unified design approach for structural concrete based on euroc
TRANSCRIPT
UNIVERSITI MALAYSIA SARAWAK
BORANG PENYERAHAN STATUS TESIS
Judul: Unified Design Approach for Structural Concrete Based on Eurocode 2
Sesi Pengajian: 2001 - 2005
Saya ADRIAN FONG WEI YI
(HURUF BESAR)
mengaku membenarkan tesis * ini disimpan di Pusat Khidmat Maklumat Akademik, Ink crsiti Malaýsia Sarawak dengan syarat-syarat kegunaan seperti berikut:
1. Tesis adalah hamilik Universiti Malaysia Sarawak.
2. Pusat Khidmat Maklumat Akademik. Universiti Malaysia SaraN%ak dihenarkan memhuat salinan untuk
tujuan pengajian sahaja.
3. Memhuat pengdigitan untuk membangunkan Pengkalan Data Kandungan "l'empatan.
4. Pusat Khidmat maklumat Akademik, Universiti Malaysia Sara\yak dihenarkan memhuat salinan tesis ini
sehagai bahan pertukaran antara institusi pengajian tinggi.
5. ** Sila tandakan ( yý ) di kotak berkenaan
SULI'I (Mengandungi maklumat yang bcrdarjah keselamatan atau kcpcntingan Malaysia scperti yang tcrmaktub di dalam AKI'A RAI ISIA RASMI I9722)
fF: RIIAD (Mengandungi maklumat 'fl? RIIAI) ýang tclah ditcntukan olch organisasi/hadan di mana penyclidikan dijalankan).
I'll)AK "I'I'. RI IAº)
4ýý
(FANI)ATANGAN PFAUI. IS)
AI, AMA"I TI ; "I'AP:
2 Regat Ipoh, Ipoh Garden. 3 1400. Ipoh Perak
Tarikh: i Ac'ýý) ýý''ý S
(I ANI)A I'AN(iAN I'I: Nti'I: I. IA)
Ass. Prof. Dr. Ng Chee Khoon
Nama Penyclia
"(arikh:
Disahkan oleh:
CATATAN * Tcsis dimaksudkan sebagai tesis ba}; i Ijazah Doktor F'alsafah, Sarjana dan Sarjana \luda lika tesis ini StTflatau IF: RIIAD, sila lampirkan sural daripada pihak herkuasa/orKanisasi hcrkenaan
dengan men}atakan sekali schab (Ian tempoh tesis ini perlu dikelaskan sebaKai St'I, fI (Ian TERIIAI).
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The following Final Year Project Report:
Title : UNIFIED DESIGN APPROACH FOR STRUCTURAL CONCRETE BASED ON EUROCODE 2
Name : ADRIAN FONG WEI Yl
Matrix Number: 7328
has been read and approved by :
ASSOCIATE PROFESSOR Date DR. NG CHEE KHOON
Project Supervisor
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P. KHIDMAT MAKLUMAT AKADEMIK UNIMAS
1111111111111111111111111 MI 1000143315
,.
'j r 'I ; ; iamaranan
UNIFIED DESIGN APPROACH FOR STRUCTURAL CONCRETE BASED
ON EUROCODE 2
ADRIAN FONG WEI Y[
A literature review report submitted in partial fulfillment of the requirement for the
Degree of Bachelor of Engineering with Honours (Civil Fngineering)
Faculty of Engineering
UNIVERSITI MALAYSIA SARAWAK
2005
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DEDICATION
To my dearest parents whom I love so much....
And to everyone who has been a part of me....
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ACKNOWLEDGEMENT
The journey began 4 years ago when I had to leave my hometown to a land far
away. Bidding farewell to my beloved family, I set my heart on completing this quest
with little knowledge of what lies ahead. Armed with just a stationery case and
writing pad, I trudged on. And with that, I met an outstanding teacher who taught me
Civil Engineering Materials and now, Final Year Project. It is an honour to have him
as my supervisor and it gives me great pleasure of saying to I)r. Ng Chee Khoon; a
million thank you is not sufficient for all the wonderful things that you have done.
