Citation
Analytical comparison of creep, elastic compliance, and shrinkage coefficents for normal and ultra high-strength concrete

Material Information

Title:
Analytical comparison of creep, elastic compliance, and shrinkage coefficents for normal and ultra high-strength concrete
Creator:
Bekhit, Elizabeth Kamal
Place of Publication:
Denver, Colo.
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
Physical Description:
xvi, 87 leaves : ; 28 cm

Thesis/Dissertation Information

Degree:
Master's ( Master of Science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Civil Engineering, CU Denver
Degree Disciplines:
Civil Engineering
Committee Chair:
Durham, Stephan A.
Committee Members:
Rens, Kevin L.
Li, Cheng Y.

Subjects

Subjects / Keywords:
Concrete -- Creep ( lcsh )
Concrete -- Expansion and contraction ( lcsh )
Elastic analysis (Engineering) ( lcsh )
High strength concrete ( lcsh )
Concrete -- Creep ( fast )
Concrete -- Expansion and contraction ( fast )
Elastic analysis (Engineering) ( fast )
High strength concrete ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaf 87).
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Elizabeth Kamal Bekhit.

Record Information

Source Institution:
|University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
655778695 ( OCLC )
ocn655778695
Classification:
LD1193.E53 2010m B44 ( lcc )

Full Text
ANALYTICAL COMPARISON OF CREEP,
ELASTIC COMPLIANCE, AND SHRINKAGE
COEFFICIENTS FOR NORMAL AND ULTRA
HIGH-STRENGTH CONCRETE
by
Elizabeth Kamal Bekhit
B.S., Colorado State LTniversity, 2006
A thesis submitted to the
University of Colorado Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
2010


Thesis for a Master of Civil Engineering
degree by
Elizabeth Kamal Bekhit
has been approved
by
Stephan A. Durham, Ph.D.
Cheng Y. Li, Ph.D.
A/y/tQ


Bekhit, Elizabeth Kamal (M.S., Civil Engineering)
Analytical Comparison of Creep, Elastic Compliance, and Shrinkage Coefficients
for Normal and Ultra High-Strength Concrete
Thesis directed by Assistant Professor Stephan Durham
ABSTRACT
Concrete experiences time-dependent deformation such as creep and shrinkage.
Creep is defined as either basic, when no movement of moisture occurs between
the concrete and the surrounding environment, or drying, when movement of
moisture occurs between the concrete and the surrounding environment.
Shrinkage is defined as the decrease in the volume of hardened concrete (Rhodes,
1997). This is due to the loss of moisture in the concrete. An analytical approach
was used to examine the affects of cement paste, quantity of aggregate and
properties of the aggregate on drying shrinkage. In addition, the properties that
affect creep, elastic compliance and shrinkage coefficients that are examined
herein include: age at time of loading, curing time, volume to surface ratio,
ambient relative humidity, cement type, and compressive strength.
Creep, elastic compliance and shrinkage coefficients were examined using the
GL2000 method. When age at time of loading and volume to surface ratio was
increased the creep coefficients decreased. When the curing time increased the


creep coefficients increased. When the ambient relative humidity decreased the
creep coefficients increased.
Results from this analysis found that when age of loading and compressive
strength increases elastic compliance decreases. Cement Type III has the least
amount of elastic deformation and cement type II has the most elastic
deformation. When curing time, volume to surface ratio, and compressive
strength increased the shrinkage coefficients decreased. When the ambient
relative humidity decreased the shrinkage coefficients increased. Cement type II
has the lowest shrinkage coefficient and cement type III has the greatest.
Therefore when ultra high-strength is used rather than normal strength concrete
the creep, elastic compliance and shrinkage coefficients will decrease.
This abstract accurately represents the content of the candidates thesis. I
recommend its publication.
Signed
Stephan A. Durham, Ph.D.


DEDICATION
I dedicate this thesis to Chris and my family for all of their support and patience.


ACKNOWLEDGEMENTS
I would like to thank my advisor, Dr. Stephan Durham, for his assistance in my
thesis. In addition, I would like to thank Dr. Kevin Rens and Dr. Cheng Yu Li for
their participation on my masters committee and their contribution towards this
thesis. Finally, I would like to thank Martin/Martin Inc. for their financial support
during my pursuit of this graduate degree.


TABLE OF CONTENTS
List of Figures..................................................................x
List of Tables.................................................................xiii
Chapter
1. Introduction..............................................................1
1.1 General....................................................,..............1
1.2 Thesis Contents.......................................................... 2
1.3 Objectives................................................................4
1.4 Scope.....................................................................5
2. Literature Review.........................................................6
2.1 Overview..................................................................6
2.2 Creep Strain and Elastic Strain...........................................8
2.2.1 Components that Cause Creep and Elasticity................................8
2.2.2 Concrete Mixture Affects on Creep and Elasticity..........................9
2.2.3 Environment Affects on Creep and Elasticity..............................10
2.2.4 Construction Affects on Creep and Elasticity.............................11
2.2.5 Calculations for Predicting Creep........................................12
2.2.6 Calculations for Predicting Elasticity...................................13
2.3 Shrinkage Strain.........................................................14
2.3.1 Components that Cause Shrinkage..........................................14
2.3.2 Concrete Mixture Affects on Shrinkage....................................15
v


2.3.3 Environment affect on Shrinkage...............................................16
2.3.4 Design and Construction Affects on Shrinkage..................................17
2.3.5 Calculations for Predicting Shrinkage.........................................18
2.4 Normal Strength Concrete......................................................18
2.5 Ultra High-Strength Concrete............................:....................19
3. Problem Statement.............................................................20
4. Development and Verification of Spreadsheet................................. 23
4.1 Spreadsheet Functionality.....................................................23
4.2 Verification with ACI 209.2R-08.............................................. 23
4.2.1 Creep Verification with ACI 209.2R-08....................................... 24
4.2.2 Elastic Compliance Verification with ACI 209.2R-08............................25
4.2.3 Shrinkage Verification with ACI 209.2R-08.....................................26
5. Coefficients due to Normal Strength Concrete.............................;....28
5.1 Overview................................................................. ;...28
5.2 Modulus of Elasticity, for Normal Strength Concrete.......................... 29
5.3 Creep Coefficients for Normal Strength Concrete............................. 29
5.3.1 Concrete age at loading Effects on Creep Coefficients for Normal Strength
Concrete................................................................... 30
5.3.2 Curing Affects on Creep Coefficients for Normal Strength Concrete.............31
5.3.3 Volume to Surface Ratio Effects on Creep Coefficients for Normal
Strength Concrete........................................................... 33
vx


5.3.4 Ambient Relative Humidity Affects on Creep Coefficients for Normal
Strength Concrete.............................................................34
5.3.5 Creep Coefficients for Normal and High Strength Concrete due to
Compressive Strength between 3,000 psi to 12,000 psi ........................36
5.4 Elastic Compliance Coefficients for Normal Strength Concrete.................36
5.4.1 Concrete age at loading Effects on Elastic Compliance Coefficients for
Normal Strength Concrete......................................................37
5.4.2 Cement Type affects on Elastic Compliance Coefficients for Normal
^Strength Concrete........................................................... 38
5.4.3 Elastic Compliance Coefficients for Normal and High Strength Concrete
due to Compressive Strength between 3,000 psi to 12,000 psi................38'
5.5 Shrinkage Coefficients for Normal Strength Concrete..........................40
5.5.1 Curing Affects on Shrinkage Coefficients for Normal Strength Concrete.........40
5.5.2 Volume to Surface Ratio Effects on Shrinkage Coefficients for Normal
Strength Concrete.............................................................42
5.5.3 Ambient Relative Humidity Affects on Shrinkage Coefficients for Normal
Strength Concrete.....:......................................................43
5.5.4 Cement Type Effects on Shrinkage Coefficients for Normal Strength
Concrete................................................................... 45
5.5.5 Shrinkage Coefficients for Normal and High Strength concrete due to
Compressive Strength between 3,000 psi to 12,000 psi........................46
vii


6. Coefficients due to Ultra High-Strength Concrete............................48
6.1 Overview....................................................................48
6.2 Modulus of Elasticity for Ultra High-Strength Concrete.................... 49
6.3 Creep Coefficients for Ultra High-Strength Concrete.........................49
6.3.1 Concrete age at loading Effects on Creep Coefficients for Ultra High-
Strength Concrete...................................................... 50
6.3.2 Curing Effects on Creep Coefficients for Ultra High-Strength Concrete.......51
6.3.3 Volume to Surface Ratio Effects on Creep Coefficients for Ultra High-
Strength Concrete..........................................................53
6.3.4 Ambient Relative Humidity Affects on Creep Coefficients for Ultra High-
Strength Concrete........................................................ 54
6.3.5 Creep Coefficients for Ultra High-Strength Concrete due to Compressive
Strengths between 13,000 psi to 19,000 psi.................................56
6.4 Elastic Compliance Coefficients for Ultra High-Strength Concrete.......... 56
6.4.1 Concrete age at loading Effects on Elastic Compliance Coefficients for
Ultra High-Strength Concrete....................................... ......57
6.4.2 Cement Type Effects on Elastic Compliance Coefficients for Ultra High-
Strength Concrete.;................................................... 57
6.4.3 Elastic Compliance Coefficients for Ultra High-Strength Concrete due to
Compressive Strength between 13,000 psi to 19,000 psi......................58
6.5 Shrinkage Coefficients for Ultra High-Strength Concrete.....................59
viii


6.5.1 Curing Effects on Shrinkage Coefficients for Ultra High-Strength
Concrete................................................................ 60
6.5.2 Volume to Surface Ratio Effects on Shrinkage Coefficients for Ultra
High-Strength Concrete....................................................61
6.5.3 Ambient Relative Humidity Effects on Shrinkage Coefficients for Ultra
High-Strength Concrete............................................. 63
6.5.4 Cement Type Effects on Shrinkage Coefficients for Ultra High-Strength
Concrete........................................................... ...64
6.5.5 Shrinkage Coefficients for Ultra High-Strength Concrete due to
Compressive Strength between 13,000 psi to 19,000 psi.........:...;..........66
7. Comparison of Results..................................... ..............68
7.1 Creep Coefficients Normal versus Ultra High-Strength..........:...........68
7.2 Elastic Compliance Coefficients Normal versus Ultra High-Strength.........71
7.3 Shrinkage Coefficients Normal versus Ultra High-Strength..................73
8. Conclusions and Recommendations.......................................... 79
8.1 Conclusion.............................................................. 79
8.2 Recommendations......................................................... 81
IX


