creep and shrinkage using different code

PSZ 19:16 (Pind. 1/07)

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(full text)

NG PING CHEW

18 JULY 1982

COMPARISON OF CREEP AND SHRINKAGE

2007/2008

820718-04-5165 ASSOC. PROF. IR. DR. WAHID OMAR

18 NOVEMBER 2008 20 NOVEMBER 2008

USING DIFFERENT CODE OF PRACTICE

DECLARATION

“I/We* hereby declare that I/We* have read this project report and in my/our*

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

award of the degree of Master of Engineering (Civil – Structure).”

Signature : ………………………….………………..

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ASSOC. PROF. IR. DR. WAHID

20 NOVEMBER 2008

COMPARISON OF CREEP AND SHRINKAGE

USING DIFFERENT CODE OF PRACTICE

NG PING CHEW

A project report submitted in fulfillment of the

requirements for the award of the degree of

Master of Engineering (Civil – Structure)

Faculty of Civil Engineering

Universiti Teknologi Malaysia

NOVEMBER 2008

ii

I declare that this project report entitled “Comparison of Creep and Shrinkage Using

Different Code of Practice” is the result of my own except as cited in the references.

The project report has not been accepted for any degree and is not concurrently

submitted in candidate of any degree.

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NG PING CHEW

18 NOVEMBER 2008

iii

DEDICATION

For my beloved family

iv

ACKNOWLEDGEMENT

The author is deeply indebted to his supervisor, Assoc. Prof. Ir. Dr. Wahid

Omar whose help, stimulating suggestions and encouragement helped him in all the

time of the study and preparation of this project.

The author wishes to thank Mr. Edgar T. Almoite, for his helpful guidance.

The author has furthermore to thank all the lecturers and staffs of Faculty of

Civil Engineering UTM, for their advice and assistance throughout the study.

Sincere appreciation also extends to all his friends for their help, support,

interest and valuable hints.

Last but not least, the author would like to express his deepest gratitude to his

parents, Ng Soon and Ken Kim Moy, for unconditional support and encouragement

to pursue his interest.

v

ABSTRACT

This project presents a study on the behavior of creep and shrinkage of concrete

specimens. Prediction of creep and shrinkage strain was studied and compared based

on British Standard 8110, Eurocode 2 and Australian Standard. The objective of this

study is to understand the concrete behavior of creep and shrinkage and to produce a

spread sheet of determining creep and shrinkage strain based on the three standards

mentioned. The spread sheet will be used to ease future engineers in estimating

creep and shrinkage strain of concrete in structural design work. Creep and

shrinkage are two important time-dependent properties of concrete as it causes

cracking and adversely affects the functionality, durability and appearance of

structure. There are many parameters that affect the concrete creep and shrinkage

strain such as concrete strength, type of cement, relative humidity, effective

thickness, days of loading, etc. In this study, relative humidity of the environment

was used as the controlled parameter in comparing the creep and shrinkage strain.

Australian Standard was found to be limited in determining creep and shrinkage

strain because it is based on climatic zones in Australia. However, prediction using

Australian Standard is still being considered as each zone has its own range of

relative humidity. Graph and formula method for Eurocode were considered in this

study. Both of the methods gave acceptable results. In creep and shrinkage strain

comparison, Eurocode present acceptable result with more conservative strain. This

code of practice is preferable in determining concrete creep and shrinkage among the

standards researched in this study.

vi

ABSTRAK

Projek ini membincangkan kajian kelakuan rayapan dan pengecutan atas spesimen

konkrit. Anggapan rayapan dan pengecutan konkrit telah dikaji dan perbandingan

telah dibuat berdasarkan British Standard 8110, Eurocode 2 dan Australian Standard.

Tujuan kajian ini adalah untuk memahami kelakuan rayapan dan pengecutan konkrit

serta menghasilkan spread sheet yang berfungsi untuk menentukan nilai rayapan dan

pengecutan berpandukan ketiga-tiga kod rekabentuk tersebut. Spread sheet ini akan

menyenangkan kerja jurutera dengan menentukan nilai rayapan dan pengecutan

konkrit dalam rekabentuk struktur. Rayapan dan pengecutan merupakan ciri-ciri

penting konkrit. Rayapan dan pengecutan akan menyebabkan keretakan konkrit,

dimana menjejaskan struktur tersebut dari segi fungsi, ketahanan dan persembahan

luarannya. Terdapat banyak parameter yang mempengaruhi rayapan dan pengecutan

konkrit seperti kekuatan konkrit, jenis simen, kelembapan bandingan, kedalaman

berkesan, masa pembebanan dan sebagainya. Dalam kajian ini, kelembapan

bandingan alam persekitaran telah digunakan sebagai parameter pengawal dalam

bandingan rayapan dan pengecutan. Didapati bahawa Australian Standard adalah

terhad dalam menentukan nilai rayapan dan pengecutan disebabkan kod tersebut

adalah berdasarkan zon cuaca Australia. Walau bagaimanapun, anggapan bagi nilai

rayapan dan pengecutan konkrit berdasarkan Australian Standard masih dilaksanakan

dalam kajian ini kerana setiap zon mempunyai kelembapan bandingannya masing-

masing. Bagi Eurocode, kaedah graf dan formula telah digunakan dalam kajian ini.

Kedua-dua kaedah tersebut telah menghasilkan keputusan yang memuaskan. Dalam

perbandingan nilai rayapan dan pengecutan, Eurocode menghasilkan keputusan

dengan konsevatif. Antara kod-kod yang digunakan, kod ini adalah lebih digemari

dalam kajian ini untuk menentukan nilai rayapan dan pengecutan.

vii

TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES xii

LIST OF FIGURES xiii

LIST OF SYMBOLS xviii

ABBREVIATION xx

1 INTRODUCTION 1

1.1 Background 1

1.2 Serviceability of Concrete Structures 5

1.3 Problem Statement 7

1.4 Objectives of Project 8

1.5 Scope of Work 9

1.6 Expected Outcome 10

2 LITERATURE REVIEW 11

2.1 Significance of Volume Changes and

Creep 11

2.2 The Gel Structure as Related to Volume

Changes 12

viii

2.3 Shrinkage of Concrete 13

2.3.1 Type of Shrinkage 14

2.3.1.1 Plastic Shrinkage 14

2.3.1.2 Autogeneous Shrinkage 15

2.3.1.3 Drying Shrinkage 16

2.3.1.4 Carbonation Shrinkage 19

2.3.2 Factors Affecting Shrinkage 22

2.3.2.1 Effect of Composition and

Fineness of Cement 23

2.3.2.2 Effect of Type and

Gradation of Aggregate 23

2.3.2.3 Effect of Cement and Water

Contents 24

2.3.2.4 Effect of Admixtures 25

2.3.2.5 Temperature and Relative

Humidity 27

2.3.2.6 Volume-to-Surface Ratio 27

2.3.2.7 Volume and Type of

Aggregate 28

2.3.2.8 Elastic Modulus of

Aggregate 29

2.3.3 Differential Shrinkage 29

2.3.4 Shrinkage-induced Cracking 32

2.3.5 Effect of Shrinkage 34

2.3.6 Methods of Controlling Shrinkage

Cracking 34

2.3.6.1 Conventional Method 36

2.3.6.2 Innovative Method 39

ix

2.4 Creep of Concrete 42

2.4.1 Creep Behavior of Concrete 44

2.4.2 Components of Creep Strain 45

2.4.3 Factors Affecting Creep 47

2.4.3.1 Effect of Stress and Age

When First Loaded 47

2.4.3.2 Effect of Water-Cement

Ratio and Mix 47

2.4.3.3 Effect of Composition and

Fineness of Cement 48

2.4.3.4 Effect of Character and

Grading of Aggregate 49

2.4.3.5 Effect of Moisture Condition

of Storage 50

2.4.3.6 Effect of Size of Mass 51

2.4.4 Effect of Creep 52

2.4.5 Test for Creep 53

2.4.5.1 Dead load 54

2.4.5.2 Spring-loaded 54

2.4.5.3 Hydraulic 54

2.4.5.4 Stabilized Hydraulic 55

3 PREDICTION METHODS 56

3.1 Introduction 56

3.2 Shrinkage 57

3.2.1 Drying Shrinkage Strain 57

3.2.2 British Standard 61

3.2.3 Australian Standard 64

3.2.3.1 Basic Shrinkage Strain 64

3.2.3.2 Design Shrinkage Strain 65

x

3.2.4 Eurocode 68

3.2.4.1 Eurocode (Annex B) 71

3.3 Creep 72

3.3.1 Creep Strain 72



3.3.3.1 Basic Creep Factor 77

3.3.3.2 Design Creep Factor 78

3.3.4 Eurocode 80

3.3.4.1 Eurocode (Annex B) 82

4 METHODOLOGY 86

4.1 Introduction 86

4.2 Information Gathering 86

4.3 Preparation of Spread Sheet 88

5 ANALYSIS OF RESULTS 89

5.1 Introduction 89

5.2 Shrinkage 89

5.2.1 Shrinkage Strain 90



5.2.4 European Standard 93

5.2.5 Comparison of Shrinkage Using

Different Standards 95

5.3 Creep 97

5.3.1 Creep Strain 98



5.3.4 European Standard 101

xi

5.3.5 Comparison of Creep Using

Different Standard 103

6 CONCLUSION AND RECOMMENDATIONS 105

6.1 Conclusions 105

6.2 Recommendations for Further Studies 107

REFERENCES 105

APPENDIX 109

xii

LIST OF TABLES

TABLE NO. TITLE PAGE

2.1 Shrinkage of neat cement in comparison with the 24

corresponding shrinkages of the same cement diluted

with a single sieve size (No. 4 to 3/8 in.) of gravel

and crushed limestone, respectively

2.2 Methods of controlling drying shrinkage 35

2.3 Aggregate type related to drying shrinkage 37

2.4 Effect of mineral character of aggregate upon creep 50

2.5 Effect of moisture condition of storage upon creep 51

3.1 Nominal unrestrained drying shrinkage values εcd,0 (%) 69

for concrete with cement CEM Class N

3.2 Values for kh 69

3.3 Basic creep factor 77

xiii

LIST OF FIGURES

FIGURE NO. TITLE PAGE

1.1 Relationship between concrete strain and time 5

2.1 Relationship between shrinkage and loss of water from 18

specimens of cement-pulverized silica pastes cured for

7 days at 21ºC and then dried

2.2 Loss of mass of concrete due to drying and carbonation 19

2.3 Drying shrinkage and carbonation shrinkage of mortar 20

at different relative humidity

2.4 Influence of the sequence of drying and carbonation of 21

mortar on shrinkage

2.5 The pattern of shrinkage as a function of cement content, 25

water content and water/cement ratio

2.6 Effect of W/C ratio and aggregate content on shrinkage 28

xiv

2.7 Relation between axial shrinkage and width of square 31

cross-section and length/width ratio of 4

2.8 Relation between ultimate shrinkage and 31

volume/surface ratio

2.9 Schematic pattern of crack development when tensile 33

stress due to restrained shrinkage is relieved by creep

2.10 Typical strain-time plot of concrete under sustained 43

load and after release of load

2.11 Recoverable and irrecoverable creep component 45

2.12 Creep components in drying specimen 46

2.13 Effect of water-cement ratio on creep 48

2.14 Creep in compression and tension for mass-cured 49

concretes

2.15 Effect of size of specimens upon creep 52

3.1 Coefficient KL 59

3.2 Coefficient Kc 59

3.3 Coefficient Ke 60

xv

3.4 Coefficient Kj 60

3.5 Drying shrinkage of normal-weight concrete 63

3.6 Shrinkage strain coefficient (k1) for various environments 66

3.7 Climatic Zones in Australia 67

3.8 Coefficient KL 73

3.9 Coefficient Km 74

3.10 Coefficient Ke 74

3.11 Effects of relative humidity, age of loading and section 76

thickness upon creep factor

3.12 Creep factor coefficient (k2) for various environments 79

3.13 Maturity coefficient (k3) 79

3.14 Method for determining the creep coefficient for concrete 82

under normal environmental conditions

5.1 Relationship between shrinkage and relative humidity 90

based on code of practice specified by Hong Kong

government

xvi


based on BS 8110


based on AS 3600


using table and formula method based on EC 2

5.5 Relationship between shrinkage and duration based on 95

EC 2

5.6 Comparison of shrinkage using different code of practice 97

5.7 Relationship between creep and relative humidity based 98

on code of practice specified by Hong Kong government

5.8 Relationship between creep and relative humidity 100

based on BS 8110


based on AS 3600


using graph and formula method based on EC 2

5.11 Comparison of creep using different standards 103

xvii

5.12 Relationship between creep and duration based on EC 2 104

xviii

LIST OF SYMBOLS

εcs / εss – shrinkage strain

cs – modification factor to allow for properties of crushed granitic

aggregate

KL – coefficient relating to the environment (shrinkage)

Kc – coefficient relating to the composition of the concrete

(shrinkage)

Ke – coefficient relating to the effective thickness of the section

(shrinkage)

Kj – coefficient defining the development of shrinkage relative to

time

Ks – reinforcement coefficient

αe – modular ratio Es/Ec

ρ – steel ratio As/Ac

As – total area of longitudinal reinforcement

Ac – gross cross-sectional concrete area

Es – modulus of elasticity of the reinforcement

Ec – short-term modulus of concrete

εcs.b – basic shrinkage strain

k1 – shrinkage strain coefficient

εsd(t) – drying shrinkage strain in time

εsd(t) – nominal unrestrained drying shrinkage

εsa – autogeneous shrinkage strain

h0 – effective thickness

u – perimeter of the member in contact with the atmosphere

xix

kh – coefficient depending on h0

fcm – the mean compressive strength (MPa)

αds1 – coefficient which depends on the type of cement

αds2 – coefficient which depends on the type of cement

E28 – static modulus of elasticity at 28 days

Et – modulus of elasticity at an age t

Eu – modulus of elasticity at age of unloading

Øc – creep coefficient depending on KL, Km, Kc, Ke, Kj

Km – coefficient relating to the hardening (maturity) of the concrete

Øcc.b – basic creep factor of concrete

k2 – creep factor coefficient

k3 – maturity coefficient

φ – creep coefficient

kσ – stress-strength ratio σc/fcm

φ0 – notional creep coefficient

φRH – factor to allow for the effect of relative humidity on the notional

creep coefficient

βc(t,t0) – coefficient to describe the development of creep with time after

loading

βH – coefficient depending on the relative humidity and the notional

member size

t – age of concrete in days at the moment considered

t0 – age of concrete at loadings in days

fcu,28 – 28 day cube strength in N/mm2

fcu,t – cube strength at an age t

σc – compressive stress in concrete

xx

ABBREVIATION

BS 8110 - British Standard 8110

AS 3600 - Australian Standard 3600

EC 2 - European Standard Eurocode 2

RH - Relative Humidity

CHAPTER 1

INTRODUCTION

1.1 Background

Concrete is a composite building material made from the combination of

aggregate and cement binder. The most common form of concrete consists of Portland

cement, mineral aggregates (generally gravel and sand) and water. Contrary to common

belief, concrete does not solidify from drying after mixing and placement. Instead, the

cement hydrates, gluing the other components together and eventually creating a stone-

like material. When used in the generic sense, this is the material referred to by the term

concrete.

The quality of concrete can be assessed from several characteristics, namely its

strength, durability, creep and shrinkage. These are the most important and common

criteria used to grade a concrete into its quality level. A concrete of good quality should

be able to work up to the structural ability for which it is designed for, and also to last

for at least the design lifetime for which it is designed for.

2

The behavior of hardened concrete can be characterized in terms of its short-term

(essentially instantaneous) and long-term properties. Short-term properties include

strength in compression, tension, bond, and modulus of elasticity [17]. The long-term

properties include creep, shrinkage, behavior under fatigue, and durability characteristics

such as porosity, permeability, freeze-thaw resistance, and abrasion resistance [17].