My journey through the 4 years is not an easy one, often at times I was
besieged by an onslaught of catastrophic events. Fortunately for me there was help
when I least expect it. The 10 of us; Dorothy Chai Sin Yee, Ling Leh Shia, Onn Yin
Wee, Ong Khin Kiat, Ong Chee Zen, Kho Joo Tiong, Chong Kah Weng, Wong Seak
Yeo, Chai Peng How and I; formed a fellowship that guided each of us through.
Many a times I had just about to give up hope, but for the bond that we have in our
fellowship, I just could not let them down.
As I approach the last of my journey, I met a lot of interesting people who
assisted me in completing my journey; especially Chua Keng Yew. Leong Chee Kin.
Kiw Wei Yuen and Lim Yar Fen. Their help, although subtle at times meant a lot.
There is still a bevy of people who will forever have a piece of my memory; Li Lung,
Pei Wen. Pei Ee, Ngiik Hua, See Ee, and Ai Lin. Though the moment was short, I will
treasure every part of it.
And so the journey ends.....
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ABSTRACT
In this project, a unified design approach was proposed for
partially prestressed concrete (PPC) which incorporates fully reinforced
concrete and fully prestressed concrete as according to Eurocode 2. The
purpose of this project is to provide a platform for solving the problems that
might occur in designing partially prestressed concrete using the new design
code of Eurocode 2. The design of partially prestressed concrete proposed
here is based on a simplified version of Eurocode 2, in which it is assimilated
with the BS8110 (1985) standards. Hence, the procedure proposed here will
be valid for the rigorous design method and also the three version of concrete
as a single system of structural concrete. The design equations used in this
project were developed according to the strain compatibility condition and
parabolic stress block for concrete. The proposal by Naaman (1992) for the
ACI Structural Journal was fundamental in providing a guideline for this
project. The unified design approach proposed here covers a wide scope of
satisfying the serviceability limit and ultimate strength requirements. Thus, a
partial prestressing ratio is introduced where it is a pre-determined value
ranging from 0 to 1 for reinforced concrete and fully prestressed concrete
respectively. In order to make the structure fail in ductile manner, a maximum
reinforcement index, Wm ax, is introduced in which it is proportionate to the
ratio x/d(,
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ABSTRAK
Dalam projek ini, satu kaedah rekabentuk penyatuan (unified
design approach) telah dikemukakan untuk konkrit pra-tegasan separa (partial
prestressing concrete) yang melibatkan konkrit bertetulang dan konkrit pra-
tegasan sepenuh sepertimana yang dicadangkan oleh Eurocode 2. Tujuan
projek im adalah sebagai satu platform untuk menyelesaikan masalah yang
mungkin muncul dalam merekabentuk konkrit pra-tegasan separa berdasarkan
kod rekabentuk Eurocode 2. Kaedah merekabentuk konkrit pra-tegasan separa
yang dikemukakan di sini adalah berdasarkan Eurocode 2 yang telah
dipermudahkan, di mana unsur-unsur BS8110 (1985) telah diterap masuk.
Oleh itu, prosedur yang dicadangkan di sini adalah sah untuk kaedah
rekabentuk yang menyeluruh dan juga untuk ketiga-tiga jenis konkrit sebagai
satu system tunggal bagi struktur berkonkrit. Dalam projek ini, persamaan-
persamaan yang diterbitkan adalah berdasarkan kepada prinsip persamaan
tegangan serta blok tegasan parabolic konkrit. Cadangan yang dikemukakan
oleh Naaman (1992) untuk Jurnal Struktur f1CI dijadikan sebagai asas yang
penting dalam projek ini. Kaedah rekabentuk penyatuan yang dikemukakan di
sini meliputi satu spectrum yang luas supaya dapat memenuhi keperluan-
keperluan kebolehkhidmatan dan kekuatan muktamad. Justeru itu, satu nisbah
pra-tegasan separa (PPR) telah dicadangkan, di mana ia merupakan satu nilai
yang akan ditentukan yang merangkumi 0 hingga I untuk konkrit hertetulang
dan konkrit pra-tegasan sepenuh masing-masing. Selain itu, indeks tetulang
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maksimum, (Omax, telah dicadangkan di mana ia adalah berkadaran kepada
nisbah x/d, , supaya mod kegagalan yang diperlukan boleh dicapai.