LIST OF FIGURES
Figure
5-1: Concrete age at loading Effects on Creep Coefficients for Normal Strength
Concrete....................................................................28
5-2: Curing Affects on Creep Coefficients for Normal Strength Concrete............29
5-3: Volume to Surface Ratio Effects on Creep coefficients for Normal
Strength Concrete............;..............................................30
5-4: Ambient Relative humidity Effects on Creep Coefficients for Normal
Strength Concrete.......................................................... 32
5-5: Elastic Compliance Coefficients for Normal and High Strength Concrete
due to Compressive Strength between 3,000 psi to 12,000 psi ................36
5-6: Curing Effects on Shrinkage Coefficients for Normal Strength
Concrete............................................................... 38
5-7: Volume to Surface Ratio Effects on Shrinkage Coefficients for Normal
Strength Concrete...........................................................39
5-8: Ambient Relative humidity Effects on Shrinkage Coefficients for Normal
Strength Concrete.......................................................... 40
5-9: Cement Type Effects on Shrinkage Coefficients for Normal Strength
Concrete.................................................................. 42
5-10: Shrinkage Coefficients for Normal and High Strength Concrete due to
Compressive Strength between 3,000 psi to 12,000 psi........................43
x


6-1: Concrete age at loading Effects on Creep Coefficients for Ultra High-
Strength Concrete.................................. .......................47
6-2: Curing Effects on Creep Coefficients for Ultra High-Strength
Concrete....................................................................48
6-3: Volume to Surface Ratio Effects on Creep coefficients for Ultra High-
Strength Concrete.......................................................... 49
6-4: Ambient Relative humidity Affects on Creep Coefficients for Ultra High-
Strength Concrete.............................................:.......... 51
6-5: Elastic Compliance Coefficients for Ultra High-Strength Concrete due to
Compressive Strength between 13,000 psi to 19,000 psi.................... 54
6-6: Curing Effects on Shrinkage Coefficients for Ultra High-Strength
Concrete............................................................... .56
6-7: Volume to Surface Ratio Effects on Shrinkage Coefficients for Ultra
High-Strength Concrete..................................................... 57
6-8: Ambient Relative Humidity Effects on Shrinkage Coefficients for Ultra
High-Strength Concrete..................................................... 59
6-9: Cement Type Effects on Shrinkage Coefficients for Ultra High-Strength
Concrete......................................................*............60
6- 10: Shrinkage Coefficients for Ultra-High Strength Concrete due to
Compressive Strength between 13,000 psi to 19,000 psi....................61
7- 1: Creep Coefficients GL2000 Method versus ACI Creep Estimation...............64
xi


66
7-2: Elastic Compliance Coefficients due to Compressive Strength between
3.000 psi to 19,000 psi..............................................
7-3: Shrinkage Coefficients Normal versus Ultra high-Strength.....................67
7-4: Shrinkage Coefficients due to Compressive Strength between 3,000 psi to
19.000 psi.................................................................68
7-5: Shrinkage Coefficients GL2000 Method versus ACI Shrinkage
Estimation,...........................................................:........70
xu


LIST OF TABLES
Table
2-1: Factors for Cement Type........................................................12
4-1: Concrete Parameters used for Verification......................................21
4-2: Values for Creep Strain Coefficients Spreadsheet Values........................21
4-3: Creep Strain Coefficients per ACI Technical Report (Videla 2008)...........:...22
4-4: Values, for Elastic Compliance Coefficients Spreadsheet Values........:........23
4-5: Elastic Compliance Coefficients per ACI Technical Report
(Videla 2008).................................................................23
4-6: Values for Shrinkage Strain Coefficients Spreadsheet Values....................23
4- 7: Shrinkage Strain Coefficients per ACI Technical Report (Videla 2008)...........24
5- 1: Creep Coefficients for Normal Strength Concrete................................26
5-2: Concrete age at loading Effects on Creep Coefficients for Normal Strength
Concrete......................................................................27
5-3: Curing Affects on Creep Coefficients for Normal Strength Concrete..............29
5-4: Volume to Surface Ratio Effects on Creep coefficients for Normal
Strength Concrete........................................................... 30
5-5: Ambient Relative humidity Effects on Creep Coefficients for Normal
Strength Concrete.............................................................31
5-6: Creep Coefficients for Normal and High Strength Concrete due to
Compressive Strength between 3,000 psi to 12,000 psi........................33
xiii


5-7: Elastic Compliance Coefficients for Normal Strength Concrete................33
5-8: Concrete age at loading affects on Elastic Compliance Coefficients for
Normal Strength Concrete....................................................34
5-9: Cement Type Effects on Elastic Compliance Coefficients for Normal
Strength Concrete...........................................................35
5-10: Elastic Compliance Coefficients for Normal and High Strength Concrete
due to Compressive Strength between 3,000 psi to 12,000 psi.................35
5-11: Shrinkage Coefficients for Normal Strength Concrete...........................37
5-12: Curing Effects on Shrinkage Coefficients for Normal Strength
Concrete................................................................. 37
5-13: Volume to Surface Ratio Effects on Shrinkage Coefficients for Normal
Strength Concrete........................................................... 39
5-14: Ambient Relative Humidity Effects on Shrinkage Coefficients for Normal
Strength Concrete......................................................... .40
5-15: Cement Type Effects on Shrinkage Coefficients for Normal Strength
Concrete................................................................... 41
5- 16: Shrinkage Coefficients for Normal and High Strength Concrete due to
Compressive Strength between 3,000 psi to 12,000 psi........................43
6- 1: Creep Coefficients for Ultra High-Strength Concrete..........................45
6-2: Concrete age at loading Effects on Creep Coefficients for Ultra High-
Strength Concrete......................................................... 46
xiv


6-3: Curing Effects on Creep Coefficients for Ultra High-Strength
Concrete...................................................................48
6-4: Volume to Surface Ratio Effects on Creep coefficients for Ultra High-
Strength Concrete..........................................................49
6-5: Ambient Relative Humidity Affects on Creep Coefficients for Ultra High-
Strength Concrete........................................................ 50
6-6: Creep Coefficients for Ultra High-Strength Concrete due to Compressive
Strength between 13,000 psi to 19,000 psi..................................52
6-7: Elastic Compliance Coefficients for Ultra High-Strength Concrete............52
6-8: Concrete age at loading affects on Elastic Compliance Coefficients for
Ultra High-Strength Concrete..;...................................... ...53
6-9: Cement Type Affects on Elastic Compliance Coefficients for Ultra High- .
Strength Concrete...................................................... 53
6-10: Elastic Compliance Coefficients for Ultra High-Strength Concrete due to
Compressive Strength between 13,000 psi to 19,000 psi......................54
6-11: Shrinkage Coefficients for Ultra High-Strength Concrete.....................55
6-12: Curing Effects on Shrinkage Coefficients for Ultra High-Strength
Concrete............................................................... 56
6-13: Volume to Surface Ratio Effects on Shrinkage Coefficients for Ultra
High-Strength Concrete....................................................-57
xv


6-14: Ambient Relative Humidity Affects on Shrinkage Coefficients for Ultra
High-Strength Concrete................................................... 58
6-15: Cement Type Affects on Shrinkage Coefficients for Ultra High-Strength
Concrete...................................................................60
6- 16: Shrinkage Coefficients for Ultra High-Strength Concrete due to
Compressive Strength between 13,000 psi to 19,000 psi......................61
7- 1: Creep Coefficients Normal versus Ultra High-Strength...................... 62
7-2: Creep Coefficients due to Compressive Strength between 3,000 psi to
19.000 psi............................................................. 63
7-3: Creep Coefficients GL2000 Method versus ACI Creep Estimation.................63
7-4: Elastic Compliance Coefficients Normal versus Ultra High-Strength......: 65
7-5: Elastic Compliance Coefficients due to Compressive Strength between
, 3,000 psi to 19,000 psi................................................:...65
7-6: Shrinkage Coefficients Normal versus Ultra High-Strength................. 67
7-7: Shrinkage Coefficients due to Compressive Strength between 3,000 psi to
19.000 psi............................................................ 68
7-8: Shrinkage Coefficients GL2000 Method versus ACI Shrinkage Estimation.......69
xvi


1. Introduction
1.1 General
Normal strength and high-strength concrete are widely used in structures around
the world. Many engineers will eventually transition to using ultra high-strength
concrete because of the smaller cross-sections and longer spans ultra high-
strength concrete will allow. Concrete that has a compressive strength of up to
6,000 psi (41 MPa) is considered normal strength (Famy, 1994), up to 12,000 psi
(83 MPa) is considered high-strength, and up to 19,000 psi (131 MPa) is
considered ultra high-strength. These high compressive strengths are achieved by
lowering the water-to-cement ratios (w/c), by increasing silica fume (Collepandi,
1990), adding a water-reducing mineral admixture such as fly ash, and/or by
adding water-reducing chemical admixture such as superplasticizers (Famy,
1994). The modulus of elasticity is dependent on several factors such as density
of the concrete, rock content and type, and on the compressive strength.
Therefore, ultra high-strength concrete has a different equation than high-strength
concrete to estimate the modulus of elasticity. As a result, ultra high-strength
concrete will allow structural members to have less shortening, when compared to
a member of the same cross-section with lower strength, which in turn makes the
member more slender, more appealing and easier to construct.