Concrete is one of the most durable construction materials. However, cracking

adversely affects its durability, functionality, and appearance. A major cause of

cracking is related to shrinkage-induced strains, creating stresses when concrete is

restrained [4]. The shrinkage of concrete is often attributed to drying of the concrete

over a long period of time, and recent observations have also focused on early age

shrinkage and creep problems. Cracked concrete typically needs to be repaired to

prevent further deterioration due to freezing and thawing, and corrosion of steel

reinforcement resulting from infiltration of water with or without chloride ions from de-

icing salts. The cracking leads to additional costs for repair to prevent premature

deterioration of the concrete and the corrosion of reinforcement steel.

The early age of concrete is known to have a significant control on the overall

performance of concrete structures. During this stage, concrete may be subjected to

severe internal actions due to thermal and hydric gradients within concrete itself and at

the same time it may be affected by the external conditions of environment and loading

[18]. All these actions may lead to different deformations within the concrete that is just

building its resistance and stiffness. Creep and shrinkage of concrete are known to have

significant effect at early age of concrete. Thus, discussing the performance of this

young age concrete with special attention to the shrinkage and creep and time dependent

deformations is of interest by many researchers.

3

In predicting the strength and serviceability of reinforced and pre-stressed

concrete structures, appropriate descriptions of the mechanical properties of the

materials are required including the prediction of the long term behavior of the concrete.

The prediction of short-term shrinkage and creep is also important to assess the risk of

concrete cracking and stripping and unshoring times [17]. The mechanical properties of

concrete are significantly affected by the temperature and availability of water during

curing, the environmental humidity and temperature after curing, and the composition of

the concrete, including the mechanical properties of the aggregates.

When concrete is subjected to sustained compressive stress, deformations

continue to increase with time due to creep and shrinkage. Creep strain is produced by

sustained stress. Shrinkage strains are independent of stress and are caused by chemical

reactions in the hydrating cement paste and by the loss of water during the drying

process. The creep and shrinkage deformations in a concrete structure are frequently

larger, and in some cases much larger than the initial deformations produced when the

external loads are first applied [7]. They thus have a significant effect on service-load

behavior.

The resistance to deformation that makes concrete a useful material means also

that volume changes of the concrete itself can have important implications in use. Any

potential growth or shrinkage may lead to complications, externally because of structural

interaction with other components or internally when the concrete is reinforced. There

may even be distress if either the cement paste or the aggregate changes dimension, with

tensile stresses set up in one component and compressive stresses in the other. Cracks

may be produced when the relatively low tensile strength of the concrete or its

constituent materials is exceeded.

4

Cracking not only impairs the ability of a structure to carry its design load but

also affect its durability and damage its appearance. In addition, shrinkage and creep

may increase deflections in one member of a structure, adversely affecting the stability

of the whole. Volume change of concrete is not usually associated with changes that

occur before the hardened state is attained. Quality and durability, on the other hand, are

dependent on what occurs from the time the concrete mix has been placed in the mold.

Control of cracking may also be done by providing appropriate reinforcement.

The reinforcement, however, does not reduce shrinkage but helps to keep cracks from

widening. The use of expansive cements, coal-combustion products containing calcium

sulfite or sulfate, and fibers is one way of counteracting shrinkage. Usually, expansive

cements and clean-coal ash produce expansion by formation of ettringite. When the

expansion is restrained by reinforcement, a compressive pre-stress is induced in

concrete, compensating shrinkage.

Figure 1.1 illustrates the relationship between various measured and derived

strain values. The figure shows that the concrete undergoes autogenous shrinkage

before drying. Once drying commences at time t0, drying shrinkage occurs. Upon

loading, both drying and basic creep occurs in the drying specimen.

5

Figure 1.1: Relationship between concrete strain and time [8]

1.2 Serviceability of Concrete Structures

For a concrete structure to be serviceable, cracking must be controlled and

deflections must not be excessive. The design for serviceability is possibility the most

difficult and least well understood aspect of the design of concrete structures. Service

load behavior depends primarily on the properties of the concrete and these are often not

known reliably at the design stage. Concrete behaves in a non-linear and inelastic

manner at service loads and the non-linear behavior that complicates serviceability

calculations is due to cracking, tension stiffening, creep, and shrinkage.

The control of cracking in a reinforced or pre-stressed concrete structure is

usually achieved by limiting the stress increment in the bonded reinforcement to some

6

appropriately low value and ensuring the bonded reinforcement is suitably distributed.

For deflection control, engineer should select maximum deflection limits that are

appropriate to the structure and its intended use. The calculated deflection must not

exceed these limits.

The quest for serviceable concrete structures must involve the development of

more reliable design procedures. It must also involve designers giving more attention to

the specification of an appropriate concrete mix, particularly with regard to the creep

and shrinkage characteristics of the mix, and sound engineering input is required in the

construction procedures.

When designing for serviceability, engineer must ensure that the structure can

perform its intended function under the day to day service loads. Deflection must not be

excessive, cracks must be adequately controlled and no portion of the structure should

suffer excessive vibration. Shrinkage cause time-dependent cracking, thereby reducing

the stiffness of a concrete structure, and is therefore a detrimental factor in all aspects of

the design for serviceability.

Excessive wide cracks can be unsightly and spoilt the appearance of an exposed

concrete surface. They allow the ingress of moisture accelerating corrosion of the

reinforcement and durability failure. In exceptional cases, they reduce the contribution

of the concrete to the shear strength of a member. Excessively wide cracks in floor

systems and walls may often be avoided by the inclusion of strategically placed

contraction joints, thereby removing some of the restraint to shrinkage and reducing the

internal tension. When cracking occurs, in order to ensure that crack widths remain

acceptably small, adequate quantities of well distributed and well-anchored

reinforcement must be included at every location where significant tension will exist.

7

Deflection problems that may affect the serviceability of concrete structures can

be classified into three main types:

a. Where excessive deflection causes either aesthetic or functional problems.

b. Where excessive deflection results in damage to either structural or non-

structural element attached to the member.

c. Where dynamics effects due to insufficient stiffness cause discomfort to

occupants.

1.3 Problem Statement

Creep and shrinkage are very important time-dependent properties of concrete.

They are in direct relation to the performance of concrete. The prediction of time-

dependent behaviour is the most uncertain part of the design of concrete structures.

Moreover, the prediction of the time-dependent behaviour is important not only for the

structural maintenance after its completion, but also for the stress and deformation

control during the erection stages of the structure.

Most of the engineers today do not consider the concrete behaviour of creep and

shrinkage in their design work because of lacking experience and understanding on the

phenomenon and the effect on concrete specimen. Most of them consider creep and

shrinkage cracks as non-structural cracks which is not important and will not cause any

serious effect on concrete specimen. This assumption and consideration is not true

because cracking deteriorate concrete’s durability and integrity. A number of analytical

8

techniques are available for the prediction of creep and shrinkage on concrete members.

However, each has its own simplifying assumptions, advantages and disadvantages.

Some of those codes are more suited to particular conditions than others such as

parameters used in BS are based on the conditions in Europe which may not be

accurately applicable in Malaysia.

Therefore, the study is mainly concentrates on the understanding of concrete

behaviour due to creep and shrinkage and to study the prediction of creep and shrinkage

strain using different code of practice.

1.4 Objectives of Project

Based on the scope of work, the objectives of the project are defined below:

(i) Study the properties and deformation of concrete due to creep and

shrinkage.

(ii) Evaluate and identify the parameters and method used in determining the

coefficient of creep and shrinkage for British Standard, Eurocode and

Australia Standard.

(iii) Develop spreadsheets that calculating the creep and shrinkage of concrete

for British Standard, Eurocode and Australia Standard.

(iv) Compare the creep and shrinkage strain using BS8110, EC2 and AS3600

under controlled parameters.

9

1.5 Scope of Work

Time-dependent concrete deformation is nowadays one of the concerns in

engineering field as it affects the serviceability and aesthetic of the concrete structures.

The main factors that cause concrete deforms due to environment and applied stress are

shrinkage and creep. Therefore, the research on this topic has been proposed in the Final

Year Project of Master Studies (Civil-Structural) in Universiti Technologi Malaysia.

In Masters Pre Project, the scope of work was mainly focused on the literature

review of related studies. Substantial information on concrete properties such as

modulus of elasticity, creep and shrinkage will be gathered through latest journals and

publications in libraries and also articles from internet. The history of concrete, effect of

admixtures on concrete properties and factors affecting deterioration on concrete and the

effects are studied in this study.

In Masters Project, detail studies on the concrete deformation due to time-

dependent factors (creep and shrinkage) will be made. The formulas, and method used

in predicting concrete deformation due to creep and shrinkage will be identified using

British Standard, EURO Code and Australia Standard. Spread sheet to determine

concrete creep and shrinkage will be produced by inputting the controlling parameters

such as strength of concrete (fcu), relative humidity, type of cement, effective thickness,

provided steel reinforcement, etc.

10

1.6 Expected Outcome

There are some outcomes to be expected through this master research studies

such as:

(i) To understand the concrete properties due to creep and shrinkage.

(ii) To be familiar with the codes in creep and shrinkage of concrete

specification.

(iii) To understand the parameter and method used in calculating concrete

creep and shrinkage for British Standard, Eurocode & Australia Standard.

CHAPTER 2

LITERATURE REVIEW

2.1 Significance of Volume Changes and Creep

If concrete is free to deform, any volume changes would be of little consequence,

but usually it is restrained by foundations, steel reinforcement, or by adjacent concrete

subject to different conditions. As the potential movement is thus restrained, stresses

will be developed which may rupture the concrete. This is particularly true when

tension is developed; thus, contractions causing tensile stress are more important than

expansions which cause compressive stress. Difference in moisture contents of the

exposed and unexposed faces of thin concrete slabs, such as highways and canal linings,

may cause curling and eventual cracking. Cracking not only may impair the ability of

any structure to carry its designed loads, but it also may affect its durability and damage

its appearance. The durability is affected by the entry of water through cracks, which

corrodes the steel, leaches out soluble components, and deteriorates the concrete when

subjected to freezing and thawing.

12

Creep, in general, tends to relieve the stress in concrete, especially when

reinforced. Thus, when a sustained load is applied to a reinforced concrete column,

creep of the concrete causes a gradual reduction in the load on the concrete and a

corresponding increase in the load on the steel. In various structural elements such as

continuous beams and slabs, creep relieves some of the stress in the most highly stressed

portions and increases the stress in adjacent portions of the concrete, so that finally the

stresses are more uniform throughout the member. This relieving of the higher stresses

serves to reduce the tendency toward cracking. However, creep may cause

objectionable sagging of thin, long-span floor slabs or other structural elements.

2.2 The Gel Structure as Related to Volume Changes

Cement, after hydration, consists of crystalline material plus a calcium silicate

gel resulting from the combination of cement and water. The amount of the gel

increases with the age of hydration and is greater for higher water-cement ratios and for

finer cements. The amount of gel also depends upon the chemical composition of the

cement, as fully hydrated dicalcium silicate is believed to be mostly gel, while hydrated

tricalcium silicate is more than half gel. For the water-cement ratios used in average

concrete, the gel has a larger volume than the crystalline portions.

The crystalline materials in cement are believed to be unaffected by ordinary

drying, but the gel is finely porous and undergoes large volume changes upon wetting

and drying. The quantity and characteristics of the calcium silicate gel, therefore,

largely determine the potential shrinkage upon drying of hydrated cement.

13

Water is held in the pores of the gel by such large attractive forces that when it is

removed from the pores by evaporation, the forces which formerly attracted the water

become effective in compressing and reducing the volume of the gel. All concretes,

then, are subject to moisture volume changes in some degree, and the problem involved

is so to control conditions that the volume changes have small or practically harmless

effects upon the integrity of the structure.

2.3 Shrinkage of Concrete

Concrete deformation due to movement of water from or to the ambient medium

when no external stress is acting is termed shrinkage. It is independent of stress and is

caused by chemical reactions in the hydrating cement paste and by the loss of water

during the drying process. Technically, shrinkage will continue for the life of the

concrete, but most shrinkage will occur within the first 90 days after placement [33].

Shrinkage cracking is a major cause of concern for concrete structures. In

addition to weakening the structure, these shrinkage cracks have the potential to allow

infiltration of moisture and chloride ions that accelerate the corrosion of steel

reinforcement and reduce the durability of concrete.

14

2.3.1 Type of Shrinkage

The four main types of shrinkage associated with concrete are plastic shrinkage,

autogenous shrinkage, drying shrinkage, and carbonation shrinkage.

2.3.1.1 Plastic Shrinkage

Plastic shrinkage is associated with moisture loss from freshly poured concrete

into the surrounding environment. Plastic shrinkage occurs only in fresh concrete. The

most common mechanism is the evaporation of water from the surface of the plastic

concrete. However, the loss of water through the sub-base or formwork can exacerbate

the effects of surface evaporation [33].

In the fresh concrete, the particles are completely surrounded by water. If water

is removed from the system, menisci are formed between particles. These menisci

generate negative capillary pressure, which pulls the cement particles together. By

pulling on the particles, the capillary stresses tend to reduce the volume of the cement

paste. Capillary pressures continue to rise as water is lost at the surface of the concrete.

When the pressures reach a critical value, the water that remains in the concrete

rearranges to form discrete zones with voids between them. Plastic shrinkage cracking

occurs at this point.

15

2.3.1.2 Autogenous Shrinkage

Autogenous shrinkage is the volume change of the cement paste due to self-

desiccation and chemical shrinkage after initial setting has occurred. Autogenous

shrinkage is a microscopic volume change occurring after the initial setting in situations

where the supply of water from outside of concrete is not enough. As the hydration of

cementitious materials progresses, very fine pores are produced within the hardened

cement paste due to the formation of calcium silicate hydrate (CSH) gel. As the

hydration further progresses, capillary pore water and gel water is consumed and

menisci are produced in these pores due to a lack of water supply from outside. As a

result of negative pressure in the pores, hardened paste shows shrinkage [18].

Autogenous shrinkage is the early shrinkage of concrete caused by the loss of

water from capillary pores due to the hydration of cementitious materials, without the

loss of water into the surrounding environment. This phenomenon is known as self-

desiccation of concrete. Self-desiccation occurs in all concrete irrespectively of the

water-cement ratio. However, its effects are very different in normal concrete and high-

performance concrete. In high-performance concrete, significantly more cementitious

materials and less mixing water are used compared with normal concrete. In normal

concrete, there is substantially more water than required for hydration of cementitious

materials particles. This excess amount of water is contained in well-connected

capillaries. Menisci created by the process of self-desiccation occur in large capillaries.

But, stresses generated in large capillaries are very low, resulting in lower autogenous

shrinkage. On the other hand, in case of high-performance concrete, pore network is

essentially composed of fine capillaries due to low water-cement ratio and high amounts

of cementitious hydration products. When self-desiccation starts to take place, very high

tensile stresses are generated in these fine pores, resulting in higher autogenous

shrinkage.

16

Although autogenous shrinkage is three-dimensional, it is usually expressed as a

linear stain so that it can be considered alongside the drying shrinkage. Typical values

of autogenous shrinkage are about 40 x 10-6 at the age of one month and 100 x 10-6 after

five years. Autogenous shrinkage tends to increase at higher temperatures, with higher

cement content, and possibly with finer cements, and with cements which have a high

C3A and C4AF content. At a constant content of blended cement, a higher content of fly

ash leads to lower autogenous shrinkage. As self-desiccation is greater at lower

water/cement ratios, autogenous shrinkage could be expected to increase but this may

not occur because of the more rigid structure of the hydrated cement paste at lower

water/cement ratios. Nevertheless, at very low water/cement ratios, autogenous

shrinkage is very high: a value of 700 x 10-6 was reported for concrete with a

water/cement ratio of 0.17 [1].

2.3.1.3 Drying Shrinkage

Drying shrinkage is different from autogenous shrinkage with regard to the

mechanism of a decrease in humidity. Drying shrinkage is caused by the diffusion of

water from concrete into the outer surrounding environment.

Drying shrinkage refers to the reduction in concrete volume resulting from the

loss of capillary water by evaporation. This shrinkage causes an increase in tensile

stress of restrained concrete, which leads the concrete to cracking, internal warping, and

external deflection, even if the concrete is not subjected to any kind of external loading.