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Pusat Khidmat R'tA. iu Mat A. k, ydeln"A UNIVERSITI MAI_A`ý(-IA SARrVrVAiti
943(1(1 KOGI Sasnaratlan
CONTENTS
Page
DEDICATION
ACKNOWLEDGEMENT
ABSTRACT
ABSTRAK
CONTENTS
LIST OF FIGURES
LIST OF TABLES
NOTATIONS
CHAPTER 1: INTRODUCTION
1.1 General
1.2 Objective
1.3 Problem Statement
1.4 Scope of Work
1.5 Organization of "Thesis
CHAPTER 2: LITERRATURE REVIEW
2.1 History of Prestressed Concrete
2.2 Classification of Concrete Structures
2.3 Partially Prestressed Concrete
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2.4 Flexural Behaviour of Prestressed Concrete Beams 10
2.5 Methods of Achieving Partial Prestressing 11
2.6 Uses of Non-Prestressed Reinforcement 12
2.7 Unified Design Approach for Partially Prestressed Beams 16
2.8 Summary 17
CHAPTER 3: METHODOLOGY
3.1 Grades of Concrete 18
3.2 Material Partial Safety Factors 19
3.3 Design of Flexural Elements at the Ultimate Limit State 19
CHAPTER 4: THE UNIFIED DESIGN APPROACH
4.1 General
4.2 Step 1: Preliminary Calculations
4.3 Step 2: Determine Partial Prestressing Ratio (PPR)
4.4 Step 3: Calculate lpe
4.5 Step 4: Estimate the Effective Depth, do
4.6 Step 5: Calculate the Factor, K
4.7 Step 6: Calculate the Reinforcement Index,
4.8 Step 7: Check Reinforcement Limit
4.9 Step 8: Calculate Tensile Forces
4.10 Step 9: Compute Neutral Axis Depth, x
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4.11 Step 10: Compute Strains
4.12 Step 11: Calculate Areas of Both Reinforcements
4.13 Step 12: Check for the Serviceability Limit State
4.14 The Flowchart of the Design Approach
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CHAPTER 5: DESIGN EXAMPLE
5.1 The Design Problem 44
5.1.1 Design Information 45
5.2 Solution 47
5.2.1 Moment Calculation 47
5.2.2 Allowable Stresses 48
5.2.3 Partial Prestressing Ratio (PPR) 49
5.2.4 Effective Prestress (fp, ) 50
5.2.5 Effective Depth (dc) 51
5.2.6 Factor K 51
5.2.7 Reinforcement Index ((w) 52
5.2.8 Maximum Reinforcement Index (c),,, j, x) 53
5.2.9 Tensile Forces 54
5.2.10 Depth of Neutral Axis (x) 54
5.2.11 Strains 55
5.2.12 Areas of Both Prestressed and Non-Prestressed Steel 58
5.2.13 Serviceability Limit State 59
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CHAPTER 6: CONCLUSION
6.1 Conclusion 61
REFERENCES 63Dem
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LIST OF FIGURES
Page
1) Fig. 2.1 Typical load-deflection curves for varying 10
degrees of prestress
2) Fig. 2.2 Uses of non-prestressed reinforcement 14
3) Fig. 3.1 Strain and stress distributions of a singly- 20
reinforced rectangular beam in accord to BS8 110 (1985)
4) Fig. 3.2 Strain and stress distributions of a doubly- 21
reinforced rectangular beam in accord to BS8110 (1985)
5) Fig. 3.3 Strain and stress distributions of a singly- 21
reinforced rectangular beam in accord to Eurocode 2
6) Fig. 3.4 Strain and stress distributions of a doubly 22
reinforced rectangular beam in accord to Eurocode 2
7) Fig. 3.5 Cross Section of a partially prestressed beam 25
8) Fig. 4.1 Cross section and stress distribution at ultimate 32
strength of a partially prestressed concrete beam
9) Fig. 4.2 Strain and stress distribution for a section with 38
prestressed and non-prestressed reinforcement
10) Fig. 4.3 Flowchart of unified design approach for 43
partially prestressed concrete structures based on EC2
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Page
11) Fig. 5.1 Cross section of beam 45
12) Fig. 5.2 Design stress-strain curve for reinforcing steel 56
13) Fig. 5.3 Design stress-strain curve for prestressing 57
tendons
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LIST OF TABLES
Page
1) Table 3.1 Comparison of notations, parameters and 23
design equations
2) Table 3.2 Relationship of cube strength to cylinder 23
strength
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NOTATIONS
a = Depth of rectangular stress block
Ac = Cross sectional area of concrete
Ap, = Area of prestressing tendon
As = Area of reinforcing steel
b = Width of section
c = Neutral axis depth
C = Total compressive forces
de = Effective depth
d� = Depth due to the centroid of compressive forces
dp = Depth due to the centroid of prestressing tendons
