concrete bridges spread across Europe, the first
national codes for reinforced concrete appeared.According to Menn
(1990), prior to the 1930s steel bridges still dominated the U.S. landscape
since they were cheaper and allowed rapid erection. In later years
reinforced concrete bridges became more common in the New World.
2.3.6.2
Concrete Arch Bridges
Robert Maillart (1872 - 1940) was exploring the structural
possibilities of the new construction material in an impressive diversity of
arch bridges in Switzerland. Located predominantly in mountainous
terrain the more than 40 bridges he designed were ingenious in their
slenderness, variability of shapes and beauty. It can be said that in his
structures all possibilities of concrete,including superior compressive
strength and formability were used to their full extent. One of his more
known structures is the daring shallow arch of the Salginatobel Bridge
that spans 90 m. In this bridge the superstructure was dissolved to a
slender arch that carried the deck with transverse wall panels. Melaragno
28
(1998, p19) in this context uses the term “structural art” to capture the
spirit of this unique family of concrete structures.
2.3.6.3
Prestressed Concrete Bridges
As early as 1888 a German engineer had examined prestressed
concrete members (Menn 1990).Yet it was Eugène Freyssinet (1879 1962), a graduate of the École des Ponts et Chaussées, who is considered
the father of prestressed concrete bridges. His most known bridge is the
Plougastel Bridge that was built between 1925 and 1930 in France. A
construction stage of this bridge is shown in Figure 2-28.
Figure 2-6: The Plougastel Bridge under Construction (taken from
Brown 1993, p122)
Three 186-m long arches of still normal reinforced concrete with a
box girder cross-section support a two level truss deck for road traffic and
railway. For this bridge Freyssinet employed large timber falsework that
was brought into place by pontoons and reused for all three arch spans.
Brown (1993) stresses the importance of this bridge with respect to
prestressing, since it was the Plougastel Bridge where Freyssinet became
aware of the phenomenon of concrete creep,which needs to be considered
29
in prestressed construction. Freyssinet implemented jacking the concrete
bridge spans apart prior to closure of the midspan gap to account for
creep. Between 1941 and 1949 a famous family of six prestressed
concrete bridges were built after Freyssinet’s design at the River Marne in
France, five of them with similar spans of 74 m (Menn1990). These
bridges were shallow frames with vertically prestressed thin girder webs
(Brown1993). Segments for these bridges were delivered by barges and
lifted into place in larger sets.Freyssinet came up with concepts for “both
pre-tensioned and post-tensioned concrete” (Menn 1990, p30) and thus
initiated the rapid development of prestressed concrete bridges.
2.4
Concrete Bridges after the Second World War
After the Second World War the European transportation
infrastructure needed to be rebuilt and extended. Steel box girders could
now be put together by welding instead of riveting. Some of the first of
these bridges were built at the Rhine by German engineer Fritz Leonhardt
(born 1909), who also designed a large number of concrete structures.
Box girders, which had been used for the arches of the Plougastel Bridge,
were more and more introduced in steel and concrete bridge construction
as better understanding of the properties and the inherent advantages of
closed hollow cross-sections grew. Prestressed concrete bridges were
built in large numbers. In Germany,Franz Dischinger (1887 - 1953) built
prestressed concrete bridges with a system different fromFreyssinet’s; he
used unbonded tendons that did not reach widespread application until
much later due to problems with loss of prestressing force (Menn 1990).
Subsequent development of different prestressing systems was therefore
based on the original Freyssinet system. Cast-in-place cantilever bridges
30
have been built for almost half a century. Ulrich Finsterwalder, student of
Dischinger, took the first step in erection with the balanced cantilevering
method when he built the 62-m long span of the Lahn Bridge at
Balduinstein in Germany between 1950 and 1951 (Fletcher 1984.
Prestressing of concrete bridges reduced deflections, prevented
cracking, and allowed higher loads to be carried by the bridges (Menn
1990). Freyssinet’s system of implementing full prestressing was not very
economical, though. Therefore, partial prestressing became prevalent as it
was introduced into the design codes. Partial prestressing permitted
limited tensile stressesin concrete and made use of mild reinforcement to
alleviate the cracking of the concrete because of these stresses.
Precast segmental construction emerged in the early 1960s, as
Menn (1990) also reports. In the following decades, solutions for the
problem of segments joints were developed, including match-casting of
the segments at the precasting yard, implementation of shear keys, and
use of epoxy agents that sealed and glued the joint faces together. In the
decades since the first prestressed concrete bridges were built many
technological achievements have been made. Research allowed better
understanding of the internal flow of forces in concrete and in the
embedded steel and helped improving material properties of these
construction materials.
2.4.1
Cable-Stayed Bridges
Cable-stayed bridges can appear in many different ways. The
bridge pylons and the bridge superstructure can be made either of
concrete or steel, or be a composite of concrete and steel members.
Pylons can be shaped in a great number of ways, including A, H, X, and
31
inverted V and Y-shapes, or combinations and variations of these. In a
cable-stayed bridge inclined straight stay cables that are attached to
pylons above the deck carry the bridge deck. A multitude of arrangements
for pylons and cable layout exists.
Furthermore, the bridge can be designed with one central or two
lateral planes of stay cables that can even be inclined toward each other.
Cable-stayed bridges can have several different arrangements for the stay
cables, as explained in Table 2-1. The respective arrangements are shown
in Figure 2-29. Cable arrangements do not necessarily have to be exactly
symmetric about the tower. Variations and combinations between these
types are possible. Cables can be anchored both on the deck and at the
pylon or can run continuously over a saddle at the top of the pylon the
anchorages for the stay cables are critical structural details that have to be
resistant to corrosion and fatigue.
Figure 2-7: Stay Cable Arrangements
32
Table 2-1: Stay Cable Arrangements
Cable-stayed bridges are not an invention of the twentieth century. Some
attempts to built bridges supported by stay cables were already made in
previous centuries, but did not prove successful, as means of calculation
for the statically highly indeterminate system and adequate materials for
the cables were lacking (Brown 1993). Cable stays were applied in the
superstructure of the Brooklyn Bridge, as mentioned in Section 2.1.5.2 to
add stiffening to the suspension system.Cable-stayed bridges were
revived after the Second World War when economical rebuilding of the
transportation infrastructure in Europe became a prime issue. Franz
Dischinger had already implemented stay cables to support the deck of a
suspended railway bridge (Brown 1993).Amongst the first modern cablestayed bridges was a family of three cable-stayed bridges over the Rhine
at Düsseldorf with steel superstructures that were built by German
engineer Leonhardt (1984) around 1952. One of them, the Oberkassel
Rhine Bridge, is shown in Figure 2-30. These slender bridges, of
remarkable clearness and simplicity in their appearance all have a harptype cable arrangement. Since then, a great number of cable-stayed
bridges have been built all over the world, of which just very few shall be
mentioned in this overview.
33
Figure 2-8: The Oberkassel Rhine Bridge, Düsseldorf, Germany
(taken from Leonhardt 1984, p260)
The first concrete cable-stayed bridge was the Lake Maracaibo
Bridge in Venezuela, which was built between 1958 and 1962.
The designer Riccardo Morandi came up with a major concrete
structure with five main spans of 235 m length (Brown 1993). He
designed uniquely shaped pier tables that had a massive complex
X-shaped substructure, which carried A-shaped towers above the
deck level. The central concrete spans were comparatively
massive to achieve stiffness and were suspended with one group
of stay cables on each side of the towers. A view of the structure
with its characteristic approaches is shown in Figure 2-31.
Figure 2-9: The Lake Maracaibo Bridge, Venezuela (taken from Leonhardt 1984, p271)
34
Later bridges incorporated a greater number of regularly spaced
cables that provided almost continuous support for the bridge
deck. Menn (1990) calls this type of multi-cable bridges the
second generation of cable-stayed bridges. He mentions the Pont
de Brotonne in France,completed in 1976, as the first example of a
bridge of the second generation. The Pont de Brotonne is shown
in Figure 2-32. Its main span of 320 m length is supported by a
single central plane of fanning stay cables. Leonhardt (1984)
specifically points at the stiffness that can be achieved with such a
structural system despite the slender deck girder, making the
bridge suitable even for railroads. With the larger dead load of
concrete bridges better damping of vibrations is achieved as
Podolny (1981) writes. Concrete is also suitable for the bridge
deck because it can withstand the longitudinal horizontal stresses
that the inclined stays induce in the bridge superstructure. Podolny
(1981) further mentions that concrete cable-stayed bridges incur
only small deflections from live load, as the ratio of live load to
dead load is relatively small.
Figure 2-10: The Pont de Brotonne, France (taken from Leonhardt 1984, p270)
35
Several advantages make cable-stayed bridges very economical
structures. Due to the almost continuous elastic support of the
deck (Podolny 1981) of multi-cable arrangements sufficient
overall stiffness can be achieved even with slender superstructure
girders. Multi-cable systems are aesthetically advantageous
because of their apparent lightness. They have a high degree of
structural redundancy and even allow repair or replacement of
single stays with relative ease. It is possible to optimize the stay
cable prestressing sequence towards a more equal stress state in
the structural system. The overall structural system allows quick
construction in comparison with e.g. suspension bridges,
especially by use of precast elements. Another major advantage is
that cable-stayed bridges do not require large anchorages at the
abutments as necessary to hold the
main cables in suspension bridges. Cable-stayed bridges are
economical especially for span ranges between about 250 and 300
m, as Swiggum et al. cite (1994). Even much longer spans have
been built up to date.With improved analytical capabilities due to
modern computer software the statically highly indeterminate
system of cable-stayed bridges can be analyzed very accurately.
Better analysis techniques for aerodynamic and seismic behavior
with scaled models in wind canals and computer simulation of the
structure allowed optimizing bridge cross-sections. The scaling
process requires special consideration because all properties of a
bridge have to be scaled for examination in a wind tunnel. A
model test e.g. included “scaled stiffness, mass, inertia,geometry
and, “we hope,” scaled damping, the most difficult aspect”
(Fairweather 1987, p. 62).The trend, according to Fairweather
(1987) in this area is to incorporate aerodynamic testing not
only for verification of an existing design, but to also use it
directly during the initial design.With aerodynamic testing it is
36
also possible to evaluate the effects of innovative details for both
aerodynamic and seismic resistance. These details can be mass
dampers or tuned damping systems at bearings, joints, and cable
anchorages, installation of interconnecting ties between the stay
cables, and special shaping and texturing of the cables sheathing
to prevent vibrations from wind and rain.Cable-stayed bridges are
ideally erected with the cantilevering method. The stay cables
hence serve to support growing cantilever arms from above and
will also be the permanent supporting system for the bridge
superstructure. Goñi (1995) gives a profound example of a major
cable-stayed bridge, the Chesapeake and Delaware Canal Bridge.
It was erected using progressive placement and was completed in
1995. According to him, the 229-m long main span consists of
two parallel box girders that are interconnected by so-called delta
frames and supported by a single plane of stays in harp-type
arrangement. It was put together from precast segments that were
placed by a crane at the tip of each cantilever. After placement of
the segments new stay cables were installed and initially
prestressed. Construction loads resulted especially from the cranes
on the cantilevers and the placement of precast segments. A
detailed computer analysis of the erection procedure that included
several
hundred
construction
steps
(e.g.
segment
placement,tendon installation, and changes in prestressing forces
or loads) was performed. With respect to
the motions of the uncompleted cantilever due to winds, Normile
(1994) points at the need to provide sufficient stiffness in the
bridge superstructure for construction.
37
2.5
Recent Bridge Projects
Several
impressive
large-span
bridges
have
been
completed in recent years. The three most important examples to
be mentioned are the Pont de Normandie in France, the Akashi
Kaikyo Bridge in Japan, and the East Bridge of the Great Belt
Link in Denmark. A brief comparison of these three breathtaking
projects will be given in Table 2-2, based on information from
Brown (1993), Robison (1993), Normile (1994) and the HonshuShikoku Bridge Authority (1998). The currently longest bridge in
the world, the Akashi Kaiyo Bridge is shown in Figure 2-11.
Table 2-2: Recent Major Bridge Projects
38
Figure 2-11: The Akashi Kaikyo Bridge, Japan (taken from Honshu-Shikoku
Bridge Authority 1998, p1)
2.6
Contributions of Modern Concrete Bridge Construction
The introduction of concrete into bridge construction
opened almost unlimited new possibilities for the profession. The
several advantages of concrete, such as free formability, strength,
and durability came to full use in bridge construction and
contributed much to successful use of concrete in other branches.
Through use of steel reinforcement to bear the tensile stresses in
the members a composite material was created that combined
positive characteristics of both concrete and steel and could be
strengthened exactly as needed for a certain structure.Prestressing
39
concrete by means of tendons that are installed in the bridge
superstructure made extremely long, yet economical spans
possible. European engineers, such as Freyssinet carried the
prestressing concepts further. Other engineers, e.g. Maillart
explored structural possibilities along with artful shaping of
concrete bridges.Along with growing understanding of the
properties of the new material went the development of a variety
of construction methods that will be presented in Section 4.2.
Choice of either cast-in- place construction, precast construction,
or a combination of both methods made it possible to adapt
construction procedures exactly to the requirements of the specific
site and the project conditions.
The concept of box girder superstructures had already
been used in bridges as e.g. the Britannia Bridge. Since the end of
the Second World War the versatile box girders have become a
widely used type of superstructure cross-section.With cablestayed bridges a relatively new type of bridge rapidly developed
in the second half of the twentieth century. Economical and
elegant long-span cable-stayed bridges were subsequently built
that were only surpassed in length by a handful of the longest of
all bridges, which are suspension bridges.
CHAPTER III
THEORITICAL BACKGROUND
3.1
Choice of Abutment
Current practice is to make decks integral with the abutments. The
objective is to avoid the use of joints over abutments and piers. Expansion
joints are prone to leak and allow the ingress of de-icing salts into the bridge
deck and substructure. In general all bridges are made continuous over
intermediate supports and decks under 60 metres long with skews not
exceeding 30°are m ade integral with their abutments.
Figure 3.1: Open Side Span
1
4
Figure 3.2:Solid Side Span
Usually the narrow bridge is cheaper in the open abutment form and the wide
bridge is cheaper in the solid abutment form. The exact transition point
between the two types depends very much on the geometry and the site of the
particular bridge. In most cases the open abutment solution has a better
appearance and is less intrusive on the general flow of the ground contours
and for these reasons is to be preferred. It is the cost of the wing walls when
related to the deck costs which swings the balance of cost in favour of the
solid abutment solution for wider bridges. However the wider bridges with
solid abutments produce a tunnelling effect and costs have to be considered in
conjunction with the proper functioning of the structure where fast traffic is
passing beneath. Solid abutments for narrow bridges should only be adopted
where the open abutment solution is not possible. In the case of wide bridges
the open abutment solution is to be preferred, but there are many cases where
economy must be the overriding consideration.
3.1.1
Design Consideration
Loads transmitted by the bridge deck onto the abutment are :
i.
eVrtical loads from self weight of deck
ii.
eVrtical loads from live loading conditions
iii.
Horizontal loads from temperature, creep movements etc and wind
iv.
Horizontal loads from breaking and skidding effects of vehicles.
2
4
These loads are carried by the bearings which are seated on the
abutment bearing platform. The horizontal loads may be reduced by
depending on the coefficient of friction of the bearings at the movement joint
in the structure.
However, the full breaking effect is to be taken, in either direction, on top of
the abutment at carriageway level.
In addition to the structure loads, horizontal pressures exerted by the fill
material against the abutment walls is to be considered. Also a vertical
loading from the weight of the fill acts on the footing.
eVhicle loads at the rear of the abutments are considered by applying a
surcharge load on the rear of the wall.
For certain short single span structures it is possible to use the bridge deck to
prop the two abutments apart. This entails the abutment wall being designed
as a propped cantilever.
3.2
Choice Of Bearing
Bridge bearings are devices for transferring loads and movements
from the deck to the substructure and foundations.
In highway bridge bearings movements are accommodated by the basic
mechanisms of internal deformation (elastomeric), sliding (PTFE), or rolling.
A large variety of bearings have evolved using various combinations of these
mechanisms.
3
4
Figure 3.3: Elastomeric Bearing
Figure 3.4:Plane Sliding Bearing
Figure 3.5 : Multiple Roller Bearing
The functions of each bearing type are :
a) Elastomeric
The elastomeric bearing allows the deck to translate and rotate, but also resists loads
in the longitudinal, transverse and vertical directions. Loads are developed, and
movement is accommodated by distorting the elastomeric pad.
b) Plane Sliding
Sliding bearings usually consist of a low friction polymer, polytetrafluoroethylene
(PTFE), sliding against a metal plate. This bearing does not accommodate rotational
movement in the longitudinal or transverse directions and only resists loads in the vertical
direction. Longitudinal or transverse loads can be accommodated by providing
mechanical keys. The keys resist movement, and loads in a direction perpendicular to the
keyway.
4
b) Roller
Large longitudinal movements can be accommodated by these bearings, but vertical
loads only can generally be resisted.
The designer has to assess the maximum and minimum loads that the deck will exert
on the bearing together with the anticipated movements (translation and rotation).
Bearing manufacturers will supply a suitable bearing to meet
Figure 3.6 : Typical Bearing Layout
Bearings are arranged to allow the deck to expand and contract, but retain the
deck in its correct position on the substructure. A 'Fixed' Bearing does not allow
translational movement. S
' liding Guid ed' Bearings are provided to restrain the deck in
all translational directions except in a radial direction from the fixed bearing. This
allows the deck to expand and contract freely. 'Sliding' Bearings are provided for
vertical support to the deck only.
3.2.1
Preliminary Design
In selecting the correct bridge type it is necessary to find a structure that will
perform its required function and present an acceptable appearance at the least cost.
Decisions taken at preliminary design stage will influence the extent to which the
actual structure approximates to the ideal, but so will decisions taken at detailed
design stage. Consideration of each of the ideal characteristics in turn will give some
indication of the importance of preliminary bridge design.
5
4
a. Safety.
The ideal structure must not collapse in use. It must be capable of
carrying the loading required of it with the appropriate factor of
safety. This is more significant at detailed design stage as generally
any sort of preliminary design can be made safe.
b. Serviceability.
The ideal structure must not suffer from local deterioration/failure,
from excessive deflection or vibration, and it must not interfere with
sight lines on roads above or below it. Detailed design cannot correct
faults induced by bad preliminary design.
c. Economy.
The structure must make minimal demands on labour and capital; it
must cost as little as possible to build and maintain. At preliminary
design stage it means choosing the right types of material for the
major elements of the structure, and arranging these in the right form.
d. Appearance.
The structure must be pleasing to look at. Decisions about form and
materials are made at preliminary design stage; the sizes of individual
members are finalised at detailed design stage. The preliminary
design usually settles the appearance of the bridge.