17

According Mehta and Monteiro the change in volume of drying concrete is not

equal to the volume of water removed [2]. The reason is that the loss of water from

large capillaries may be considered as free water, and its removal does not cause volume

change. Loss of water held by capillary tension in small capillaries may cause shrinkage

of concrete. It is also possible that shrinkage is related to the removal of interlayer

water, which is also known as zeolite water. It has been suggested that a monomolecular

water layer between the layers of CSH is strongly held by hydrogen bonding. This

water is associated with CSH structure and the interlayer water is lost only on strong

drying.

The drying shrinkage of hydrated cement paste begins at the surface of the

concrete. Depending on the relative humidity of the ambient air and the size of

capillaries in the cement paste structure, drying shrinkage progresses more or less

rapidly through concrete. The drying in ordinary concrete is, therefore, rapid because

the capillary network is well connected and contains large capillaries. In the case of

high-performance concrete, drying shrinkage is slow because the capillaries are very

fine and soon get disconnected by hydration products.

The influence of the gel particle size on drying is shown by the low shrinkage of

the much more coarse-grained natural building stones and by the high shrinkage of fine

grained shale [3]. Also, high-pressure steam-cured cement paste, which is

microcrystalline and has a low specific surface, shrinks 5 to 10 times [4], and sometimes

even 17 times [5], less than a similar paste cured normally.

It is possible also that shrinkage, or a part of it, is related to the removal of

intracrystalline water. Calcium silicate hydrate has been shown to undergo a change in

lattice spacing from 1.4 to 0.9 nm on drying [6]; hydrated C4A and calcium

sulfoaluminate show similar behavior [7]. It is thus not certain whether the moisture

18

movement associated with shrinkage is inter- or intracrystalline. But, because paste

made with both Portland and high-alumina cements, and also with pure ground calcium

monoaluminate, exhibit essentially similar shrinkage, the fundamental cause of

shrinkage must be sought in the physical structure of the gel rather than in its chemical

and mineralogical character [6].

The relation between the mass of water lost and shrinkage is shown in Figure

2.1. For neat cement pastes, the two quantities are proportional to one another as no

capillary water is present and only adsorbed water is removed. However, mixes to

which pulverized silica has been added and which, for workability reasons, require a

higher water/cement ratio, contain capillary pores even when completely hydrated.

Emptying of the capillaries causes a loss of water without shrinkage but, once the

capillary water has been lost, the removal of adsorbed water takes place and causes

shrinkage in the same manner as in a neat cement paste.

Figure 2.1: Relationship between shrinkage and loss of water from specimens of

cement-pulverized silica pastes cured for 7 days at 21ºC and then dried [3]

19

2.3.1.4 Carbonation Shrinkage

In addition to shrinkage upon drying, concrete undergoes shrinkage due to

carbonation, and some of the experimental data on drying shrinkage include the effects

of carbonation. Drying shrinkage and carbonation shrinkage are, however quite distinct

in nature.

Carbonation shrinkage is caused by the chemical reactions of various cement

hydration products with carbon dioxide present in the air. This type of shrinkage is

usually limited to the surface of the concrete. Because of carbon dioxide is fixed by the

hydrated cement paste, the mass of the latter increases. Consequently, the mass of

concrete also increases. When the concrete dries and carbonates simultaneously, the

increase in mass on carbonation may at some stage give the misleading impression that

the drying process has reached stage of constant mass, i.e. equilibrium (see Figure 2.2).

Figure 2.2: Loss of mass of concrete due to drying and carbonation [8]

20

Carbonation shrinkage is probably caused by the dissolving of crystals of

Ca(OH)2 while under a compressive stress (imposed by the drying shrinkage) and

depositing of CaCO3 in spaces free from stress; the compressibility of the hydrated

cement paste is thus temporarily increased. If carbonation proceeds to the stage of

dehydration of C-S-H, this also produces carbonation shrinkage.

Figure 2.3 shows the drying shrinkage of mortar specimens dried in CO2 – free

air at different relative humidity, and also the shrinkage after subsequent carbonation.

Carbonation increases the shrinkage at intermediate humidity, but not at 100 per cent or

25 per cent. In the latter case, there is insufficient water in the pores within the cement

paste for CO2 to form carbonic acid. On the other hand, when the pores are full of

water, the diffusion of CO2 into the paste is very slow; it is also possible that the

diffusion of calcium ions from the paste leads to precipitation of CaCO3 with a

consequent clogging of surface pores.

Figure 2.3: Drying shrinkage and carbonation shrinkage of mortar at different relative

humidity [9]

21

The sequence of drying and carbonation greatly affects the total magnitude of

shrinkage. Simultaneous drying and carbonation produces lower total shrinkage than

when drying is followed by carbonation (Figure 2.4) because, in the former case, a large

part of the carbonation occurs at relative humidity above 50 per cent; under such

conditions carbonation shrinkage is reduced. Carbonation shrinkage of high-pressure

steam-cured concrete is very small.

Figure 2.4: Influence of the sequence of drying and carbonation of mortar on

shrinkage [9]

When concrete is subjected to alternating wetting and drying in air containing

CO2, shrinkage due to carbonation becomes progressively more apparent. The total

shrinkage at any stage is greater than if drying took place in CO2 – free air. However,

carbonation of concrete prior to exposure to alternating wetting and drying reduces the

moisture movement.

22

2.3.2 Factors Affecting Shrinkage

Generally, plastic shrinkage results from surface evaporation due to

environmental conditions, such as humidity, wind speed or ambient temperature. ACI

305R, Hot Weather Concreting [10], provides guidance for placement of concrete to

minimize plastic shrinkage cracking.

Several factors which may be expected to influence the magnitude of volume

changes in mortars and concretes caused by variations in moisture conditions, which

take place with time and the simultaneous hardening of the cement paste are [34]:

(i) Composition and fineness of the cement

(ii) Cement and water contents

(iii) Type and gradation of aggregate

(iv) Admixtures

(v) Age at first observation

(vi) Duration of tests

(vii) Moisture and temperature conditions

(viii) Size and shape of specimen

(ix) Absorptiveness of forms

(x) Amount and distribution of reinforcement

23

2.3.2.1 Effect of Composition and Fineness of Cement

Cement properties and cement content in concrete influence concrete shrinkage.

As the fineness of cement increases, so does the hydration rate of cement, leading to an

increase to an increase in autogenous shrinkage of concrete. Small autogenous

expansion as opposed to shrinkage may be produced through the use of coarser cements.

Therefore, early age cracking could be possibly being avoided. Although coarser

particles of cement are relatively beneficial in minimizing early age cracking, they may

be detrimental to long-term strength. Mehta and Monteiro [2] state that the variation in

fineness and composition of Portland cement affect the rate of hydration, but not the

volume and characteristics of hydration products. Therefore, normal changes in fineness

and composition of cement have negligible effect on drying shrinkage of concrete.

Higher cement content with lower W/C in concrete results in higher autogenous

shrinkage due to self-desiccation and chemical shrinkage, but may reduce drying

shrinkage due to dense microstructure and poor pore connectivity.

2.3.2.2 Effect of Type and Gradation of Aggregate

The drying shrinkage of concrete is not related to a fraction of neat cement as the

aggregate particles not only dilute the paste but they reinforce it against contraction.

Tests have shown that if the aggregate were readily compressible, as when using porous

but nonabsorbent rubber particles, the concrete would shrink as much as neat cement.

The ability of normal aggregates to restrain the shrinkage of a cement paste depends

upon (1) extensibility of the paste, (2) degree of cracking of the paste, (3)

compressibility of the aggregate, and (4) volume change of aggregate due to drying. In

table A is shown the shrinkage of neat cement in comparison with the corresponding

24

shrinkages of the same cement diluted with a single sieve size (No. 4 to 3/8 in.) of gravel

and crushed limestone, respectively. The reduction in shrinkage due to the aggregate is

greater than would be expected considering its relative volume. It is possible that

internal cracking of the paste due to the restraint of the aggregate is a factor.

Table 2.1: Shrinkage of neat cement in comparison with the corresponding shrinkages

of the same cement diluted with a single sieve size (No. 4 to 3/8 in.)

of gravel and crushed limestone, respectively [35]

2.3.2.3 Effect of Cement and Water Contents

The water content is probably the largest single factor influencing the shrinkage

of cement paste and concrete. Tests have shown that for cements having normal

shrinkage characteristics, the shrinkage of the cement paste varies directly with the

water-cement ratio [33].

Figure 2.5 shows the pattern of shrinkage as a function of cement content, water

content, and water/cement ratio where the concrete is moist-cured for 28 days, thereafter

dried for 450 days [11]. At a constant water/cement ratio, shrinkage increases with an

25

increase in the cement content because this results in a larger volume of hydrated cement

paste which is liable to shrinkage. However, at a given workability, which

approximately means a constant water content, shrinkage is unaffected by an increase in

the cement content, or may even decrease, because the water/cement ratios is reduced

and the concrete is therefore, better able to resist shrinkage.

Figure 2.5: The pattern of shrinkage as a function of cement content, water content and

water/cement ratio [11]

2.3.2.4 Effect of Admixtures

Admixtures can adversely affect the shrinkage potential of concrete. For

instance, water reducers can be used to reduce the paste volume and thereby enhance the

creep capacity without the loss of workability. Set retarders can be used to delay set and

to decrease the amount of heat of hydration. A lower heat of hydration will decrease the

thermal shock on the hydrating concrete [33]. However, overly long retardations will

increase the potential for plastic shrinkage cracking. Proper curing is necessary with the

26

use of a set retarder. Conversely, set accelerators increase the heat of hydration and

early-age shrinkage. This combination will increase transverse shrinkage and the

resulting cracking.

Shrinkage-reducing admixtures (SRAs) are also available. These admixtures

reduce the drying shrinkage by reducing the surface tension of the water in the capillary

pores. If the surface tension of the water is reduced, there is less tension transferred to

the capillary walls, and consequently less shrinkage. Laboratory evaluations have

shown a slight decrease in compressive strength when an SRA is used. Taking

advantage of the water-reducing properties of SRAs can offset the decrease in strength.

Shrinkage of concrete made with high-alumina cement is of the same magnitude

as when Portland cement is used, but it takes place much more rapidly [12]. Including

either fly ash or ground granulated blastfurnace slag in the mix increases shrinkage.

Specifically, at a constant water/cement ratio, a higher proportion of fly ash or slag in

the blended cement leads to higher shrinkage by some 20 percent with the former

material and by up to 60 percent at very high contents of slag [13]. Silica fume

increases the long-term shrinkage [14].

Water-reducing admixtures per se probably cause a small increase in shrinkage.

Their main effect is indirect in that the use of an admixture may result in a change in the

water content or in the cement content of the mix, or in both, and it is the combined

action of those changes that influences shrinkage. Superplasticizers have been found to

increase shrinkage by some 10 to 20 percent. However, the changes in the observed

shrinkage are too small to be accepted as reliable and generally valid.

27

Entrainment of air has been found to have no effect on shrinkage [15]. Added

calcium chloride increases shrinkage, generally between 10 and 50 percent [16],

probably because a finer gel is produced and possibly because of greater carbonation of

the more matures specimens with calcium chloride.

2.3.2.5 Temperature and Relative Humidity

A high temperature and low relative humidity of the ambient environment

accelerate the diffusion of the adsorbed water and capillary water into the atmosphere,

and consequently, increases the drying shrinkage of concrete. An increase in the

atmospheric humidity slows down the rate of moisture flow from the interior to the outer

surface of concrete. Mehta and Monteiro [2] states that at 0% relative humidity, it is

assumed that the drying shrinkage of concrete is zero.

2.3.2.6 Volume-to-Surface Ratio

The size and shape of a concrete element have a considerable effect on the rate

and total amount of shrinkage. The size and shape are often considered together as the

volume-to-surface area ratio. A high volume-to-surface ratio usually results in lower

shrinkage magnitudes.

28

2.3.2.7 Volume and Type of Aggregate

Drying shrinkage of concrete is a fraction of that of neat cement because the

aggregate particles not only dilute the paste but reinforce it against contraction. The size

and grading of aggregate do not, by themselves, influence the magnitude of shrinkage,

but an aggregate incorporating larger sizes permits the use of a mix with less cement and

hence a lower shrinkage.

The shrinkage of aggregates themselves may be of considerable importance in

determining the shrinkage of concrete. Some fine-grained sandstones, slate, basalt, trap

rock and aggregates containing clay show large shrinkage while concretes low in

shrinkage often contain quartz, limestone, granite or feldspar. The pore structure of

aggregate particles may have a strong effect on autogenous shrinkage. Aggregate

particles may contain water in coarse pores, which provides the “internal curing” for

hydrating cement paste hence reducing autogenous shrinkage. Figure 2.6 indicates the

relationship between W/C ratio, aggregate content and shrinkage.

Figure 2.6: Effect of W/C ratio and aggregate content on shrinkage [36]

29

2.3.2.8 Elastic Modulus of Aggregate

Modulus of elasticity is the most important property of aggregate that directly

influences drying shrinkage of concrete. When readily compressible aggregate is used,

concrete will shrink as mush as neat cement, and that expanded shale leads to shrinkage

more than that of ordinary aggregate. Steel aggregate on the other hand, leads to

shrinkage less than that of ordinary concrete. The drying shrinkage of concrete

increased 2.5 times [17] when an aggregate with high elastic modulus was substituted by

an aggregate with low elastic modulus.

2.3.3 Differential Shrinkage

It was mentioned earlier that the potential shrinkage of neat cement paste is

restrained by the aggregate. In addition, some restraint arises also from non-uniform

shrinkage within the concrete member itself. Moisture loss takes place only at the

surface so that a moisture gradient is established in the concrete specimen, which is thus

subjected to differential shrinkage. The potential shrinkage is compensated by the

strains due to internal stresses, tensile near the surface and compressive in the core.

When drying takes place in an unsymmetrical manner, warping (curling) can result.

It may be useful to point out that the values of shrinkage generally quoted are

those of free shrinkage, or potential shrinkage, that is, contraction unrestrained either

internally or by external constraints on a structural member. In considering the effect of

the constraining forces on the actual shrinkage, it is important to realize that the induced

stresses are modified by relaxation, which may prevent the development of cracking.

30

Because relaxation occurs only slowly, it may prevent cracking when shrinkage

develops slowly; however, the same magnitude of shrinkage occurring rapidly may well

induce cracking. It is shrinkage cracking that is of paramount interest.

Because drying takes place at the surface of concrete, the magnitude of shrinkage

varies considerably with the size and shape of the specimen, being a function of the

surface/volume ratio. A part of the size effect may also be due to the pronounced

carbonation shrinkage of small specimens. Thus, for practical purposes, shrinkage

cannot be considered as purely an inherent property of concrete without reference to the

size of the concrete member.

Many investigations have, in fact, indicated an influence of the size of the

specimen on shrinkage. The observed shrinkage decreases with an increase in the size

of the specimen but, above some value, the size effect is small initially as shown in

Figure 2.7. The shape of the specimen also appears to enter the picture but, as a first

approximation, shrinkage can be expressed as a function of the volume/surface ratio of

the specimen. There appears to be a linear relation between this ratio and the logarithm

of shrinkage as shown in Figure 2.8.

The effect of shape is secondary. I-shaped specimens exhibit less shrinkage than

cylindrical ones of the same volume/surface ratio, the difference being 14 percent on the

average [18]. The difference, which can be explained in terms of variation in the mean

distance that the water has to travel to the surface, is thus not significant for design

purposes.

31

Figure 2.7: Relation between axial shrinkage and width of concrete prisms of

square cross-section and length/width ratio of 4 [37]

Figure 2.8: Relation between ultimate shrinkage and volume/surface ratio [18]

32

2.3.4 Shrinkage-induced Cracking

As mentioned in connection with differential shrinkage, the importance of

shrinkage in structures is largely related to cracking. Strictly speaking, we are

concerned with the cracking tendency because the advent or absence of cracking

depends not only on the potential contraction but also on the extensibility of concrete, its

strength, and its degree of restraint to the deformation that may lead to cracking.