d, = Depth due to the centroid of reinforcing steels
Ec = Secant modulus of elasticity of concrete
Eps = Modulus of elasticity of prestressing tendon
E, = Modulus of elasticity of reinforcing steel
Fi = Initial prestressing force
f 1 Initial concrete strength
fcu = Characteristic concrete cube strength at 28 days
ffk = Characteristic compressive cylinder strength of concrete at 28 days
fph = Design tensile stress in the tendons at failure
fpe = Design effective prestress in the tendons alter all losses
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fp; = Initial prestress in tendons
fps = Stress in prestressing steel at ultimate limit
fp� = Characteristic strength of prestressing tendon
fpy = Yield strength of tendon taken at 0.2% of permanent strain
fs
f,,
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= Stress in reinforcing steel
= Yield strength of reinforcing steel according to BS8110 (1985)
= Yield strength of reinforcing steel according to Eurocode 2
= Depth of section
= Second moment of area
K = Factor defined in Clause 3.4.4.4: Part 1: BS8110: 1985
ki, k2 = Characteristic ratios of parabolic stress block
kb = Depth from centroid of concrete to lower limit of central kern
kt = Depth from centroid of concrete to upper limit of central kern
L = Span of beam
M = Bending moment
MIMIX = Maximum moment
M,,,;,, = Minimum moment
M� = Nominal moment strength of a section
Mu = Ultimate bending moment
(Mu)iý = Ultimate resisting moment due to prestressing steel
(M01"s = Ultimate resisting moment due to total steel
Np = Number of tendons required
= Number of non-prestressed steels required
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PPR = Partial prestressing ratio
T = Total tensile forces
TI, = Tensile force due to prestressing tendon
Ts = Tensile force due to reinforcing steel
Wco�c = Self-weight of concrete beam
W[) = Dead load
W DI = Factored dead load
WL = Live load
Will = Factored live load
x = Neutral axis depth
Yb = Distance from centroid of concrete to extreme bottom fibre
y, = Distance from centroid of concrete to extreme top fibre
Z = Lever arm
Zi, = Section modulus with respect to the bottom fibre
Zt = Section modulus with respect to the top fibre
7n, = Partial safety factor of materials
7C = Specific weight of concrete
FCC = Effective strain in concrete
= Ultimate concrete strain
Eph = Ultimate strain in tendon
ErC = Effective prestrain in tendon
E5 = Strain in reinforcing steel
FU = Ultimate strain
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w = Combined reinforcement index
wmax = Maximum reinforcement index
wr = Reinforcement index due to tendons
ws = Reinforcement index due to reinforcing steel
ß,, ß, = Bond coefficients
rl; = Coefficient of short term losses
Ili, = Coefficient of long term losses
ac; = Allowable temporary compressive stress in the concrete
6ti = Allowable temporary tensile stress in the concrete
6cs = Allowable service compressive stress in the concrete
Gts = Allowable service tensile stress in the concrete
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CHAPTER I
INTRODUCTION
1.1 GENERAL
The European construction market was officially established in
January 1993. An important instrument in this connection is the 'Construction
products directive', adopted by the EU-Commission in December 1988. This
directive sets out the conditions under which a construction product (e. g.
cement, ready-mixed concrete, reinforcement, precast element) can be
imported and exported and used for its intended purposes without impediment
in EU countries. According to The Concrete Society (1997), a set of
'Technical specifications'; that is, harmonized European standards, or, where
these are lacking European technical approvals - are necessary I'Or tile
practical applications of this directive. This standards system will quantify
requirements for concept, design, detailing and execution of structures. On the
basis of provisional mandates of the EU. a code of practice for concrete
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structures is being established by the European Committee for Standardization
(CEN) which, in the long term, will replace national standards.