3.2.2
Constraint
The construction depth available should be evaluated. The economic
implications of raising or lowering any approach embankments should then be
considered. By lowering the embankments the cost of the earthworks may be
reduced, but the resulting reduction in the construction depth may cause the deck to
be more expensive. If the bridge is to cross a road that is on a curve, then the width of
the opening may have to be increased to provide an adequate site line for vehicles on
6
4
the curved road.
It is important to determine the condition of the bridge site by carrying out a
comprehensive site investigation. BS 5930: Code of practice for Site Investigations
includes such topics as:
3.3
i.
Soil survey
ii.
Existing services (Gas, Electricity, Water, etc)
iii.
Rivers and streams (liability to flood)
iv.
Existing property and rights of way
v.
Access to site for construction traffic
Selection of Bridge Type
Span
Deck Type
Insitu reinforced concrete.
Up to 20m
Insitu prestressed post-tensioned concrete.
Prestressed pre-tensioned inverted T beams with insitu fill.
Insitu reinforced concrete voided slab.
Insitu prestressed post-tensioned concrete voided slab.
16m to 30m
Prestressed pre-tensioned M and I beams with insitu slab.
Prestressed pre-tensioned box beams with insitu topping.
Prestressed post-tensioned beams with insitu slab.
Steel beams with insitu slab.
Prestressed pre-tensioned SYbeams with insitu slab.
30m to 04m
Prestressed pre-tensioned box beams with insitu topping.
Prestressed post-tensioned beams with insitu slab.
Steel beams with insitu slab.
30m to 250m Box girder bridges - As the span increases the construction tends to go from a' ll
7
4
concrete' to s' teel box /concrete deck' to a' ll steel'.
Truss bridges - for spans up to 50m they are generally less economic than plate
girders.
150m to 350m Cable stayed bridges.
350m >
Suspension bridges.
Table 3.1 : selection of bridge type for various span length
3.3.1
Preliminary Design Consideration
1. A span to depth ratio of 20 will give a starting point for estimating
construction depths.
2. Continuity over supports
i.
Reduces number of expansion joints.
ii.
Reduces maximum bending moments and hence construction
depth or the material used.
3. Increases sensitivity to differential settlement. Factory made units
i.
Reduces the need for soffit shuttering or scaffolding; useful
when headroom is restricted or access is difficult.
ii.
Reduces site work which is weather dependent.
iii.
Dependent on delivery dates by specialist manufactures.
iv.
Specials tend to be expensive.
v.
Special permission needed to transport units of more than
29m long on the highway
.
4
Length of structure
i.
The shortest structure is not always the cheapest. By
increasing the length of the structure the embankment,
8
4
retaining wall and abutment costs may be reduced, but the
deck costs will increase.
5. Substructure
i.
The structure should be considered as a whole, including
appraisal of piers, abutments and foundations. Alternative
designs for piled foundations should be investigated; piling
can increase the cost of a structure by up to 20%
.
The preliminary design process will produce several apparently viable schemes.
The procedure from this point is to:
i.
Estimate the major quantities.
ii.
Apply unit price rates - they need not be up to date but should reflect any differential
variations.
iii.
3.3.2
Obtain prices for the schemes.
Design Standard for preliminary design
The final selection will be based on cost and aesthetics. This method of
costing assumes that the scheme with the minimum volume will be the cheapest, and
will be true if the structure is not particularly unusual
i.
BS 54
00: Part 1: General Statement
ii.
BS 54
00: Part 2: Specification for Loads
iii.
BS 5930: Code of Practice for Site Investigations
9
4
3.4
Reinforced Concrete Deck
The three most common types of reinforced concrete bridge decks are:
Figure 3.7 : Various of Deck Slab
Solid slab bridge decks are most useful for small, single or multi-span bridges and are
easily adaptable for high skew.
oVided slab and beam and slab bridges are used for larger, single or multi-span
bridges. In circular voided decks the ratio of d[ epth of void] / d[ epth of slab] should
be less than 0.79; and the maximum area of void should be less than 94%
of the deck
sectional area
3.4.1
Analysis of Deck
For decks with skew less than 25°a si mple unit strip method of analysis is
generally satisfactory. For skews greater than 25°t hen a grillage or finite element
method of analysis will be required. Skew decks develop twisting moments in the
slab which become more significant with higher skew angles. Computer analysis will
produce values for Mx, My and Mxy where Mxy represents the twisting moment in the
slab. Due to the influence of this twisting moment, the most economical way of
reinforcing the slab would be to place the reinforcing steel in the direction of the
50
principal moments. However these directions vary over the slab and two directions
have to be chosen in which the reinforcing bars should lie. Wood and Armer have
developed equations for the moment of resistance to be provided in two
predetermined directions in order to resist the applied moments Mx, My and Mxy.
Extensive tests on various steel arrangements have shown the best positions as
follows
Figure 3.8 : Aspect Ratio vs Skew angle graf
3.4.2
Design Standard for concrete Deck
British Standard
i.
BS 54
00: Part 2: Specification for Loads
ii.
BS 54
00: Part :4Code of Practice for the Design of Concrete
Bridges
51
3.4.3
Prestressed Concrete Deck
There are two types of deck using prestressed concrete :
i.
Pre-tensioned beams with insitu concrete.
ii.
Post-tensioned concrete.
The term pre-tensioning is used to describe a method of prestressing in which
the tendons are tensioned before the concrete is placed, and the prestress is
transferred to the concrete when a suitable cube strength is reached.
Post-tensioning is a method of prestressing in which the tendon is tensioned
after the concrete has reached a suitable strength. The tendons are anchored
against the hardened concrete immediately after prestressing.
There are three concepts involved in the design of prestressed concrete :
i.
Prestressing transforms concrete into an elastic material.
By applying this concept concrete may be regarded as an elastic
material, and may be treated as such for design at normal working
loads. From this concept the criterion of no tensile stresses in the
concrete was evolved.
In an economically designed simply supported beam, at the
critical section, the bottom fibre stress under dead load and
prestress should ideally be the maximum allowable stress; and
under dead load, live load and prestress the stress should be the
minimum allowable stress.
Therefore under dead load and prestress, as the dead load moment
reduces towards the support, then the prestress moment will have
to reduce accordingly to avoid exceeding the permissible stresses.
In post-tensioned structures this may be achieved by curving the
tendons, or in pre-tensioned structures some of the prestressing
strands may be deflected or de-bonded near the support.
52
ii.
Prestressed concrete is to be considered as a combination of steel
and concrete with the steel taking tension and concrete
compression so that the two materials form a resisting couple
against the external moment. (Analogous to reinforced concrete
concepts).
This concept is utilized to determine the ultimate strength of
prestressed beams.
iii.
Prestressing is used to achieve load balancing.
It is possible to arrange the tendons to produce an upward load
which balances the downward load due to say, dead load, in
which case the concrete would be in uniform compression.
3.4.4
Pre-Tension Bridge Deck
Pre-tensioned bridge decks are composed of prestressed beams, which
have been prestressed off site, together with insitu concrete forming a slab
and in some cases filling the voids between the beams.
T-Beam
M-Beam
Y-Beam
Figure 3.9 : Type of Girder
Types of beams in common use are inverted T-beams, M-beams and
Ybeam s. Inverted T-beams are generally used for spans between 7 and 16
53
metres and the voids between the beams are filled with insitu concrete thus
forming a solid deck. M-Beams are used for spans between 14an d 30 metres
and have a thin slab cast insitu spanning between the top flanges. The -Y
beam was introduced in 1990 to replace the M-beam. This lead to the
production of an SY
-bea m which is used for spans between 32 and 40 m etres.
Post-tensioned bridge decks are generally composed of insitu concrete in
which ducts have been cast in the required positions..
T-Beam
Span <35m
oVided Slab
20m <Span <35m
Box
Span >30m
Figure 3.10 : Types of Beam-Slab
When the concrete has acquired sufficient strength, the tendons are
threaded through the ducts and tensioned by hydraulic jacks acting against
the ends of the member. The ends of the tendons are then anchored.
Tendons are then bonded to the concrete by injecting grout into the ducts
after the stressing has been completed.
It is possible to use pre-cast concrete units which are post-tensioned
together on site to form the bridge deck.
Generally it is more economical to use post-tensioned construction for
continuous structures rather than insitu reinforced concrete at spans
greater than 20 metres. For simply supported spans it may be economic to
use a post-tensioned deck at spans greater than 20 metres.
54
3.5
Composite Deck
Composite Construction in bridge decks usually refers to the
interaction between insitu reinforced concrete and structural steel.
Three main economic advantages of composite construction are :
i. For a given span and loading system a smaller depth of beam can be used
than for a concrete beam solution, which leads to economies in the approach
embankments.
ii. The cross-sectional area of the steel top flange can be reduced because the
concrete can be considered as part of it.
iii. Transverse stiffening for the top compression flange of the steel beam can
be reduced because the restraint against buckling is provided by the
concrete deck.
Figure 3.11: Typical Composite Deck
3.5.1
Construction Method
It is possible to influence the load carried by a composite deck section
in a number of ways during the erection of a bridge.
55
By propping the steel beams while the deck slab is cast and until it has gained
strength, then the composite section can be considered to take the whole of
the dead load. This method appears attractive but is seldom used since
propping can be difficult and usually costly.
With continuous spans the concrete slab will crack in the hogging regions and
only the steel reinforcement will be effective in the flexural resistance, unless
the concrete is prestressed.
Generally the concrete deck is 220mm to 250mm thick with beams or plate
girders between 2.5m and 3.5m spacing and depths between span/20 and
span/30.
Composite action is developed by the transfer of horizontal shear forces
between the concrete deck and steel via shear studs which are welded to the
steel girder.
3.6
Steel Box Girder
Box girders have a clean, uninterrupted design line and require less
maintenance because more than half of their surface area is protected from
the weather. The box shape is very strong torsionally and is consequently
stable during erection and in service; unlike the plate girder which generally
requires additional bracing to achieve adequate stability.
Figure 3.12 : Cross section of Steel Box Girder
56
The disadvantage is that box girders are more expensive to fabricate
than plate girders of the same weight and they require more time and effort to
design.Box girders were very popular in the late 1960's, but, following the
collapse of four bridges, the Merrison Committee published design rules in
1972 which imposed complicated design rules and onerous fabrication
tolerances. The design rules have now been simplified with the publication of
BS54
00 and more realistic imperfection limits have been set.
The load analysis and stress checks include a number of effects which are
generally of second order importance in conventional plate girder design such
as shear lag, distortion and warping stresses, and stiffened compression
flanges. Special consideration is also required for the internal intermediate
cross-frames and diaphragms at supports.
3.6.1
Steel Deck Truss
Trusses are generally used for bridge spans between 30m and 150m
where the construction depth (deck soffit to road level) is limited. The small
construction depth reduces the length and height of the approach
embankments that would be required for other deck forms. This can have a
significant effect on the overall cost of the structure, particularly where the
approach gradients cannot be steep as for railway bridges.
Figure 3.13 : Type of truss
57
High fabrication and maintenance costs has made the truss type deck less
popular in the UK
; labour costs being relatively high compared to material
costs. Where material costs are relatively high then the truss is still an
economical solution. The form of construction also allows the bridge to be
fabricated in small sections off site which also makes transportation easier,
particularly in remote areas.
3.6.2
Choice of Truss
Figure 3.14 : Bridge Truss
The underslung truss is the most economical as the deck provides
support for the live load and also braces the compression chord. There is
however the problem of the headroom clearance required under the deck
which generally renders this truss only suitable for unnavigable rivers or over
flood planes.
Where underslung trusses are not possible, and the span is short, it
may be economical to use a half-through truss. Restraint to the compression
flange is achieved by U frame action.
58
When the span is large, and the underslung truss cannot be used, then the
through girder provides the most economic solution. Restraint to the
compression flange is provided by bracing between the two top chords; this is
more efficient than U frame support. The bracing therefore has to be above
the headroom requirement for traffic on the deck.
3.7
Cable Stay Deck
Cable stayed bridges are generally used for bridge spans between
150m and 350m. They are often chosen for their aesthetics, but are generally
economical for spans in excess of 250m.
Figure 3.15 : Simple Cable Stay Bridge
Cable stayed girders were developed in Germany during the reconstruction
period after the last war and attributed largely to the works of Fritz
Leonhardt. Straight cables are connected directly to the deck and induce
significant axial forces into the deck. The structure is consequently self
anchoring and depends less on the foundation conditions than the suspension
bridge.
The cables and the deck are erected at the same time which speeds up the
construction time and reduces the amount of temporary works required. The
cable lengths are adjusted during construction to counteract the dead load
deflections of the deck due to extension in the cable
59
Decks are usually of orthortropic steel plate construction however composite
slabs can be used for spans up to about 250m. Either box girders or plate
girders can be used in the deck, however if a single plane of cables is used
then it is essential to use the box girder construction to achieve torsional
stability.
3.8
Suspension Bridges
Suspension bridges are used for bridge spans in excess of 350m.
Figure 3.16 : Suspension Bridge
Plans have now been approved to build a 3300m span suspension bridge
across the Strait of Messina.A number of early suspension bridges were
designed without the appreciation of wind effects. Large deflections were
developed in the flexible decks and wind loading created unstable
oscillations. The problem was largely solved by using inclined hangers.
The suspension bridge is essentially a catenary cable prestressed by dead
weight. The cables are guided over the support towers to ground anchors. The
stiffened deck is supported mainly by vertical or inclined hangers.
The Design Manual for Roads and Bridges BD 52/93 defines a
Parapet as "A protective fence or wall at the edge of a bridge or similar
structure.
60
Figure 3.17 : Types of Parapet
Manufacturers have developed and tested parapets to meet the containment
standards specified in the codes. Much of the earlier testing work was
involved with achieving a parapet which would absorb the impact load and
not deflect the vehicle back into the line of adjacent traffic. The weight of
vehicle, speed of impact and angle of impact influence the behaviour of the
parapet. Consequently a level of containment has been adopted to minimise
the risk to traffic using the bridge (above and below the deck).
The Design Manual for Roads and Bridges BD 52/93 Specifies a Group
Designation for various containment levels as follows :
Parapet Group
Application
Designation
P1
eVhicle parapets for brid ges carrying motorways or
roads to motorway standards (excluding motorway
bridges over railways and high risk locations).
P2
eVhicle/pedestrian parape ts for bridges carrying all
purpose roads and for accommodation bridges
(excluding bridges over railways and high risk
locations).
P4
Pedestrian parapets for use on footbridges and
bridges carrying bridleways (excluding bridges over
railways).
Containment for which
designed
1.5t vehicle at 113 km/h
and 20°angl e of impact.
1.5t vehicle at 113 km/h
and 80 km/h and 20°
angle of impact.
1.4kN/m
perpendicular
to the parapet.
61
P5
Parapets for use over railways (excluding use on
bridges at high risk railway locations).
i. on bridges carrying motorways or roads to
motorways or roads to motorway standards
P6
As for P1
ii. on bridges carrying all purpose roads
As for P1
iii. on footbridges
As for P4
High Containment vehicle and vehicle/pedestrian
parapets at high risk locations (excluding
accommodation bridges).
30t vehicle at 64km/h
and 20°angle of impact.
Table 3.2 : The Design Manual for Roads and Bridges BD 52/93 Specifies a Group
Designation
The Group Designation in the table above have the equivalent level of
containment as defined in BS 6779 as follows :
i.
P1 &
P2 (113) : Normal level of containment.
ii.
P2 (80) : Low level of containment.
iii.
P5 (excluding Footbridges) : Normal level of containment.
iv.
P6 : High level of containment.
v.
3.8.1
Design Consideration
Normal and low level of containment strength requirements for
parapet posts and rails are given in terms of the products of the plastic moduli
of their geometric sections and the minimum yield stress of the material used.
Consequently the parapet will deform to absorb the impact load. Higher loads
than the designed containment load will fail the member at impact. If the
parapet post fails then the rails will mobilise lengths of the parapet adjacent to
the failed section to retain the vehicle. Concrete parapets are ideal for high
containment parapets due to their significant mass.
62
Steel parapets are generally the cheapest solution for the normal and
low level containment. This is significant if the site is prone to accidents and
parapet maintenance is likely to be regular. The steelwork does however
require painting and is usually pretreated with hot-dip galvanising.
Aluminium parapets do not require surface protection and
maintenance costs will be reduced if the parapet does not require replacing
through damage. The initial cost is however high and special attention to
fixing bolts is required to prevent them from being stolen for their high scrap
value. Aluminium also provides a significant weight saving over the steel
parapet. This is sometimes important for parapets on moving bridges.
3.9
Choice of Pier
Wherever possible slender piers should be used so that there is
sufficient flexibility to allow temperature, shrinkage and creep effects to be
transmitted to the abutments without the need for bearings at the piers, or
intermediate joints in the deck.
A slender bridge deck will usually look best when supported by
slender piers without the need for a downstand crosshead beam. It is the
proportions and form of the bridge as a whole which are vitally important
rather than the size of an individual element viewed in isolation.
63
Figure 3.18 : Different Pier Shape
3.9.1
Design Consideration
Loads transmitted by the bridge deck onto the pier are :
i.
eVrtical loads from self weight of deck
ii.
eVrtical loads from live loading conditions
iii.
Horizontal loads from temperature, creep movements etc and
wind
iv.
Rotations due to deflection of the bridge deck.
The overall configuration of the bridge will determine the
combination of loads and movements that have to be designed for. For
example if the pier has a bearing at its top, corresponding to a structural pin
joint, then the horizontal movements will impose moments at the base, their
magnitude will depend on the pier flexibility.
Sometimes special requirements are imposed by rail or river authorities if
piers are positioned within their jurisdiction. In the case of river authorities a
c' ut water ' may be required to assist the river flow, or independent fenders to
protect the pier from impact from boats or floating debris. A similar
arrangement is often required by the rail authorities to prevent minor
derailments striking the pier. Whereas the pier has to be designed to resist
64
major derailments. Also if the pier should be completely demolished by a
train derailment then the deck should not collapse.
3.10
Choice Of Wingwalls
Wing walls are essentially retaining walls adjacent to the abutment.
The walls can be independent or integral with the abutment wall.
Figure 3.19 : Load acting on Retaining Wall
Providing the bridge skew angle is small (less than 20°), an d the
cutting/em bankment slopes are reasonably steep (about 1 in 2), then the wing
wall cantilevering from the abutment wall is likely to give the most
economical solution.
Figure 3.20 : Distribution Surcharge Load
65
Splayed wing walls provide even more of an economy in material costs but
the detailing and fixing of the steel reinforcement is more complicated than
the conventional wall.
3.10.1 Design Consideration
Loads effects to be considered on the rear of the wall are:
i.
Earth pressures from the backfill material.
ii.
Surcharge from live loading or compacting plant.
iii.
Hydraulic loads from saturated soil conditions.