Restraint in the form of reinforcing bars or a gradient of stress increases extensibility of

concrete in that it allows it to develop strain well beyond that corresponding to

maximum stress. A high extensibility of concrete is generally desirable because it

permits concrete to withstand greater volume changes.

The schematic pattern of crack development when stress is relieved by creep is

shown in Figure 2.9. Cracking can be avoided only if the stress induced by the free

shrinkage strain, reduced by creep, is at all times smaller than the tensile strength of the

concrete. Thus, time has two-fold effect: the strength increases, thereby reducing the

danger of cracking but, on the other hand, the modulus of elasticity also increases so that

the stress induced by a given shrinkage becomes larger. Furthermore, the creep relieves

decreases with age so that the cracking tendency becomes greater. A minor practical

point is that, if the cracks due to restrained shrinkage form at an early stage, and

moisture subsequently has access to the crack, many of the cracks will become closed by

autogenous healing.

One of the most important factors in cracking is the water/cement ratio of the

mix because its increase tends to increase shrinkage and, at the same time, to reduce the

strength of the concrete. An increase in the cement content also increases shrinkage and,

therefore, the cracking tendency, but the effect on strength is positive. This applies to

drying shrinkage. Carbonation, although it produces shrinkage, reduces subsequent

33

moisture movement, and therefore is advantageous from the standpoint of cracking

tendency. On the other hand, the presence of clay in aggregate leads both to higher

shrinkage and to greater cracking.

The use of admixtures may influence the cracking tendency through interplay of

effects on hardening, shrinkage, and creep. Specifically, retarders may allow more

shrinkage to be accommodated in the form of plastic shrinkage and also probably

increase the extensibility of concrete, and therefore reduce cracking. On the other hand,

if concrete has attained rigidity too rapidly, it cannot accommodate the would-be plastic

shrinkage and, having a low strength, cracks.

The temperature at the time of placing determines the dimensions of concrete at

the moment when it ceases to deform plastically. A subsequent drop in temperature will

produce potential contraction. Thus, placing concrete in hot weather means a high

cracking tendency. Steep temperature or moisture gradients produce severe internal

restraints and thus represent a high cracking tendency. Likewise, restraint by the base of

a member, or by other members, may lead to cracking.

Figure 2.9: Schematic pattern of crack development when tensile stress due to

restrained shrinkage is relieved by creep [33]

34

2.3.5 Effect of Shrinkage

Virtually all concrete is subject to some form of restraint, such as steel

reinforcement, forms, subgrade, or adjacent members. Each of these forms of restraint

involve the imposition of a gradually increasing tensile force on the concrete which may

lead to time-dependent cracking, increases in deflection and a widening of existing

cracks.

The advent of shrinkage cracking depends on the degree of restraint to shrinkage,

the extensibility and strength of the concrete in tension, tensile creep and the load

induced tension existing in the member. Cracking can be avoided if the gradually

increasing tensile stress induced by shrinkage, and reduced by creep, is at all times less

than the tensile strength of the concrete. The existence of load induced tension in

uncracked regions accelerates the formation of time-dependent cracking. The control of

such cracking requires two important steps. First, the shrinkage-induced tension and the

regions where shrinkage cracks are likely to develop must be recognized by the

structural engineer. Second, an adequate quantity and distribution of anchored

reinforcement must be included in these regions to ensure that the cracks remain fine

and the structure remains serviceable.

2.3.6 Methods of Controlling Shrinkage Cracking

Specific methods to properly control shrinkage cracking have been developed

and researched. Conventional methods, which include proper material selection,

mixture proportioning, and good construction techniques, can be used to a certain extent

to control and limit the shrinkage cracking of concrete. Unfortunately, because these

methods are hard to control, and environmental conditions can vary so much, the

35

shrinkage cracking cannot be entirely prevented. For example, concrete in hot, dry, and

windy conditions can have much higher rates of water evaporation, thus making them

more susceptible to shrinkage cracking. Innovative methods of controlling shrinkage

cracking have been found in literature and developed by numerous researches to help

control and eliminate shrinkage cracking. These include using fiber-reinforced concrete,

shrinkage-reducing admixtures, shrinkage-compensating concrete, and extensible

concrete. The categories of methods are summarized in Table 2.2.

Table 2.2: Methods of controlling drying shrinkage [31]

Methods Description

Conventional • Proper Material Selection

o Aggregates

o Cement type

o Admixtures

• Mixture Proportioning

o Cement Content

Innovative • Fiber Reinforcement

o Polypropylene

o Steel

• Shrinkage-Compensating Concrete

• Shrinkage-Reducing Admixtures

• Extensible Concrete

36

2.3.6.1 Conventional Method

Shrinkage cracking in concrete is currently being controlled through

conventional methods, which consist of the proper selection of materials and concrete

mixtures, along with good construction techniques.

2.3.6.1.1 Aggregates

The type of aggregate used in concrete mixtures, as well as the aggregate

content, can influence the amount of shrinkage in concrete. The aggregate type was the

most significant factor affecting when concrete cracked [19]. Specifically, limestone-

aggregate concretes proved to be the most resistant to cracking, while Eau Claire river

gravel had the shortest time-to-cracking of the aggregates tested. Burrows (1998) also

studied the effect of the type of aggregate used on the drying shrinkage of concrete.

Again, limestone was found to be one of the aggregates exhibiting the least drying

shrinkage while, in the study, sandstone exhibited the highest amount of drying

shrinkage. The amount of aggregate used in a concrete mixture can also help to reduce

shrinkage. Research has shown that a higher aggregate content can help to reduce

shrinkage. Table 2.3 shows the aggregate type related to drying shrinkage according to

Burrows report in 1998.

37

Table 2.3: Aggregate type related to drying shrinkage [18]

Aggregate One-year shrinkage (percent)

Sandstone 0.097

Basalt 0.068

Granite 0.063

Limestone 0.050

Quartz 0.040

2.3.6.1.2 Cement Content and Type

The amount of cement proportioned in concrete mixtures has an impact on the

amount of shrinkage that concrete will undergo. Specifically, concrete cracking has

been more prevalent when higher cement contents have been used. Krauss and Rogalla,

using a ring shrinkage test, found that cracking occurred sooner as the cement content of

the concrete mixes was increased [19]. Water-cement ratio also influences shrinkage

behavior in concrete. Krauss and Rogalla found that the concrete with more water

shrinks and creeps more than concrete with less water, but it may not crack sooner

because it has higher creep [19]. Burrows contends that although concrete mixes with

lower water-cement ratios produce stronger concrete, that same concrete can be much

more vulnerable to cracking. The type of cement used also plays an important role in

reducing shrinkage cracking. Krauss and Rogalla noted that cements that are ground

finer and have higher sulfate contents increase the early strength of concrete while also

increasing the early modulus of elasticity and heat of hydration [19]. For example, Type

III cement could increase the risk of cracking because of the rapid early strength gains.

38

2.3.6.1.3 Admixtures

Fly ash, silica fume, set retarders, and accelerators are all admixtures that have

been investigated for shrinkage by a number of researchers.

Fly ash has been found to reduce early concrete temperatures and the rate of

strength gain, thus reducing concrete cracking. The process of using fly ash to replace

cement is referred to as the creation of extensible concrete and is described in detail

following this section.

Silica fume, a by-product of silicon metal or ferrosilicon alloys in electric arc

furnaces, has been found to increase the cracking of concrete. The silica fume product

has an average fineness of about two orders of magnitude finer than Portland cement,

which causes the bleeding rate of concrete to decrease, and the subsequent water loss

resulting from evaporation cannot be replaced. Silica fume is found to be a problem

with cracking tendency specifically when the concrete is not cured properly.

Retarders have not been proven either to be the cause of concrete cracking or to

help reduce the risk of thermal cracking. Plastic cracking could be caused by the

addition of retarders, while retarders have also been found to reduce the risk of thermal

cracking by reducing early heat of hydration in concrete.

39

2.3.6.2 Innovative Method

Because of the extreme variance of the conventional methods used to control

drying shrinkage, innovative methods should be used to help reduce cracking tendencies

of concrete. These include fiber-reinforced concrete, shrinkage-reducing admixtures,

shrinkage-compensating concrete, and extensible concrete.

2.3.6.2.1 Fiber-Reinforced Concrete

Many studies have shown that adding fibers to concrete significantly reduces

shrinkage cracking. Various parameters that were investigated include the addition of

fibers at low volumes as compared to high volumes, as well as the different types of

fibers to be used.

Steel fibers can affect the properties of concrete, but the reinforced properties

depend on the percentage of fiber addition, the aspect ratio of the fibers, and the strength

of the concrete paste. Longer fibers provide more strength but decrease workability.

For this reason, fibers with an aspect ratio of less than 100 are commonly used. Steel

fiber reinforced concrete has been shown to increase the tensile strength, flexural

strength, and compressive strength of concrete through research. Tests have shown that

steel fibers do not affect the shrinkage strain of concrete, but the fibers can reduce the

amount of cracking associated with the shrinkage strain.

40

Low volume of polypropylene fibers can significantly reduce the plastic

shrinkage of concrete. For low-volume fiber reinforcement typically 0.1%-0.3% has

little effect on the properties of the hardened concrete. However, high volumes of fiber,

generally greater than 2%, can increase the ductility and toughness of concrete. At high

volumes, polypropylene fibers can be used to prevent shrinkage cracking. The

shrinkage stress produced in the concrete is transferred to the fibers, which can better

withstand the tensile stresses than the concrete.

2.3.6.2.2 Shrinkage-Reducing Admixtures

A great deal of research has been performed regarding the development of SRAs

used to control shrinkage cracking of concrete. These chemical admixtures, which are

added to concrete work by lowering the surface tension of the pore water inside

hardened concrete. The pore water evaporates from capillary pores in the hardened

concrete during drying, and the tension in the liquid is transferred to the capillary walls,

resulting in shrinkage. Any stresses generated during drying are proportional to the

surface tension of the pore water solution. This surface tension is lowered by SRAs,

thus reducing the overall drying shrinkage. Therefore, there are fewer tendencies for

shrinkage and resultant stress to occur in the concrete when the pore water initially

evaporates. SRAs affect the nature of the pore water, rather than limiting or reducing

the amount of water from concrete during drying.

41

2.3.6.2.2 Shrinkage-Compensating Concrete

Shrinkage-compensating concrete is an innovative material that causes expansion

of concrete during curing, which in turn reduces the effects of drying shrinkage. If the

expansion is properly restrained, the concrete will be subjected to compression the first

few days after concrete placement. Although the shrinkage-compensating concrete will

shrink as much as normal concrete once exposed to drying conditions, the net shrinkage

will be negligible because the concrete started out with an initial expansion. The

mechanism of expansion in the shrinkage-compensating concrete is a result of the early

formation and stability of ettringite. The ettringite crystals need water to expand, and

therefore, moist curing must provide this water, or else minimal expansion will result.

2.3.6.2.3 Extensible Concrete

Extensible concrete is a term that refers to a combination of factors that are

useful for reducing the cracking in concrete. Basically, some of the conventional

materials and methods mentioned previously can be used in an innovative manner to

achieve this type of behavior. A typical extensible concrete would have a high volume

of fly ash, low cement content, and a high water-cement ratio. These factors would

produce a low heat of hydration, thereby reducing thermal stresses in the concrete while

also producing a low elastic modulus and high creep, minimizing shrinkage cracking.

42

2.4 Creep of Concrete

Creep of concrete, resulting from the action of a sustained stress, is a yielding of

the concrete. It may be due partly to viscous flow of the cement-water paste, closure of

internal voids and crystalline flow in aggregates, but it is believed that the major portion

is caused by seepage of colloidal water from the gel that is formed by hydration of the

cement. Although water may exist in the mass as chemically combined water, and as

free water in the pores between the gel particles, neither of these is believed to be

involved in creep. The rate of expulsion of the colloidal water is a function of the

applied compressive stress and of the friction in the capillary channels. The greater the

stress, the steeper the pressure gradient with resulting increase in rate of moisture

expulsion and deformation. The phenomenon is closely associated with that of drying

shrinkage.

Creep is defined as the increase in strain under a sustained stress. There is an

instantaneous strain on concrete which is called the “elastic” deformation when the

sample is unloaded. It is observed that there is a gradual increase in strain for days after

a stress has been applied to concrete. This is called the “creep” strain. Since this

increase can be several times as large as the strain on loading, creep is of considerable

importance in structural mechanics. The deformation of concrete with time is

schematically shown in Figure 2.10. The rate of creep is relatively rapid at early ages

after loading and then decreases gradually, until after a few years it becomes

insignificant. Roughly, about one-fourth of the ultimate creep occurs within the first

month or so, and one-half occurs within the first year.

43

Figure 2.10: Typical strain-time plot of concrete under a sustained load

and after release of load [16]

Creep in concrete is a post-elastic phenomenon. In practice, drying shrinkage

and viscoelastic behavior such as creep usually take place simultaneously. Considering

the various combinations of loading, restraining, and humidity conditions, the following

terms is defined:

i. True or Basic Creep

Defined as the creep that occurs under conditions that there is no drying

shrinkage or moisture movement between concrete and ambient

environment.

ii. Specific Creep

- Defined as creep strain per unit of applied stress.

- Specific Creep = εcr / σ

44

iii. Drying Creep

- Is the additional creep that occurs when the specimen under load is also

drying.

iv. Creep Coefficient

- Is defined as the ratio of creep strain to elastic coefficient.

- Creep Coefficient = εcr / εE

2.4.1 Creep Behavior of Concrete

Creep in concrete can have both positive as well as negative effects on the

performance of concrete structures. On the positive side, creep can relieve stress

concentrations induced by shrinkage, temperature changes, or the movement of supports.

For indeterminate beam with two fixed ends, creep deformation will be very useful in

reducing tensile stress caused by shrinkage and temperature variation.

In some concrete structures, creep can do hard to the safety of the structures.

Creep can lead to an excessive deflection of structural members, buckling or other

serviceability problems, especially in high-rise building, eccentrically loaded columns

and long bridges [8]. In mass concrete, creep may be a cause of cracking when a

restrained concrete mass undergoes a cycle of temperature change due to the

development of heat of hydration and subsequent cooling [8].

45

2.4.2 Components of Creep Strain

There are two components of creep strain which occur in a concrete member,

recoverable creep and irrecoverable creep [30], as show in Figure 2.11. the recoverable

component also know as delayed elastic strain εd(t), which is caused by the elastic

aggregates acting on the viscous cement paste after the applied stress is removed.

Figure 2.11: Recoverable and irrecoverable creep component [30]

While the irrecoverable component, also can be referred as flow, εf(t). It is

subdivided into rapid initial flow εfi(t), basic flow εfb(t) and drying flow εfd(t). Rapid

initial flow happens in the first 24 hours after loading and is the remaining flow which

develops gradually with time. While basic flow or basic creep is not dependent upon the

loss of moisture from the concrete and will occur with concrete protected from drying.

46

Meanwhile drying creep is the additional creep which occurs in a drying specimen.

However, drying creep, like drying shrinkage, is dependent upon the loss of moisture

from the concrete to its environment [31]. In normal structural engineering application,

one does not distinguish between basic and drying creep [33].

Therefore, the creep strain can be expressed as [30]

εf(t) = εd(t) + εf(t)

or

εf(t) = εd(t) + εfi(t) + εfb(t) + εfd(t)

as illustrated in Figure 2.12.

Figure 2.12: Creep components in a drying specimen [30]

47

2.4.3 Factors Affecting Creep

The magnitude of the creep depends upon several factors relating to the quality

of the concrete such as the aggregate-cement ratio, water-cement ratio, kind of aggregate

and its grading, composition and fineness of cement, and the age at time of loading. It

also depends upon the intensity and duration of stress, moisture content of the concrete,

the humidity of the ambient air, and the size of the mass.

2.4.3.1 Effect of Stress and Age When First Loaded

The greater the degree of hydration of the cement at the time of load application,

the lower the rate and total amount of creep. One explanation of this is that the

expulsion of moisture from the gel becomes more difficult as the porosity is decreased

through hydration. Since the extent of the hydration is indicated by the strength of a

given concrete, it can be said that creep varies inversely as the strength.