Concrete members experience time-dependent deformations such as creep and
shrinkage. Creep is defined as the time-dependent increase of strain in hardened
concrete subjected to sustained stress (Rhodes, 1997). Creep is defined as either
basic, when no movement of moisture occurs between the concrete and the
surrounding environment, or drying, when movement of moisture occurs between
the concrete and the surrounding environment. Shrinkage is defined as the
decrease in the volume of hardened concrete (Rhodes, 1997). This-is due to the
loss of moisture in the concrete. This study focuses on drying shrinkage afid this
is governed by the cement paste and the quantity and properties of the, aggregate
(McDonald 2005).
1.2 Thesis Contents
This thesis provides in chapter two a literature review of creep, elastic
compliance, shrinkage, normal strength concrete, ultra high-strength concrete, and
the GL2000 method created by Gardner and Lockman that calculates creep,
elastic compliance and shrinkage coefficients. Each of these properties are
defined below:
Creep- is defined as the increase of strain in hardened concrete subjected
to sustained stress due to either basic, when no movement of moisture
occurs between the concrete and the surrounding environment, or drying,
2


when movement of moisture occurs between the concrete and the
surrounding environment (Rhodes, 1997).
Elastic Compliance- is defined as the initial strain at loading per unit stress
applied. It is the inverse of the mean modulus of elasticity of concrete
when loading starts (Rhodes, 1997).
Shrinkage- is defined as the decrease in the volume of hardened concrete
(Rhodes, 1997) due to the loss of moisture in the concrete.
Chapter three defines the need for this research and the concrete properties used
for the analytical analysis. Chapter four describes the development of the
spreadsheet used to calculate creep, elastic compliance, and shrinkage and
provides verification of the calculations. Chapter five contains the coefficient
values for creep, elastic compliance, and shrinkage of normal strength concrete,
the effects of concrete age at time of loading on creep and elastic compliance
coefficients, the effects of curing time on creep and shrinkage, and the effect of
volume to surface on creep and shrinkage. In addition, the influence of relative
humidity on creep and shrinkage, the effect of cement type on elastic compliance
and shrinkage, and the effect of compressive strength on elastic compliance and
shrinkage are included in this chapter. Chapter six contains the coefficient values
for creep, elastic compliance, and shrinkage of ultra high-strength concrete, the
effects of concrete age at time of loading on creep and elastic compliance
coefficients, the effects of curing time on creep and shrinkage, and the effect of
3


volume to surface on creep and shrinkage. In addition, the influence of relative
humidity on creep and shrinkage, the effect of cement type on elastic compliance
and shrinkage, and the effect of compressive strength on elastic compliance and
shrinkage are included in this chapter. Chapter seven provides comparisons of
creep, elastic compliance, and shrinkage coefficients between normal strength to
ultra high-strength concrete. Where normal strength according to GL200Q is
considered to be up to 11,890 psi (82 MPa) (Videla 2008), therefore the concrete
compressive strengths analyzed in this chapter are between 3,000 psi (21 MPa) to
19,000 psi (131 MPa), Chapter, eight includes the conclusions and
recommendations fi;om this study. Appendix A provides a hand calculation of the
creep, elastic compliance, and shrinkage coefficients of normal strength and ultra
high-strength concrete.
1.3 Objectives
This thesis compares both normal strength and ultra high-strength concrete effects
on creep, elastic compliance, and shrinkage coefficients of hardened concrete.
This was accomplished by incorporating documented empirical equations derived
in previous research for normal strength concrete. These equations were modified
in this research for ultra-high strength concrete. The primary objective of this
thesis is to examine the influences of increased compressive strength on the
shrinkage and creep behavior of concrete. Specifically, ultra high-strength
4


concrete with compressive strengths greater than 12,000 psi (83 MPa) was
researched. It was expected that ultra high-strength concrete would decrease the
amount of shortening in hardened concrete.
1.4 Scope
An analytical study was conducted to examine the effects of normal strength and
ultra high-strength concrete on time-dependent deformations using a method
called GL2000 created by Gardner and Lockman. This method was created to
analytically analyze concrete compressive strengths up to 11,890 psi (82 MPa).
The method has been manipulated for this studys purpose to account for concrete
compressive strengths up to 19,000 psi (131 MPa).
5


2. Literature Review
2.1 Overview
Creep and shrinkage are time-dependent deformations. The GL2000 method
along with other methods were developed to estimate these deformations. The
GL2000 method was created by Gardner and Lockman (2001), with minor
modification introduced by Gardner (2004). The method is a modification of the
GZ Atlanta 97 model made to conform to the AC! 209 model. Prediction of creep
and shrinkage by the GL2000 model is found to be the closest to experimental
results (Goel 2007). The model only requires input of data that is available to the
engineer at the time of design.
This method requires (Videla 2008):
age of concrete when drying begins, usually taken at the end of the moist
curing;
Age of concrete at time of loading;
Ambient Relative humidity expressed as a decimal;
Volume-to-surface ratio;
Cement type;
Average concrete compressive strength at 28 days of age.
6


These requirements are parameters that impact creep and shrinkage. The method
uses these parameters to estimate the amount of creep and shrinkage a member
may experience over the members lifetime.
This method was developed for normal strength concrete. Normal strength
concretes are defined as concretes with an average compressive strength at 28
days of age between 2,321 psi (16 MPa) but not more than 11,890 psi (82 MPa)
according to the GL2000 method (Videla 2008). Where as normal strength
concrete is usually define as concretes with compressive strengths up to 6,000 psi
(41 MPa). According to Gardner and Lockman, the method can be used
regardless of type and quantity of chemical admixtures or supplementary
cementitious materials used in the concrete, ambient temperature, or curing
regime. The predicted values can be improved by simply measuring concrete
strength development and modulus of elasticity with time (Videla 2008).
7


The limitations for the Gardner and Lockman method are (Lockman 2000):
2321 psi (16 MPa) < 28 day of age compressive strength (f cm28) < 11,890
psi (82 MPa)
0.4 < water-to-cement ratio (w/c) < 0.6
0.2 < ambient relative humidity (h) < 1.0
0.75 in (19 mm) < volume-to-surface ratio (v/s) < oo
Time of curing (tc) > 1 day
Time load is applied (t0) > 1 day
tc 2.2 Creep Strain and Elastic Strain
Creep and elastic strains are time-dependent. Altering the concrete properties,
environment, and construction of a concrete member will change the amount of
creep and elastic strains over time. This affects the strains by either increasing or
decreasing the strain coefficients.
2.2.1 Components that Cause Creep and Elasticity
The five primary components of creep and elasticity: load induced strains, initial
strain at time of loading (also known as nominal elastic strain), creep strain, basic
creep, and drying creep. Load induced strain is the time-dependent strain due to
the constant sustained load applied. The initial strain at time of loading is the
8


short term strain at the instantaneous moment of loading. Creep strain represents
the time dependent increase in strain under sustained constant load taking place
after the initial strain at loading. Basic creep strain represents the time dependent
increase in strain under sustained constant load of a concrete specimen in which
there are no moisture losses or gains. Drying creep depends on the size and shape
of the specimen. It occurs when the specimen is exposed to the environment that
allows the specimen to dry (McDonald 2005).
2.2.2 Concrete Mixture Affects on Creep and Elasticity
Factors affecting creep due to mixture proportions are quantity of aggregate, size
and grading of aggregate, aggregate properties, lightweight aggregates, water and
cement content, slump, air content, and admixtures. An increase in aggregate
quantity will decrease the amount of creep (McDonald 2005) because it results in
less paste and aggregate is much stiffer than paste. Aggregate size affects the
bond between the paste and the aggregate (McDonald 2005), where a better bond
will decrease the creep. Thus as aggregate size decreases it will create a better
bond with the paste. The elastic properties of the aggregate significantly
influence basic and drying creep. Dimensional changes in the cement paste can
deform softer aggregates easier than stiffer aggregates (McDonald 2005). Moduli
of elasticity are typically between 10,000 ksi to 20,000 ksi for aggregates.
Lightweight aggregate concrete tends to have a greater basic and drying creep
9


than normal weight aggregate. This is primarily due to the lower modulus of
elasticity of these aggregates. Generally decreasing the water to cement ratio
(w/c) by increasing the cement content usually increases basic and drying creep.
This causes the member to have less moisture and when the member experiences
a decrease in moisture more basic and drying creep occurs. Increasing air content
will increase basic and drying creep. In addition, mineral and chemical
admixtures such as water-reducing and high-range water-reducing admixtures will
increase both basic and drying creep. Silica fume will also increase creep.
Whereas, fly ash will decrease creep (McDonald 2005).
2.2.3 Environment Affects on Creep and Elasticity
Ambient relative humidity, cyclic ambient relative humidity, and temperature are
environmental factors that affect elasticity and creep. Ambient relative humidity
affects drying creep. Concrete in water or environments where drying cannot
occur may have only a quarter of drying creep. Cyclic ambient relative humidity
proves that a constant ambient relative humidity at 65% exhibited slightly lower
drying creep than ambient relative humidity cycled between 40%-90%
(McDonald 2005). Due to the fluctuation of temperature the member will
experience expansion and contraction which will cause an increase in creep.
Temperature affects basic and drying creep (McDonald 2005) because when
10


moisture is removed from the concrete member the basic and drying creep is
increased.
2.2.4 Construction Affects on Creep and Elasticity
Load, curing time, heat or steam curing, size and shape, and time of loading are
factors that affect creep due to the construction and structural design of the
concrete members. Basic and drying creep are generally assumed linearly related
to applied stress up to 40% of the compressive strength (fc). Increasing the
period of moist curing before loading will decrease basic and diying creep
(McDonald 2005) due to increasing the moisture in the concrete member. Heat
and steamed curing significantly reduces the basic and drying creep of concrete as
this type of curing increases the strength of concrete at early ages. Drying creep
is significantly affected by the thickness of the concrete member. Thicker
members have a lower rate of creep. Concrete loaded at later ages will have less
creep (McDonald 2005).
11


2.2.5 Calculation for Predicting Creep
Equation 2.1 predicts creep strain according to the Gardner and Lockman Method
(GL2000) in the AC1 209.2R-08 technical report.
\as
<*>28 W = #C)
I,-*.!
/_Y
+

\li ~{o +7
+2.5(l-1.08ft2]
t~h
ti -t0 +77x
W2
wy y
Eq. 2.1
Where,
028 (t) = Creep coefficient at time i due to load at time t0
h Relative humidity (decimal)
^ = Concrete volume to surface ratio (in)
tf = Age of concrete at the time being considered (days)
to =Age of concrete at time of loading (days)
o>(0 =
f .
1-
t, -t.
t, c + 77 x
If (<><,)
Eq. 2.2
Where,
0(tc ) = Drying before time of loading factor, remains constant at the initial value
throughout the relaxation period, remains constant at the value at the time of
loading.
12


tc =Time of moist curing (days)
= Concrete volume to surface ratio
(in)
tt = Age of concrete at the time being considered (days)
2.2.6 Calculation for Predicting Elasticity
Equation 2.3 predicts elastic strain according to the Gardner and Lockman
Method (GL2000) in the AC1209.2R-08 technical report.
ElasticStrain 1 / Ecmt Eq. 2.3
Where,
Ecm = 500,000 + 52,000Jf'cmt Elastic modulus at time of loading
/' = /?,2 /cm28 Concrete strength at time of loading
Relates to the strength development to cement type
Where s factor is a Comite euro-international du beton, Euro-International
Committee of Concrete, (CEB) 1993 style strength development parameter
(Videla 2008). See Table 2-1. Type I cement is a general-purpose cement suitable
for all uses. Type II cement is used in normal structures or elements exposed to
soil or ground waters where sulfate concentrations are considered moderate. Type
III cement is a higher early strength cement used when forms need to be removed
13


as soon as possible (Kosmatka 2002). The coefficients s (strength gain
coefficient) and K (shrinkage constant) are factors that depend on cement type.
These factors should be determined from test data whenever possible (Videla,
2008).
Table 2-1: Factors for Cement Type
Cement Type s K
1 0.335 1.00
11 0.40 0.75
III 0.13 1.15
2.3 Shrinkage Strain
Shrinkage is affected by the surrounding environment and the specimen
configuration. Altering the concrete properties, environment, and construction of
a concrete member will change the amount of shrinkage strain over time. This
affects the strains by either increasing or decreasing the strain coefficients.
2.3.1 Components that Cause Shrinkage
There are five types of shrinkage: autogenous, drying, carbonation, plastic
shrinkage, and swelling. Autogenous shrinkage, also known as basic shrinkage, is
the shrinkage that occurs in the absence of moisture exchange. T'his shrinkage is
usually small but may become significant for concrete with a w/c of less than
14