The stability of the wall is generally designed to resist a' c tive' earth
pressures (K
a); whilst the structural elements are designed to resist a' t rest'
earth pressures (K
o). The concept is that a' t rest' pressures are developed
initially and the structural elements should be designed to accommodate these
loads without failure. The loads will however reduce to a' ctive' pressure w hen
the wall moves, either by rotating or sliding. Consequently the wall will
stabilise if it moves under a' t rest' pressures providing it is designed to resist
a' ctive' earth pressures.
CHAPTER IV
METHODOLOGY
4.1
Introduction
This chapter discuss the ways on how to compare the different
usage of code of practices and the steps for each codes in getting a result
of design of structure members. In this case, we redesign an existing
bridge structure that available in our selecting bridge in Malaysia.This
bridge was designed using the usual code in Malaysia known as BS 54
00.
In our research, we take this existing of structure and try redesign
by using another method or code of practice to compare a size and cost of
structure when using different code of practices. For this case, we select
AASHTO-SEISMIC design code as our comparison code. We have
defined for value of seismic or reading based on previous event that
occurred in our country.For peninsular Malaysia, a reading of seismic
value we assign as 0.075 g (75 gal). Meanwhile for Sabah and Sarawak,
we assign as 0.15 g (150 gal).We get these both values from Malaysia
Meteorological Services Department.
Section 4.2 will show the design flow chart for each codes that we
apply i.e. sequence of steps in design calculation of members.After that,
our result will be described in section .43 by analyzing the outcome from
67
both codes in scope of member required i.e. Steel Area that we need and
cost of the material.
4.2
Design Flowchart
In general, two different code of practices were compared in this
study.The scope of structure element that we have compared are
Slab,Girder,Pier and Abutment.Section 4.2.1 describe the flowchart for
each code of practice for member design and overall design of structure.
4.2.1 BS 5400 and AASHTO-Seismic Design Flowchart
Seismic Design
Chart
Multi-Span
Bridge
No
No seismic
analysis is
required
Y
es
eYs
Seismic
one 2,3,
Z
and 4
No
68
Y
es
Critical
Bridge
Essential
Bridges
No
No
Y
es
Y
es
Other Bridge
Regular
Regular
eYs
No
Yes
Z
one m ethod
2
MM
3
MM
4
TH
Z
one m ethod
2
MM
3
TH
4
TH
Z
one m
2
3
4
eYs
ethod
SM/UL
MM
MM
No
No
Z
one m
2
3
4
ethod
MM
MM
MM
Z
one m
2
3
4
ethod
SM/UL
SM/UL
SM/UL
Z
one m
2
3
4
ethod
SM
MM
MM
69
Select Modification Factor
R
Design Components
based on F/R
Design Detail : Connections between
superstructure and substructure, and
seat width
END
SM-Single Mode Spectral Method
UL-Uniform Load Method
MM-Multi mode Spectral Method
TH-Time History
Figure 4.1 : AASHTO–LRFD seismic design flowchart
70
Safety : Ideal
structure,loading
and appropriate
Economy :Minimal
demands on labour
and capital
Appearance : Decision
about form and
material,sizes of
individual members
Factory made units
71
Length of structure i.e. retaining
wall,abutment, girder,slab and
pier
Substructure :
Appraisal of
Piers,abutments and
foundation
Costing and Final
Selection
END
Figure 4.2 : BS 5400 design flowchart
72
DESIGN FLOWCHART OF PRESTRESSED COMPOSITE
CONCRETE I GIRDER BRIDGE ACCORDING TO AASHTO
Determine Impact and Distribution Factors
Calculate Moment of Inertia of Composite Section
Calculate Dead Load on Prestressed Girder
Compute Dead Load Moments
Calculate Live Load Plus Impact Moment
Calculate Stresses at Top fiber of Girder
73
Calculate Stresses at Bottom fiber of Girder
Calculate Stresses at Bottom fiber of Girder
Calculate Initial Prestressing Force
Calculate fiber Stresses in Beam
Determine and Check Required Concrete Strength
Define Draping of Tendons
Check Required Concrete Strength
Check Ultimate Flexural Capacity
Finish
Figure 4.3 : Design Flowchart of I Girder Bridge according to AASHTO
74
DESIGN FLOWCHART OF PRESTRESSED COMPOSITE
CONCRETE I GIRDER BRIDGE ACCORDING TO BS5400
Calculate Moment
V
ariation
(live load +finishes)
Stress limit
(Structure class concrete grade)
Min. Section Modulus
Trial Section
(Shape,Depth,Web,Flange limit,cover,Loss allowance)
Self weight +dead load mom ent
Total moment
Min. prestress force
Serviceability
L.S
75
(Cable zone width limit, max eccentricity)
Design prestress force
Tendon profile
Transfer stresses
Check final stresses
Serviceability L.S
Check deflection
Design end block
(Prestress system)
Ultimate mom. of resistance
Untensioned Reinforced
Shear design
Finish
Check end block (unbonded)
Ultimate L.S
76
Figure 4.4 : Design flowchart of I-Girder Bridge according to BS 5400
ANALY
SIS OF COLUMN BENT PIER
UNDER SEISMIC LOADING ACCORDING TO AASHTO
Determine Type of Seismic Analysis and Other Criteria
Compute stiffness of the Pier
Compute Load due to Longitudinal Motion
Compute Load due to Transverse Motion
Summarizes Loads Acting On Pier Column
Check for Effects of Slenderness
Compute Moment Magnification Factor
77
Determine Required Reinforcing Steel
END
Figure 4.5: Design Flowchart of Column Bent Pier according to AASHTO
ANALY
SIS OF COLUMN BENT PIER
ACCORDING TO BS 5400
Calculate nominal load
Adopt size of pier
-Determine self weight
Design
bearing
design dowel
bar
design capping
beam
design column
design pile cap
short column
design as beam
design piles
Long column
Load
at SLS
Load
combination
determine structural
capacity of piles
Load at ULS
Load Combination
Calculate maximun reaction
Type of piles and nos
Check maximun reaction
Design pile cap
78
Design load capacity of piles
Based on soil data
-design length of piles
- Geotechnical capacity
Figure 4.6: Design Flowchart of Column Bent Pier according to BS 5400
DESIGN OF A STUB ABUTMENT WITH SEISMIC DESIGN CODE
ACCORDING TO AASHTO
Determine Type of seismic Analysis
and Other Criteria
Compute Seismic active earth Pressure
Compute Static Active Earth Pressure
Compute Equivalent Pressure
Compute Abutment Loads
Compute Active Earth Pressure for Stem
and Wall
Compute Abutment Stiffness
Compute Earthquake Load On Abutment
79
Compute Shears and moments
Design
Reinforcement
for Stem
Figure 4.7: Design Flowchart of Stub Abutment according to AASHTO
DESIGN OF A STUB ABUTMENT WITH SEISMIC DESIGN CODE
ACCORDING TO BS 5400
Strength at the Ultimate limit state
Stresses at the serviceability limit state
Crack widths at the serviceability limit state
Overtunning.
Restoring moment>m ax. overturning moment
(unfactored nominal load)
Factor of safety against sliding and soil pressures
(Due to nominal load)
Design reinforcement for moment
Figure 4.8: Design Flowchart of Column Bent Pier according to BS 5400
80
4.3
Result and Analysis
Table 4.1 and table 4.3 show the va
lue of require steel area for
usage of different codes.According to the table, we can see that percentage
of difference steel area for each members that use difference type of
codes.
Codes of Practices
Amount of Steel
Area (mm2)
Deck
Girder
Column
Abutment (Moment Steel +
Shear)
AASHTO
BS5400
1341 (H16-150)
7*3039 (4.71 in 2 )
=21273
6*17710 (22H32)
=
106260
2*(7543 +2095)
=19360
1006 (H16-200)
7*
54
00
=37800
16,905 (21H32)
=101430
2*(5892)
=11784
Percent of
Difference
( %)
33.30
3.72
4
.76
4
64
.29
Table 4.1 : Steel Area for different code of practice.Consider for seismic reading 0.15 g
Codes of Practices
Cost of Steel
Area (RM2000/tonne)
Deck
Girder
Column
Abutment (Moment Steel +
Shear)
Overall Cost
AASHTO
BS5400
RM 632
7*(RM1432)
RM10024
=
6*(RM 2113) =
RM12678
2*
(RM 855) =
RM1710
RM 24,142
RM 474
7*(RM2542)
=RM17794
6*(RM 2017) =
RM12102
2*
(RM 647) =
RM 1294
RM 31664
Percent of
Difference
( %)
33.30
3.67
4
.76
4
32.15
22.90
Table 4.2 : Cost of steel area for different code.Consider seismic reading 0.15 g
81
Table 4.2 and table 4.4show
the steel area cost for usage of different
codes.According to the table, we can see that percentage of difference
steel area cost for each members that use difference type of codes.
Codes of Practices
Amount of Steel
Area (mm2)
Deck
Girder
Column
Abutment (Moment Steel +
Shear)
AASHTO
BS5400
1341 (H16-150)
7*3039
=21273
6*17710 (22H32)
=
106260
2*(5632 +1609)
=14482
1006 (H16-200)
7*
5400
=37800
16,905 (21H32)
=101430
2*(5892)
=
11784
Percent of
Difference
( %)
33.30
3.67
4
.76
4
22.89
Table 4.3 : Steel Area for different code of practice.Consider for seismic reading 0.075 g
Codes of Practices
Cost of Steel
Area (RM2000/tonne)
Deck
Girder
Column
Abutment (Moment Steel +
Shear)
Overall Cost
AASHTO
BS5400
RM 632
7*(RM1432)
RM10024
=
6*(RM 2113) =
RM12678
2*
(RM 729)
=
RM 1458
RM 474
7*(RM2542)
=RM17794
6*(RM 2017) =
RM12102
2*
(RM 64
7)
=RM 1294
RM 24792
RM 31664
Percent of
Difference
( %)
33.30
2.61
4
.76
4
12.67
21.70
Table 4.4 : Cost of steel area for different code.Consider seismic reading 0.075g
82
Graphically Result :
Steel area for different code of practices
Amount of steel area (mm^2)
120000
100000
80000
60000
40000
20000
0
Deck
Girder
Column
Abutment
American Code
1341
21273
106260
19360
British Code
1006
37800
101430
11784
Figures 4.9 : Steel Area for different code of practice.Consider for seismic reading 0.15 g
Amount of steel area (mm^2)
Steel area for different code of practices
120000
100000
80000
60000
40000
20000
0
Deck
Girder
Column
Abutment
American Code
1341
21273
106260
14482
British Code
1006
37800
101430
11784
Figures 4.10 : Steel Area for different code of practice.Consider for seismic reading 0.075 g
83
Cost of steel area for 0.15 g seismic reading
20000
Cost (RM)
15000
10000
5000
0
Deck
Girder
Column
Abutment
American Code
632
10024
12678
1710
British Code
474
17794
12102
1294
Figures 4.11 : Cost of steel area for different code.Consider seismic reading 0.15 g
Cost of steel area for 0.075 g seismic reading
20000
Cost (RM)
15000
10000
5000
0
Deck
Girder
column
Abutment
American Code
632
10024
12678
1458
British Code
474
17794
12102
1294
Figures 4.12 : Cost of steel area for different code.Consider seismic reading
0.075g
Meanwhile , table .45 and table 4.6
indicated the result of Time
History Analysis in order end member force (Girder) among both codes of
practices.
84
Member
Joint
1
(Girder)
2
(Girder)
3
(Girder)
4
(Column)
5
1
2
2
3
3
4
5
2
6
3
(Column)
Axial
(kN)
386.40
-189.51
181.57
145.49
-219.48
416.37
-53.21
-53.21
-56.93
-56.93
Shear-Y
(kN/m2)
MomentZ
74.7 8
122.11
162.99
164. 07
120.65
76.25
98.48
7.94
39.87
73.99
156.03
-582.05
720.80
-737.08
564. 28
-164.6 6
-182.68
-138.76
-43.24
172.80
Axial
Capacity
of the
Column
(MN)
2,218.82
2,218.82
2,218.82
2,218.82
Moment
Capacity of
Girder
(kN.m)
9,231.30
9,231.30
9,231.30
9,231.30
9,231.30
9,231.30
Shear
Capacity of
Structure
(MN/m2)
3270.30
3270.30
3270.30
3270.30
3270.30
3270.30
3,48 7.76
3,48 7.76
3,48 7.76
3,48 7.76
Table 4.5 : Time History Analysis due to End Member of Force by using British code
analysis (Staad-Pro)
Member
Joint
Axial
(kN)
ShearY
(kN/m 2)
1
(Girder)
2
(Girder)
3
(Girder)
4
(Column)
5
(Column)
1
2
2
3
3
4
5
2
6
3
438. 34
-211.79
208.89
167.44
-246.2 2
472. 77
53.21
53.21
56.93
56.93
86.24
140.32
187.63
188.71
138.86
87.70
-103.53
-2.90
-35.08
-78.77
MomentZ
180.89
-667.61
830.70
-846.9 1
649. 93
-189.47
-194.1 6
-163.09
-31.05
196.98
Axial
Capacity
of the
Column
(MN)
2,218.82
2,218.82
2,218.82
2,218.82
Moment
Capacity of
Girder
(kN.m)
9,231.30
9,231.30
9,231.30
9,231.30
9,231.30
9,231.30
Shear
Capacity of
Structure
(MN/m 2)
3270.30
3270.30
3270.30
3270.30
3270.30
3270.30
3,48 7.76
3,48 7.76
3,48 7.76
3,48 7.76
Table 4.6 : Time History Analysis due to End Member of Force by using American code
analysis (Staad-Pro)
85
Table 4.7 and table 4.8 show the re sult of Time History Analysis
due to joint displacement of bridge structure among both codes of
practices.
Joint
1
XTrans
0.000
Y–
Trans
0.000
Z–
Trans
0.000
2
0.000
0.000
0.000
0.000
0.0000
0.0000
1
0.000
0.000
0.000
0.000
0.0000
0.0000
2
-0.0504
0.000
0.000
0.000
0.0000
-0.0005
1
2
0.000
-0.0558
0.000
0.000
0.000
0.000
0.000
0.000
0.0000
0.0000
0.0000
0.0005
1
0.000
0.000
0.000
0.000
0.0000
0.0000
2
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
2
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
2
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
Load
X–
Y–
Rotation Rotation
0.000
0.0000
Z–
Rotation
0.0000
1
2
3
4
1
5
6
Table 4.7 : Time History Analysis due to joint displacement by using American code
analysis (Staad-Pro)
86
Joint
Load
1
XTrans
0.000
Y–
Trans
0.000
Z–
Trans
0.000
X–
Y–
Rotation Rotation
0.000
0.0000
Z–
Rotation
0.0000
2
0.000
0.000
0.000
0.000
0.0000
0.0000
1
0.000
0.000
0.000
0.000
0.0000
0.0000
2
-0.0483
0.000
0.000
0.000
0.0000
-0.0005
1
2
0.000
-0.0509
0.000
0.000
0.000
0.000
0.000
0.000
0.0000
0.0000
0.0000
0.0005
1
0.000
0.000
0.000
0.000
0.0000
0.0000
2
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
2
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
2
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1
2
3
4
1
5
6
Table 4.8 : Time History Analysis due to joint displacement by using British code
analysis (Staad-Pro)
87
Finally , table 4.9 and table 4.10 show the result of Time history Analysis
due to support reaction among both codes.
Joint
1
FORCE
-X
0.00
FORCE
-Y
0.00
FORCE
-Z
0.00
MOM
-X
0.00
MOM
-X
0.00
Z–
Rotation
0.00
2
38.34
4
86.24
0.00
0.00
0.00
180.89
1
0.00
0.00
0.00
0.00
0.00
0.00
2
72.76
4
87.70
0.00
0.00
0.00
-189.4
6
1
2
0.00
103.53
0.00
53.21
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-194.16
1
0.00
0.00
0.00
0.00
0.00
0.00
2
35.02
56.89
0.00
0.00
0.00
-30.95
2
0.00
0.00
0.00
381.16
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1
0.00
0.00
0.00
0.00
0.00
0.00
2
0.00
0.00
0.00
0.00
0.00
Load
1
4
5
6
1
2
3
384
.4
6
Table 4.9 : Time History Analysis due to support reaction by using American code
analysis (Staad-Pro)
88
Joint
1
FORCE
-X
0.00
FORCE
-Y
0.00
FORCE
-Z
0.00
MOM
-X
0.00
MOM
-X
0.00
Z–
Rotation
0.00
2
961.15
184.36
0.00
0.00
0.00
358.34
1
0.00
0.00
0.00
0.00
0.00
0.00
2
998.93
186.16
0.00
0.00
0.00
-368.59
1
2
0.00
106.28
0.00
53.21
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-199.98
1
0.00
0.00
0.00
0.00
0.00
0.00
2
30.37
56.89
0.00
0.00
0.00
-18.17
2
0.00
0.00
0.00
806.42
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1
0.00
0.00
0.00
0.00
0.00
0.00
2
0.00
809.69
0.00
0.00
0.00
0.00
Load
1
4
5
6
1
2
3
Table 4.10 : Time History Analysis due to support reaction by using British code
analysis (Staad-Pro)
89
4.13 ) Mode Shape of bridge structure during earthquake event for each codes of
practices design
Fig 4.13 a : Mode Shape of bridge structure during earthquake event for American code
design
90
Fig 4.13 b : Mode Shape of bridge structure during earthquake event for American code
design
Fig 4.13.c: Natural Frequency vs Participation graph
91
6
5
Acceleration (m/sec^2)
4
3
Series1
2
1
0
0
5
10
15
20
25
30
35
40
Period (Sec)
Fig. 4.13.d : Time History Analysis graph for American code design
Fig 4.14. a : Mode Shape of bridge structure during earthquake event for British code
design by using Lusas Software
92
Fig 4.14. b : Mode Shape of bridge structure during earthquake event for British code
design by using Lusas Software
Fig 4.14.c. : Natural Frequency vs Participation graph
.
93
Response Spectrum Analysis for BS 5400 Bridge
6
Acceleration (m/sec^2)
5
4
Series1
3
2
1
0
0
5
10
15
20
25
30
35
40
Period (Sec)
Fig. 4.14.d. : Time History Analysis graph for British code design
4.4
Discussion and Conclusion
Based on the result and analysis, we can see that cost for using
different code is decrease in term of amount of steel area if we apply
AASHTO-Seismic Design Code.This case occurred because the reading
value of seismic in Malaysia is consider to small compare to another area
country.But for amount of steel is increase except Girder Steel Area if
AASHTO-Seismic Design code is apply.
We can conclude that by applying AASHTO-Seismic Design code
for bridge design it’s more save than BS 5400 in term of Malaysia
situation.We can save almost 22 %
cost for steel area.