2.4.3.2 Effect of Water-Cement Ratio and Mix

Strength of concrete is determined by the water/cement ratio. The strength of

concrete reduces with the increasing of water/cement ratio. Concrete experience higher

creep due to higher water/cement ratio because the concrete has insufficient restraint due

to the tension force induced in the concrete. A higher water-cement ratio increases the

48

size of the pores in the paste structure, so that water may the more readily escape, and

then under a sustained load the water of adsorption may be expelled more readily to

cause a high rate of creep as shown in Figure 2.13.

Figure 2.13: Effect of water-cement ratio on creep [34]

2.4.3.3 Effect of Composition and Fineness of Cement

Cement is the most important factor in creep because the hydrated cement paste

is the source of the phenomenon. The influence of cement is twofold: that arising from

the physical and chemical properties of the cement. The composition of cement affects

the creep primarily through its influence upon the degree of hydration. Slow-hardening

cements such as low-heat Portland and Portland-pozzolan cements creep more than

cements which hydrate more rapidly. Creep seems to be inversely proportional to the

rapidly of hardening of the cement used. The more hardened the paste the more rigid it

is and the lower its creep potential at a given applied stress.

49

Figure 2.14: Creep in compression and tension for mass-cured concretes [34]

Figure 2.14 indicates that in both tension and compression the creep of concrete

made with low-heat cement is about one-third greater than for concrete made with

normal cement. This serves to explain why low-heat Portland and Portland-pozzolan

cements have served so effectively in relieving stresses in large dams as the mass cools

and have shown superior resistance to cracking.

2.4.3.4 Effect of Character and Grading of Aggregate

Aggregates play an important role in creep of concrete. Coarse aggregate

reduces creep deformation by reducing the cement paste content and restraining the

cement paste against contraction. Generally, concretes made with an aggregate, which is

hard and dense and have low absorption and high modulus of elasticity, are desirable

when low creep strain is needed.

50

The effect of mineral character of aggregate is shown in Table 2.4 for six

concretes. Same mineral aggregate was used from fine to coarse; the grading was the

same for all mixes. After carrying a sustained stress of 800 psi for about 5 years the

maximum creep (1300 millionths) was exhibited by the sandstone concrete and the

minimum (550 millionths) by the limestone.

Table 2.4: Effect of Mineral Character of Aggregate upon Creep [28]

As all aggregates were batched in a saturated, surface-dry condition, and their

absorption factors were generally low, the large variations in creep were not due to the

moisture conditions and the aggregates. Neither were they due to seepage from the

identical paste used in each mix. It is possible that variations in crystalline slip, particle

shape, surface texture, and pore structure of the aggregates may have had some

influence.

2.4.3.5 Effect of Moisture Conditions of Storage

Creep appears to be influenced by the humidity of the air in so far as it affects the

seepage of moisture from the concrete. Naturally, an increase in the humidity of the

atmosphere reduces the rate of loss of moisture or water vapor to the surrounding

atmosphere, slows down the flow of moisture or water vapor to the outer surface, and

51

thus reduces the seepage. Another factor affecting compressive creep is that drying

shrinkage at or near the surface results in a reduction of the cross-sectional area

remaining in compression and therefore causes higher stresses on the central core. A

high temperature and low relative humidity of the ambient environment accelerate the

diffusion of the adsorbed water and capillary water into the atmosphere, and

consequently, increases the creep of concrete. Therefore, the creep of concrete can be

concluded to be inversely proportional to the relative humidity.

The magnitude of creep for various moisture conditions of storage is shown in

Table 2.5. Although these values indicate that for a concrete loaded to 800 psi at the age

of 28 days the creep in air at 70 percent relative humidity was about double that for

water storage, for similar concrete loaded at 3 months to 1,200 psi the creep for the air

storage condition at 70 percent relative was about 2½ times that for water storage.

Table 2.5: Effect of Moisture Condition of Storage upon Creep [5]

2.4.3.6 Effect of Size of Mass

The larger the mass subjected to sustained loading, the less the creep. This is

probably due to the reduced seepage, as the path traveled by the expelled water is greater

with a resulting increase in the frictional resistance to the flow of water from the interior.

The general effect of size of specimen upon creep is shown in Figure 2.15, which

52

includes 6-, 8-, and 10-in. diameter cylinders stored in fog to eliminate the effect of

surface drying. These results show that creep in the 10-in. cylinder is only about one-

half that for the 6-in. cylinder. For storage in dry air, seepage may occur much more

readily from small specimens, and the effect of size on creep may become more

pronounced. Models were prepared using aggregate-cement ratio of 6.95 by weight;

water-cement ratio 0.61 by weight; age at loading 28 days; sustained stress 800 psi;

storage in fog before and after loading.

Figure 2.15: Effect of size of specimens upon creep [5]

2.4.4 Effect of Creep

Creep of plain concrete does not by itself affect strength, although under very

high stresses creep hastens the approach of the limiting strain at which failure takes

place. The influence of creep on the ultimate strength of a simply supported, reinforced

concrete beam subjected to a sustained load is insignificant, but deflection increases

considerably and may in many cases be a critical consideration in design. Another

53

instance of the adverse effects of creep is its influence on the stability of the structure

through increase in deformation and consequent transfer of load to other components.

Thus, even when creep does not affect the ultimate strength of the component in which it

takes place, its effect may be extremely serious as far as the performance of the structure

as a whole is concerned.

Loses of pre-stress due to creep is well known and accounted for the failure of all

early attempts of pre-stressing. Only with the introduction of high tensile steel did pre-

stressing become a successful operation. The effects of creep may thus be harmful. On

the whole, however, creep unlike shrinkage is beneficial in relieving stress

concentrations and has contributed to the success of concrete as a structural material.

2.4.5 Test for Creep

The majority of creep tests are performed on compression specimens subjected to

a uniaxial stress. Generally, there are four loading methods:

i. Dead load

ii. Spring-loaded

iii. Hydraulic

iv. Stabilized hydraulic

54

2.4.5.1 Dead load

The dead load system is hardly used because for the usual size of specimens it

requires large dead weight and is, therefore, cumbersome and often impractical.

2.4.5.2 Spring-loaded

The spring-loaded system, one or more heavy coil springs are held in a

compressed position against a suitable frame. This procedure improves the constancy of

the applied load. The main difficulties lie in the application of the proper load

sufficiently rapidly so that no creep takes place.

2.4.5.3 Hydraulic

In the hydraulic system, high loads can be applied more easily and can be

maintained to a high degree of accuracy. This system is compact and flexible. The

application of the desired load is simple and reliable. However, the maintenance of a

sustained load is sensitive and often there is an unavoidable small leakage of the

hydraulic fluid.

55

2.4.5.4 Stabilized hydraulic

The stabilized hydraulic loading system can be used for a number of specimens

at the same time. This system solves the difficulties encountered in the hydraulic

system.

CHAPTER 3

PREDICTION METHODS

3.1 Introduction

There are various methods for predicting the creep coefficient and shrinkage

strain. Those methods vary in complexity. Some are simple and easy to use, while

others are much more complicated. But the increasing in complexity does not mean an

increasing inaccurary. In this study, predictions from British Standared 8110, Eurocode

2 and Australian Standard 3600 are considered. Besides, there is a prediction of

concrete creep and shrinkage is specified in website. It is used and analyzed as a

comparison for the three specified codes mentioned above.

57

3.2 Shrinkage

Prediction of concrete shrinkage strain is analyzed in this report based on BS

8110, EC 2 and AS 3600.

3.2.1 Drying Shrinkage Strain [32]

An estimate of the drying shrinkage strain of plain concrete εcs at any instant is

given by the product of five partial coefficients:

jecLscs KKKKc=ε [32]

Where

cs is the modification factor to allow for properties of the crushed granitic

aggregate

KL is the coefficient relating to the environment, see figure 3.1

Kc is the coefficient relating to the composition of the concrete, see figure

3.2

Ke is the coefficient relating to the effective thickness of the section, see

figure 3.3

Kj is the coefficient defining the development of shrinkage relative to time,

see figure 3.4

58

The shrinkage to be expected over an interval of time should be taken as the

difference between the shrinkage calculated for the beginning and the end of the

interval.

The values of shrinkage, which are for plain concrete, should be multiplied by

the reinforcement coefficient Ks to obtain the corresponding shrinkage strain for

reinforced concrete.

( )e

sKρα+

=

1

1 [32]

Where

αe is the modular ratio Es/Ec

ρ is the steel ratio As/Ac

As is the total area of longitudinal reinforcement

Ac is the gross cross-sectional concrete area

Es is the modulus of elasticity of the reinforcement

Ec Is the short-term modulus of concrete

59

Figure 3.1: Coefficient KL [32]

Figure 3.2: Coefficient Kc [32]

60

Figure 3.3: Coefficient Ke [32]

Figure 2.12: Coefficient Kj (Shrinkage)

Figure 3.4: Coefficient Kj [32]

61

3.2.2 British Standard [25]

Drying shrinkage consideration is specified in BS8110: Part 2: 1985, section 7.4.

Estimation of drying shrinkage of plain concrete may be obtained from Figure 3.5.

Recommendations for effective section thickness and relative humidity are given in

section 7.3 (BS 8110) [25].

Figure 3.5 relates to concrete of normal workability made without water reducing

admixtures; original water content of about 190 L/m3. Concrete is known to have

different water content; shrinkage may be regarded as proportional to water content

within the range of 150 L/m3 to 230 L/m3.

The shrinkage of plain concrete is dependent on the relative humidity of the air

surrounding, the surface area of concrete and mix proportions. It is increased slightly by

carbonation and self-desiccation and reduced by prolonged curing. Concrete made up of

aggregates with high moisture content increase the initial drying shrinkage. Aggregates

with low modulus of elasticity may lead to higher shrinkage than normal concrete.

Concrete exposed to the outdoor climate in the UK will exhibit seasonal cyclic

strains of ± 0.4 times the 30 year shrinkage superimposed on the average shrinkage

strain.

62

For symmetrically reinforced concrete sections, shrinkage estimation may be

obtained from:

( )ρ

εε

K

sh

ss+

=

1 [25]

Where

εsh = shrinkage of the plain concrete

ρ = area of steel relative to the concrete

K = coefficient, taken as 25 for internal exposure and 15 for external

exposure

For non-symmetrically reinforced concrete sections, the influence of shrinkage

on curvature and deflection is more complex and is outlined in section 3.4.6 of BS 8110:

Part 1: 1985.

Section 3.4.6.7 from BS 8110: Part 1: 1985 indicates the consideration of

concrete deflection due to creep and shrinkage. Permissible span/effective depth ratio

obtained from Table 3.9 to 3.11 (BS 8110) take into account of normal creep and

shrinkage deflection only. The permissible span/effective ratio should be reduced if the

creep or shrinkage of the concrete is expected to be particularly high or in other

abnormal adverse conditions.

63

Figure 3.5: Drying shrinkage of normal-weight concrete [25]

64

3.2.3 Australian Standard [26]

Shrinkage consideration is specified in AS 3600, Clause 6.1.7 [26]. Basic

shrinkage strain and design shrinkage strain are considered in the standard in which they

are mainly affected by the type of environment.

3.2.3.1 Basic shrinkage strain

The basic shrinkage strain of concrete (εcs.b), may be:

a. Normal-class concrete

i. determined from measurements on similar local concrete; or

ii. taken as equal to 850 x 10-6

b. Special-class concrete

i. determined from measurements on similar local concrete; or

ii. determined by tests after eight weeks drying, in accordance with AS

1012.13

65

3.2.3.2 Design shrinkage strain

The design shrinkage strain (εcs) shall be determined from the basic shrinkage

strain (εcs.b) by any accepted mathematical model for shrinkage behavior, calibrated such

that εcs.b is also predicted by the chosen model. In the absence of more accurate

methods, the design shrinkage strain at any time after commencement of drying

shrinkage may be taken as

bcscs k .1εε = [26]

where

k1 is obtained from Figure 3.6

Figure 3.7 classified the climatic zones in Australia. AS 3600 specified that the

consideration shall be given to the fact that εcs has a range of ±40%.

66

Figure 3.6: Shrinkage strain coefficient (k1) for various environments [26]

67

Figure 3.7: Climatic Zones in Austalia [26]

68

3.2.4 Eurocode [27]

Clause 3.1.4 specifies concrete material properties on shrinkage [27]. The total

shrinkage strain is composed of two components, the drying shrinkage strain and the

autogenous shrinkage strain. The drying shrinkage strain develops slowly, since it is a

function of the migration of the water through the hardened concrete. The autogenous

shrinkage strain develops during hardening of the concrete. The major part therefore

develops in the early days after casting. Autogenous shrinkage is a linear function of the

concrete strength. It should be considered specifically when new concrete is cast against

hardened concrete. Hence the values of the total shrinkage strain εcs follow from

cacdcs εεε += [27]

where:

εcs is the total shrinkage strain

εcd is the drying shrinkage strain

εca is the autogenous shrinkage strain

The final value of the drying shrinkage strain, εcd,∞ is equal to kh.εcd,0. εcd,0 may

be taken from Table 3.1 (expected mean values, with a coefficient of variation of about

30%).

69

Table 3.1: Nominal unrestrained drying shrinkage values εcd,0 (%) for concrete with

cement CEM Class N [27]

Relative Humidity (%) fck/fck,cube

(MPa) 20 40 60 80 90 100

20/25 0.62 0.58 0.49 0.30 0.17 0.00

40/50 0.48 0.46 0.38 0.24 0.13 0.00

60/75 0.38 0.36 0.30 0.19 0.10 0.00

80/95 0.30 0.28 0.24 0.15 0.08 0.00

90/105 0.27 0.25 0.21 0.13 0.07 0.00

The development of the drying shrinkage strain in time follows from:

( ) ( ) 0,.., cdhsdscd kttt εβε = [27]

where:

kh is a coefficient depending on the notional size h0 according to Table

3.2

Table 3.2: Values for kh [27]

h0 kh

100

200

300

≥ 500

1.0

0.85

0.75

0.70

70

( )( )

( )3

004.0,

htt

tttt

s

s

sds

+−

−

=β [27]

where:

t is the age of the concrete at the moment considered, in days

ts is the age of the concrete (days) at the beginning of drying

shrinkage (or swelling). Normally this is at the end of curing

h0 is the notional size (mm) of the cross-section (2Ac/u)

Ac is the concrete cross-sectional area

u is the perimeter of that part of the cross section which is exposed to

drying

The autogenous shrinkage strain follows from:

( ) ( ) ( )∞= caasca tt εβε . [27]

where:

( ) ( )610105.2 −

×−=∞ ckca fε [27]

( ) ( )5.02.0exp1 ttas −−=β [27]

71

3.2.4.1 Eurocode (Annex B) [27]

Euro Code Annex B introducing concrete shrinkage using basic equations as well

[27]. The equations are shown below.

Basic equations for determining the drying shrinkage strain

1. the basic drying shrinkage strain εcd,0 is calculated from:

( ) RH

cmo

cm

dsdscdf

fβααε .10..exp..11022085.0 6

210,−

−+= [27]

−=

3

0

155.1RH

RHRHβ [27]

where:

fcm is the mean compressive strength (MPa)

fcmo = 10 MPa

αds1 is a coefficient which depends on the type of cement

= 3 for cement Class S

= 4 for cement Class N

= 6 for cement Class R

αds2 is a coefficient which depends on the type of cement

= 0.13 for cement Class S

72

= 0.12 for cement Class N

= 0.11 for cement Class R

RH is the ambient relative humidity (%)

RH0 = 100%

3.3 Creep

Prediction of concrete creep strain is analyzed in this report based on BS8110,

EC2, AS3600.