0.40. Drying shrinkage occurs in specimens that are exposed to the environment
and allowed to dry. Carbonation shrinkage is caused by the reaction of calcium
hydroxide within the cement matrix with atmospheric carbon dioxide. Plastic
shrinkage occurs while the cement paste, mortar, grout and concrete is plastic
(during placement). Swelling occurs when concrete is placed in water (McDonald
2005).
2.3.2 Concrete Mixture Affects on Shrinkage
Factors affecting shrinkage due to mixture proportions are as follows: quantity of
aggregate, size and grading of aggregate, water and cement content, slump, elastic
properties of aggregate, clay containing aggregates, lightweight aggregates,
cement characteristics, air content, and admixtures. The quantity of the aggregate
affects shrinkage due to the aggregates ability to restrain shrinkage of the cement
paste. An increase in the size of aggregates will decrease the paste content. Thus
decreasing the shrinkage as a result of less cement paste. Increasing water and
cement will increase shrinkage since this will increase the quantity of cement
paste and decrease aggregate content in the mixture. Increasing the slump by
adding water will increase shrinkage. If slump is increased by using water
reducing admixtures then shrinkage will decrease if the water content of the
concrete mixture is decreased. Concrete with a high modulus of elasticity will
tend to decrease shrinkage when compared to concrete with low modulus of
15


elasticity values. Aggregates containing clay with minerals such as breccia tend
to increase shrinkage due to their high water demand. Light-weight aggregate
increases shrinkage because they are typically more porous than normal strength
aggregate and can absorb more water (McDonald 2005). In addition, high levels
of sulfates often present in groundwater can cause sulfate attacks; cracking and
expansion of the concrete and/or softening and disintegration of cement paste
(Mindness, 2002). Therefore, concreted with high sulfate levels may exhibit
increased shrinkage. When the air content is less than 8% there is generally no
shrinkage due to minimum air content the concrete specimen will experience less
drying where in turn will decrease shrinkage. Admixtures also affect shrinkage.
For example, water-reducing and high-range water-reducing admixtures, as well
as ground slag will increase shrinkage. On the other hand, silica fume will
decrease shrinkage and fly ash has no effect (McDonald 2005).
2.3.3 Environment Affects on Shrinkage
Factors affecting shrinkage due to the environment are ambient relative humidity,
cyclic ambient relative humidity, and temperature. Ambient relative humidity
refers to the air surrounding the concrete which can affect shrinkage. For
example, in deserts and heated buildings there is an increase in drying and
subsequently, in shrinkage. Cyclic ambient relative humidity is an environment
that cycles between 40-90% humidity. In this type of environment, specimens
16


exhibit less drying shrinkage than specimens stored at a constant 65% ambient
relative humidity. This cyclic ambient relative humidity provides greater
moisture to the specimen and results in less drying. Temperature doesnt affect
shrinkage as significantly as can ambient relative humidity (McDonald 2005).
2.3.4 Design and Construction Affects on Shrinkage
Factors affecting shrinkage due to design and construction are curing time, heat
and steam curing, and size and shape of specimen. Extended periods of moist
curing will typically reduce the amount of shrinkage occurring by 10%-20% in
the concrete; however this depends upon w/c. Heat and steam curing can
significantly reduce shrinkage of concrete by as much as 30% (McDonald 2005).
Typically concrete cures for seven (7) days in the field. The longer the concrete
cures, the more C-S-H (calcium-silicate-hydrates) that will be produced, thereby
reducing shrinkage. In addition, the member will develop more strength. The
specimen size and shape affects shrinkage due to the slower rate of drying of the
larger members. Thick concrete members shrink at a slower rate than thin
concrete members (McDonald 2005),
17


2.3.5 Calculation for Predicting Shrinkage
Equation 2.4 will predict the shrinkage strain according to the Gardner and
Lockman Method (GL2000) in the ACI 209.2R-08 technical report.
= ZshuPhPn Eq- 2A
eshu =900xA^ |----- xlO 6 Ultimate shrinkage
V fun2%
fcmi% = 1 -l/'c +700 Mean (actual) 28 day concrete compressive strength
Ph-\-1.18/;4 Relative humidity factor
0.5
A =
tt r
t, -1' + 77 x
Time factor
2.4 Normal Strength Concrete
Normal strength concrete is defined as concrete with compressive strength up to
6,000 psi (41 MPa). The modulus of elasticity equation 2.5 used by the GL2000
method for normal strength concrete is:
-Efm,o =500,000 +52,000//'cmI[
Eq. 2.5
18


This equation can be used for high-strength concrete as well. It complies with
compressive strengths as high as 11,890 psi (82 MPa).
2.5 Ultra High-strength Concrete
Ultra high-strength concrete is defined as concrete with compressive strength of
12,000 psi (83 MPa) to 19,000 psi (131 MPa). A best-fit regression analysis was
applied to test data of different types of curing to determine the function that
accurately represents the behavior and the simplest function to calculate the
modulus of elasticity (Graybeal 2006). Equation 2.6 (Gravbeal 2006) used to
estimate the modulus of elasticity of ultra high-strength concrete up to 19,000 psi
(131 MPa) is:
7,100,000 x e

1 V44000 j
2 ' 1.7

Eq. 2.6
This equation has been compared to other modulus of elasticity equations and it is
the closest approximation to the real values. Other modulus of elasticity
equations over estimated or underestimated the modulus of elasticity values for
ultra high-strength concrete.
19


3. Problem Statement
Historically, there have been many accidents due to shortening of columns in
buildings, such as causing floor framing to slope over the maximum amount
allowed, damaging ducked work, and sometimes as bad as buildings collapsing.
For most cases the maximum floor sloping allowed is approximately 1/8 in (3.175
mm). There have been structures designed in the past that have had floor framing
sloping over 3 in (76.2 mm). When floors slope over the maximum allowed,
several problems may arise: visibility to the occupants, objects rolling and sliding
off desks and doors continually staying open. This is a result that is two fold: (1)
initial shortening from axial loading and (2) shortening caused from creep and
shrinkage. This thesis focuses on creep and shrinkage.
Creep and shrinkage occurs after the building has been constructed. Creep and
shrinkage are time-dependent deformations in concrete. Creep is defined as the
time-dependent increase of strain in hardened concrete subjected to sustained
stress. (Rhodes, 1997) Shrinkage is defined as the decrease in the volume of
hardened concrete. (Rhodes, 1997) The total strain on a member is the sum of
creep, elastic, and shrinkage strain. These time-dependent deformations are
complicated properties to predict because of the large amount of parameters that
affect each strain. Several factors include fresh and hardened concrete properties,
the design of the concrete mixtures, environments conditions, and member
20


construction. This thesis examines many of these properties such as: compressive
strength, modulus of elasticity, age of concrete at time of loading, curing time,
volume-to-surface ratio, ambient relative humidity, and cement type.
Normal strength concrete compressive strength is defined as concrete with
compressive strengths up to 6,000 psi (41 MPa), high strength concrete is defined
as concrete with compressive strengths up to 12,000 psi (83 MPa) and ultra high-
strength concrete is defined as concrete with compressive strengths up to 19,000
psi (131 MPa).
This thesis focuses on the comparison of normal and ultra high-strength concrete
on creep and shrinkage using the Gardner and Lockman method. In order to
analytically analyze the effects of compressive strength, all other properties of the
concrete remained the same for both concrete strengths. The analytical analysis
of both concrete strengths was found using:
Cement Type I
Seven days for moist curing
Time of loading of 14 days for of age
Ambient relative humidity of 70%, and
Volume to surface ratio of 10 in (254 mm).
21


The compressive strength for normal strength concrete was analytically analyzed
at 4,000 psi (28 MPa) and the compressive strength for the ultra high-strength
concrete was analytically analyzed at 17,000 psi (117 MPa). The creep, elastic
compliance and shrinkage coefficients were found at 28, 60, 90, 180, and 365
days. Increasing and decreasing different properties such as compressive
strength, modulus of elasticity, age of concrete at time of loading, curing time,
volume-to-surface ratio, ambient relative humidity, and cement type were
analytically analyzed.
Creep, elastic compliance, and shrinkage coefficients were analytically analyzed
using various f c that ranged between 3,000 psi (21 MPa) to 19,000 psi (131 MPa)
to find the effects of increasing fc. The properties used in this analytical analysis
are as follows:
Cement Type 1
Seven days for moist curing
Time of loading of 14 days of age
Ambient relative humidity of 70%
Volume to surface ratio of 10 in (254 mm), and
Time in consideration at 60 days.
22


4. Development and Verifications of Spreadsheet
4.1 Spreadsheet Functionality
This spreadsheet was created to predict the creep, elastic compliance, and
shrinkage coefficients using the GL2000 method. The input parameters for this
spreadsheet are the s and K factors of the cement type (see Table 2-1), the
compressive strength in pounds per square inch, the moist curing period in days,
the ambient relative humidity percentage in decimal form, the time of loading,
and the time that is being considered in days. This spreadsheet will convert the
compressive strength into the mean compressive strength at 28 days. The
spreadsheet will formulate this conversion because the GL2000 method calculates
the creep, elastic compliance and shrinkage coefficients based off of the mean
compressive strength at 28 days. The difference between the mean compressive
strength at 28 days and the compressive strength is that as concrete ages the
compressive strength increases and the GL2000 method uses the mean
compressive strength at 28 days to account for this increase.
4.2 Verification with ACI 209.2R-08
The values found for creep, elastic compliance, and shrinkage strain coefficients
on hardened concrete from the created spreadsheet were proven to equal the
values of ACI209.2R-08 technical report.
23