CHAPTER V
CONCLUSION AND SUGGESTION
5.0
Introduction
As we mentioned in last chapter I, our target in comparison
between these both codes are to investigate percentage of cost whether
increase or decrease in term of seismic design consideration in our bridge
in Malaysia.In fact of that, we also make study on behaviour of existing
bridge capacity in Malaysia towards to seismic loading.
We also try find out the level of design strength for our current
bridge design code and new bridge design code (AASHTO-Seismic
Design) that we supposed to invesigate to determine capability in resisting
the seismic loading to bridge structure.
We conduct this study by redesign existing bridge in Malaysia with
a new code of practices.In our case, our new design code that we adopt
and apply is AASHTO-Seismic Design.We redesign all structure
component by manually hand calculation without using any kinds of
software design.This is because, we try understand deeply the application
of seismic design consideration before we perform using software design
i.e LUSAS,Cosmos,SAP 90,Staad-Pro etc.
95
5.1
Future Research
The study of comparison between both different code in our
country toward our bridge in Malaysia is just beginning.There are a lot of
improvement that can be done to get a better and accurate result or
outcome so that we can recover our currently backdraw practice in design
of our bridge structure in Malaysia.We plan to perform this bridge case by
using software design that just concentrate only to seismic loading
independently.We decide to use LUSAS software application in doing our
case study.
5.1.1.
Future Challenges in Bridge Engineering
Having given an overview of more than two millennia in bridge
building with some discussion of the impact of developments on later
bridge engineering, the following paragraphs shall look ahead. The second
half of this chapter will give an overview of the wide spectrum of future
challenges. As opposed to the history of bridges, for which an abundance
of literature can be found in any library, books or articles on the future of
bridge construction are more rare.How can predictions be made at all? The
basic approach is to identify current problem areas and trends in research
interests. With some imagination, it is then possible to derive ideas of
where bridge engineering may be heading. These predictions will certainly
not be exact, but they give an impression of future challenges. New
concepts are emerging, yet there is still very little experience with the
practical application of these. It will take creativity and sometimes also
courage to face them.
96
The following sections will outline these areas of challenge for
coming generations of bridge engineers. Three main areas are identified:
Dealing with the engineering approach towards the complete project lifecycle, including design, construction, maintenance, and rehabilitation;
secondly new or improved materials; and finally new types of structures
are discussed.
5.2 Improvements in Design, Construction, Maintenance, and
Rehabilitation
The construction industry is unique in the way that most of its
structures are one-of-a-kind products. As opposed to industrial
manufacturing, the construction industry in most cases produces structures
that are adapted to the owner’s specific wishes and to constraints imposed
by site conditions and technical possibilities. The processes that lead to the
complete structure are discussed in much more detail in Chapter 3. Here,
some areas of possible improvements shall be pointed out.
5.2.1 Improvements in Design
Since the construction of a real structure is the ultimate goal of all
design, the design process inevitably needs to consider the requirements
and limitations of construction methods. Current issues in improving
design for construction focus on better designs through an increased team
effort of all parties involved. Construction engineering concepts, such as
Design-Build Construction and Partnering all deal with trying to foster
close cooperation and improve communication to achieve better overall
97
project performance.Apart from managerial improvements, especially the
development of prestressed concrete segmental bridges has given
designers a wide range of possibilities at hand. In addition to the
possibilities inherent to this kind of concrete, designers are able to choose
from improved or newly developed materials. More information on highperformance materials is given in Section 2.2.2. Use of advanced materials
of higher strength, less weight, and improved durability will allow smaller
structural members for substructures and superstructures and less dead
load of the structures that they form. Up to a certain point these
improvements remain well within the classic design methodology, but as
Podolny (1998, p26) writes, with enhanced materials and new structural
concepts necessity can arise “to deal with new limit states, such as user
sensitivity to vibration or claustrophobic reaction to long tubular structures
or tunnels.” With these advanced materials in innovative structures, the
center of attention may shift even more to the serviceability of the
structures. Podolny and Muller (1982) state that at some time a situation is
reached where stress criteria are not determining anymore, but are
overruled by limitations to deformations. They also point at the increased
necessity to examine special failure modes of slender, yet strong structural
members, such as buckling. Fabrication tolerances would have to be
included in these considerations.In the past two decades, the enormous
development of computer capabilities has certainly provided engineers
with much better tools for performing a vast amount of analytical
calculations in very short time. Still, it has to be cautioned about too much
relying on computer results and the models on which they are based.
5.2.2 Improvements in Construction
The core issues governing the actual construction process are
safety and economy, with the latter one referring especially to a smooth
98
construction process on budget and within time scheduled. Quality control
is necessary to ensure that the structure and its parts are built according to
the specifications. Control of all these goals is the main task of
construction management.Depending on the actual construction method
employed to the specific project, various ways of simplifying and
speeding up construction works for economy exist. Examples provided in
technical literature are e.g. increased use of precast elements to speed up
construction on site, such as prefabricating webs for cast-in-place box
girders (Mathivat 1983). Podolny and Muller (1982) give an example of a
modified method of incremental launching, where the concrete deck for a
steel superstructure is cast and launched forward stepwise, thus reducing
the need for formwork considerably. More methods of combining different
erection methods and implementing both precast and cast-in-place
segments where advantageous are conceivable. In future, introduction of
more automated equipment on site can help accomplish certain repetitive
tasks. The uniqueness and complex conditions of every site, as well as the
multitude of tasks to be performed during construction yet still make such
automation very difficult. Use of improved equipment, e.g. modular
formwork and shoring systems, are but small steps towards the goals
outlined above.
5.2.3 Improvements in Maintenance and Rehabilitation
Bridges have to withstand a large variety of environmental
influences during their service life.The natural environment induces
stresses in the structure e.g. through temperature gradients.Strong winds,
flood events and seismic events put the structural stability and integrity to
a test.Corrosive chemicals in water and air, as well as present through
99
deicing agents for roadways affect the soundness of the materials.
Dynamic loads from traffic and winds generate fatigue.Construction
details, as e.g. joints, bearings, and anchorages suffer from wear and tear.
Apart from these influences various forms of impact, e.g. from passing
vehicles or ship traffic need to be anticipates in design of the structure.
Maintenance of bridges comprises regular inspections, renewal of e.g.
protective exterior coatings, replacement of parts as e.g. worn out bridge
bearings, and other minor repairs. A certain percentage of total
construction cost is commonly budgeted for annual maintenance of
bridges under service. Inspections are required in order to keep informed
on the current state of the bridge. Future development of technical systems
could support or even replace these inspections. Sensors built into the
structure could then be used to measure the current state of deterioration,
e.g. in the bridge deck and to detect weaknesses. Links with computer
databases and software for so-called bridge management systems could
then help interpreting the data collected. Accessing these data will allow
for decisions as to the measures required to keep the structure at a
serviceable condition. Measures that simplify construction work can also
make repair and rehabilitation work easier.
Modularization of structural members and good accessibility of the
whole assembly will contribute to performing repair and rehabilitation
work with greater ease. Structural details affected by wear and tear and
thus most susceptible to corrosion are traditionally bearings and joints.
Reducing the number of complicated details and focussing efforts on good
detailing of these will contribute to a longer service life of the whole
structure. Good design will also anticipate easy replacement of these parts.
Another most important factor for the length of bridge service life
is materials. Less weight of structural members due to stronger materials
will simplify handling these members. Workability is another factor that
100
can determine the high performance of a material. In the area of materials
for repair and rehabilitation development of coatings, epoxy grouts, fiber
reinforcement, and other materials enables the repairs to be very specific
adapting to the problem.
5.3
Conclusion
With the prospects and possibilities presented above one can say
that the future of bridges has just begun. The three main areas of future
development that were pointed out in the previous sections show that the
range of ideas to be explored is very wide. Some of these ideas may prove
impractical within the technical environment, while others will become
feasible once the existing technologies have been developed further. The
approaches mentioned will contribute to the development of amazing new
structures. Only the fascination that is characteristic for bridge engineering
field will remain the same that it has always been, during the many
centuries that have passed since the first bridges were erected.
REFERENCES
Standard Specifications for Highway Bridges, 15th ed, American Association
of State highway and Transportation Officials, Washington, D.C, 1993.
Standard Plans for Highway Bridges, vol. I,Concrete Superstructures, U.S
department of Transportation ,Federal Highway Administration,Washington,
D.C,1990.
Winter,George and Nolson,Arthur H., Design of Concrete Structures, 9th
ed.,McGraw-Hill,New York,1979.
Gutkowski,Richard M. and Williamson,Thomas G., “Timber Bridges:State of
Art,” Journal of Structural Engineering,American Society of Civil
Engineers,pp.2175-2191,vol.109,No.9,September,1983.
Standard details for Highway Bridges,New york State Deparment of
Transportation,Albany,1989.
Elliot,Arthur L.,”Steel and Concrete Bridges,”Structural Engineering
Handbook,Edited by Gaylord,Edwin H., Jr., and Gaylord,Charles N.,
McGraw-Hill,New York,1990.
AASHTO Manual for Bridge Maintenance,American Association of State
Highway and Transportation Officials,pp.77-104,Washington,D.C.,1987.
Bridge Design Practice Manual,CaliforniaDepartment of Transportation,p.111,Sacramento,1983.
102
Robert A.et al., Goals,Opportunities, and Priorities for the USGSEartquake
Hazard Reduction Program,U.S. geological Survey,p.366,Wahington,
D.C.,1992.Bridge Design Practice Manual, 3rd ed., California Department of
Transportation, Sacramento.,1971.
Steinman ,D.B., and Watson , S.R., Bridges and Their Builders,2nd ed., Dover
Publications Inc., New York,1957.
Starzewski,K., “Earth Reatining Structures and Culverts.”The Design and
Construction of Engineering Foundation,Edited by Hendry, F.D.C.,
Chapman and Hall, New York, 1986.
Bowles,Joseph E., Foundation Analysis and Design, 2 nd ed., McGrawHill,New York,1977.
Standard Specification for Highway Bridges, 15th ed., American
Association of State Highway and Transportation Officials, p. 646,
Washington, D.C., 1993.
Walley,W.J., and Purkiss, J.A., “Bridge Abutment and Piers,” pp. 821 –
884,The Design and Construction of Engineering Foundations,Edited by
Henry, F.D.C., Chapman and Hall, New York, 1986.
Standard Specifications for Highway Bridges, 15th ed, American
Association of State highway and Transportation Officials, Washington,
D.C, 1993.
Standard Specifications for Highway Bridges, 15th ed, American
Association of State highway and Transportation Officials,
Washington,pp. 646 D.C, 1993.
103
Winter , George, and Nilson, Arthur H., Design of Concrete Structures,9th
ed.,McGraw-Hill,New York,1979.
APPENDIX A
Design of reinforced concrete deck slab
Problem : Design the transversely reinforced concrete deck slab.
Given :
1. Bridge to carry two traffic lanes.
2. Bridge loading specified to be HS20-44.
3. Concrete strength fc’ = 4,500 psi = C40
4. Grade 60 reinforcement fs = 24,000 psi
5. Account for 25 psf future wearing surface.
6. Deck has integrated wearing surface.
Step 1 : Compute the Effective Span Length
From table 3.6 (AASHTO) effective span length criteria for concrete slabs,for a slab
supported on concrete stringer and continuous over more than two longitudinals supports:
S = Clear Span (Clear distances between faces of supports)
= 5.75 ft
Step 2 : Compute Moment due to Dead Load
Dead load includes slab and future wearing surfaces,so that the total dead load on the slab
is
DL = (thickness of slab)(Weight of concrete ) + Future WS
= [(8 in)(1 ft/12 in)(150 Ib/ft3) + (25 Ib/ft2)](1 ft Strip)
= 125.0 Ib /ft.
MDL =
WS 2
(125.0 Ib/ft)(5.75 ft)2
=
10
10
= 0.41 ft-kips
Step 3 : Compute Moment Due Live Load + Impact
Live load is computed as per equation 3.18
§S 2·
§ 5.75 2 ·
MLL = 0.8 ¨
¸ P = 0.8 ¨
¸ 16
© 32 ¹
© 32 ¹
= 3.1 ft- kips
Impact factor for spans 98.4 ft :
50
L 125
I=
=
50
98.4 125
= 0.22
Therefore,
MLL+I = (3.10)(1.22)
= 3.78 ft-kips
Step 4 : Compute Total Bending Moment
Mb = MDL + MLL+I =( 0.41 + 3.78) ft-kips
= 4.19 ft-kips
Step 5 : Compute Effective Depth of Slab
First,find the modular ratio n:
Es
EC
29,000 ksi
n=
3,824ksi
n=
where : Es = Modulus of Elasticity for steel
= 29,000,000 psi (ACI 8.5.2)
EC = Modulus of Elasticity for concrete
n = 7.0
= 57,000 f 'C = 57,000 4,500 psi
= 3,823,676.242 psi (ACI 8.5.2)
Next,find the stress ratio r :
r=
fS
fC
where : fs = Allowable stress for steel
= 24,000 psi (ACI A.3.2)
24,000 psi
r=
1,800 psi
fc = Allowable stress for concrete
= 0.40fc = 0.40(4,500)
r = 13.3
= 1,800 psi (AASHTO)
Now,compute the coefficients,k and j:
k=
n
7 .0
=
= 0.36
nr
7.0 13.3
,
j= 1-
k
0.36
= 1= 0.88
3
3
For a rectangular beam,the minimun depth required is given as :
d=
2 Mb
fC kjb
where : b = Unit width of slab
= 1.0 ft
d=
2( 4.19 ft kips)(12in / ft )
(1.8kip / in2 )(0.36)(0.88)(12in)
= 3.83 in
Step 6 : Compute Required Main Reinforcement
DACTUAL = 7.87 slab- 1.96 Integral W.S – 1.96 cover-(0.75Dia/2)
= 3.58 < 3.83 in minimun u
Therefore, use d = 4.0 in
AS =
s
=
Mb
f S jd
( 4.19 ft.k )(12in / ft )
( 24 ksi )(0.88)( 4.0in)
= 0.60 in2 /ft = 1,267 mm2/m
Step 7 : Determine number of Bars and Spacing
From predefined tables (see Appendix) we can select various numbers of bars at a given
spacing.
Therefore,use # 4 @ 3.5 in- spacing( 0.50 in Dia) = 0.67 in2 / ft
Or H16-125 (1609 mm2)
Step 8 : Compute Distribution Steel in Bottom of Slab
D=
220
220
=
= 91.7 % > 67% so use
S
5.75
Distribution Steel = (AS)(67 %) = (0.22 in2 / ft)(0.67) = 0.15 in2 / ft
Use # 3 @ 8 in-spacing (0.375 in Dia) = 0.17 in2 / ft
Design of Prestressed Composite Concrete I Girder Bridge
Problem : Design the interior stringer for a simple 98 ft simple span structure using a
standard AAHTO PCI girder.
Given :
1. Simply supported span.
2. Design Span length = 98 ft
3. Type V AASHTO-PCI girders.
4. HS20-44 live loading.
5. Steel : f ‘S = 270,000 psi
6. Concrete : f ‘C = 5,500 psi = C40
7. 3.00 in wearing course.
8. Deck and girder made of same strength concrete.
9. Barrier area = 2.91 ft2
Step 1 : Determine Impact and distribution Factors.
By equation 3.10,the impact factor is :
I=
50
50
=
= 0.22
L 125
98 125
So, use I = 1.22
By table 3.4,the distribution factor is calculated for a bridge with:
1. Concrete Floor
2. Two or more traffic lanes
3. On prestressed Concrete Girders
DF =
S
5.75
=
= 1.05
5.5
5 .5
Step 2 : Calculate Moment of Inertia of Composite Section
ELEMENT
SLAB
GIRDER
TOTALS
A (in2)
543.0
1013.0
1556.00
AY (in3)
36348.42
32375.48
68723.9
Y (in)
66.94
31.96
98.90
AY2 (in4)
2433163.235
1034720.34
3467883.58
= 3991862.32 in2
IZ = ¦ I O + ¦ AY 2 = 523978.74 + 3467883.58
Y’=
IO (in4)
2798.74
521,180
523978.74
¦ AY 68723 .90
=
¦A
1556.00
= 44.17 in
I = IZ – ( ¦ A )( ¦ Y ' )2 = 3991862.32 – (1556)(44.17)2
= 956123.59 in4
7.87 in thickness of slab
+
+
e = 27.96 in
C.G SECTION
44.17 in
C.G GIRDER
31.96 in
Assumed C.G PS Force
+
4.0 in
Step 3 : Calculate Dead Load on Prestressed Girder
The dead load is composed of the following items :
DL slab
= (beff)(Slab thickness)(wConc)
= (5.75)(7.87 in)(1 ft/12 in)(0.150 k/ft3)
= 0.566 k/ft
63”
DL haunch = (Haunch width)( Haunch thickness)(Wconc)
= (1.33 ft)(1 in)(1 ft/12 in)(0.150 k/ft3)
DLGIRDER
= 0.017 k/ft
= (girder area)(Wconc)
= (1013 in2)(1 ft/144 in2)(0.150 k/ft3)
DL Barrier
= 1.06 k/ft
= (2 barriers)(barrier area)(wConc)/7
= (2)(2.61 ft2)(0.150 k/ft3)/7
DL Wearing
= 0.11 k/ft
= (W.C thickness)(1/12 ft)(pave.width)(W pave)/7
= (2.0 in)(1ft/12in)(34.4 ft)(0.150 k /ft3)/7
= 0.12 k/ft
Step 4 : Compute Dead Load Moments
Dead Load moments by equation:
WL2 (0.566 0.017 )(98.0 ft )
=
8
8
2
(1.06 k / ft )(98.0) 2
WL
=
Mgirder =
8
8
2
(0.157 k / ft )(98.0 ft ) 2
WL
=
Mbarrie =
8
8
2
(0.12 k / ft )(98 ft ) 2
WL
=
Mwearing =
8
8
Mslab
=
= 700.0 ft-k
=1272.5 ft-k
= 188.5 ft-k
=144.06 ft-k
Total MDL = 2305.06 ft-k
Step 5 : Calculate Live Load Plus Impact Moment from figure below,
We locate the HS20-44 truck as shown below:
C/L
4k
16 k
14 ‘0”
2’4”
16 k
11’8”
Bearing
A
Bearing
49’
98.0 ft
49’ B
First,solve for the reaction by summing moment about Point A:
Assume positive direction for clockwise, ¦ M A = 0:
(4k x 32.7) + (16k x 46.7) + (16k x 60.7) – (RB x 98ft) = 0
1849 .2
= 18.87 k
so, RA = 36 k – 18.87 k = 17.13 k
98
Now,compute the maximun live load moment:
RB =
MLL = MMAX = (RA x 46.7) - (4 k x 14.0) = 772.0 ft-k
Apply the impact and wheel load distribution factors:
MLL +I = MLL x DF x I
MLL+I = (772)(1.05)(1.22)
MLL+I = 988.93 ft-k
4k
16 k
14.0’
C
A
46.7’
Step 6 : Calculate Stresses at Top Fiber of Girder
Recapping from step 2,the centroid distances and moments of inertia for composite and
noncomposite sections are:
NONCOMPOSITE
COMPOSITE
Type III Girder
7.87 ” Slab & Type III Girder
I = 521,180 in4
956123.59 in4
YT = (63-31.96)in = 31.04 in
YT = (63-44.17)in = 18.83 in
31.96 in
44.17 in
The stresses at the top fiber of the girder is calculated using the standard expression
defined by equation (fC = Mc / I):
Equation
Element
NonComposite
Slab
(700.0)(12in / ft )(31.04)
521180 in 4
= 0.50
Type III
(1272.5)(12in / ft )(31.04)
521180 in4
= 0.91
LL + I
(989 )(12in / ft )(18.83)
956123.59in4
= 0.23
Barrier
(189)(12in / ft )(18.83)
956123.59in4
= 0.045
Wearing
(145)(12in / ft )(18.83)
956123 .59in 4
= 0.034
Girder
Composite
Top Fiber
Course
Total
fTOP = 1.719 ksi
Step 7: Calculate Stresses at Bottom Fiber of Girder
Recapping from step 2,the centroid distances and moments of inertia for the composite
and noncomposite section are:
NONCOMPOSITE
COMPOSITE
Type III Girder
7.87 ” Slab & Type III Girder
I = 521,180 in4
956123.59 in4
YT = (63-31.96)in = 31.04 in
YT = (63-44.17)in = 18.83 in
YB = 31.96 in
YB = 44.17 in
The stresses at the top fiber of the girder is calculated using the standard expression
defined by equation (fC = Mc / I):
Equation
Element
NonComposite
Slab
(700.0)(12in / ft )(31.96)
521180 in 4
= 0.52
Type III
(1272.5)(12in / ft )(31.96)
521180 in4
= 0.94
LL + I
(989)(12in / ft )( 44.17 )
956123 .59in 4
= 0.55
Barrier
(189 )(12in / ft )( 44.17 )
956123 .59in4
= 0.10
Wearing
(145)(12in / ft )( 44.17 )
956123.59in4
= 0.08
Girder
Composite
Bottom Fiber
Course
Total
FBOT = 2.19 ksi
Step 8 : Calculate Initial Prestressing Force
In step 2, we assumed an eccentricity of : e = 27.96 in.