3.3.1 Creep Strain [32]

The creep strain in concrete εcc at a particular time after casting can be predicted

from

ccc φσ

ε ×

Ε

=

28

[32]

Where

E28 is the 28-day value of concrete secant modulus which may be taken from

Ec = 3.46√fcu + 3.21

73

Øc is the creep coefficient, Øc = KLKmKcKeKj

Where

KL is the coefficient relating to environment conditions, see figure 3.8

Km is the coefficient relating to the hardening (maturity) of the concrete, see

figure 3.9

Kc is the coefficient relating to the composition of the concrete, see figure

3.2

Ke is the coefficient relating to the effective thickness of the section, see

figure 3.10

Kj is the coefficient defining the development of shrinkage relative to time,

see figure 3.4

Figure 3.8: Coefficient KL [32]

74

Figure 3.9: Coefficient Km [32]

Figure 3.10: Coefficient Ke [32]

75

3.3.2 British Standard [25]

In BS 8110: Part 2: 1985; section 7.3 specifies the creep of concrete [25]. The

final (30 year) creep strain in concrete, εcc can be predicted from

φσ

ε ×

Ε

=

t

cc [25]

Where

Et = modulus of elasticity of the concrete at the age of loading t

Ø = creep coefficient

The creep coefficient may be estimated from Figure 3.11 and the effective

section thickness is defined as twice the cross-sectional area divided by the exposed

perimeter for uniform section. The effective thickness should be taken as 600 mm if

drying is prevented by immersion in water or by sealing. For general purposes, suitable

relative humidity for indoor and outdoor exposure in the UK is 45% and 85%.

However, the relative humidity used in UK might not be applicable in Malaysia.

The creep of concrete can be assumed that about 40%, 60% and 80% of the final

creep develops during the first month; 6 months and 30 months under load respectively,

when concrete is exposed to conditions of constant relative humidity.

76

Creep is partly recoverable with a reduction in stress. The final creep recovery

after 1 year is approximately

0.3 x stress reduction / Eu [25]

Where

Eu = modulus of elasticity of the concrete at the age of unloading

Figure 3.11: Effects of relative humidity, age of loading and section

thickness upon creep factor [25]

77

3.3.3 Australian Standard [26]

Clause 6.1.8.1 in AS 3600 specifies the creep consideration [26]. Basic creep

factor and design creep factor are considered in the standard in which they are mainly

affected by the type of environment and maturity of the hardened concrete.

3.3.3.1 Basic creep factor

The basic creep factor of concrete (Øcc.b) is the ratio of ultimate creep strain to

elastic strain for a specimen loaded at 28 days under a constant stress of 0.4f’c and may

be:

i. Taken as the values given in Table 3.3

ii. Determined from measurements on similar local concrete; or

iii. Determined by tests in accordance with AS 1012.16

Table 3.3: Basic creep factor [26]

Characteristic

strength (f’c), MPa

20 25 32 40 ≥ 50

Creep factor Øcc.b 5.2 4.2 3.4 2.5 2.0

78

3.3.3.2 Design creep factor

The design creep factor (Øcc) for concrete shall be determined from the basic

creep factor (Øcc.b) by any accepted mathematical model for creep behavior, calibrated

such that Øcc.b is also predicted by the chosen model.

cc.b32cc ØØ kk= [26]

where

k2 is obtained from Figure 3.12 [26]

k3 is obtained from Figure 3.13 [26]

Consideration shall be given to the fact that Øcc has a range of approximately

±30%.

79

Figure 3.12: Creep factor coefficient (k2) for various environments [26]

Figure 3.13: Maturity Coefficient (k3) [26]

80

3.3.4 Eurocode [27]

Clause 3.1.4 specifies the concrete material properties on creep [27]. The creep

coefficient, φ(t,t0) is related to Ec, the tangent modulus, which may be taken as 1.05Ecm.

The value found from Figure A may be considered as the creep coefficient, provided that

the concrete is not subjected to a compressive stress greater than 0.45fck(t0) at an age t0,

the age of concrete at the time of loading. The creep deformation of concrete

( ) ( )

Ε

∞=∞

c

c

cc ttσ

ϕε .,, 00 [27]

When the compressive stress of concrete at an age t0 exceeds the value

0.45fck(t0), creep non-linearity should be considered. Such a high stress can occur as a

result of pre-tensioning, e.g. in precast concrete members at tendon level. In such cases,

the non-linear notional creep coefficient should be obtained as follows:

( ) ( ) ( )[ ]45.05.1exp.,, 00 −∞=∞σ

ϕϕ kttk [27]

where:

φk(∞,t0) is the non-linear notional creep coefficient, which replaces φ(∞,t0)

kσ is the stress-strength ratio σc/fcm(t0), where σc is the compressive

stress and fcm(t0) is the mean concrete compressive strength at the

time of loading.

81

The values given in Figure 3.14 are valid for ambient temperatures between -

40ºC and +40ºC and a mean relative humidity RH = 40% and RH = 100%. The

following symbols are used:

φ(∞,t0) is the final creep coefficient

t0 is the age of the concrete at time of loading in days

h0 is the notional size= 2Ac/u, where Ac is the concrete cross-sectional

area and u is the perimeter of that part which is exposed to drying

S is Class S (cement of strength Classes CEM 32.5 N)

N is Class N (cement of strength Classes CEM 32.5 R)

R is Class R (cement of strength Classes CEM 42.5 R, CEM 52.5 N

and CEM 52.5 R)

82

Figure 3.14: Method for determining the creep coefficient for concrete under

normal environmental conditions [27]

3.3.4.1 Eurocode (Annex B) [27]

Euro Code Annex B introducing concrete creep using basic equations as well

[27]. The equations are shown below.

Note: - intersection point between lines 4

and 5 can also be above point 1 - for t0 > 100 it is sufficiently

accurate to assume t0 = 100 (and use the tangent line)

83

Basic equations for determining the creep coefficient:

the creep coefficient may be calculated from:

( ) ( )000 ,., tttt cβϕϕ = [27]

where:

φ0 is the notional creep coefficient and may be estimated from

( ) ( )00 .. tf cmRH ββϕϕ = [27]

φRH is the factor to allow for the effect of relative humidity on the

notional creep coefficient:

3

01.0

100/11

h

RHRH

×

−+=ϕ [27]

213

0

..1.0

100/11 ααϕ

×

−+=

h

RHRH [27]

RH is the relative humidity of the ambient environment in %

β(fcm) is a factor to allow for the effect of concrete strength on the

notional creep coefficient:

( )

cm

cmf

f8.16

=β [27]

for fcm ≤ 35 MPa

for fcm > 35 MPa

84

fcm is the mean compressive strength of concrete in MPa at the age of

28 days

β(t0) is a factor to allow for the effect of concrete age at loading on the

notional creep coefficient

( )

( )20.0

0

01.0

1

tt

+

=β [27]

h0 is the notional size of the member in mm where:

u

Ah c2

0 = [27]

Ac is the cross-sectional area

u is the perimeter of the member in contact with the atmosphere

βc(t,t0) is a coefficient to describe the development of creep with time

after loading, and may be estimated using the following

expression:

( )( )

( )

3.0

0

00,

−+

−

=

tt

tttt

H

cβ

β [27]

t is the age of concrete in days at the moment considered

t0 is the age of concrete at loading at days

t – t0 is the non-adjusted duration of loading in days

βH is a coefficient depending on the relative humidity and the

notional member size. It may be estimated from:

85

for fcm ≤ 35 MPa

( )[ ] 1500250012.015.1 0

18≤++= hRHHβ [27]

for fcm > 35 MPa

( )[ ] 330

181500250012.015.1 ααβ ≤++= hRHH [27]

α1/2/3 are coefficients to consider the influence of the concrete strength

7.0

1

35

=

cmfα

2.0

1

35

=

cmfα

5.0

1

35

=

cmfα [27]

CHAPTER 4

METHODOLOGY

4.1 Introduction

This research is a theoretical work on studying and analyzing concrete properties

due to creep and shrinkage. Therefore, task was completed by gathering information

from all sources and to study in detail what are the parameters that affect creep and

shrinkage. Spread sheet was created based on British Standard, Australian Standard and

European Standard in this research to ease future engineers’ work to determine concrete

creep and shrinkage.

4.2 Information Gathering

Concrete properties due to creep and shrinkage are commonly discussed in

website. The information is repetitive and therefore, reference books and journals are

87

very important in this research. Reference books from UTM library and journals from

several famous authors were used to carry out the literature review in this research.

There are a lot of complicated parameters specified in journals to discuss creep and

shrinkage according to the specific author. However, those complicated parameters are

not discussed in this research.

British Standard (BS8110), Australian Standard (AS3600) and European

Standard (EC2) were also used as a reference in this research as well because one of the

tasks was to produce spread sheet using these standards. The parameters, tables and

graphs from these standards were studied and analyzed in detail during the process of

producing spread sheet.

Other than reference books, discussion on concrete material properties was made

with Mr. Edgar, assistant manager of WorleyParsons Services Sdn Bhd (Infrastructure

Department). He had couple years of experience in mega projects such as constructing

concrete dam using various types of concrete admixtures to reduce the heat of hydration

and to minimize concrete creep and shrinkage with the purpose to reduce cracking on

concrete structures.

88

4.3 Preparation of Spread Sheet

Spread sheet in calculating concrete creep and shrinkage are produced in this

research. The spread sheet is able to determine the final creep and shrinkage of concrete

by inputting some controlled parameters such as concrete strength, relative humidity of

the environment, size of concrete specimen, provided steel reinforcement, concrete

density, applied stress, day of consideration, etc.

The spread sheet was produced separately according to the standards and finally

they were compared to each other to determine their differences by controlling the

parameters. In this research, relative humidity of the environment was used as the

controlled parameter in comparing the final creep and shrinkage of concrete.

CHAPTER 5

ANALYSIS AND RESULTS

5.1 Introduction

In this chapter, the analysis and results from the spread sheet that have been

carried out through this study are analyzed and discussed. The results were

subsequently compared among the standards, BS 8110, AS 3600 and EC 2 by using

relative humidity of the environment as the controlled parameter.

5.2 Shrinkage

Shrinkage is the deformation caused by evaporation of internal water in hardened

concrete. This occurs when chemically free water evaporates from concrete in a dry

environment. Concrete properties due to shrinkage are specified in all codes and below

are the discussion on the shrinkage prediction mentioned in BS 8110, AS 3600, EC 2.

90

5.2.1 Shrinkage Strain

Shrinkage strain prediction in this section is based on the code of practice

documented by Hong Kong government. There are few parameters govern in this code

are not specified in other standards such as cement content, water cement ratio, etc.

Figure 5.1 indicates the relationship between shrinkage and relative humidity based on

the parameters mentioned above. As shown in Figure 5.1, the shrinkage strain of

concrete is 4.70E-04 at relative humidity of 40%. The shrinkage strain is shown to be

zero at relative humidity of 100%.

Shrinkage, εcs

vs Relative Humidity (%)

0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

5.00E-04

0 20 40 60 80 100 120

Relative Humidity (%)

Shrinkage, ε

cs

Figure 5.1: Relationship between Shrinkage, εcs and Relative Humidity (%)

Based on code of practice specified by Hong Kong government

91

5.2.2 British Standard

British Standard is commonly used in Malaysia for structural design. However,

there are some assumed values in BS especially in concrete shrinkage and creep are

obtained from United Kingdom and this might not be applicable in this country because

of the difference in relative humidity.

Generally, shrinkage prediction using BS is based on Figure 3.5. It is found that

there are some limitations by using this standard as there are only 6 month (short term)

and 30 year (long term) duration to be considered. This graph could not accurately give

the shrinkage value for duration such as 5 years or 100 days because interpolation could

not be performed through this graph.

Therefore, it can be said that Figure 3.5 is limited in determining concrete

shrinkage at various duration. It can only be used by assuming short term duration as 6

month period and long term duration as 30 year period.

Figure 5.2 indicates the relationship between shrinkage, εcs and relative humidity

(%). It is shown that at RH of 20%, shrinkage of concrete is about 1.70E-04 while RH

of 100% gives shrinkage value of -8.40E-05.

92

Shrinkage, εcs


-1.00E-04

-5.00E-05

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

0 20 40 60 80 100 120


Shrinkage, ε

cs


Based on BS 8110

5.2.3 Australian Standard

Concrete shrinkage prediction using Australian Standard is found to be limited

There is no specific relative humidity specified in this standard. The parameter, k1

needed in the shrinkage prediction is based on the climatic zones of Australia (Figure

3.7) which is not applicable in other countries. However, a graph of shrinkage versus

the type of environment in Australia was plotted as shown in Figure 5.3. It is found that

relative humidity is increasing at the environment of Arid, Interior, Temperate Inland

and Tropical relatively. At the zone of Tropical and Near-Coastal, the shrinkage strain

is about 2.36E-04.

93

Shrinkage, εcs


0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

5.00E-04

0 20 40 60 80 100 120


Shrinkage, ε

cs


Based on AS 3600

5.2.4 European Standard

European Standard specifies concrete shrinkage in Clause 3.1.4 using table

method and using formula method in Annex B. EC 2 considers autogenous shrinkage

of concrete which does not specified in other codes. This might cause the results to be

more accurate. However, there is no statement mentioning about reinforced concrete

shrinkage which include the ratio of reinforcement area to concrete specimen ratio as

specified in other codes.

Arid

Interior

Temperate

Tropical & Near-Coastal

94

Figure 5.4 show the comparison of predicting concrete shrinkage using table

method and formula method, relative humidity as the controlled parameter. It is shown

that both of the methods are almost the same. At RH of 20%, the shrinkage is about

3.24E-04 and at RH of 100%, the shrinkage value is at about 5.00E-05.

Shrinkage, εcs


0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

3.00E-04

3.50E-04

0 20 40 60 80 100 120


Shrinkage, ε

cs

EC2

(Graph)

EC2

(Formula)


using Table and Formula Method Based on EC 2

Figure 5.5 indicates the relationship between shrinkage strain and duration in

days using the formula specified in EC 2. From the figure, it is found that the rate of

concrete shrinkage is higher at the beginning stage (first year) and is decreasing at the

entire duration. This might be due to the rate of chemical reaction in concrete

component where the rate is decreasing with the increase in time.

95

Shrinkage, ε cs vs Duration (days)

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

3.00E-04

3.50E-04

4.00E-04

0 500 1000 1500 2000 2500 3000 3500 4000

Duration (days)

Sh

rin

kag

e, ε

cs

Figure 5.5: Relationship between Shrinkage, εcs and Duration (days)

Based on EC 2

5.2.5 Comparison of Shrinkage Using Different Standards

Figure 5.6 shows the comparison of concrete shrinkage prediction using AS

3600, BS 8110, EC 2 and code specified by Hong Kong government. Relative humidity

is used as controlling parameter rather than duration, t because all codes consider long

term shrinkage except EC 2 formula method. Therefore, time of consideration is not

preferable in this section.

96

As shown in the figure below, the shrinkage strain values are almost similar.

Shrinkage prediction using BS 8110 is less conservative compare to the others. This

might be due to the parameter of duration. British Standard only considers 6 month and

30 year shrinkage. Shrinkage at duration other than 6 months and 30 years are unlikely

to be predicted because interpolation from the graph is difficult. Besides, the estimation

and assumption of shrinkage parameters in BS is based on United Kingdom environment

which might not be applicable in other countries.

Figure 5.6 indicates that shrinkage prediction using Eurocode is more

conservative. Although AS 3600 present higher value, it shouldn’t be considered in this

comparing purpose because Australian Standard does not include the effect of specific

relative humidity in the calculation. Only climatic zones is specified in the AS 3600.

Therefore, Eurocode is preferable in determining shrinkage strain as it considers the

effect of autogeneous shrinkage which does not be specified in other codes. Another

advantage of using Eurocode is that the shrinkage strain at varies duration can be

predicted easily. In short, Eurocode is preferable and more general in determining

concrete shrinkage strain.

97

Shrinkage, εcs


-2.00E-04

-1.00E-04

0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

5.00E-04

0 20 40 60 80 100 120


Sh

rin

kag

e, ε

cs

HK govern.

BS8110

EC2 (Graph)

EC2 (Formula)

AS3600

Figure 5.6: Comparison of Shrinkage Using Different Standards

5.3 Creep

Creep is the deformation of hardened concrete caused by a long-lasting constant

load applied on it. Concrete properties due to creep is specified in all codes and below

are the discussion on the creep prediction specified in BS 8110, AS 3600, EC 2 and code

documented by Hong Kong government.