4.2.1 Creep Verification with ACI 209.2R-08
Using the parameters in Table 4-1 the creep strain coefficients were calculated at
14, 28, 60, 90, 180, and 365 days of concrete age. The creep coefficients
presented in Table 4-2 are proven to match the values of Table 4-3 from the ACI
209.2R-08 technical report.
Table 4-1: Concrete Parameters used for Verification
Age of concrete ti 28 days
Age of concrete at loading to 14 days
Age of concrete cured tc 7 days
Relative Humidity h 0.7
Volume-Surface Ratio v/s 4in
Cement Type s 0.335
Concrete compressive strength fcm28 3626 psi
Table 4-2: Values for Creep Strain Coefficients Spreadsheet Values
Creep strain Coefficients
Time Being Considered Time load is applied Drying Before Loading Factor Basic Creep 1 st Term Basic Creep 2nd Term Basic Creep Drying Creep 3rd Term Creep Coefficients
ti (days) to=tj (days) (tc) if tj>tc 28(t)
14 14 0.962 0.000 0.000 0.000 0.000 0.000
28 14 0.962 0.272 0.577 0.850 0.124 0.936
60 14 0.962 0.368 0.659 1.026 0.222 . 1.201
90 14 0.962 0.415 0.677 1.092 0.282 1.321
180 14 0.962 0.497 0.693 1.190 0.403 1.532
365 14 0.962 0.586 0.700 1.286 0.551 1.767
24


Table 4-3: Creep Strain Coefficients per ACI Technical Report (Videla 2008)
SI units | in.-lh units

Effect of drying before loading factor Efiect id drying beiWe loading i actor
(In .rt.) = 11061 t A- ;;A1 cV t AAs Ipl = 0 062 I H A t jfc (A- p :'i 1
Basic creep ctnHik ion)
1st term 2|f14)1
2nd term
6 days 1 si. term 2nd term Baste vici'p voidikiciii 1, class 1st lenn 2nd term Baste creep coefficient
14 0.000 OOfHI OfXXl 14 0 IKXI it 000 0 000
:.s 0.272 0.577 0.850 28 0.272 0,577 0 850
m 0 >6K (4656 1.026 611 0.368 0650 1,026
00 0 415 0,677 1.002 00 0415 0.677 1 o-O
ISO 0.4M7 OoOs 1,1 Oft ISO 0 407 0 603 1.100
365 0.5N6 0,71X1 1 286 565 0.586 6 706 1.286
Drying creep coefficient
Ambient relative humidity factor 2.5M I.OSWrj
1.170
Time function + > kivvsi'n"' Tune tuncimn ii/,r> = |u-r<(i/|o -ri + 7?f V7S>?
/. days tiu, ,< Diy mg accp coctficicnl 3rd term i. days j itj> Drying jvp etKifieient 3rd term
14 0.(100 0.000 14 0.000 0 iiOO
28 0.107 0 126 0.106 0 124
ist) 0.J02 0 225 60 0 .0 8) 6.222
vO 0 244 0.285 <*.) 0 241 0.282
ISO 0,540 0.40S ISO 0 345 0.403
365 0.476 0 556 365 If 471 0.551
Creep coefficient
= f. days Basic + drying creep 1. days Basic + drying creep C>;xl U!
14 0.01 NJ 0.000 14 0000 - OOfXi
28 0.075 0.037 28 0.074 0,036.
60 1 251 1.203 60 1.248 1.201
90 . 1.377 1 324 90 1.374 1321
1 so 1.5 VS 1.536 ISO 1.593t .1.532
56? 1.S43 1.771 365 1X37 1,767 '
4.2.2 Elastic Compliance Verification with ACI 209.2R-08
Using the parameters in Table 4-1 the elastic compliance coefficients were
calculated in Table 4-4 and proven to match the values of Table 4-5 from the ACI
209.2R-08 technical report.
25


Table 4-4: Values for Elastic Compliance Coefficients Spreadsheet Values
Elastic Strain Coefficients
Strength Development to Cement Type Be 0.933
Concrete Strength at time to fcmto (psi) 4081
Elastic Modulus at time to Ecmto (psi) 3821941
Elastic Strain 1/Ecmto (1/psi) 2.62E-07
Table 4-5: Elastic Compliance Coefficients per ACI Technical Report (Videla
2008)
SI umi< in. -Ih uiuK
Cement type !
V = t! VV5 < ]: i*
fs , = exp|s/>! 1 -(
Mean strength at ape IV = o.o*
.W = IVT
= MPa t : 'M '= 40.S1.1 psi ( V a-!
Mean elastic mmlulus at Eos*.'MPa- = >500 + 4*1 JIN/ ffS ,K!or- i ') P -a' = 5(H),ooo + 5:.< 5 i . A i
iige 7,, £^,= >.>71 MPa ti t Etiuh, = XS21 .OJo psi i !
J-.I.i'tK compliance Ml= UE MU' i > ;
, = i|X s Ur' i IMI',1 1 = 0.2tO y. 1 <, |/psii (A- i
4.2.3 Shrinkage Verification with ACI 209.2R-08
Using the parameters in Table 4-1 the shrinkage strain coefficients were
calculated at 7, 14, 28, 60, 90, 180, and 365 days of concrete age. Table 4-6
provides these values and are proven to match the values of Table 4-7 from the
ACI 209.2R-08 technical report.
26


Table 4-6; Values for Shrinkage Strain Coefficients Spreadsheet Values
Shrinkage Strain Coefficients
Time Being Considered Time Load is Applied Correction Term for the Effect of Time Shrinkage Strain at Time ti
ti (days) to=ti (days) pti esiwx10A-6
7 14 0 0
14 ' 14 0.075 47
28 14 0.129 80
60 14 0.203 126
90 14 0.251 156
. 180. 14 0.351 218
365 14 0.475 295
Table 4-7: Shrinkage Strain Coefficients per ACI Technical Report (Videla
2008)
M units in.-lb iimis
Cement type la-ioi k= I.not) IT:;:-: V :-i
Ultimate shrinkage strain :->i.\-. = Oill/141-51 >0 .yKi5 0^ (- ; a
= .7 x Ml-t i:i ; o
Ambient relative humidity la-. ! -i ({(/;.! = I | MS/!4! < -
[t'/ll =0.717 >
Shrinkage time timenon |t-.' J/ r +l> LM'-Sr- J]' \ > l,r.. f_ i |.i.. r, 1 + -7.\ Sr '
Shimkaee strains l;j/.f;.i,i = i:!y>l/njtil~i>i
L Jays !)i|-l(.l 1^.0..',.?. xtir6 r, days flu lt.) x nr*
7 0.000 0 7 OIKIO 0
14 0 076 47 14 0075 -47
2S OI3I SI 2S 0120 80
60 0.206 128 60 0.203 126
'£) 0254 158 m 0355 220 iso 0.351 21S
.i65 0 479 297 365 0.475 295
27


5. Coefficients Due to Normal Strength Concrete
5.1 Overview
The analytical analysis of normal strength concrete with a compressive strength of
4,000 psi (28 MPa) was found using cement Type I with 7 days of moist curing,
time of loading of 14 days, ambient relative humidity at 70%, and the volume to
surface ratio of 10 in (254 mm). The creep, elastic compliance and shrinkage
coefficients were found at 28, 60, 90, 180, and 365 days.
Creep, elastic compliance, and shrinkage coefficients were analytically analyzed
using various f c that ranged between 3,000 psi (21 MPa) to 12,000 psi (83 MPa).
The properties used in this analytical analysis are as follows:
Cement Type I
Seven days for moist curing
Time of loading of 14 days for of age
Ambient relative humidity of 70%
Volume to surface ratio of 10 in (254 mm), and
Time in consideration at 60 days.
28


5.2 Modulus of Elasticity for Normal Strength Concrete
The modulus of elasticity, ECi used for normal strength concrete for the GL2000
method is illustrated in equation 2.5 and repeated in equation 5.1 for convenience
(Videla 2008). The modulus of elasticity is a function of the compressive strength,
fc
500,000 + 52,000^/7'^,
(5.2.1)
5.3 Creep Coefficients for Normal Strength Concrete
The creep coefficients took into account the following factors: age of the concrete
at time of loading, the period of moist curing, the volume to surface ratio, and
relative humidity. The creep coefficients do not change depending on the
modulus of elasticity nor on the compressive strength. The Creep coefficients at
28, 60, 90, 180, and 365 days are shown in Table 5-1.
Table 5-1: Creep Coefficients for Normal Strength Concrete
Time being considered Creep Coefficient
ti (days) 28(t)
28 0.8859
60 1.0996
90 1.1890
180 1.3394
365 1.5072
29


5.3.1 Concrete age at loading Effects on Creep Coefficients for Normal
Strength Concrete
Creep coefficients decrease the older the concrete is before loading due to
additional time for the concrete to harden. The creep calculation takes into
account age of concrete at time of loading for this reason. Table 5-2 and Figure
5-1 shows the affect of analytically increasing the age of concrete at time of
loading by doubling the age from 14 days to 28 days. The creep coefficient is
equal to zero for age of loading at 28 days due to the loading age equaling the age
of consideration. The creep coefficients decrease by about approximately 23% at
60.days, 20% at 90 days, 17% at 180 days, and 15% at 365 days. As concrete
ages the gap between creep coefficients lessens and over time will equalize and
the differences between the creep coefficients loaded at 14 days or 28 days will
become insignificant.
Table 5-2: Concrete age at loading Effects on Creep Coefficients for Normal
Strength Concrete ____________________________________________________________
Time being considered Creep Coefficient Creep Coefficient
ti (days) '£*>-*52* 1 -* < J/// Load at age 14 days Load at age 28 days
28 0.8859 0
60 1.0996 0.8415
90 1.1890 0.9481
180 1.3394 1.1091
365 1.5072 1.2806
30


Figure 5-1: Concrete age at loading Effects on Creep Coefficients for Normal
Strength Concrete
5.3.2 Curing Effects on Creep Coefficients for Normal Strength Concrete
When the period of time for moist curing is analytically increased the creep
coefficients also increase by approximately 1.5%. Typically creep coefficients
decrease when the curing period increases due to the increase in the moisture in
the concrete. In this case the creep coefficient increased due to loading occurring
the same time the curing period completes. If loading time occurred after the
curing period was completed then the creep coefficient would have decreased..
The creep calculation takes into account the period of time for moist curing for
31


this reason. Table 5-3 and Figure 5-2 illustrates the affect of analytically
increasing the period of curing by increasing it from 7 to 14 days.
Table 5-3: Curing Effects on Creep Coefficients for Normal Strength
Concrete
Time being considered Creep Coefficient Creep Coefficient
ti (days) 28(t) 28(t)
Moist Cure Period of 7 days Moist Cure Period of 14 days
28 0.8859 0.8996
60 1.0996 1.1166
90 1.1890 1.2073
180 1.3394 1.3600
365 1.5072 1.5304
Figure 5-2: Curing Effects on Creep Coefficients for Normal Strength
Concrete
32