The square of radius of gyration is calculated as:
r2 =
521,180in4
I
=
= 514.49 in2
1013
A
Calculate effective prestressing force :
C = Pf =
( 2.19)(1013in2 )
f bot A
= 788.4 k
=
( 27.96)(31.96)
ey
1
1 2b
514.49
r
Calculate effective stress :
fe = Allowable Initial Stress – Assumed Losses
By AASHTO 9.15.1 for low relaxation strands :
Allowable Initial Stress = 0.75 fs ‘ = (0.75)(270 ksi) = 202.50 ksi
By table 3.25 for pretensioned strands :
Assumed losses = 35 ksi
fe = 202.50 ksi – 35.0 ksi = 167.50 ksi
Calculate area of steel:
AS =
Pf
fe
=
788.4 k
= 4.71 in2
167.5ksi
Assume losses due to elastic shortening , So:
Losses After Transfer = 35 ksi- 13 ksi = 22 ksi
The initial prestressing force is:
Pi = Pf + (Losses After Transfer)(AS) = 788.4 k + (22 ksi)(4.71 in2)
Ÿ PI = 892.02 k
Step 9 : Calculate Fiber Stresses in Beam
Compute stresses at top and bottom using equation:
TOP FIBER
ey
1 + 2t
r
( 27.96)( 31.04)
1+
= -0.67
514.49
P
fTOP = -0.67
+/- ftime
A
BOTTOM FIBER
ey
1 + 2b
r
( 27.96)(31.96)
1+
= 2.74
514.49
P
fBOT = 2.74
+/- ftime
A
Time of Stress
Top
Fiber
At time of
prestressing
At time slab is
placed
At design load
At time of
prestressing
-0.67x
-0.67x
Equation
Stress
892.02 k
- 0.91
1013in 2
= -0.32 ksi T
788.4 k
-1.41
1013in 2
= -0.89 ksi C
788.4 k
- 1.719
1013in 2
892.02 k
2.74 x
+ 0.94
1013in 2
-0.67x
= -1.20 ksi C
= - 1.47 ksi C
At time slab is
placed
At design load
2.74 x
788.4 k
+ 1.46
1013in 2
= - 0.67 ksi C
2.74 x
788.4 k
+ 2.19
1013in 2
= 0.058 ksi C
Step 10 : Determine and Check Required Concrete Strength
By AASHTO 9.15.2.1,the allowable temporary compressive stress for pretensioned
members prior to creep shrinkage is :
Compressiv eStress 1.20 ksi
=
= 2.0 ksi
0.60
0.60
0.60f ‘ C , So : f ‘ C =
Ÿ specify a minimun strength of f ‘ C = 2,000 psi.
By AASHTO 9.15.2.1 ,the allowable temporary tensile stress for pretensioned members a
prior to creep shrinkage is :
3
f 'c = so: 3 5,500 psi = 222.49 psi = 0.222 ksi > -0.32 ksi ¥
By AASHTO 9.15.2.1,the allowable service load compressive stress for pretensioned
members after losses have occurred:
0.40 f ‘ C so: f ‘ C =
Compressiv eStress 1.20 ksi
=
= 3.0 ksi
0.40
0.40
3,000 psi < 4,000 psi.¥
By AASHTO 9.15.2.1,the allowable service load tensile stress for pretensioned members
after losses have occurred:
6 4000 psi =379.5 psi
Step 11 : Define Draping of Tendons
Drape tendon with two holddown positions as illustrated below:
L/3=32.7 ‘
L/3=32.7 ‘
L/3=32.7 ‘
A
B
Moment at third point moment to midspan moment is then:
§ L·
W¨ ¸
WL2
WX ( L X )
L
3
MX =
at X =
: M L = © ¹ ( L – L/3) =
X
2
9
2
3
3
The ratio of third point moment to midspan moment is then :
MMID =
WL2
WL2 / 9
8
so :
= = 0.89
2
8
WL / 8
9
Compare this to the ratio of live load moments at L/3 and midspan:
¦ M A = 0:
46.7 ‘
32.7 ‘
18.7 ‘
98.0 ‘
RA
RB
( 4 x 18.7) + ( 16 x 32.7) + (16 x 46.7) – ( RB x 98)
RB = 13.73 k
Mx
l/3
RA = 36 – 13.73 = 22.27 k
= (RA x 32.7) – (4k x 14 ft) = 664.23 ft-k
The maximun moment (near midspan) calculated earlier in step 5 was found earlier to be
: MMAX = 772.0 ft-k
The ratio of third point to midpoint moments can be taken as :
664.23 ft k
= 0.86 Since this is relatively close to 0.89 we will use 0.89 as our
772.0 ft k
multiplier.
Step 12 : Fiber stresses at Third Points of Beam
The multiplier is applied to the “time dependant” stresses calculated in steps 6 and 7.
Time of Stress
Top
Fiber
At time of
prestressing
At time slab is
placed
At design load
Bottom
Fiber
At time of
prestressing
At time slab is
placed
At design load
Equation
-0.67x
-0.67x
892.02 k
- (0.91)(0.89)
1013in 2
= -0.22 ksi T
788.4 k
-(1.41)(0.89)
1013in 2
= -0.73 ksi C
788.4 k
- (1.719)(0.89)
1013in 2
892.02 k
+ (0.94)(0.89)
2.74 x
1013in 2
788.4 k
2.74 x
+ (1.46)(0.89)
1013in 2
-0.67x
2.74 x
Stress
788.4 k
+ (2.19)(0.89)
1013in 2
= -1.01 ksi C
= - 1.57 ksi C
= - 0.83 ksi C
= -0.18 ksi C
Step 13 : Check Required Concrete Strength
By AASHTO 9.15.2.1, the allowable temporary compressive stress for pretensioned
members prior to creep shrinkage is :
0.60 f ‘C
so : f ‘C =
Compressiv eStress 1.57 ksi
=
= 2.62 ksi < 4.0 ksi ¥
0.60
0.60
By AASHTO 9.15.2.1,the allowable temporary tensile stress for pretensioned members
prior to creep shrinkage is :
3
f 'C = 3 5,500 = 222.49 psi = 0.1897 ksi > -0.22 ksi ¥
This does satisfy the requirement AASHTO 9.15.2.1 specifies,however,that bonded
reinforcement may be provided to resist the total tension in concrete provided that:
Maximun Tensile Stress < 7.5
f 'C
7.5 5,500 psi = 556.21 psi so : -220 psi < 556.21 psi ¥
Determine the number of conventional reinforcing bars required :
Distances to Neutral Axis =
(63in)( 220 psi )
= -10.3 in
220 psi 1570 psi
42 in
N.A = 10.3 in
5 in
63 in
2620 psi
Tensile force = (1/2) ft)(AC)
§ 220ksi ·
=¨
¸ (42 in)(10.3 in)
© 2 ¹
=47,586 Ib
For 24 ksi steel,required area:
A=
47586 Ib
= 1.98 in2
24,000 psi
Use 5 - # 6
A = 2.20 in2 > 1.98 in2 ¥
Step 14 : Check Ultimate Flexural Capacity
Compute prestressing steel ratio defined as :
P*=
AS *
bd
As* = 4.71 in2 (step 8)
B = Effective Flange Width = 5.75 ft
D = Girder – Slab Depth above PS = (63 in +1in+8in)-(4 in) = 68 in
P* =
4.71in2
= 1.0 x 10-3
(5.75 ft )(12in / ft )(68in)
By AASHTO 9.17.4 compute average stress in prestressing steel at ultimate load for
bonded members:
ª § y*
f*SU = f ‘ S «1 ¨¨
«¬ © E1
· § p * f 'S
¸¸ ˜ ¨¨
¹ © f 'C
·º
¸¸»
¹»¼
p* = 1.0 x 10-3 (above)
f ‘ S = 270 ksi (given)
f ‘C = 5,500 psi = 5.5 ksi
ª § (0.5)(1.0 x10 3 )( 270 ksi ) º
= 270 ksi «1 ¨¨
» = 263 ksi
5
.
5
ksi
©
¬
¼
By AASHTO 9.17.3 the neutral axis for ultimate load is located in the web if the flange
thickness is less than the following:
1.4 ˜ d ˜ p * ˜ f *SU
(1.4)(68.0in)(0.001)( 263ksi )
=
= 4.55 in
f 'C
5.5ksi
Thickness of slab = 8 in so,since 4.45 in < 8.0 in :
Neutral axis is located in the flange meaning that we design for a rectangular section.
For a rectangular section,we must check that :
p * f *SU
(0.001)( 263ksi )
=
= 0.05
f 'C
5.5ksi
…does not exceed the following limit (AASHTO 9.18.1) :
0.36 E 1 = (0.36)(0.85) = 0.31 so : 0.05 < 0.31 ¥
By AASHTO 9.17.2 , the flexural strength of a rectangular section is taken as :
I ˜ Mn
ª
§
¨
©
I ˜ « A *S ˜ f *SU ˜d ˜ ¨1 0.6 ˜
I ˜ Mn
«¬
>
p * f *SU
f 'C
·º
¸¸»
¹»¼
1.0 4.71in2 ( 263)(68in)(1 0.6 x0.05
12in / ft
= 6809 ft-k
=
@
Taking the moment defined by the load factored group loading (see Table 3.2):
M= J ˜ [ E DL ˜ M DL E LL I M LL I ]
Using the dead load moment determined in step 4 and the live load plus impact moment
found in step 5 :
M = 1.3[(1.0)(2305.06 ft-k) + (1.67)(989 ft-k)] = 5144 ft-k
So,since we are O.K since we have :
5144 ft-k < 6809 ft-k ¥
ANALYSIS OF A COLUMN BENT PIER UNDER SEISMIC
LOADING
PROBLEM : Analyze an existing column bent pier to see if a column in the pier can
accommodate seismic loading.
C/L
5.74’ (TYP)
3.94’
2.95’
14.8’
14.8’
ELEVATION
GIVEN :
1. A 3 span (18’-29’-18’) essential bridge crossing a highway.
2. 9 pairs of piles at 8.8’ center to center along length of footer.
3. 3 bays at 14.8’ center to center of column.
4. Concrete strength f’c = 4,400 psi.
5. 1950 ‘s vintage reinforcement fS = 27,000 psi.
6. Deck weight = 21.75 k / ft.
7. Geografic area has acceleration coeficient A = 0.075g
Step 1 : Determine Type of Seismic Analysis and Other Criteria
For an “essential bridge” by AASHTO 3.3 I-A we have:
IC = Importance Classification = I
With an importance classification of “I” by AASHTO 3.4 I-A for :
0.09 < A < 0.19 and IC = I
SPC = Seismic Performance Category = B
The bridge has an unchanging cross section,with similar supports, and a uniform mass
and stiffness,so it is considered to be :
Regular (By AASHTO 4.2 I-A)
For a Regular Bridge, SPC = B, and 2 or more spans, use:
Method 1 = Single-Mode Spectral Analysis (By AASHTO 4.2 I-A)
For stiff clay,by AASHTO 3.5 I-A:
Soil Profile Type II: S = Site Coefficient = 1.2
Response Modification Factor (AASHTO 3.6 I-A)
Multiple Column Bent: R = 5 (Treat as a wall-type pier)
Pier footing: R
= One-Half R for Multiple Column Bent
= R/2 = 5/2 = 2.25 (AASHTO 4.7.2 I-A)
Combination of Seismic Forces (AASHTO 4.4 I-A):
Case I : [100% Longitudinal Motion] + [30% Tranverse Motion]
Case II : [30% Longitudinal Motion] + [100 % Tranverse Motion}
Load Grouping (AASHTO 4.7.1 I-A) :
1.0(DL + Buoyancy + Stream Flow + Earth Pressure + Earthquake)
(N/A)
(N/A)
Step 2 : Compute Stiffness of the Pier
G
G
h = 24’
Longitudinal Earthquake
Motion
Transverse Earthquake
Motion
Longitudinal Motion
Ph3
G
3EI
4
Sd
S ( 2.95' ) 4
I=
3.72 ft 4
64
64
E = 3,300 ksi = 475,200 ksf
Transverse Motion
Ph3
Ph3
Ph3
G
12 E6I 12 E ˜ 6 I 72 EI
Sd 4 S ( 2.95' ) 4
I=
3.72 ft 4
64
64
E = 3,300 ksi = 475,200 ksf
Compute Deflection Due to Longitudinal Motion with P = 1:
G =
(1)( 24 ft )3
= 2.607 x 10-3 ft / k
4
(3)( 475,200 ksf )(3.72 ft )
k = Stiffness = 1/ G = 383.625 k / ft
For 3 column use : k = 1150.875 k / ft (Longitudinal Motion)
Step 3 : Compute Stiffness of the Pier (Continued)
Compute Deflection Due to Transverse Motion with P = 1:
G
(1)( 24 ft )3
= 108.613 x 10-6 ft / k
(72)( 475,200ksf )(3.72 ft 4 )
k = 1/ G = 1 / 108.613 x 10-6
= 9207 k / ft (Transverse Motion)
Step 4 : Compute Load due to Longitudinal Motion
18 m
29 m
18 m
Weight of Deck Slab
= 30.00 k / ft
VS
Compute static displacement vS with PO = 1:
VS =
(1)(98.04 ft )
= 85.19 x 10-3
1150.875
PO L
k
Compute single-mode factors D , E , J (AASHTO Division I-A 5.3) :
L
D =
-3
³ v ( x )dx = vS L = (85.19x 10
0
S
L
E
³ w( x )v ( x ) dx
J
³
0
L
0
S
w( x )vS ( x )2 dx
ft)(98.04 ft) = 8.352 ft2
Dw (8.352)(30.00k / ft ) = 250.56 ft-k
Evs
Compute period of oscillation :
( 250.56)(85.19 x10 3 ) = 21.35 ft2-k
J
T = 2S
PO gD
= 2S
21.35
(1k )(32.2 ft / sec 2 )(8.352)
= 1.770 sec
Compute elastic seismic response coefficient :
A = Acceleration coefficient = 0.075g (Given)
S = Site coefficient = 1.2 (Step 1)
CS =
1.2 AS
T
2
3
=
(1.2)(0.075)(1.2)
1.770
2
3
= 0.0738
AASHTO Division I-A 5.2.1 states that CS need not exceed 2.5A :
CS = 2.5A = 2.5(0.075) = 0.1875 > 0.1476 .: So use 0.1476
Compute equivalent static earthquake loading :
Pe (x) =
=
ECS
w( x )vS ( x )
J
( 250.56)(0.1875)
(30.0)(85.19 x10 3 ) = 5.624 k / ft
21.35
Compute force due to longitudinal motion acting on pier :
VY =
Pe ( x ) ˜ L
RPIER
(5.624)(98.04)
= 110.27 k
5
Step 5 : Compute Load Due to Transverse Motion
Compute force due to transverse motion acting on pier:
The force due to transverse motion is :
Compute static displacement vS with PO = 1:
VS =
(1)(39.4 ft )
= 4.28 x 10-3
9207
PO L
k
Compute single-mode factors D , E , J (AASHTO Division I-A 5.3) :
L
D =
-3
³ v ( x )dx = vS L = (4.28 x 10
0
S
L
E
³ w( x )v ( x ) dx
J
³
S
0
L
0
w( x )vS ( x )2 dx
ft)(39.4 ft) = 0.1687 ft2
Dw (0.1687)(30.00k / ft ) = 5.058 ft-k
Evs
(5.058)( 4.28x10 3 ) = 0.0216 ft2-k
Compute period of oscillation :
J
T = 2S
PO gD
= 2S
0.0216
(1k )(32.2 ft / sec 2 )(0.1687)
= 0.3962 sec
Compute elastic seismic response coefficient :
A = Acceleration coefficient = 0.075g (Given)
S = Site coefficient = 1.2 (Step 1)
CS =
1.2 AS
T
2
3
=
(1.2)(0.075)(1.2)
0.3962
2
3
= 0.2000
AASHTO Division I-A 5.2.1 states that CS need not exceed 2.5A :
CS = 2.5A = 2.5(0.075) = 0.1875 < 0.2000 .: So use 0.1875
Compute equivalent static earthquake loading :
Pe (x) =
=
ECS
w( x )vS ( x )
J
(5.058)(0.1875)
(30.0)( 4.28 x10 3 ) = 5.638 / ft
0.0216
Compute force due to Transverse motion acting on pier :
VX =
Pe ( x ) ˜ L
RPIER
(5.638)(39.4)
= 44.42 k
5
Step 6 : Summarize Loads Acting on Pier Column
PIER COLUMN
LOAD CASE I
Case 1 : 100% Longitudinal Motion + 30% Transverse Motion
VY = (110.27 k)(1.0) / 3 Columns = 36.76 k / column
MY = (36.76)(17.2) = 632.272 ft-k
VX = (44.25 k)(0.30) = 13.33 k
MX = (13.33 k)(13.13) = 174.97 ft-k
M=
2
2
M X M Y = 174.97 632.2722 = 656.04 ft-k
PU = Maximun Axial Load = 476.52 k
Total Dead Load = 1.873 k / ft
MDL = Dead Load Moment = 2,531.627 k-ft
A check of load case II produces a total moment of 378.4 ft-k.so load case II controls.