98

5.3.1 Creep Strain

Shrinkage strain prediction in this section is based on the code of practice

documented by Hong Kong government. Generally, the concrete creep is affected by

several factors such as relative humidity, effective thickness, concrete strength, applied

stress, composition of concrete, etc. Figure 5.7 shows the relationship between creep

and relative humidity based on the parameters mentioned above. As shown in Figure

5.7, the creep of concrete is about 1.37E-03 at relative humidity of 40%. The creep is

shown to be 4.35E-03 at relative humidity of 100%.

Creep, ε cc vs Relative Humidity (%)

0.00E+00

3.00E-04

6.00E-04

9.00E-04

1.20E-03

1.50E-03

0 20 40 60 80 100 120


Cre

ep, ε

cc

Figure 5.7: Relationship between Creep, εcc and Relative Humidity (%)

Based on Code of Practice specified by Hong Kong government

99

5.3.2 British Standard

As discussed in section 5.2.2, the assumed values in BS especially in concrete

shrinkage and creep are obtained from United Kingdom and this might not be applicable

in this country because of the difference in relative humidity.

The creep factor used in BS is obtained in Figure 3.11. The values from the

graph show reasonable as it includes the effect of relative humidity and the age of

loading applied to the concrete specimen.

Figure 5.8 show relationship between creep, εcc and relative humidity (%). It is

shown that at RH of 40%, creep of concrete is about 1.92E-03 while RH of 100% gives

creep value of 7.36E-04.

100


0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

0 20 40 60 80 100 120


Cre

ep, ε

cc


Based on BS 8110

5.3.3 Australian Standard

Concrete creep prediction using Australian Standard is found to be limited as

discussed in section 5.2.3 because it is based on the climatic zones of Australia as shown

in Figure 3.7. The parameter, k2 needed in the creep strain prediction is depends on

climatic zones of Australia which is not applicable in other countries. However, a graph

of creep strain versus different type of environment in Australia was plotted as shown in

Figure 5.9. At the environment of Tropical and Near-Coastal zone, creep strain is about

1.51E-03.

101


0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

0 20 40 60 80 100 120


Cre

ep

, ε

cc


Based on AS 3600

5.3.4 European Standard (EC 2)

European Standard specifies concrete creep in Clause 3.1.4 using graph method

and using formula method in Annex B. The graph method is limited because it is only

applicable at relative humidity of 50% and 80%. Interpolation could not be performed

through the graph and therefore, creep value at other relative humidity such as 20%

could not be obtained. Furthermore, the maximum day of applied stress is only 100 days

which is limited as well. The figure of obtaining creep is shown in Figure 3.14.

Arid Interior

Temperate

Tropical & Near-Coastal

102

The method of using formula to obtain creep of concrete is straight forward. It is

affected by mean compressive strength, relative humidity, type of cement, modulus of

elasticity, etc. This method is preferable because it is more general and applicable for

various relative humidity of environment. Varies in duration manage to provide the

creep strain prediction by using this method.

Figure 5.10 show the comparison of predicting concrete creep using graph and

formula method, relative humidity as the controlling parameter. It is shown that

although they are from the same basis, the results are slightly different. However, the

results are acceptable.


0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

0 20 40 60 80 100 120


Cre

ep

, ε

cc


using Graph and Formula Method Based on EC 2

103

5.3.5 Comparison of Creep Using Different Standard

Figure 5.11 shows the comparison of concrete creep prediction using AS 3600,

BS 8110, EC 2 and code specified by Hong Kong government. The parameter, relative

humidity is preferable rather than duration, t in this section because only EC 2 manage

to give creep strain prediction at specific duration. Other codes only consider long term

creep.

As shown in the figure below, the creep values are almost similar. From the

graph below, it is stated that creep strain prediction using these standards are acceptable.

Eurocode give more conservative result compare to the others it is preferable as creep

strain at varies duration can be predicted using this code of practice.


0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

0 20 40 60 80 100 120


Cre

ep

, ε

cc

HK govern.

BS8110

EC2 (Graph)

EC2 (Formula)

AS3600

5.11: Comparison of Creep Using Different Standards

104

Figure 5.12 indicates the relationship between creep strain and duration in days

using the formula specified in EC 2. From the figure, it is found that the rate of concrete

creep is higher at the beginning stage (first year) and is decreasing at the entire duration.

This might be due to the rate of chemical reaction in concrete component where the rate

is decreasing with the increase in time.

Creep, ε cc vs Duration (days)

0.00E+00

2.00E-04

4.00E-04

6.00E-04

8.00E-04

1.00E-03

1.20E-03

1.40E-03

1.60E-03

0 500 1000 1500 2000 2500 3000 3500 4000

Duration (days)

Cre

ep

, ε

cc

Figure 5.12: Relationship between Creep, εcc and Duration (days)

Based on EC 2

CHAPTER 6

CONCLUSIONS AND RECOMMENDATIONS

6.1 Conclusions

From the results of this study, the following conclusions can be drawn:

i. Both the concrete creep and shrinkage induce tension force in the concrete

elements and cause cracking on the concrete specimen. They are affected by

few parameters such as concrete strength, cement properties, days to be

considered, relative humidity, etc. This research shows that the creep and

shrinkage decrease proportionally with the relative humidity of the

environment as specified in Chapter 5.

ii. From the shrinkage strain study, BS 8110 gives lower value compare with

other codes of practice. Furthermore, prediction using BS is limited because

it only considers long term and short term duration. In the comparison,

Eurocode give acceptable result. The shrinkage strain is more conservative

106

compare to the others under controlled parameters. Besides, strain at varies

duration is predictable and it considers the effect of autogeneous shrinkage.

iii. From the creep strain study, all codes present similar result. There is no big

difference in the creep strain prediction. However, Eurocode is preferable in

determining the strain because value at varies duration is predictable.

iv. The code of BS 8110, Eurocode 2 and Australian Standards are based on

environment from Europe and Australia, where the weather conditions are

very much different from tropical countries, such as Malaysia. Therefore,

those design codes are just a guide to predict concrete creep and shrinkage.

They are unable to determine the exact creep and shrinkage strain of concrete

as measured at site.

v. The rate of creep and shrinkage strain is higher at the beginning stage (first

year) and is decreasing at the entire duration. The rate of deformation is due

to the rate of chemical reaction in concrete components.

107

6.2 Recommendations for Further Research

1. This study is a theoretical work which does not carry out laboratory test.

Therefore, laboratory test is required to clarify and compare with the results from

calculation by controlling the parameters such as concrete strength, cement

content, applied stress, relative humidity, etc which are specified in the spread

sheet. The results might be used to verify which code of practice gives a closer

result to the actual concrete creep and shrinkage.

2. There are many articles specify the effect of admixtures such as Shrinkage

Reducing Agent (SRA) on the concrete properties in order to minimize the

concrete creep and shrinkage. However, the effects of natural admixtures such

as Fly Ash and Rice Husk Ash on concrete properties are just briefly discussed.

Therefore, studies on the effects of natural admixtures on concrete can be

continued to improve this research. The spread sheet can be improved by

including the effect of admixtures as well.

3. This study only concentrates on British Standards, Australian Standards and

European Standards. To improve this study, other codes such as American

Standards, Chinese Standards, etc could be considered so that comparison

between different codes of practice can be done more precisely.

108

4. Other parameters such as concrete strength could be used as controlling

parameter in comparing the creep and shrinkage strain based on different codes

of practice.

REFERENCES

1. T. Tazawa and S. Miyazawa. Eds Z. P. Bazant and I. Carol Proc. 5th International

RILEM Symposium. Autogenous shrinkage of concrete and its importance in

concrete, in Creep and Shrinkage in Concrete. 1993: 159-168.

2. Mehta, P.K., and Monteiro, P., Concrete-Structure, Properties, and Materials,

The McGraw-Hill Companies, Inc., New York, 1993.

3. T.C. Powers. J. Portl. Cem. Assoc. Research and Development Laboratories.

Causes and control of volume change. 1959: 29-39.

4. R. L’Hermite. Proc. 4th Int. Symp. On the Chemistry of Cement, Washington

DC. Volume changes of concrete. 1960: 659-694.

5. J. D. Bernal, J. W. Jeffery and H. F. W. Taylor. Mag. Concr. Res. first report on

investigations in progress Crystallographic research on the hydration of

Portland cement. 1952: 49-54.

6. J. D. Bernal. Proc. 3rd Int. Symp. On the Chemistry of Cement, London. The

structures of cement hydration compounds. 1952: 216-36.

7. F. M. Lea. On the Chmistry of Cement, Washington DC. Cement research:

Retrospect and prospect, Proc. 4th

Int. Symp. 1960: 5-8.

8. S.E. Pihlajavaara. On Evaluation of the Performance of External Surfaces of

Buildings. Carbonation – an important effect on the surfaces of cement based

materials, RILEM/ASTM/CIB Symp.

9. G.J. Verbeck. ASTM. Sp. Tech. Publ. Carbonation of hydrated Portland cement.

1958(205): 17-36.

10. American Concrete Institute. Hot Weather Concreting. Farmington Hills,

Michigan. ACI 305R-99. 1999

106

11. M. Shoya. Transactions of the Japan Concrete Institute. Drying shrinkage and

moisture loss of superplasticizer admixed concrete of low water cement ratio,

1979: 103-110.

12. F. M. Lea. The Chemistry of Cement and Concrete. Arnold, London. 1970.

13. J. J. Brooks and A. Neville. Creep and Shrinkage of Concrete: Effect of

Materials and Environment. Creep and shrinkage of concrete as affected by

admixtures and cement replacement materials. 1992: 19-36.

14. E. J. Sellevold. Nordic Concrete Research. Shrinkage of concrete: effect of

binder composition and aggregate volume fraction from 0 to 60%. 1992: 139-

152.

15. P. W. Keene. Cement Concrete. Assoc. Tech. Report TRA/331. The effect of air-

entrainment on the shrinkage of concrete stored in laboratory air. 1960.

16. J. J. Shideler. J. Amer. Concr. Inst.. Calcium chloride in concrete. 1952: 537-

559.

17. Troxell, G.E., Raphael, J.E., Davis, R.W., 1958. Long-time creep and shrinkage

tests of plain and reinforced concrete. Proc. ASTM 58, 1101 – 1120.

18. T. C. Hansen and A. H. Mattock. J. Amer. Concr. Inst.. The influence of size and

shape of member on the shrinkage and creep of concrete. 1966: 267-290.

19. Krauss, P. D., and Rogalla, E. A., Transverse Cracking in Newly Constructed Bridge

Decks, NCHRP Report 380, Transportation Research Board, National Research

Council, Washington, D.C., 1996

20. Burrows, R. D., The Visible and Invisible Cracking of Concrete, American

Concrete Monograph No. 11, 1998.

21. American Concrete Institute. Prediction of Creep, Shrinkage, and Temperature

Effects in Concrete Structures. Detroit, Michigan. ACI Committee 209. 1999.

22. American Concrete Institute. Standard Practice for the Use of Shrinkage

Compensating Concrete. Detroit, Michigan. ACI Committee 223. 1998.

23. Neil Jackson and Ravindra K. Dhir. Civil Engineering Materials. 1996.

107

24. Concrete Manual Eight Edition. A Manual for the Control of Concrete

Construction. U.S. Department of the Interior Water and Power Resources

Services. 1981.

25. British Standard Institution. Structural use of concrete. London, BS8110. 1997

26. Australian Standard: Concrete Structures. Australia, AS3600-2001.

27. European Standard. Eurocode 2: Design of concrete structures. Europe, EN

1992-1-1. 2004

28. Davis, R. E., H. E. Davis, and J. S. Hamilton. Proc. ASTM. Plastic Flow of

Concrete under Sustained Stress. 34(1934): 354-386.

29. South African Bureau of Standards. The Structural use of Concrete. Pretoria.

SABS 0100: 1992, Part 1 and 2. 1992.

30. Gilbert, R. I., Time Effects in Concrete Structures. Elsevier Science Publishers.

1988.

31. Lee, Y., Yi, Seng-Tae, Kim, Min-Su and Kim, Jin-Keun. Cement and Concrete

Research. Evaluation of a Basic Creep Model With Respect to Autogenous

Shrinkage. 2006. 36(2006): 1268-1278.

32. http://www.bd.gov.hk/english/ducuments/code/concrete/Concrete2004_reprinted

3.pdf

33. A. M. Neiville, Properties of Concrete, Fourth and Final Edition, Standards

updated to 2002: 412-474

34. George Earl Troxell, Harmer E. Davis, Composition and Properties of Concrete,

1956: 228-251

35. Carlson, R. W.: „The Chemistry and Physics of Concrete Shrinkage,“ Proc.

ASTM, vol. 35, pt. II (1935), pp. 419-437

36 S. T. A. ÖDMAN, Effects of variations in volume, surface area exposed to

drying and composition of concrete on shrinkage, RILEM/CEMBUREAU Int.

Colloquium on the Shrinkage of Hydraulic Concretes, 1, 20 pp. (Madrid, 1968)

108

37 R. G. L’HERMITE, Quelques problèmes mal connus de la technologie du béton,

Il Cemento, 75, No. 3, pp. 231-46 (1978)

APPENDIX

110

Creep and Shrinkage

1. Shrinkage for plain concrete

Cs = 3.0, the modification factor to allow for properties of the crushed granitic aggregate

KL = the coefficient relating to the environment, see graph 1

Kc = the coefficient relating to the composition of the concrete, see graph 2

Ke = the coefficient relating to the effective thickness of the section, see graph 3

Kj = the coefficient defining the development of shrinkage relative to time, see graph 4

ε cps = csKLKcKeKj

Graph 1: Coefficient KL (Shrinkage)

0

110

200

275

330

380

420

y = -0.0702x2 + 2.9405x + 411.43

0

50

100

150

200

250

300

350

400

450

30405060708090100

Relative humidity of air, %

Sh

rin

kag

e K

L x

10

-6

Graph 2: Coefficient KC (Creep / Shrinkage)

y = 4.3285x2 + 0.7103x

y = 3.2408x2 + 0.737x

y = 1.6816x2 + 0.9725x

y = 1.5075x2 + 0.4063x

0

0.5

1

1.5

2

2.5

3

3.5

4

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Water / cement ratio

Cre

ep

/ S

hri

nkag

e K

C

500

400

300

200

Graph 3: Coefficient Ke (Shrinkage)

1.2

1

0.8

0.650.55

0.5

y = 3E-06x2 - 0.0033x + 1.3302

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 100 200 300 400 500 600

Sh

rin

kag

e K

e

Cement content kg/m3

Effective thickness

111

0

0 100 200 300 400 500 600

Effective thickness, hA, mm

112

Table 1: Cube strength at an age of, fcu,t

Grade

7 days 2 months 3 months 6 months 1 year

N/mm2 N/mm2 N/mm2 N/mm2 N/mm2

20 13.5 22 23 24 25

25 16.5 27.5 29 30 31

30 20 33 35 36 37

40 28 44 45.5 47.5 50

50 36 54 55.5 57.5 60

1.1 Shrinkage for reinforced concrete

ε cs = the shrinkage for reinforced concrete

ε cps = the shrinkage for plain concrete

α e = E s / E c

ρ = As / Ac

E c,t = E c,28 ( 0.4 + 0.6 f cu,t / f cu,28 )

E c,28 = ( w / 2400 )2 x ( Ko + 0.2 f cu,28 )

t0 = time since loading, days

E s = modulus of elasticity of reinforcement

E c = modulus of elasticity of concrete

As = area of steel reinforcement

Ac = area of concrete

w = concrete density in kg/m3

Ko = a constant closely related to the modulus of elasticity of the aggregate

(taken as 20 kN/mm2 for normal-weight concrete)

ε cs = ε cps / ( 1 + ρα e )

Characteristic Cube strength at an age of:

strength, f cu,28

N/mm2

20

25

30

40

50

Graph 4: Coefficient Kj (Creep / Shrinkage)