5.3.3 Volume to Surface Ratio Effects on Creep Coefficients for Normal
Strength Concrete
When the volume to surface ratio is analytically increased the creep coefficients
decrease. The creep calculation takes into account the volume to surface ratio for
this reason. Table 5-4 and Figure 5-3 shows the effect of analytically increasing
the volume to surface ratio by increasing it from 10 to 20 inches (254 to 508 mm).
The creep coefficients decrease at approximately 2% at 28 days, 3% at 60 days,
4% at 90 days, 5.5% at 180 days, and 7% at 365 days. This proves that concrete
experiences less creep as it ages due to the increase in the volume to surface ratio.
Table 5-4: Volume to Surface Ratio Effects on Creep Coefficients for Normal
Strength Concrete
Time being considered Creep Coefficient Creep Coefficient
ti (days) 4>28(t) 28(t)
. \ iiiffiBBai?' V/S = 10 inches V/S = 20 inches
28 0.8859 0.8680
60 1.0996 1.0635
90 1.1890 1.1410
180 1.3394 1.2661
365 1.5072 1.3997
33


1.6000
1.4000
1.2000
in
1 1.0000
o
t
o 0.8000
O
Q.
2 0.6000
O
0.4000
0.2000
0.0000
0 100 200 300 400
. Time (days)
Figure 5-3: Volume to Surface Ratio Effects on Creep Coefficients for
Normal Strength Concrete
5.3.4 Ambient Relative Humidity Effects on Creep Coefficients for Normal
Strength Concrete
As the ambient relative humidity decreases the creep coefficients increase due to
the concrete drying at an accelerated rate as the ambient relative humidity
decreases. Table 5-5 and Figure 5-4 shows the effect of analytically decreasing
the ambient relative humidity form 70% to 50%. The creep coefficients increase
by 3% at 28 days, 4% at 60 days, 5% at 90 days, 6.5% at 180 days, and 8% at 365
days. This demonstrates that concrete experiences more creep due to the
reduction in ambient relative humidity as concrete ages.
V/S at 10 inches
" V/S at 20 inches
34


Table 5-5: Ambient Relative Humidity Effects on Creep Coefficients for
Normal Strength Concrete
Time being considered Creep Coefficient Creep Coefficient
ti (days) 28(t) 0>28(t)
S fttf "Wffl 1: Relative Humidity = 0.7 Relative Humidity = 0.5
28 0.8859 0.9132
60 1.0996 1.1491
90 1.1890 1.2524
180 1.3394 1.4326
365 1.5072 1.6411
Figure 5-4: Ambient Relative Humidity Effects on Creep Coefficients for
Normal Strength Concrete
35


5.3.5 Creep Coefficients for Normal and High Strength Concrete due to
Compressive Strength between 3,000 psi to 12,000 psi
The creep coefficients do not change depending on the modulus of elasticity nor
on the compressive strength. Therefore the creep coefficients remained constant
due to compressive strength varying between 3,000 psi (21 MPa) to 12,000 psi
(83 MPa) as shown in Table 5-6.
Table 5-6: Creep Coefficients for Normal and High Strength Concrete due to
Compressive Strength between 3,000 psi to 12,000 psi
Compressive Strength Creep Coefficient
fc (psi) 3000 1.0996
4000 1.0996
5000 1.0996
6000 1.0996
7000 1.0996
8000 1.0996
9000 1.0996
10000 1.0996
11000 1.0996
12000 1.0996
5.4 Elastic Compliance Coefficients for Normal Strength Concrete
The elastic compliance coefficients took into account the following factors age of
the concrete at time of loading, the strength gain coefficient s (where s depends on
cement type), the average compressive strength at 28 days of age, and the
modulus of elasticity of the compressive strength at 28 days of age. The elastic
compliance coefficients are shown in Table 5-7. The elastic compliance
coefficients change depending on the modulus of elasticity.
36


Table 5-7: Elastic Compliance Coefficients for Normal Strength Concrete
Elastic Compliance Coefficients
Strength Development to Cement Type Be 0.9330
Concrete Strength at time to fcmto (psi) 4439
Elastic Modulus at time to Ecmto (psi) 3964629
Elastic Strain 1/Ecmto (1/psi) 2.5223E-07
5.4.1 Concrete age at loading Effects on Elastic Compliance Coefficients for
Normal Strength Concrete
The older the concrete is before loading the more the elastic compliance
coefficients decrease. The elastic compliance calculation takes into account age
of concrete at time of loading for this reason. Table 5-8 shows the effect of
analytically increasing the concrete age at time of loading by increasing the age
from 14 days to 28 days. The elastic compliance coefficient decreased by
approximately 6% due to the additional time for the concrete to harden.
Table 5-8: Concrete age at loading Effects on Elastic Compliance Coefficients
for Normal Strength Concrete____________________________________________________
Elastic Compliance Coefficients
J * ] ** Load at age 14 days Load at age 28 days
Strength Development to Cement Type Be 0.9330 1
Concrete Strength at time to fcmto (psi) 4439 5100
Elastic Modulus at time to Ecmto (psi) 3964629 4213542
Elastic Strain 1/Ecmto (1/psi) 2.5223E-07 2.3733E-07
37


5.4.2 Cement Type Effects on Elastic Compliance Coefficients for Normal
Strength Concrete
As cement type changes the elastic compliance coefficients change. The elastic
compliance calculation takes into account cement type for this reason. Table 5-9
shows the affect of cement type by analytical changing s (where ,v is the strength
gain coefficient of the cement type). Cement Type III has the least amount of
elastic deformation due to cement Type III having finely ground cement, where
finely ground cement can be deformed easier than coarse ground cement. Cement
Type II has coarse ground cement which in turn creates an increase in elastic
strain (McDonald, 2005).
Table 5-9: Cement Type Effects on Elastic Compliance Coefficients for
Normal Strength Concrete ___________________________________________.
Elastic Compliance Coefficients
i. V-_irHgV?tj L r" j j ,i, : Cement Type I Cement Type II Cement Type III
Strength Development to Cement Type Pe 0.9330 0.9205 0.9734
Concrete Strength at time to femto (psi) 4439 4321 4832
Elastic Modulus at time to Ecmto (psi) 3964629 3918300 4114893
Elastic Strain 1/Ecmto (1/psi) 2.5223E-07 2.5521 E-07 2.4302E-07
5.4.3 Elastic Compliance Coefficients for Normal and High Strength
Concrete due to Compressive Strength between 3,000 psi to 12,000 psi
The elastic compliance coefficients change depending on the modulus of elasticity
and on the compressive strength. When compressive strength analytically
increases the elastic compliance coefficients decrease as shown in Table 5-10 and
Figure 5-5.
38


Table 5-10: Elastic Compliance Coefficients for Normal and High Strength
Concrete due to Compressive Strength between 3,000 psi to 12,000 psi
Compressive Strength Elastic Strain
fc (psi) 1/Ecmto (1/psi)
3000 2.8024E-07
4000 2.5223E-07
5000 2.3148E-07
6000 2.1528E-07
7000 2.0217E-07
8000 1.9126E-07
9000 1.8199E-07
10000 1.7398E-07
11000 1.6698E-07
12000 1.6078E-07
Figure 5-5: Elastic Compliance Coefficients for Normal and High Strength
Concrete due to Compressive Strength between 3,000 psi to 12,000 psi
39


5.5 Shrinkage Coefficients for Normal Strength Concrete
The shrinkage coefficients take into account the following factors: period of moist
curing, the volume to surface ratio, the correction term for humidity, the
shrinkage constant K (where K depends on the cement type), and the average
compressive strength at 28 days of age. The shrinkage coefficients do not change
depending on the modulus of elasticity; however, change depending on the
compressive strength. The shrinkage coefficients at 28, 60, 90, 180, and 365 days
are shown in Table 5-11.
Table 5-11: Shrinkage Coefficients for Normal Strength Concrete
Time being considered Shrinkage Strain at time i
ti (days) tsiw x10A-6
28 31.0672
60 49.2529
90 61.5168
180 88.3042
365 125.5615
5.5.1 Curing Effects on Shrinkage Coefficients for Normal Strength Concrete
When the period of time for moist curing is analytically increased, the shrinkage
coefficients decrease as a result of increased production of C-S-H. Table 5-12
and Figure 5-6 shows the effect of analytically increasing the period of time for
moist curing by increasing it from 7 to 14 days of age. At 28 days of age the
shrinkage coefficients decreased by approximately 18%, 7% at 60 days, 4% at 90
days, 2% at 180 days, and 1% at 365 days. This demonstrates that as the
40


concrete ages the period of curing does not significantly influence concrete
shrinkage. However, shrinkage at early ages are greatly influenced.
Table 5-12: Curing Effects on Shrinkage Coefficients for Normal Strength
Concrete
Time being considered Shrinkage Strain at time i Shrinkage Strain at time i
ti (days) csiwx10A-6 csiwx10A-6
Moist Cure Period of 7 days Moist Cure Period of 14 days
28 31.0672 25.3777
60 49.2529 45.9059
90 61.5168 58.8921
180 88.3042 86.5378
365 125.5615 124.3819
i
7 Day Cure Period |
* 14 Day Cure Period j
Figure 5-6: Curing Effects on Shrinkage Coefficients for Normal Strength
Concrete
41


5.5.2 Volume to Surface Ratio Effects on Shrinkage Coefficients for Normal
Strength Concrete
When the volume to surface ratio is analytically increased the shrinkage
coefficients decrease. Table 5-13 and Figure 5-7 shows the effect of analytically
increasing the volume to surface ratio by increasing it from 10 to 20 inches (254
to 508 mm). The shrinkage coefficients decrease by approximately 50% due to
the increase in the volume to surface ratio.
Table 5-13: Volume to Surface Ratio Effects on Shrinkage Coefficients for
Normal Strength Concrete
Time being considered Shrinkage Strain at time i Shrinkage Strain at time i
ti (days) £siwx10A-6 tsiwx10A-6
S|llllli;ay V/S = 10 inches V/S = 20 inches
28 31.0672 15.5494
60 49.2529 24.6898
90 61.5168 30.8822
180 88.3042 44.5205
365 125.5615 63.8536
42