Step 7 : Checks for Effects of Slenderness
Unsupported Column Length (AASHTO 8.16.5.2.1) :
LU = 26 ft
Radius of Gyration (AASHTO 8.16.5.2.2):
k=1.0
k=2.0
r = qlS = (0.25 for circular member)(4ft) = 1.0 ft
Effective length factor :
The effective length factor used will vary
depending on the earthquake motion and
the corresponding orientation of the pier.
Keep in the mind the following :
‰
Transverse Earthquake Motion
Longitudinal Pier Direction
‰
Longitudinal Earthquake Motion
Transverse Motion
Longitudinal Motion
Transverse Pier Direction
Pier direction are in reference to bridge centerline.
Check Slenderness Ratio Limit (AASHTO 8.16.5.2.5) :
k ˜ LU
r
(1.0)( 26 ft )
= 26 > 22 : Column is SLENDER for Transverse Motion.
1.0
k ˜ LU
r
( 2.0)( 26 ft )
= 52 > 22 : Column Is SLENDER for Longitudinal Motion.
1 .0
Step 8 : Compute Moment Magnification Factor
Approximation Effects of Creep (AASHTO 8.16.5.2.7 ) :
Ed
TotalDeadLoad
TotalEarthquakeMoment
2531.627
656.04
= 3.86
Moment of Inertia of Gross Concrete Section :
Ig =
SD 4
S ˜ [( 2.95) (12in / ft )]4
64
64
=77.09 x 10 3 in4
Compute Flexural Rigidity (Equation 4.28) :
EC I g
EI = 2.5
1 E
3,300,000 psi(77.09 x103 )
2 .5
= 1.047 x 1011 Ib in2
1 3.86
Compute Factor Relating Actual Moment Diagram to Equivalent :
CM = 1.0
Compute Critical Buckling Load (Equation 4.26 ):
PC =
S 2 EI
S 2 (1.047 x1011 )
( kLU ) 2
(( 2.0)( 26 ft )(12in / ft )) 2
= 2653,855.35 k
Compute Moment Magnification Factor (Service Load Approach):
G
Cm
1 .0
=
= 1.00045
2.50 PU
( 2.50)( 476.52 k )
1
1
I ˜ PC
1.0( 2653,855.35k )
Step 9 : Determine Required Reinforcing Steel :
Compute Properties for Interaction Diagrams
PU= (476.52)( G )= (476.52)(1.00045) = 476.73 k
M = 607.10 ft-k( G ) = 656.04(1.00045) = 656.34 ft-k
Ag =
St 2
S (35.4" ) 2
4
4
P
f 'C ˜ Ag
M
f 'C tAg
= 984.2 in2
476.730
4,400(984.2)
= 0.11
(608860)(12)
= 4.77 x 10-2
4,400(35.4)(984.2)
gt = 31.6 in So : g = 31.6 in /35.6 in = 0.888 (must interpolate)
Enter into figure 4.14 (AASHTO) with x = 0.0477 and y = 0. 11
U g = 0.029
[ g = 0.8]
Enter into figure 4.15 (AASHTO) with x = 0.0477 and y = 0.11
U g = 0.027
[ g= 0.9]
Interpolate for g = 0.888
§ 0.8 0.888 ·
U g = 0.029 - ¨
¸ ˜ 0.029 0.027 = 0.02724
© 0 .8 0 .9 ¹
A
U g = S or : AS = U g ˜ A = (0.02724)(984.2) = 26.81 in2 = 17,296.49 mm2
Ag
Provide : 22H32 (17,710 mm2)
ANALYSIS OF A COLUMN BENT PIER UNDER SEISMIC
LOADING
PROBLEM : Analyze an existing column bent pier to see if a column in the pier can
accommodate seismic loading.
C/L
5.74’ (TYP)
3.94’
2.95’
14.8’
14.8’
ELEVATION
GIVEN :
1. A 3 span (18’-29’-18’) essential bridge crossing a highway.
2. 9 pairs of piles at 8.8’ center to center along length of footer.
3. 3 bays at 14.8’ center to center of column.
4. Concrete strength f’c = 3,000 psi.
5. 1950 ‘s vintage reinforcement fS = 27,000 psi.
6. Deck weight = 21.75 k / ft.
7. Geografic area has acceleration coeficient A = 0.15g
Step 1 : Determine Type of Seismic Analysis and Other Criteria
For an “essential bridge” by AASHTO 3.3 I-A we have:
IC = Importance Classification = I
With an importance classification of “I” by AASHTO 3.4 I-A for :
0.09 < A < 0.19 and IC = I
SPC = Seismic Performance Category = B
The bridge has an unchanging cross section,with similar supports, and a uniform mass
and stiffness,so it is considered to be :
Regular (By AASHTO 4.2 I-A)
For a Regular Bridge, SPC = B, and 2 or more spans, use:
Method 1 = Single-Mode Spectral Analysis (By AASHTO 4.2 I-A)
For stiff clay,by AASHTO 3.5 I-A:
Soil Profile Type II: S = Site Coefficient = 1.2
Response Modification Factor (AASHTO 3.6 I-A)
Multiple Column Bent: R = 5 (Treat as a wall-type pier)
Pier footing: R
= One-Half R for Multiple Column Bent
= R/2 = 5/2 = 2.25 (AASHTO 4.7.2 I-A)
Combination of Seismic Forces (AASHTO 4.4 I-A):
Case I : [100% Longitudinal Motion] + [30% Tranverse Motion]
Case II : [30% Longitudinal Motion] + [100 % Tranverse Motion}
Load Grouping (AASHTO 4.7.1 I-A) :
1.0(DL + Buoyancy + Stream Flow + Earth Pressure + Earthquake)
(N/A)
(N/A)
Step 2 : Compute Stiffness of the Pier
G
G
h = 24’
Longitudinal Earthquake
Motion
Transverse Earthquake
Motion
Longitudinal Motion
Ph3
G
3EI
4
Sd
S ( 2.95' ) 4
I=
3.72 ft 4
64
64
E = 3,300 ksi = 475,200 ksf
Transverse Motion
Ph3
Ph3
Ph3
G
12 E6I 12 E ˜ 6 I 72 EI
Sd 4 S ( 2.95' ) 4
I=
3.72 ft 4
64
64
E = 3,300 ksi = 475,200 ksf
Compute Deflection Due to Longitudinal Motion with P = 1:
G =
(1)( 24 ft )3
= 2.607 x 10-3 ft / k
4
(3)( 475,200 ksf )(3.72 ft )
k = Stiffness = 1/ G = 383.625 k / ft
For 3 column use : k = 1150.875 k / ft (Longitudinal Motion)
Step 3 : Compute Stiffness of the Pier (Continued)
Compute Deflection Due to Transverse Motion with P = 1:
G
(1)( 24 ft )3
= 108.613 x 10-6 ft / k
(72)( 475,200ksf )(3.72 ft 4 )
k = 1/ G = 1 / 108.613 x 10-6
= 9207 k / ft (Transverse Motion)
Step 4 : Compute Load due to Longitudinal Motion
18 m
29 m
18 m
Weight of Deck Slab
= 30.00 k / ft
VS
Compute static displacement vS with PO = 1:
VS =
(1)(98.04 ft )
= 85.19 x 10-3
1150.875
PO L
k
Compute single-mode factors D , E , J (AASHTO Division I-A 5.3) :
L
D =
-3
³ v ( x )dx = vS L = (85.19x 10
0
S
L
E
³ w( x )v ( x ) dx
J
³
0
L
0
S
w( x )vS ( x )2 dx
ft)(98.04 ft) = 8.352 ft2
Dw (8.352)(30.00k / ft ) = 250.56 ft-k
Evs
Compute period of oscillation :
( 250.56)(85.19 x10 3 ) = 21.35 ft2-k
J
T = 2S
PO gD
= 2S
21.35
(1k )(32.2 ft / sec 2 )(8.352)
= 1.770 sec
Compute elastic seismic response coefficient :
A = Acceleration coefficient = 0.15g (Given)
S = Site coefficient = 1.2 (Step 1)
CS =
1.2 AS
T
2
3
=
(1.2)(0.15)(1.2)
1.770
2
3
= 0.1476
AASHTO Division I-A 5.2.1 states that CS need not exceed 2.5A :
CS = 2.5A = 2.5(0.15) = 0.375 > 0.1476 .: So use 0.1476
Compute equivalent static earthquake loading :
Pe (x) =
=
ECS
w( x )vS ( x )
J
( 250.56)(0.1476)
(30.0)(85.19 x10 3 ) = 4.4270 k / ft
21.35
Compute force due to longitudinal motion acting on pier :
VY =
Pe ( x ) ˜ L
RPIER
( 4.4270 )(98.04)
= 86.80 k
5
Step 5 : Compute Load Due to Transverse Motion
Compute force due to transverse motion acting on pier:
The force due to transverse motion is :
Compute static displacement vS with PO = 1:
VS =
(1)(39.4 ft )
= 4.28 x 10-3
9207
PO L
k
Compute single-mode factors D , E , J (AASHTO Division I-A 5.3) :
L
D =
-3
³ v ( x )dx = vS L = (4.28 x 10
0
S
L
E
³ w( x )v ( x ) dx
J
³
S
0
L
0
ft)(39.4 ft) = 0.1687 ft2
Dw (0.1687)(30.00k / ft ) = 5.058 ft-k
w( x )vS ( x )2 dx
Evs
(5.058)( 4.28x10 3 ) = 0.0216 ft2-k
Compute period of oscillation :
J
T = 2S
PO gD
= 2S
0.0216
(1k )(32.2 ft / sec 2 )(0.1687)
= 0.3962 sec
Compute elastic seismic response coefficient :
A = Acceleration coefficient = 0.15g (Given)
S = Site coefficient = 1.2 (Step 1)
CS =
1.2 AS
T
2
3
=
(1.2)(0.15)(1.2)
0.3962
2
3
= 0.4004
AASHTO Division I-A 5.2.1 states that CS need not exceed 2.5A :
CS = 2.5A = 2.5(0.15) = 0.375 < 0.4004 .: So use 0.375
Compute equivalent static earthquake loading :
Pe (x) =
=
ECS
w( x )vS ( x )
J
(5.058)(0.375)
(30.0)( 4.28 x10 3 ) = 11.275k / ft
0.0216
Compute force due to Transverse motion acting on pier :
VX =
Pe ( x ) ˜ L
RPIER
(11.275)(39.4)
= 88.85 k
5
Step 6 : Summarize Loads Acting on Pier Column
PIER COLUMN
LOAD CASE I
Case 1 : 100% Longitudinal Motion + 30% Transverse Motion
VY = (86.80 k)(1.0) / 3 Columns = 28.933 k / column
MY = (28.933)(17.2) = 497.65 ft-k
VX = (88.25 k)(0.30) = 26.48 k
MX = (26.48 k)(13.13) = 347.77 ft-k
M=
2
2
M X MY =
347.77 497.652 = 607.12 ft-k
PU = Maximun Axial Load = 476.52 k
Total Dead Load = 1.873 k / ft
MDL = Dead Load Moment = 2,531.627 k-ft
A check of load case II produces a total moment of 378.4 ft-k.so load case II controls.
Step 7 : Checks for Effects of Slenderness
Unsupported Column Length (AASHTO 8.16.5.2.1) :
LU = 26 ft
Radius of Gyration (AASHTO 8.16.5.2.2):
k=1.0
k=2.0
r = qlS = (0.25 for circular member)(4ft) = 1.0 ft
Effective length factor :
The effective length factor used will vary
depending on the earthquake motion and
the corresponding orientation of the pier.
Keep in the mind the following :
‰
Transverse Earthquake Motion
Longitudinal Pier Direction
‰
Longitudinal Earthquake Motion
Transverse Motion
Longitudinal Motion
Transverse Pier Direction
Pier direction are in reference to bridge centerline.
Check Slenderness Ratio Limit (AASHTO 8.16.5.2.5) :
k ˜ LU
r
(1.0)( 26 ft )
= 26 > 22 : Column is SLENDER for Transverse Motion.
1.0
k ˜ LU
r
( 2.0)( 26 ft )
= 52 > 22 : Column Is SLENDER for Longitudinal Motion.
1 .0
Step 8 : Compute Moment Magnification Factor
Approximation Effects of Creep (AASHTO 8.16.5.2.7 ) :
Ed
TotalDeadLoad
TotalEarthquakeMoment
2531.627
607.12
= 4.17
Moment of Inertia of Gross Concrete Section :
Ig =
SD 4
S ˜ [( 2.95) (12in / ft )]4
64
64
=77.09 x 10 3 in4
Compute Flexural Rigidity (Equation 4.28) :
EC I g
EI = 2.5
1 E
3,300,000 psi(77.09 x103 )
2 .5
= 1.968 x 1010 Ib in2
1 4.17
Compute Factor Relating Actual Moment Diagram to Equivalent :
CM = 1.0
Compute Critical Buckling Load (Equation 4.26 ):
PC =
S 2 EI
S 2 (1.968 x1010 )
( kLU ) 2
(( 2.0)( 26 ft )(12in / ft )) 2
= 498,834 k
Compute Moment Magnification Factor (Service Load Approach):
G
Cm
1. 0
=
= 1.00239
2.50 PU
( 2.50)( 476.52 k )
1
1
I ˜ PC
1.0( 498,834 k )
Step 9 : Determine Required Reinforcing Steel :
Compute Properties for Interaction Diagrams
PU= (476.52)( G )= (476.52)(1.00239) = 477.66 k
M = 607.10 ft-k( G ) = 607.10(1.0029) = 608.86 ft-k
Ag =
St 2
S (35.4" ) 2
4
4
P
f 'C ˜ Ag
M
f 'C tAg
= 984.2 in2
477660
4,400(984.2)
= 0.11
(608860)(12)
= 4.77 x 10-2
4,400(35.4)(984.2)
gt = 31.6 in So : g = 31.6 in /35.6 in = 0.888 (must interpolate)
Enter into figure 4.14 (AASHTO) with x = 0.0477 and y = 0. 11
U g = 0.029
[ g = 0.8]
Enter into figure 4.15 (AASHTO) with x = 0.0477 and y = 0.11
U g = 0.027
[ g= 0.9]
Interpolate for g = 0.888
§ 0.8 0.888 ·
U g = 0.029 - ¨
¸ ˜ 0.029 0.027 = 0.02724
© 0 .8 0 .9 ¹
A
U g = S or : AS = U g ˜ A = (0.03784)(984.2) = 26.81 in2 = 17,296.49 mm2
Ag
Provide : 22H32 (17,710 mm2)
DESIGN OF A STUB ABUTMENT WITH SEISMIC CODE
PROBLEM : Design a stub abutment to accommodate given reactions from a composite
steel superstructure.
2.62’
V
13.73’
2.62’
4.43’
6.56’
Given :
1. A 3 span ( 59’-98’-59’) essential bridge crossing a highway.
2. 2.0 ‘ diameter concrete piles – 50 ft long.Capacity = 140 ton
3. 9 pairs of piles at 9’ center to center along length of footer.
4. Concrete strength f ‘C = 7,300psi = C50
5. Grade 50 reinforcement f ‘S = 27,000 psi =
6. Total reaction from all stringer R = 387 k.
7. Deck weight = 21.74 k/ft
8. Geografic area has acceleration coefficient : A = 0.075.
9. Soil test indicate stiff clay with angle of friction : I
30q
Step 1 : Determine Type of Seismic Analysis and Other Criteria
For an “essential bridge” by AASHTO 3.3 I-A we have :
IC = Importance Classification = I
With an importance classification of “I” by AASHTO 3.4 I-A for :
0.09<A<0.19 and IC = II
SPC = Seismic Performance Category = B
The bridge has an unchanging cross section,with similar supports,and a uniform mass and
stiffness,so it is considered to be :
Regular (By AASHTO 4.2 I-A)
For a Regular Bridge,SPC = B,and or more spans,use :
Method 1 = Single Mode Spectral Analysis (BY AASHTO 4.2 I-A)
For stiff clay, by AASHTO 3.5 I-A:
Soil Profile Type II:S = Site Coefficient = 1.2
Response Modification Factor (AASHTO 3.6 I-A)
Abutment Stem : R = 2 (Treat as a wall-type pier)
Abutment Footing : R = One – half R for abutment stem.