0

0.2

0.4

0.6

0.8

1

1.2

1 10 100 1000 10000

Time since loading, days

Cre

ep

/ S

hri

nkag

e K

j

50

100

200

400

800

Effective Thickness

113

Input

Concrete section

width, b = 250 mm

depth, d = 400 mm

4 T 20

Ac = 100000 mm2 f cu,28 = 25 N/mm2

As = 1257 mm2

ρ = 0.0126

w = 2400 kg/m3 (normal-weight concrete = 2400 kg/m3 )

Ko = 20 kN/mm2 (range from 14 kN/mm2 to 26 kN/mm

2 )

E s = 200 kN/mm2

E c,28 = 25 kN/mm2

90 days

t0 = 28 days

f cu,t = 28.55 Mpa

E c,t = 27.13 kN/mm2

α e = 7.37

R.H = 100 %

KL = 3.48E-06

W/C = 0.5

Cement content = 500 kg/m3

KC = 1.4373

Eff. Thickness = 154 mm

Ke = 0.8935

Time since loading = 90 days

Kj = 0.32

ε cps = 4.29E-06

ε cs = 3.93E-06

Steel provided =

Shrinkage at t =

(From Table 1)

(t ≥ 3 days)

(From Graph 3)

(From Graph 1)

(From Graph 2)

(From Graph 4)

114

2. Creep strain in concrete

E 28 = 28-day value of concrete secant modulus which may be taken from E c = 3.46√f cu + 3.21

Øc = creep coefficient, Øc = KLKmKcKeKj

Kc = the coefficient relating to the composition of the concrete, see graph 2

Kj = the coefficient defining the development of shrinkage relative to time, see graph 4

KL = the coefficient relating to environment conditions, see graph 5

Km = the coefficient relating to the hardening (maturity) of the concrete, see graph 6

Ke = the coefficient relating to the effective thickness of the section, see graph 7

ε cc = (stress / E 28 ) x Øc

Graph 5: Coefficient KL (Creep)

1

1.5

2.35

2.95

3.3

y = -0.0003x2 + 0.0061x + 3.3956

0

0.5

1

1.5

2

2.5

3

3.5

0102030405060708090100110

Relative humidity of air, %

Cre

ep

KL

Graph 6: Coefficient Km (Creep)

1.8

1.6

1.4

1

0.850.75

0.630.5

1.7

1.4

1.1

0.9

0.70.58

0.50.4

0.3

1.2y = 2.019x-0.222

y = 1.8791x-0.2982

0

1

2

1 10 100 1000Age of concrete at time of loading (T=20˚C)

Cre

ep

Km

Wa

ter

Sto

rag

e

No

rma

l a

ir

Ve

ry d

ry a

ir

Ve

ry m

ois

t a

ir

115

R.H = 100 %

KL = 1.0056

Age of concrete at time of loading, t0 = 28 days

Type of cement: 1

1. Ordinary Portland Cement

2. Rapid Hardening Portland Cement

Km = 0.9635

Eff. Thickness = 154 mm

Ke = 0.9063

E 28 = 3.46√f cu + 3.21

= 20.51 kN/mm2

Ø c = 0.4456

20 N/mm2

ε cc = 4.35E-04

Total creep & shrinkage = 4.38E-04

Applied stress, σ =

(From Graph 6)

(From Graph 7)

(From Graph 5)

Graph 7: Coefficient Ke (Creep)

1.2

1

0.850.75 0.72 0.7

y = 3.0412x-0.2404

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 100 200 300 400 500

Effective thickness, he, mm

Cre

ep

Ke

115

Creep and Shrinkage


Ambient relative humidity = 100 %

Effective thickness = 154 mm

Shrinkage period = 90 days

ε sh = 200 x 10-6

British Code

BS 8110 - 1997

Structural use of Concrete

Figure 1: Drying shrinkage of normal-weight concrete

(From Figure 1)

116

1.1 Shrinkage for reinforced concrete

ε ss = the shrinkage for reinforced concrete

ε sh = the shrinkage of the plain concrete

K = the coefficient, taken as 25 for internal exposure and as 15 for

external exposure

ρ = the area of steel relative to that of the concrete

Input

Concrete section

width, b = 250 mmdepth, d = 400 mm

4 T 20

Ac = 100000 mm2

As = 1257 mm2

ρ = 0.0126

K = 15

ε ss = 1.68E-04

2. Creep strain in concrete

E t = the modulus of elasticity of the concrete at the age of loading

Ø = the creep coefficient

σ = applied stress

E c,t = E c,28 ( 0.4 + 0.6 f cu,t / f cu,28 )

E c,28 = ( w / 2400 )2 x ( Ko + 0.2 f cu,28 )

w = concrete density in kg/m3

Ko = a constant closely related to the modulus of elasticity of the aggregate

(taken as 20 kN/mm2 for normal-weight concrete)

w = 2400 kg/m3(normal-weight concrete = 2400 kg/m

3)

Ko = 20 kN/mm2(range from 14 kN/mm

2 to 26 kN/mm

2)

f cu,28 = 25 N/mm2

ε ss = ε sh / ( 1 + K ρ )

Steel provided =

εcc = (σ / E t ) x Ø

117

28 days

f cu,t = 24.09 N/mm2

E c,28 = 25 kN/mm2

E c,t = 24.45 kN/mm2

Figure 2: Effects of relative humidity, age of loading and section thickness upon creep factor

RH = 100 %

Ø = 0.9

σ = 20 N/mm2

ε cc = 7.36E-04


Age of loading, t =

(Refer Table 1)

(t ≥ 3 days)

(From Figure 2)

118

Creep and Shrinkage


Basic shrinkage strain, εcs.b

a) Normal-class concrete

i. Determined from measurements on similar local concrete

ii. Taken as equal to 850 x 10-6

b) Special-class concrete

i. Determined from measuremnets on similar local concrete

ii. Determined by tests after eigth weeks drying, in accordance with AS 1012.13

ε cs.b = 8.50E-04

Design shrinkage strain, εcss

th = 154 mm

90 days

k 1 = 0.33

ε css = 2.81E-04

Shrinkage for reinforced concrete

As = the cross-sectional area of reinforcement

Ag = the gross cross-sectional area of a member

Input

Concrete section

width, b = 250 mm

depth, d = 400 mm

4 T 20

Ag = 100000 mm2

As = 1257 mm2

ε cs = 2.36E-04

(From Figure 1) Type of environment = Tropical and Near-Coastal

Days for shrinkage strain =

(From Graph 4)

ε cs = ε css / ( 1 + 15 As/Ag)

ε css = k 1 ε cs.b

Australian Standard

AS 3600 - 2001

Concrete Structures

Steel provided =

119

Graph 2: INTERIOR ENVIRONMENTS (Shrinkage)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 10 100 1000 10000 100000Days

k1

400

200

100

50

37.5

Graph 3: TEMPERATE INLAND (Shrinkage)

0

0.2

0.4

0.6

0.8

1

1.2

1 10 100 1000 10000 100000Days

k1

400

200

100

50

Graph 1: ARID (Shrinkage)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 10 100 1000 10000 100000Days

k1

400

200

100

50

120

Figure 1: Climatic Zones

Graph 4: TROPICAL AND NEAR-COASTAL (Shrinkage)

0

0.2

0.4

0.6

0.8

1

1 10 100 1000 10000 100000Days

k1

400

200

100

50

121

Creep strain in concrete

Basic creep factor, Øcc.b

Ø cc.b = the ratio of ultimate creep strain to elastic strain for a specimen loaded at 28 days

under a constant stress of 0.4 f' c and may be -

(a) taken as the values given in Table 1; or

(b) determined from measurements on similar local concrete; or

(c) determined by tests in accordance with AS 1012.6

f' c = characteristic compressive cylinder strength of concrete at 28 days

f cm = mean value of the compressive strength of concrete at the relevant age

Table 1 : Basic Creep Factor

5.2 4.2 3.4 2.5 2

f' c = 20 Mpa

f cm = 28 Mpa

Ø cc.b = 5.2

Strength ratio (f cm /f' c ) = 1.4

Design creep factor, Øcc

Ø cc = k 2 k 3 Ø cc.b

th = 154 mm

90 days

k 2 = 0.45

k 3 = 0.90

Ø cc = 2.106

(From Graph 9)

(From Graph 8)

Type of environment = (From Figure 1)

Days for shrinkage strain =

40

Tropical and Near-Coastal

≥ 5020 25 32

Creep factor Ø cc.b

Characteristic strength

(f' c ) , Mpa

122

Creep for concrete

σ i = the sustained stress in the concrete

E c = the mean value of the modulus of elasticity of concrete at 28 days

σ i = 20 N/mm2

E c = 20.51 kN/mm2

ε cc = 2.05E-03


ε cc = (σ i / E c ) x Ø cc

Graph 5 : ARID (Creep)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 10 100 1000 10000 100000Days

k2

400

200

100

50

Graph 6 : INTERIOR ENVIRONMENTS (Creep)

0

0.2

0.4

0.6

0.8

1

1.2

1 10 100 1000 10000 100000Days

k2

400

200

100

75

50

123

Graph 7 : TEMPERATE INLAND (Creep)

0

0.2

0.4

0.6

0.8

1

1.2

1 10 100 1000 10000 100000Days

k2

400

200

100

50

Graph 8 : TROPICAL AND NEAR-COASTAL (Creep)

0

0.2

0.4

0.6

0.8

1

1 10 100 1000 10000 100000Days

k2

400

200

100

50

Graph 9 : Maturity Coefficient (k 3 ) (Creep)

0.7

0.9

1.1

1.3

1.5

1.7

0.5 0.7 0.9 1.1 1.3 1.5 1.7

Strength Ratio (f cm / f' c )

Ma

turi

ty C

oe

ffic

ien

t (k

3)

124

Creep and Shrinkage

1. Shrinkage

ε cs is the total shrinkage strain

ε cd is the drying shrinkage strain

ε ca is the autogenous shrinkage strain

Drying shrinkage, ε cd (t)

t = the age of the concrete at the moment considered, in days

ts = the age of the concrete (days) at the beginning of drying shrinkage

(or swelling). Normally at the end of curing

h0 = the notional size (mm) of the cross-section (2A c/u )

h0 kh

100 1

200 0.85

300 0.75

≥ 500 0.7

20 40 60 80 90 100

20/25 0.62 0.58 0.49 0.30 0.17 0.00

40/50 0.48 0.46 0.38 0.24 0.13 0.00

60/75 0.38 0.36 0.30 0.19 0.10 0.00

80/95 0.30 0.28 0.24 0.15 0.08 0.00

90/105 0.27 0.25 0.21 0.13 0.07 0.00

f ck is the characteristic compressive cylinder strength of concrete at 28 days

f ck, cube is the characteristic compressive cube strength of concrete at 28 days

f ck /f ck,cube

(MPa)Relative Humidity (%)

Eurocode 2

European Standard

Design of Concrete Structures

ε cs = ε cd + ε ca

ε cd (t) = β ds (t,ts) . kh . ε cd,0

Table 1: Values for k h

Table 2: Nominal unrestrained drying shrinkage values ε cd,0 (‰) for concrete

withcement CEM Class N

( )( )

( )3

004.0,

htt

tttt

s

ssds

+−

−=β

125

t = 90 days

ts = 2 days

h0 = 154 mm

f ck = 20 MPa

RH = 100 %

f cm = 28 MPa

β ds (t,ts) = 0.5355

kh = 0.9172

ε cd,0 = 1.13E-04

ε cd (t) = 5.55E-05

Autogenous shrinkage, ε ca (t)

β as (t) = 2.5 (f ck - 10) x 10-6

= 2.50E-05

ε ca (∞) = 1 - (exp (-0.2 t0.5)

8.50E-01

ε ca (t) = 2.13E-05

ε cs = 7.68E-05

ε ca (t) = β as (t) . ε ca (∞)

126

2. Creep

t0 = the age of the concrete at time of loading in days

= 28 day (t0 > 3 days)

φ (∞,t0) = 2.3

σc = 20 N/mm2

Type of cement = N

s = 0.25

β cc (t0) = exp {s [1 - (28/t0)1/2] }

1.0000

f cm (t0) = 28 MPa

f ck (t0) = 20 MPa

φ(∞,t0) exp [1.5 (kσ - 0.45)] kσ = σc/fcm(t)

= 3.42 = 0.7143

E cm = 29.96 kN/mm2

E cm (t0) = E cm x [f cm (t0) / f cm ]0.3

29.96 kN/mm2

E c (t0) = 1.05 x E cm (t0)

31.46 kN/mm2

ε cc = 2.17E-03


φ k (∞,t0) =

(From Figure 1 )

ε cc (∞,t0) = φ k (∞,t0) . (σc/E c )

σc > 0.45 fck(t0)

Cement Type

1. Class N

2. Class R

3. Class S

127

Figure 1: Method for determining the creep coefficient for concrete under normal environmental conditions

128

Creep and Shrinkage

1. Shrinkage

Drying shrinkage, ε cd (t)

t is the age of the concrete at the moment considered, in days

ts is the age of the concrete (days) at the beginning of drying shrinkage

(or swelling). Normally at the end of curing

h0 is the notional size (mm) of the cross-section (2A c/u )

h0 kh

100 1

200 0.85

300 0.75

≥ 500 0.7

f cm is the mean compressive strength (MPa)

f ck is the characteristic compressive cylinder strength of concrete at 28 days

f cmo = 10 MPa

α ds1 is a coefficient which depends on the type of cement

= 3 for cement Class S

= 4 for cement Class N

= 6 for cement Class R

α ds2 is a coefficient which depends on the type of cement

= 0.13 for cement Class S

= 0.12 for cement Class N

= 0.11 for cement Class R

RH is the ambient relative humidity (%)

RH0 = 100%

ε cd (t) = β ds (t,ts) . kh . ε cd,0

European Standard

Eurocode 2

Design of Concrete Structures

Table 1: Values for k h

ε cs = ε cd + ε ca

( )( )

( )3

004.0

,

htt

tttt

s

s

sds

+−

−

=β

( )RH

cmo

cm

dsdscdf

fβααε .10..exp..11022085.0 6

210,−

−+=

−=

3

0

155.1RH

RHRHβ

129

Type of cement = N

f ck = 20 MPa

RH = 100 %

t = 90 days

ts = 2 days

h0 = 154 mm

f cm = 28 MPa

α ds1 = 4

α ds2 = 0.12

ε cd,0 = 0.00E+00

kh = 0.9172

0.5355

ε cd (t) = 0.00E+00

Autogenous shrinkage, ε ca (t)

β as (t) = 2.5 (f ck - 10) x 10-6

= 2.50E-05

ε ca (∞) = 1 - (exp (-0.2 t0.5)

8.50E-01

ε ca (t) = 2.13E-05

ε cs = 2.13E-05

ε ca (t) = β as (t) . ε ca (∞)

β ds (t,ts) =

130

2. Creep

φ (t,t0) = φ 0 . β c (t,t0)

φ 0 = φ RH . β (f cm ) . β (t0)

t = 10950 days

t0 = 28 days (age of concrete at loading in days)

α 1 = (35/f cm )0.7= 1.17

α 2 = (35/f cm )0.2= 1.05

α 3 = (35/f cm )0.5= 1.12

φ RH = 1 + { (1-RH/100) / [0.1 x h0^(1/3)] }

= 1.0000

β (f cm ) = 16.8 / √f cm

= 3.1749

β (t0) = 1 / (0.1 + t00.2)

= 0.4884

β H = 1.5[1+(0.012RH)^18]h0+250≤1500

= 1500

β c(t,t0) = [ (t-t0) / (β H + t - t0) ]0.3

= 0.9621

φ 0 = 1.5508

φ (t,t0) = 1.4920

s = 0.25

β cc (t) = exp {s [1 - (28/t0)1/2] }

1.0000

f cm (t0) = 28 MPa

σc = 20 N/mm2

E cm = 29.96 kN/mm2

E cm (t0) = E cm x [f cm (t0)/ f cm ]0.3

29.96 kN/mm2

E c (t0) = 1.05 x E cm (t0)

31.46 kN/mm2

ε cc = 9.49E-04


ε cc (t,t0) = φ (t,t0) . (σc/E c )

creep and shrinkage using different code

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