- V/S at 10 inches I
V/S at 20 inches
Figure 5-7: Volume to Surface Ratio Effects on Shrinkage Coefficients for
Normal Strength Concrete
5.5.3 Ambient Relative Humidity Effects on Shrinkage Coefficients for
Normal Strength Concrete
As the ambient relative humidity analytically decreases the shrinkage coefficients
increase as a result of the concrete drying at a more accelerated rate when the
ambient relative humidity decreases. Table 5-14 and Figure 5-8 demonstrates the
effect of analytically decreasing the ambient relative humidity from 70% to 50%.
The shrinkage coefficients increase by approximately 23% due to the decrease in
the relative humidity. The influence of ambient relative humidity is greater with
concrete age.
43


Table 5-14: Ambient Relative Humidity Effects on Shrinkage Coefficients for
Normal Strength Concrete
Time being considered Shrinkage Strain at time i Shrinkage Strain at time i
ti (days) tsiwx10A-6 tsiwx10A-6
Relative Humidity = 0.7 Relative Humidity = 0.5
28 31.0672 40.1516
60 49.2529 63.6551
90 61.5168 79.5052
180 88.3042 114.1256
365 125.5615 162.2774
Figure 5-8: Ambient Relative Humidity Effects on Shrinkage Coefficients for
Normal Strength Concrete
44


5.5.4 Cement Type Effects on Shrinkage Coefficients for Normal Strength
Concrete
As cement type changes the shrinkage coefficients change. Table 5-15 and Figure
5-9 demonstrates the effect of cement type by analytically changing K (where K
is the shrinkage constant of the cement type). The least amount of shrinkage
occurs in cement Type II due to the cement having coarser ground cements.
Aggregate restrains shrinkage of the cement paste. Cement Type III typically has
finely ground cement resulting in greater shrinkage than coarser ground cement
(McDonald 2005).
Table 5-15 Cement Type Effects on Shrinkage Coefficients for Normal
Strength Concrete:_____________________________________________________________
Time being considered Shrinkage Strain at time i Shrinkage Strain at time i Shrinkage Strain at time i
ti (days) Esiwx10A-6 Esiwx10A-6 Esiwx10A-6
Cement Type I Cement Type II Cement Type III
28 31.0672 23.3004 35.7272
60 49.2529 36.9397 56.6408
90 61.5168 46.1376 70.7444
180 88.3042 66.2282 101.5499
365 125.5615 94.1711 144.3957
45


--Type I
Type II
_ Type III
Time (days)
Figure 5-9 Cement Type Effects on Shrinkage Coefficients for Normal
Strength Concrete
5.5.5 Shrinkage Coefficients for Normal and High Strength Concrete due to
Compressive Strength between 3,000 psi to 12,000 psi
The shrinkage coefficients change depending on the modulus of elasticity and on
the compressive strength. When compressive strength analytically increases the
shrinkage coefficients decrease as shown in Table 5-16 and Figure 5-10.
46


Table 5-16: Shrinkage Coefficients for Normal and High Strength Concrete
Compressive Strength Shrinkage Strain at time i
fc (psi) esiwx10A-6
3000 55.6143
4000 49.2529
5000 44.6705
6000 41.1676
7000 38.3775
8000 36.0873
9000 34.1636
10000 32.5180
11000 31.0894
12000 29.8338
Figure 5-10: Shrinkage Coefficients for Normal and High Strength Concrete
due to Compressive Strength between 3,000 psi to 12,000 psi
47


6. Coefficients Due to Ultra High-Strength Concrete
6.1 Overview
The analytically analysis of ultra high-strength concrete with a compressive
strength of 17,000 psi (117 MPa) was found using the following factors: cement
Type I with 7 days of moist curing, time of loading of 14 days, ambient relative
humidity at 70%, and the volume to surface ratio at 10 in (254 mm). The creep,
elastic compliance and shrinkage coefficients were found at 28, 60, 90, 180, and
365 days.
Creep, elastic compliance, and shrinkage coefficients were analytically analyzed
using various fc that ranged between 13,000 psi (90 MPa) to 19,000 psi (131
MPa). The properties used in this analytically analysis are as follows:
Cement Type I
Seven days for moist curing
Time of loading of 14 days for of age
Ambient relative humidity of 70%
Volume to surface ratio of 10 in (254 mm), and
Time in consideration at 60 days.
48


6.2 Modulus of Elasticity for Ultra High-Strength Concrete
The modulus of elasticity, Ec used for ultra high-strength concrete is illustrated in
equation 2.6 and repeated in equation 6.1 for convenience (Graybeal, 2006). The
modulus of elasticity is a function of the compressive strength, f c.
E
cmt0
= 7,100,000 x
6.1
6.3 Creep Coefficients for Ultra High-Strength Concrete
The creep coefficients took into account the following factors: age of the concrete
at time of loading, the period of moist curing, the volume to surface ratio, and
relative humidity. The creep coefficients do not change depending on the
modulus of elasticity nor on the compressive strength. The creep coefficients at
28, 60, 90, 180, and 365 are shown in Table 6-1. Thus the creep coefficients are
the same for normal strength and ultra high-strength concrete.
Table 6-1: Creep Coefficients for Ultra High-Strength Concrete
Time being considered Creep Coefficient
ti (days) 028(t)
28 0.8859
60 1.0996
90 1.1890
180 1.3394
365 1.5072
49


6.3.1 Concrete age at loading Effects on Creep Coefficients for Ultra High-
Strength Concrete
The older the concrete is before loading the more the creep coefficients decrease.
The creep calculation takes into account age of concrete at time of loading for this
reason. Table 6-2 and Figure 6-1 shows the affect of analytically increasing the
age of concrete at time of loading by increasing the age from 14 days to 28 days.
The creep coefficients decrease by approximately 23% at 60 days, 20% at 90
days, 17% at 180 days, and 15% at 365 days. These reductions are equal to the
reductions from normal strength concrete.
Table 6-2: Concrete age at loading Effects on Creep Coefficients for Ultra
High-Strength Concrete______________________________________________
Time being considered Creep Coefficient Creep Coefficient
ti (days) lllliiliilj Load at age 14 days Load at age 28 days
28 0.8859 0
60 1.0996 0.8415
90 1.1890 0.9481
180 1.3394 1.1091
365 1.5072 1.2806
50


1.6000
- Load at age 14 days
* Load at age 28 days
Time (days)
Figure 6-1: Concrete age at loading Effects on Creep Coefficients for Ultra
High-Strength Concrete
6.3.2 Curing Effects on Creep Coefficients for Ultra High-Strength Concrete
When the period of time for moist curing is analytically increased the creep
coefficients also increase by approximately 1.5% which is equal to the increase
due to the curing increase for normal strength concrete. This is due to loading the
member at the same time that the curing period is completed. Table 6-3 and
Figure 6-2 illustrates the affect of analytically increasing the period of curing by
increasing it from 7 to 14 days.
51


Table 6-3: Curing Effects on Creep Coefficients for Ultra High-Strength
Concrete
Time being considered Creep Coefficient Creep Coefficient
ti (days) 28(t) 28(t)
Moist Cure Period of 7 days Moist Cure Period of 14 days
28 0.8859 0.8996
60 1.0996 1.1166
90 1.1890 1.2073
180 1.3394 1.3600
365 1.5072 1.5304
7 day Cure Period
14 day Cure Period
Figure 6-2: Curing Effects on Creep Coefficients for Ultra High-Strength
Concrete
52


6.3.3 Volume to Surface Ratio Effects on Creep Coefficients for Ultra High-
Strength Concrete
When the volume to surface ratio is analytically increased the creep coefficients
also increase. The creep calculation takes into account the volume to surface ratio
for this reason. Table 6-4 and Figure 6-3 illustrates the effect of analytically
increasing the volume to surface ratio by increasing it from 10 to 20 inches (254
to 508 mm). The creep coefficients decrease at approximately 2% at 28 days, 3%
at 60 days, 4% at 90 days, 5.5% at 180 days, and 7% at 365 days. These
reductions are equal to the reductions from normal strength concrete.
Table 6-4: Volume to Surface Ratio Effects on Creep Coefficients for Ultra
High-Strength Concrete
Time being considered Creep Coefficient Creep Coefficient
ti (days) 4>28(t) V/S = 10 inches V/S = 20 inches
28 0.8859 0.8680
60 1.0996 1.0635
90 1.1890 1.1410
180 1.3394 1.2661
365 1.5072 1.3997
53


1.6000
1.4000
1.2000
to
I 1.0000
o
£
o 0.8000
O
Q.
s> 0.6000
o
0.4000
0.2000 ---------------------------------------------------
0.0000 J------------1-----------1------------1------------1
0 100 200 300 400
Time (days)
Figure 6-3: Volume to Surface Ratio Effects on Creep Coefficients for Ultra
High- Strength Concrete
6.3.4 Ambient Relative Humidity Affects on Creep Coefficients for Ultra
High-Strength Concrete
As the ambient relative humidity decreases, the creep coefficients increase due to
the concrete drying at an accelerated rate as the ambient relative humidity
decreases. Table 6-5 and Figure 6-4 illustrates the effect of analytically
decreasing the ambient relative humidity form 70% to 50%. The creep
coefficients increase by 3% at 28 days, 4% at 60 days, 5% at 90 days, 6.5% at 180
days, and 8% at 365 days. These reductions are equal to the reductions for normal
strength concrete.
54


Table 6-5: Ambient Relative Humidity Affects on Creep Coefficients for
Ultra High-Strength Concrete
Time being considered Creep Coefficient Creep Coefficient
ti (days) 28(t) Relative Humidity = 0.7 Relative Humidity 0.5
28 0.8859 0.9132
60 1.0996 1.1491
90 1.1890 1.2524
180 1.3394 1.4326
365 1.5072 1.6411
j Relative Humidity 70%
1 j Relative Humidity 50%
Time (days)
Figure 6-4: Ambient Relative Humidity Effects on Creep Coefficients for
Ultra High-Strength Concrete
55