= R/2 = 2/2 = 1 (AASHTO 4.7.2 I-A)
Combination of Seismic Performance (AASHTO 4.4 I-A) :
Case I : 100 % Longitudinal Motion + 30% Tranverse Motion
Case II : 30% Longitudinal Motion + 100 % Tranverse Motion
Load Grouping (AASHTO 4.7.1 I-A):
1.0(DL = Buoyancy + Stream Flow + Earth Pressure + Earthquake
Step 2 : Compute Seismic Active Earth Pressure
Using the Monokobe- Okabe Equation (AASHTO C6.3.2 I-A) :
PAE =
1
˜ J ˜ H 2 ˜ (1 K V ) ˜ K AE
2
Where the seismic active pressure coefficient is defined as :
KAE =
cos2 (I T E )
Z ˜ cosT ˜ cos2 cos(G E T )
Where :
I
G
I
E
= Angle of Friction of soil = 30 ˚ (Given)
= Angle of friction between soil and abutment = 0 (Smooth)
= Backfill slope angle = 0 (Level Backfill)
= Slope of soil face = 0 (Vertical Rear Face of Stem)
and where :
§ kh
© 1 kV
T = ATAN ¨¨
·
¸¸
¹
§ 0.1125 ·
¸
© 1 0.045 ¹
T = ATAN ¨
kh = Horizontal acceleration Coefficient
= 1.5A = (1.5)(0.075) = 0.1125
kV = Vertical Acceleration Coefficient
T = 6.72˚ § 7 ˚
0.3kh < kV < 0.5kh
(0.3)(0.1125) < kV < (0.5)(0.1125)
0.03375 < kV < 0.05625 So use :
kV = 0.045
Check horizontal acceleration coefficient (AASHTO C6.3.2 I-A):
Kh < (1-kV)tan( I -I) so : 0.045 < (1-0.045)(tan(30-0)) < 0.5514 ¥
ª
sin(I G ) ˜ sin(I T i º
< = «1 »
cos(G E T ) ˜ cos(i E ) ¼
¬
ª
sin(30 0) ˜ sin(30 7 ) º
< = «1 »
cos(0 0 7 ) ˜ cos(0) ¼
¬
< = 1.1969
2
2
Recall that the seismic active pressure coefficient is defined as :
KAE =
=
cos2 (I T E )
< ˜ cosT ˜ cos2 E ˜ cos(G E T )
cos2 (30 7 0)
= 0.7183
(1.1969) ˜ cos(7 ) ˜ cos2 (0) ˜ cos(0 0 7 )
Also recall that the Monokobe- Okabe Equation is defined as :
PAE =
1
˜ J ˜ H 2 ˜ (1 kV ) ˜ k AE
2
So for the whole wall :
PAE =
1
˜ (120 Ib / ft 3 )(14) 2 (0.955) = 11,230.8 Ib / ft
2
Step 3 : Compute Static Active Earth Pressure
The static active earth pressure coefficient is defined as :
KA =
cos2 (I E )
\ ˜ cos2 E ˜ cos(G E )
Where :
2
ª
ª
sin(I G ) ˜ sin(I i) º
sin(30) ˜ sin(30) º
< = «1 » = «1 »
cos(G E ) ˜ cos(i E ) ¼
cos(0) ˜ cos(0) ¼
¬
¬
= 2.25
KA =
=
cos2 (I E )
\ ˜ cos2 E ˜ cos(G E )
cos2 (30 0)
= 0.3333
( 2.25) ˜ cos2 (0) ˜ cos(0 0)
So the static active earth pressure is defined as :
PA =
1
˜J ˜ H 2 ˜ KA
2
So for the whole wall :
PA =
1
˜ (120 Ib / ft 3 )(14) 2 (0.3333) = 3916.08 Ib/ft
2
Step 4 : Compute Equivalent Pressure
2
Determine a single,equivalent pressure based on :
‰
‰
Static pressure acting at H/3
Seismic pressure acting at 0.6H
F ‘T =
PA ˜
H
> PAE PA ˜ 0.60 H @
3
H
PA ˜
3
3916.08 ˜
F ‘T =
14
>11,230.8 Ib / ft 3916.08 Ib / ft ) ˜ 0.60 ˜ 14 ft @
3
14 ft
(3916.08 Ib / ft ) ˜ (
)
3
Use an equivalent pressure of : PAE = F ‘ TPA = (4.3622)PA
Step 5 : Compute Abutment Loads
For all dimensions refer to figure on calculation in step 1
DL
NOTE :
For all loads Wi and DL there is a
Kh W1
corresponding load kVWi and kVDL
acting upward (kV > 0) or
downward (kV <0)
All Wi loads are based on a per pile
VY
pair basis.Recall that the distance
between piles along the length of
footing was given as 9’ = 9 ft
Kh W2
Use the following unit weights :
CONCRETE = 145 Ib/ft3
PAE
W2
KhW3
R3
W3
R2
Compute all Wi loads from abutment and soil:
SOIL = 120 Ib/ft3
Wi = (Height)(Width)(Pile Distance)(Weight)
W1 = (5.66ft)(2.62 ft)(9.0 ft)(0.150 k / ft3) = 20.0 k
W2 = (2.62ft)(5.09ft)(9.0 ft)(0.150 k/ft3) = 18.0 k
W3 = (4.43 ft)(8.2 ft)(9.0 ft)(0.150 k/ft3) = 49.0 k
W4 = (8.40 ft)(1.312)(9.0ft)(0.120 k/ft3) = 11.90 k
Recall that the dead load from the superstructure was given as :
DL = 387 k / 9 pairs of piles = 43.0 k / pair
Step 6 : Compute Active Earth Pressure for Stem and Wall
H = 9.30’ (STEM)
H = 14 ‘ (WHOLE WALL)
PA
3.1’ Stem
PA
WALL
Using Rankie equation for :
4.7 ‘
I = 0 Level backfill
E = 0 Vertical Rear Face
G = 0 No friction Between Backfill and Backwall
PA =
1
˜ J ˜ H 2 ˜ K A Recall from step 3 : KA = 0.3333
2
1
˜ (0.120 k / ft 3 )(9.30 ft )2 (0.333) = 1.73 k/ft
2
PA = (1.73 k/ft)(9.0 ft between piles) = 15.57 k / pair
STEM
PA =
WALL
PA =
1
˜ (0.120 k / ft 3 )(14 ft ) 2 (0.3333) = 3.92 k/ft
2
PA = (3.92 k/ft)(9.0 ft between piles) = 35.28 k /pair
Step 7 : Compute Abutment Stiffness
5.08 ‘
G
KNOWN GEOMETRY :
The following are known geometric
parameters regarding the abutment
and bridge.
Backwall Width = 39.2 ‘
Span 1 = 59 ‘
Span 2 = 98 ‘
Span 3 = 59 ‘
H = 2.62’
G = 0.4E = 190080 ksf
Modulus of Elasticity for concrete
is given by :
EC = 33wC1.5 3,000 psi
= 33(150 pcf)1.5 3,000 psi
=3,300,000 psi
=475,200 ksf.
Compute Deflection Considering Effects of Shear with P = 1 :
G=
Ph3 1.2 Ph
3EI
AG
Where :
or : G
h3
1.2 h
3EI 0.4 EA
12 h3
1.2 h
3
3Ebd
0.4 Ebd
The equation above can be rewritten as :
H = 2.62’
3
D = 5.08’
G
§h·
§h·
4 ˜ ¨ ¸ 3˜ ¨ ¸
©d ¹
©d ¹
E ˜b
4 ˜ (0.52)3 3 ˜ (0.52)
( 475,200)(39.2' )
B = 39.2’
= 0.000000113 ft/k
H
D
2.62'
5.08'
0.52
k = stiffness = 1/ G = 8,776,648.7 k/ft
Step 8 : Compute Earthquake Load on Abutment
59 ‘
98 ‘
w = weight of deck = 21.74 k/ft
vS
Compute static displacement vS with PO = 1 :
59 ‘
(1)(98.0 ft)
PO ˜ L
= 11.17 x 10 -6
=
k
8776648.7 k / ft
VS =
Compute single-mode factors D , E , J (AASHTO Division I-A 5.3)
D
³
E =
v ( x ) dx = vSL = (11.17 x 10 –6)(98) = 1.09x 10 –3 ft2
L
0 S
³
L
0
³
L
0
w( x )vS ( x ) dx
Dw = (1.09 x 10 –3 ft2)(21.74 k/ft)
= 23.80 x 10 –3 ft k
J
=
w( x )vS ( x ) 2 dx
EvS = (23.80 x 10-3)(11.17 x 10-6)
= 265.82x 10-9 ft2 k
Compute period of oscillation :
J
T=2ɩ
PO gD
2S
265.82 x1098 ft 2 k
(1k )(32.2 ft / sec 2 )(1.09 x10 3 )
= 0.0173 sec
Compute Elastic Seismic Response Coefficient :
A = Acceleration Coefficient = 0.075 (Given)
S= Site coefficient = 1.2 (step 1)
CS =
1.2 AS
T
2
3
=
1.2(0.075)(1.2)
0.0173
2
3
= 1.61
AASHTO Division I-A 5.2.1 states that CS need not exceed 2.5A :
CS = 2.5A = (2.5)(0.075) = 0.1875 < 1.61 ¥ Use : CS = 0.1875
Compute equivalent static earthquake loading :
Pe(x) =
ECS
w( x )vS ( x )
J
( 23.80 x103 ft ˜ kx0.1875)
x (21.74 k /ft)(11.17x 10-6)
265.82 x10 9
= 4.0785 k / ft
=
Compute force acting on abutment :
VY =
pe ( x ) ˜ L
RSTEM
( 4.0785k / ft )(98 ft )
= 199.85 k
2 .0
Step 9 : Compute Shears and Moments
8”
NOTE :
12 ”
For all loads Wi and DL there is a
DL
corresponding load kVWi and kVDL
acting upward (kV > 0) or downward
VY
6’
KhW2
(kV < 0).
PAE
5.6’
3.1’
W2
1.31’
A
Previously Determined Values
DL = 43.0 k , W2 = 18 k , kh = 0.1125
W1 = 20.0 k
,kV = 0.045
Active pressure acting on stem :
PA = 15.57 k / pair
Step 6
PAE = 4.3622 PA = 4.3622 (15.57 k /Pair) = 67.92 k/pair
step 4
Superstructure loads acting on a pair of piles :
VY = 199.85 k
step 8
VY = (199.85 k) / 9 pairs of piles
= 22.21 k
6 V= 0:
-(DL + W1 + W2)(1-kV) kV > 0
= - (43.0 k + 20.0 k + 18.0 k )(1-0.045)
6 V= 0:
-(DL + W1 + W2 )(1+kV)
Ÿ -77.36 k
kV < 0
= - (43.0 k + 20.0 k + 18.0 k)(1 + 0.045)
6 H = 0:
Ÿ -84.65 k
khDL + khW1 + khW2 +VY + PAE
= (0.1125)(43.0 k) + (0.1125)(20.0 k) + (0.1125)(18) k + 22.21 k + 67.92
Ÿ 99.24 k
Axial Force:
FA =
V MAX
84.65k
=
=
Dist.Between piles
9.0 ft
Ÿ FA = 9.41k/ft
Shear Force :
V=
H
99.24 k
=
=
Dist.Between piles
9.0 ft
6 MA = 0:
Ÿ V = 11.03 k / ft
[kh < 0][kV>0]
5.6VY+ 1.0DL (1+kV) + 3.1PAE + 6khW1 + 2W2kh – 0.67W1(1+ kV)
(5.6)(22.21k) = 124.38 ft-k
Controlling Moment:
(1.0)(43.0 k)(1.045) = 44.94 ft-k
M=
(3.1)(67.92 k) = 210.55 ft-k
=
Worst case moment
Dist . between piles
383.42 ft k
9.0 ft
(6)(0.1125)(20) = 13.5 ft-k
Ÿ M = 42.60 ft-k /ft
(2)(18)(0.1125) = 4.05 ft-k
-(0.67)(20)(1+0.045) = -14.00 ft-k
TOTAL
= 383.42 ft-k
Step 10 : Design Reinforcement for Stem
Concrete and reinforcing steel parameters :
f’C = 7,300 psi (Given)
fC = 0.40f’C
n=
29,000ksi
ES
§6
=
4,923ksi
EC
r=
27,000 psi
fS
=9
=
fC
2,920 psi
k=
6
n
=
= 0.40
nr
69
= (0.40)(7,300 psi)
=2,920 psi
fS = 27,000 psi (Given)
fY = 50,000 psi (Given)
d = (5.09 ‘) – (2” cover) – ½(#6 bar)
= 58.71 in
Check for slenderness :
j = 1-
0.40
k
= 1= 0.867
3
3
LU = Unsupported length
By AASHTO 8.16.5.2.5 effect of
= 2.62 ft
slenderness may be ignored if the
slenderness ratio is less than 22
( 2.0)( 2.62)
k ˜ LU
=
= 5.24 < 22 ¥
r
1. 0
r = radius of gyration
= (0.30)(3.333) = 1.0
Therefore member is not slender
k= effective length factor
= 2.0
Design required main reinforcement :
AS =
( 42.60)(12in / ft )
M
=
f S jd
27 ksi(0.867 )(58.71in)
= 0.372 in2 / ft of wall = 791.998 mm2/ meter
for right and left moment, 791.998 x 7.0 meter = 5,543.99 mm2
So : Use , 7H32 (5632 mm2)
Compute design moment strength (AASHTO 8.16.3.2) :
IM N
a=
ª
a ·º
§
= I « AS fY ¨ d ¸»
2 ¹¼
©
¬
AS fY
0.85 f 'C b
So :
a=
(0.34inch2 )(50,000 Ib / in2 )
= 0.2283 in
0.85(7,300 Ib / in2 )(12in)
MU = IM n = 0.9[(0.34 in)(50,000 Ib/in2)(58.71 in -
0.2283
)]
2
= 896,516.51 in.b = 74.71 ft-k > 35.56 ft-k ¥
Design for shear – friction (AASHTO 8.15.5.4) :
Avf = Required Shear – Friction reinforcement =
V = 11.03 k/ft
V
fS P
step 9
fS = 27 ksi (Given)
P = 0.60 O (AASHTO 8.15.5.4.3(c)) = (0.60)(1.0)
Avf =
11.03k / ft
= 0.68 in2 / ft of wall = 1450 mm2 / meter
27(0.60)
H16-125 (1609 mm2)
Temperature Steel:
Ÿ # 5 bars @ 12 inch (0.31 inch2)
DESIGN OF A STUB ABUTMENT WITH SEISMIC CODE
PROBLEM : Design a stub abutment to accommodate given reactions from a composite
steel superstructure.
2.62’
V
13.73’
2.62’
4.43’
6.56’
Given :
1. A 3 span ( 59’-98’-59’) essential bridge crossing a highway.
2. 2.0 ‘ diameter concrete piles – 50 ft long.Capacity = 140 ton
3. 9 pairs of piles at 9’ center to center along length of footer.
4. Concrete strength f ‘C = 7,300psi = C50
5. Grade 50 reinforcement f ‘S = 27,000 psi =
6. Total reaction from all stringer R = 387 k.
7. Deck weight = 21.74 k/ft
8. Geografic area has acceleration coefficient : A = 0.15.
9. Soil test indicate stiff clay with angle of friction : I
30q
Step 1 : Determine Type of Seismic Analysis and Other Criteria
For an “essential bridge” by AASHTO 3.3 I-A we have :
IC = Importance Classification = I
With an importance classification of “I” by AASHTO 3.4 I-A for :
0.09<A<0.19 and IC = II
SPC = Seismic Performance Category = B
The bridge has an unchanging cross section,with similar supports,and a uniform mass and
stiffness,so it is considered to be :
Regular (By AASHTO 4.2 I-A)
For a Regular Bridge,SPC = B,and or more spans,use :
Method 1 = Single Mode Spectral Analysis (BY AASHTO 4.2 I-A)
For stiff clay, by AASHTO 3.5 I-A:
Soil Profile Type II:S = Site Coefficient = 1.2
Response Modification Factor (AASHTO 3.6 I-A)
Abutment Stem : R = 2 (Treat as a wall-type pier)
Abutment Footing : R = One – half R for abutment stem.
= R/2 = 2/2 = 1 (AASHTO 4.7.2 I-A)
Combination of Seismic Performance (AASHTO 4.4 I-A) :
Case I : 100 % Longitudinal Motion + 30% Tranverse Motion
Case II : 30% Longitudinal Motion + 100 % Tranverse Motion
Load Grouping (AASHTO 4.7.1 I-A):
1.0(DL = Buoyancy + Stream Flow + Earth Pressure + Earthquake
Step 2 : Compute Seismic Active Earth Pressure
Using the Monokobe- Okabe Equation (AASHTO C6.3.2 I-A) :
PAE =
1
˜ J ˜ H 2 ˜ (1 K V ) ˜ K AE
2
Where the seismic active pressure coefficient is defined as :
KAE =
cos2 (I T E )
Z ˜ cosT ˜ cos2 cos(G E T )
Where :
I
G
I
E
= Angle of Friction of soil = 30 ˚ (Given)
= Angle of friction between soil and abutment = 0 (Smooth)
= Backfill slope angle = 0 (Level Backfill)
= Slope of soil face = 0 (Vertical Rear Face of Stem)
and where :
§ kh ·
¸¸
© 1 kh ¹
T = ATAN ¨¨
§ 0.225 ·
¸
© 1 0.09 ¹
T = ATAN ¨
kh = Horizontal acceleration Coefficient
= 1.5A = (1.5)(0.15) = 0.225
kV = Vertical Acceleration Coefficient
T = 13.89 ˚ § 14 ˚
0.3kh < kV < 0.5kV
(0.3)(0.225) < kV < (0.5)(0.225)
0.0675 < kV < 0.1125 So use :
kV = 0.09
Check horizontal acceleration coefficient (AASHTO C6.3.2 I-A):
Kh < (1-kV)tan( I -I) so : 0.225 < (1-0.09)(tan(30-0)) < 0.525 ¥
ª
sin(I G ) ˜ sin(I T i º
< = «1 »
cos(G E T ) ˜ cos(i E ) ¼
¬
ª
sin(30 0) ˜ sin(30 14) º
< = «1 »
cos(0 0 14) ˜ cos(0) ¼
¬
< = 1.896
2
2
Recall that the seismic active pressure coefficient is defined as :
KAE =
=
cos2 (I T E )
< ˜ cosT ˜ cos2 E ˜ cos(G E T )
cos2 (30 14 0)
= 0.5388
(1.896) ˜ cos(18) ˜ cos2 (0) ˜ cos(0 0 18)
Also recall that the Monokobe- Okabe Equation is defined as :
PAE =
1
˜ J ˜ H 2 ˜ (1 kV ) ˜ k AE
2
So for the whole wall :
PAE =
1
˜ (120 Ib / ft 3 )(14) 2 (0.91) = 10,701.6Ib / ft
2
Step 3 : Compute Static Active Earth Pressure
The static active earth pressure coefficient is defined as :
KA =
cos2 (I E )
\ ˜ cos2 E ˜ cos(G E )
Where :
2
ª
ª
sin(I G ) ˜ sin(I i) º
sin(30) ˜ sin(30) º
< = «1 » = «1 »
cos(G E ) ˜ cos(i E ) ¼
cos(0) ˜ cos(0) ¼
¬
¬
= 2.25
KA =
=
cos2 (I E )
\ ˜ cos2 E ˜ cos(G E )
cos2 (30 0)
= 0.3333
( 2.25) ˜ cos2 (0) ˜ cos(0 0)
So the static active earth pressure is defined as :
PA =
1
˜J ˜ H 2 ˜ KA
2
So for the whole wall :
PA =
1
˜ (120 Ib / ft 3 )(14) 2 (0.3333) = 3916.08 Ib/ft
2
Step 4 : Compute Equivalent Pressure
2
Determine a single,equivalent pressure based on :
‰
‰
Static pressure acting at H/3
Seismic pressure acting at 0.6H
F ‘T =
PA ˜
H
> PAE PA ˜ 0.60 H @
3
H
PA ˜
3
3916.08 ˜
F ‘T =
14
>10701.6 Ib / ft 3916.08 Ib / ft ) ˜ 0.60 ˜ 14 ft @
3
14 ft
(3916.08 Ib / ft ) ˜ (
)
3
Use an equivalent pressure of : PAE = F ‘ TPA = (4.1189)PA
Step 5 : Compute Abutment Loads
For all dimensions refer to figure on calculation in step 1
DL
NOTE :
For all loads Wi and DL there is a
Kh W1
corresponding load kVWi and kVDL
acting upward (kV > 0) or
downward (kV <0)
All Wi loads are based on a per pile
VY
pair basis.Recall that the distance
between piles along the length of
footing was given as 9’ = 9 ft
Kh W2
Use the following unit weights :
CONCRETE = 145 Ib/ft3
PAE
W2
KhW3
R3
W3
R2
Compute all Wi loads from abutment and soil:
SOIL = 120 Ib/ft3
Wi = (Height)(Width)(Pile Distance)(Weight)
W1 = (5.66ft)(2.62 ft)(9.0 ft)(0.150 k / ft3) = 20.0 k
W2 = (2.62ft)(5.09ft)(9.0 ft)(0.150 k/ft3) = 18.0 k
W3 = (4.43 ft)(8.2 ft)(9.0 ft)(0.150 k/ft3) = 49.0 k
W4 = (8.40 ft)(1.312)(9.0ft)(0.120 k/ft3) = 11.90 k
Recall that the dead load from the superstructure was given as :
DL = 387 k / 9 pairs of piles = 43.0 k / pair
Step 6 : Compute Active Earth Pressure for Stem and Wall
H = 9.30’ (STEM)
H = 14 ‘ (WHOLE WALL)
PA
3.1’ Stem
PA
WALL
Using Rankie equation for :
4.7 ‘
I = 0 Level backfill
E = 0 Vertical Rear Face
G = 0 No friction Between Backfill and Backwall
PA =
1
˜ J ˜ H 2 ˜ K A Recall from step 3 : KA = 0.3333
2
1
˜ (0.120 k / ft 3 )(9.30 ft )2 (0.333) = 1.73 k/ft
2
PA = (1.73 k/ft)(9.0 ft between piles) = 15.57 k / pair
STEM
PA =
WALL
PA =
1
˜ (0.120 k / ft 3 )(14 ft ) 2 (0.3333) = 3.92 k/ft
2
PA = (3.92 k/ft)(9.0 ft between piles) = 35.28 k /pair
Step 7 : Compute Abutment Stiffness
5.08 ‘
G
KNOWN GEOMETRY :
The following are known geometric
parameters regarding the abutment
and bridge.