Eurocode 2 `Design of concrete structures; Part 1-1: General rules and
rules for buildings' was issued as European Prestandard ENV 1992-1-1 by the
European Committee for Standardization (CEN). Consequently, the first parts
of the future European system of harmonized standards for concrete structures
are available in the form of ENV 1992-1-1 (EC2) and the Prestandard ENV
206 for concrete technology. According to Beeby and Narayanan (1995), the
gaps, which are due to the lack of further ENV standards, including covering
constituent materials for concrete, reinforcement, prestressing steel, quality
control, are covered by National Application Documents (NAD). This is to
enable the provisional application of the new European standards as
recommended by the EU.
The design concept of EC2 does not differentiate between prestressed
and non-prestressed structural members. Likewise, no distinction is made
between full, limited or partial prestressing. EC2 is divided into `Principles'
and `Application rules'. `Principles' comprise verbally defined general
requirements (e. g. regarding structural safety), to which no alternative is
permitted. On the whole, these are definitions and obvious requirements
which can be adopted by all EU countries. The `Application rules' are
generally recognizes rules (for example detailing rules) that follow the
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`Principles' and satisfy their requirements. It is permissible to use alternative
design rules provided that it is shown that these rules accord with the relevant
`Principles' and that they are at least equivalent to those in EC2. Similar
questions regarding methods have yet to be resolved. However, the principle
of interchangeability of rules is generally anchored in the national codes of
practice. A further characteristic of EC2 is the so-called `indicative' values,
i. e. figures given as an indication (e. g. the partial safety factors) and identified
in the text by a `box'. During an interim period, at least, they can be
determined nationally by the individual EU countries. Where necessary, such
modifications are given in special cases in the National Applications
Documents (NAD) during provisional applications of EC2.
1.2 OBJECTIVE
With the BS 81 10 about to give way to Furocode 2 in the year 2008 as
the structural design code in the UK, this project seeks to look into the details
of EC2 and obtain a unified approach for reinforced and prestressed concrete.
Derivation of formulas for design of reinforced, partially prestressed and fully
prestressed concrete structures will he based on Furocode 2.
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1.3 PROBLEM STATEMENT
When Eurocode 2 is to be introduced in the future, most engineers will
need to be assured that it can be used as a practical concrete design tool, as
well as producing economic results. If they are not assured of this, practices
will continue to use BS 8110 in preference to adopting the new code.
Furthermore, the general philosophy of EC2 is quite different from that found
in BS 8110. Eurocode 2 makes no attempt to be a design 'guide'; it is a code
giving general rules. There are no simplified tables of moment or shear factors
for example, as one might expect to look for these in separate design guides or
standard textbooks. Therefore, it is necessary that the transition to Eurocode 2
will be aided by the availability of necessary guidance in the form of
explanatory literature, process flowcharts, spreadsheets and other design
software.
1.4 SCOPE OF WORK
There are 3 types of structures in which this project will look into,
reinforced, partially prestressed and fully prestressed concrete structures. The
design formulas for reinforced concrete structures are based on stress and
strain compatibility and force equilibrium. The derivation of the formulas for
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prestressed and partially prestressed concrete structures will be based from
this first principle.
1.5 ORGANIZATION OF THESIS
This thesis is divided into 6 chapters. The First Chapter is an
introduction to the Eurocode 2, in which a brief history and background of
Eurocode 2 and its application are mentioned. In Chapter Two, a review on
the materials used in this project such as journals, books and articles is given.
In Chapter Three, an explanation of the materials used for prestressed
concrete as well as a comparison of both Eurocode 2 and BS8110 (1985). For
Chapter Four, the derivation of the formulas of partially prestressed concrete
structures for Eurocode 2 is covered whereas in Chapter Five, examples of the
derived formulas in design are shown. In the last part of the thesis, Chapter
Six, a conclusion will be drawn to summarise the overall project as a whole.
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