Backwall Width = 39.2 ‘
Span 1 = 59 ‘
Span 2 = 98 ‘
Span 3 = 59 ‘
H = 2.62’
G = 0.4E = 190080 ksf
Modulus of Elasticity for concrete
is given by :
EC = 33wC1.5 3,000 psi
= 33(150 pcf)1.5 3,000 psi
=3,300,000 psi
=475,200 ksf.
Compute Deflection Considering Effects of Shear with P = 1 :
G=
Ph3 1.2 Ph
3EI
AG
Where :
or : G
h3
1.2 h
3EI 0.4 EA
12 h3
1.2 h
3
3Ebd
0.4 Ebd
The equation above can be rewritten as :
H = 2.62’
3
D = 5.08’
G
§h·
§h·
4 ˜ ¨ ¸ 3˜ ¨ ¸
©d ¹
©d ¹
E ˜b
4 ˜ (0.52)3 3 ˜ (0.52)
( 475,200)(39.2' )
B = 39.2’
= 0.000000113 ft/k
H
D
2.62'
5.08'
0.52
k = stiffness = 1/ G = 8,776,648.7 k/ft
Step 8 : Compute Earthquake Load on Abutment
59 ‘
98 ‘
w = weight of deck = 21.74 k/ft
vS
Compute static displacement vS with PO = 1 :
59 ‘
(1)(98.0 ft)
PO ˜ L
= 11.17 x 10 -6
=
k
8776648.7 k / ft
VS =
Compute single-mode factors D , E , J (AASHTO Division I-A 5.3)
D
³
E =
v ( x ) dx = vSL = (11.17 x 10 –6)(98) = 1.09 x 10 –3 ft2
L
0 S
³
L
0
³
L
0
Dw = (1.09 x 10 –3 ft2)(21.74 k/ft)
w( x )vS ( x ) dx
= 23.80 x 10 –3 ft k
J
=
EvS = (23.80 x 10-3)(11.17 x 10-6)
w( x )vS ( x ) 2 dx
= 265.82 x 10-9 ft2 k
Compute period of oscillation :
J
T=2ɩ
PO gD
2S
265.80 x10 9 ft 2 k
(1k )(32.2 ft / sec 2 )(1.09 x10 6 )
= 0.0173 sec
Compute Elastic Seismic Response Coefficient :
A = Acceleration Coefficient = 0.15 (Given)
S= Site coefficient = 1.2 (step 1)
CS =
1.2 AS
T
2
3
=
1.2(0.15)(1.2)
0.0173
2
3
= 3.23
AASHTO Division I-A 5.2.1 states that CS need not exceed 2.5A :
CS = 2.5A = (2.5)(0.15) = 0.375 < 3.23 ¥ Use : CS = 0.375
Compute equivalent static earthquake loading :
Pe(x) =
ECS
w( x )vS ( x )
J
( 23.80 x103 ft ˜ kx0.375)
x (21.74 k /ft)(11.17 x 10-6)
265.80 x10 9
= 8.160 k / ft
=
Compute force acting on abutment :
VY =
pe ( x ) ˜ L
RSTEM
(8.160 k / ft )(98 ft )
= 399.84 k
2 .0
Step 9 : Compute Shears and Moments
8”
NOTE :
12 ”
For all loads Wi and DL there is a
DL
corresponding load kVWi and kVDL
acting upward (kV > 0) or downward
VY
6’
KhW2
(kV < 0).
PAE
5.6’
3.1’
W2
1.31’
A
Previously Determined Values
DL = 43.0 k , W2 = 18 k , kh = 0.225
W1 = 20.0 k
,kV = 0.09
Active pressure acting on stem :
PA = 15.57 k / pair
Step 6
PAE = 4.1189 PA = 4.1189(15.57 k /Pair) = 64.13 k/pair
step 4
Superstructure loads acting on a pair of piles :
VY = 399.84 k
step 8
VY = (399.84 k) / 9 pairs of piles
= 44.43 k
-(DL + W1 + W2)(1-kV)
6 V= 0:
kV > 0
= - (43.0 k + 20.0 k + 18.0 k )(1-0.09)
6 V= 0:
-(DL + W1 + W2 )(1+kV)
Ÿ -73.71 k
kV < 0
= - (43.0 k + 20.0 k + 18.0 k)(1 + 0.09)
6 H = 0:
Ÿ -88.29 k
khDL + khW1 + khW2 +VY + PAE
= (0.225)(43.0 k) + (0.225)(20.0 k) + (0.225)(18) + 44.43 + 64.13
Ÿ 126.79 k
Axial Force:
FA =
V MAX
88.29 k
=
=
Dist.Between piles
9.0 ft
Ÿ FA = 9.81 k/ft
Shear Force :
V=
H
126.79 k
=
=
Dist.Between piles
9.0 ft
6 MA = 0:
Ÿ V = 14.10 k / ft
[kh < 0][kV>0]
5.6VY+ 1.0DL (1+kV) + 3.1PAE + 6khW1 + 2W2kh – 0.67W1(1+ kV)
(5.6)(44.43 k) = 248.81 ft-k
Controlling Moment:
(1.0)(43.0 k)(1.09) = 46.87 ft-k
M=
(3.1)(64.13 k) = 198.80 ft-k
=
Worst case moment
Dist . between piles
514.97 ft k
9.0 ft
(6)(0.225)(20) = 27 ft-k
Ÿ M = 57.22 ft-k /ft
(2)(18)(0.225) = 8.1 ft-k
-(0.67)(20)(1+0.09) = -14.61 ft-k
TOTAL
= 514.97 ft-k
Step 10 : Design Reinforcement for Stem
Concrete and reinforcing steel parameters :
f’C = 7,300 psi (Given)
fC = 0.40f’C
n=
29,000ksi
ES
§6
=
4,923ksi
EC
r=
27,000 psi
fS
=9
=
fC
2,920 psi
k=
6
n
=
= 0.40
nr
69
= (0.40)(7,300 psi)
=2,920 psi
fS = 27,000 psi (Given)
fY = 50,000 psi (Given)
d = (5.09 ‘) – (2” cover) – ½(#6 bar)
= 58.71 in
Check for slenderness :
j = 1-
0.40
k
= 1= 0.867
3
3
LU = Unsupported length
By AASHTO 8.16.5.2.5 effect of
= 2.62 ft
slenderness may be ignored if the
slenderness ratio is less than 22
( 2.0)( 2.62)
k ˜ LU
=
= 5.24 < 22 ¥
r
1. 0
r = radius of gyration
= (0.30)(3.333) = 1.0
Therefore member is not slender
k= effective length factor
= 2.0
Design required main reinforcement :
AS =
(57.22)(12in / ft )
M
=
f S jd
27 ksi(0.867 )(58.71in)
= 0.4996 in2 / ft of wall = 1063.7 mm2/ meter
for right and left moment, 10 x 7.0 meter = 7,445.9 mm2
So : Use , 6H40 (7543 mm2)
Compute design moment strength (AASHTO 8.16.3.2) :
IM N
a=
ª
a ·º
§
= I « AS fY ¨ d ¸»
2 ¹¼
©
¬
AS fY
0.85 f 'C b
So :
a=
(0.34inch2 )(50,000 Ib / in2 )
= 0.2283 in
0.85(7,300 Ib / in2 )(12in)
MU = IM n = 0.9[(0.34 in)(50,000 Ib/in2)(58.71 in -
0.2283
)]
2
= 896,516.51 in.b = 74.71 ft-k > 35.56 ft-k ¥
Design for shear – friction (AASHTO 8.15.5.4) :
Avf = Required Shear – Friction reinforcement =
V = 14.10 k/ft
V
fS P
step 9
fS = 27 ksi (Given)
P = 0.60 O (AASHTO 8.15.5.4.3(c)) = (0.60)(1.0)
Avf =
14.10 k / ft
= 0.87 in2 / ft of wall = 1853.04 mm2 / meter
27(0.60)
H20-150 (2095 mm2)
Temperature Steel:
Ÿ # 5 bars @ 12 inch (0.31 inch2)
APPENDIX B
APPENDIX C
Data for El Centro 1940 North South Component (Peknold Version)
1559 points at equal spacing of 0.02 sec
"Points are listed in the format of 8F10.5, i.e., 8 points
across in"
a row with 5 decimal places
The units are (g)
*** Begin data ***
0.00630
0.00364
0.00099
0.00428
0.00758
0.01087
0.00682
0.00277
-0.00128
0.00368
0.00864
0.01360
0.00727
0.00094
0.00420
0.00221
0.00021
0.00444
0.00867
0.01290
0.01713 -0.00343 0.02400 -0.00992
0.00416
0.00528
0.01653
0.02779
0.03904
0.02449
0.00995
0.00961
0.00926
0.00892 -0.00486 -0.01864 -0.03242 -0.03365 0.05723 -0.04534
-0.03346 -0.03201 -0.03056 -0.02911 -0.02766 -0.04116 0.05466 -0.06816
-0.08166 -0.06846 -0.05527 -0.04208 -0.04259 -0.04311 0.02428 -0.00545
0.01338
0.03221
0.05104
0.06987
0.08870
0.04524
0.00179 -0.04167
-0.08513 -0.12858 -0.17204 -0.12908 -0.08613 -0.08902 0.09192 -0.09482
-0.09324 -0.09166 -0.09478 -0.09789 -0.12902 -0.07652 0.02401
0.02849
0.08099
0.13350
0.18600
0.23850
0.21993
0.20135
0.18277
0.16420
0.14562
0.16143
0.17725
0.13215
0.08705
0.04196 0.00314 -0.04824
-0.09334 -0.13843 -0.18353 -0.22863 -0.27372 -0.31882 0.25024 -0.18166
-0.11309 -0.04451
0.02407
0.09265
0.16123
0.22981
0.29839
0.23197
0.16554
0.09912
0.03270 -0.03372 -0.10014 -0.16656 0.23299 -0.29941
-0.00421
0.29099
0.22380
0.15662
0.08943
0.02224 0.04495
0.01834
0.08163
0.14491
0.20820
0.18973
0.17125
0.13759
0.10393
0.07027
0.03661
0.00295 -0.03071 -0.00561
0.01948
0.04458
0.06468
0.08478
0.10487
0.05895
0.01303 -0.03289 -0.07882 -0.03556
0.00771
0.05097
0.01013 -0.03071
0.07304 -0.03294
0.00715 -0.06350
0.03513
0.11510
0.19508
0.12301
0.03995
0.10653
0.17311
0.11283
0.04737
0.06573
0.02021 -0.02530
0.01709
0.03131
-0.02278 -0.07686
0.06034 -0.01877
0.02280 -0.00996
0.01459 -0.05022
-0.08585 -0.12148
0.13453 -0.08761
-0.04069
0.00623
0.04808 -0.00138
0.05141
0.10420
0.07734 -0.01527
-0.10789 -0.20051
0.07945 -0.12753
-0.17561 -0.22369
0.18128
0.14464
0.10800
0.07137
0.18296
0.14538
0.10780
0.07023
0.10337
0.07257
0.04177
0.01097
0.10416
0.03551
-0.03315 -0.10180
0.02025 -0.05543
-0.09060 -0.12578
0.05127 -0.00298
-0.01952 -0.03605
0.02699
0.02515
0.01770
0.02213
0.06294 -0.02417
0.01460
0.05337
0.02274
0.00679
-0.00915 -0.02509
0.00454 -0.01138
-0.00215
0.00708
0.01141
0.00361
0.01863
0.03365
0.02441
0.01375
0.01099
0.00823
0.02461 -0.04230
-0.05999 -0.07768
0.03777
0.01773
-0.00231 -0.02235
0.00418 -0.02496
-0.04574 -0.02071
0.02086
0.00793
-0.00501 -0.01795
0.02519 -0.05693
-0.07156
-0.11240
-0.15324
-0.11314
-
-0.13415
-0.20480
-0.12482
-0.04485
0.05094
-0.02113
-0.09320
-0.02663
0.05255
-0.00772
0.01064
0.02900
-0.07081
-0.04107
-0.01133
0.00288
-0.13095
-0.18504
-0.14347
-0.10190
-
-0.04272
-0.02147
-0.00021
0.02104
-
-0.15711
-0.19274
-0.22837
-0.18145
-
0.05316
0.10008
0.14700
0.09754
0.15699
0.20979
0.26258
0.16996
-0.06786
0.06479
0.01671
-0.03137
-0.27177
-0.15851
-0.04525
0.06802
0.03473
0.09666
0.15860
0.22053
0.03265
0.06649
0.10033
0.13417
-0.01983
0.04438
0.10860
0.17281
-0.07262
-0.04344
-0.01426
0.01492
-
-0.16095
-0.19613
-0.14784
-0.09955
-
-0.05259
-0.04182
-0.03106
-0.02903
-
0.02656
0.00419
-0.01819
-0.04057
-
0.02428
-0.00480
-0.03389
-0.00557
-0.04103
-0.05698
-0.01826
0.02046
0.00496
0.00285
0.00074
-0.00534
-
0.04867
0.03040
0.01213
-0.00614
-
0.00547
0.00812
0.01077
-0.00692
-
-0.09538
-0.06209
-0.02880
0.00448
0.01791
0.05816
0.03738
0.01660
0.00432
0.02935
0.01526
0.01806
-0.03089
-0.01841
-0.00593
0.00655
-
-
-
-0.04045 -0.02398
0.00642 -0.01156
-0.02619 -0.04082
0.05634 -0.04303
-0.02972 -0.01642
0.05011
0.02436
-0.00139 -0.02714
0.05773
0.04640
0.03507
0.03357
0.03637
0.01348
-0.00942 -0.03231
0.01984 -0.01379
-0.00775 -0.01449
0.12463
0.16109
0.12987
0.09864
0.00345
0.00269
-0.05922 -0.12112
0.06740
0.13001
0.08373
0.03745
0.13763 -0.10278
-0.06794 -0.03310
0.06417
0.09883
0.13350
0.05924
0.04164
0.01551
-0.01061 -0.03674
0.01508
0.04977
0.08446
0.05023
0.06769 -0.04870
-0.02970 -0.01071
0.00234 -0.06714
-0.04051 -0.01388
0.02351 -0.00541
-0.03432 -0.06324
0.01137
0.02520
0.06177
0.04028
0.12184
0.06350
0.00517 -0.05317
0.03283
0.03109
0.02935
0.04511
0.02245 -0.01252
0.00680
0.02611
0.07347 -0.03990
-0.00633
0.02724
0.03564 -0.00677
0.02210
0.05098
0.03706
0.02636
0.05822
0.09009
0.03689
0.01563
-0.00564 -0.02690
0.11521 -0.11846
-0.12170 -0.12494
0.06129 -0.01337
0.03455
0.08247
0.11235
0.13734
0.12175
0.10616
0.09037
0.06208
-0.00750
0.00897
0.00384
-0.00129
-
-0.05545
-0.04366
-0.03188
-0.06964
-
-0.00311
0.01020
0.02350
0.03681
-0.00309
0.02096
0.04501
0.06906
0.03207
0.03057
0.03250
0.03444
-0.02997
-0.03095
-0.03192
-0.02588
-0.02123
0.01523
0.05170
0.08816
0.06741
0.03618
0.00495
0.00420
-0.18303
-0.12043
-0.05782
0.00479
0.06979
0.10213
-0.03517
-0.17247
-0.03647
-0.03984
-0.00517
0.02950
-0.01503
-0.08929
-0.16355
-0.06096
-0.06287
-0.08899
-0.05430
-0.01961
0.01600
-0.01823
-0.05246
-0.08669
-
0.00829
-0.00314
0.02966
0.06246
-
0.01274
0.00805
0.03024
0.05243
-0.09215
-0.12107
-0.08450
-0.04794
0.01880
0.04456
0.07032
0.09608
-0.03124
-0.00930
0.01263
0.03457
0.06087
0.07663
0.09239
0.05742
0.04543
0.01571
-0.01402
-0.04374
-
0.06080
0.03669
0.01258
-0.01153
-
0.07985
0.06915
0.05845
0.04775
0.12196
0.10069
0.07943
0.05816
-0.04817
-0.06944
-0.09070
-0.11197
-
-0.16500
-0.20505
-0.15713
-0.10921
-
0.07576
0.06906
0.06236
0.08735
0.09057
0.07498
0.08011
0.08524
-
-
-
0.03378
0.00549
0.01201 -0.02028
-0.02855 -0.06243
0.02337 -0.03368
-0.01879 -0.00389
0.00840
0.00463
0.01766
0.03069
0.04456 -0.03638
-0.02819 -0.02001
0.05882 -0.06795
-0.07707 -0.08620
0.03496
0.04399
0.05301
0.03176
0.00186
0.05696
0.01985 -0.01726
0.11499
0.07237
0.02975 -0.01288
0.01853
0.00383
0.00342 -0.02181
0.08317 -0.04362
-0.00407
0.03549
0.00387
0.00284
0.00182 -0.05513
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*** End Data ***
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