6.3.5 Creep Coefficients for Ultra High-Strength Concrete due to
Compressive Strength between 13,000 psi to 19,000 psi
The creep coefficients do not change depending on the modulus of elasticity nor
on the compressive strength. Therefore the creep coefficients remained constant
due to compressive strength varying between 13,000 psi (90 MPa) to 19,000 psi
(131 MPa) as shown in Table 6-6.
Table 6-6: Creep Coefficients for Ultra High-Strength Concrete due to
Compressive Strength Creep Coefficient
fc (psi) 28(t)
13000 1.0996
14000 1.0996
15000 1.0996
16000 1.0996
17000 1.0996
18000 1.0996
19000 1.0996
6.4 Elastic Compliance Coefficients for Ultra High-Strength Concrete
The elastic compliance coefficients took into account the following factors: age of
the concrete at time of loading, the strength gain coefficient s (where s depends on
cement type), the average compressive strength at 28 days of age, and the
modulus of elasticity of the compressive strength at 28 days of age. The elastic
compliance coefficients are shown in Table 6-7. The elastic compliance
coefficients change depending on the modulus of elasticity.
56


Table 6-7: Elastic Compliance Coefficients for Ultra High-Strength Concrete
Elastic Compliance Coefficients
Strength Development to Cement Type Pe 0.9330
Concrete Strength at time to femto (psi) 16886
Elastic Modulus at time to Ecmto (psi) 6058237
Elastic Strain 1/Ecmto (1/psi) 1.6506E-07
6.4.1 Concrete age at loading Effects on Elastic Compliance Coefficients for
Ultra High-Strength Concrete
The older the concrete is before loading the more the elastic compliance
coefficients decrease. Table 6-8 illustrates the effect of analytically increasing the
concrete age at time of loading by increasing the age from 14 to 28 days. The
elastic compliance coefficient decreased by approximately 4%.
Table 6-8: Concrete age at loading Effects on Elastic Compliance Coefficients
for Ultra High-Strength Concrete__________________________
Elastic Compliance Coefficients
.'--l rV. Load at age 14 days Load at age 28 days
Strength Development to Cement Type pe 0.9330 1
Concrete Strength at time to femto (psi) 16886 19400
Elastic Modulus at time to Ecmto (psi) 6058237 6322216
Elastic Strain 1/Ecmto (1/psi) 1 6506E-07 1.5817E-07
6.4.2 Cement Type Effects on Elastic Compliance Coefficients for Ultra
High-Strength Concrete
As cement type changes the elastic compliance coefficients change. Table 6-9
illustrates the affect of cement type by analytically changing s (where s is the
strength gain coefficient of the cement type). Cement Type III has the least
57


amount of elastic deformation and Cement Type II has the greatest amount of
elastic deformation which also is true for normal strength concrete.
Table 6-9: Cement Type Effects on Elastic Compliance Coefficients for Ultra
High-Strength Concrete________________________________________________
Elastic Compliance Coefficients
iiiiiiiii Cement Type I Cement Type II Cement Type III
Strength Development to Cement Type Be 0.9330 0.9205 0.9734
Concrete Strength at time to fern to (psi) 16886 16438 18383
Elastic Modulus at time to Ecmto (psi) 6058237 6003673 6223359
Elastic Strain 1/Ecmto (1/psi) 1.6506E-07 1.6656E-07 1.6068E-07
6.4.3 Elastic Compliance Coefficients for Ultra High-Strength Concrete due
to Compressive Strength between 13,000 psi to 19,000 psi
The elastic compliance coefficients change depending on the modulus of elasticity
and on the compressive strength. When compressive strength analytically
increases the elastic compliance coefficients decrease as shown in Table 6-10 and
Figure 6-5.
Table 6-10: Elastic Compliance Coefficients for Ultra High-Strength
Concrete due to Compressive Strength between 13,000 psi to 19,000 psi
Compressive Strength Elastic Strain
fc (psi) 1/Ecmto (1/psi)
13000 1.8182E-07
14000 1.7664E-07
15000 1.7221E-07
'16000 1.6839E-07
17000 1.6506E-07
18000 1.6216E-07
19000 1.5961E-07
58


20000
Q. 14000
£
b> c s? 12000 -
CO 0) > 10000 -
Q. £ 6000
o 4000 -
2000
0 -
1.55E-07 1.60E-07 1.65E-07 1.70E-07 1.75E-07
Elastic Strain (1/psi)
1.80E-07 1.85E-07
I
Figure 6-5: Elastic Compliance Coefficients for Ultra High-Strength
Concrete due to Compressive Strength between 13,000 psi to 19,000 psi
6.5 Shrinkage Coefficients for Ultra High-Strength Concrete
The shrinkage coefficients account for the period of moist curing, the volume to
surface ratio, the correction term for humidity, the shrinkage constant K (where K
depends on the cement type), and the average compressive strength at 28 days of
age. The shrinkage coefficients do not change depending on the modulus of
elasticity; however, changes depending on the compressive strength. The
shrinkage coefficients at 28, 60, 90, 180, and 365 days are demonstrated in Table
6-11.
59


Table 6-11: Shrinkage Coefficients for Ultra High-Strength Concrete
Time being considered Shrinkage Strain at time i
ti (days) csiw x10A-6
28 15.9289
60 25.2532
90 31.5412
180 45.2758
365 64.3785
6.5.1 Curing Effects on Shrinkage Coefficients for Ultra High-Strength
Concrete
When the period of time for moist curing is analytically increased, the shrinkage
coefficients decrease as a result of increased production of more C-S-H Table 6-
12 and Figure 6-6 demonstrates the effect of analytically increasing the period of
time for moist curing by increasing it from 7 to 14 days of age. At 28 days of age,
the shrinkage coefficients decreased by approximately 18%,7% at 60 days, 4% at
90 days, 2% at 180 days, and 1% at 365 days. These reductions are equal to the
reductions due to the curing increase for normal strength concrete.
Table 6-12: Curing Effects on Shrinkage Coefficients for Ultra High-
Strength Concrete______________________________________________________________
Time being considered Shrinkage Strain at time i Shrinkage Strain at time i
ti (days) csiwx10A-6 csiw x10A-6
Jit* _r LJ. % l c ^ Moist Cure Period of 7 days Moist Cure Period of 14 days
28 15.9289 13.0118
60 25.2532 23.5371
90 31.5412 30.1954
180 45.2758 44.3700
365 64.3785 63.7737
60


70.0000
7 day Cure Period i
i
14 day Cure Period |
| 0 100 200 300 400
| Time (days)
Figure 6-6: Curing Effects on Shrinkage Coefficients for Ultra High-Strength
Concrete
6.5.2 Volume to Surface Ratio Effects on Shrinkage Coefficients for Ultra
High-Strength Concrete
When the volume to surface ratio is analytically increased the shrinkage
coefficients decrease. Table 6-13 and Figure 6-7 illustrates the effect of
analytically increasing the volume to surface ratio by increasing it from 10 to 20
inches (254 to 508 mm). The shrinkage coefficients decrease by approximately
50% which is equal to the decrease due to the volume to surface ratio increase for
normal strength concrete.
61


Table 6-13: Volume to Surface Ratio Effects on Shrinkage Coefficients for
Ultra High-Strength Concrete______________________________________________
Time being considered Shrinkage Strain at time i Shrinkage Strain at time i
ti (days) tsiw x10A-6 tsiw x10A-6
- V/S = 10 inches V/S = 20 inches
28 15.9289 7.9726
60 25.2532 12.6591
90 31.5412 15.8341
180 45.2758 22.8268
365 64.3785 32.7393
! V/S at 10 inches [
j V/S at 20 inches j
Figure 6-7: Volume to Surface Ratio Effects on Shrinkage Coefficients for
Ultra High-Strength Concrete
62


6.5.3 Ambient Relative Humidity Effects on Shrinkage Coefficients for Ultra
High-Strength Concrete
As the ambient relative humidity analytically decreases the shrinkage coefficients
increase as a result of the concrete drying at a more accelerated rate when the
ambient relative humidity decreases. Table 6-14 and Figure 6-8 shows the effect
of analytically decreasing the ambient relative humidity from 70% to 50%. The
shrinkage coefficients increase by approximately 23% which is equal to the
increase due to the ambient relative humidity decrease for nonnal strength
concrete.
Table 6-14: Ambient Relative Humidity Effects on Shrinkage Coefficients for
Ultra High-Strength Concrete
Time being considered Shrinkage Strain at time i Shrinkage Strain at time i
ti (days) esiw x10A-6 esiw x10A-6
Relative Humidity = 0.7 Relative Humidity = 0.5
28 15.9289 20.5867
60 25.2532 32.6375
90 31.5412 40.7643
180 45.2758 58.5150
365 64.3785 83.2036
63


90.0000
80.0000
co 70.0000
<
O
* 60.0000

c
0 50.0000
o 40.0000
£ 30.0000
c
w
w 20.0000
10.0000
0.0000 A----------.----------.---------.----------1
0 100' 200 300 400
Time (days)
Figure 6-8: Ambient Relative Humidity Effects on Shrinkage Coefficients for
Ultra High-Strength Concrete
6.5.4 Cement Type Effects on Shrinkage Coefficients for Ultra High-Strength
Concrete
As cement type changes the shrinkage coefficients also change. Table 6-15 and
Figure 6-9 illustrates the effect of cement type by analytically changing K (where
K is the shrinkage constant of the cement type). The least amount of shrinkage
occurs in Type 11 cement and the most amount occurs in Type III which is also
true for normal strength concrete.
64


t
Table 6-15: Cement Type Effects on Shrinkage Coefficients for Ultra High-
Strength Concrete
Time being Shrinkage Strain Shrinkage Strain Shrinkage Strain
considered at time i at time i at time i
ti (days) tsiw x10A-6 ESiw x10A-6 tsiw x10A-6
Cement Type I Cement Type II Cement Type III
28 15.9289 11.9467 18.3182
60 25.2532 18.9399 29.0411
90 31.5412 23.6559 36.2724
180 45.2758 33.9568 52.0671
365 64.3785 48.2839 74.0352
Figure 6-9: Cement Type Effects on Shrinkage Coefficients for Ultra High-
Strength Concrete
65


6.5.5 Shrinkage Coefficients for Ultra High-Strength Concrete due to
Compressive Strength between 13,000 psi to 19,000 psi
The shrinkage coefficients change depending on the modulus of elasticity and on
the compressive strength. When compressive strength analytically increases the
shrinkage coefficients decrease as shown in Table 6-16 and Figure 6-10.
Table 6-16: Shrinkage Coefficients for Ultra High-Strength Concrete due to
Compressive Strength between 13,000 psi to 19,000 psi
Compressive Strength Shrinkage Strain at time i
fc (psi) esiwx10A-6
13000 28.7191
14000 27.7207
15000 26.8196
16000 26.0011
17000 25.2532
18000 24.5663
19000 23.9326
66


Compressive Strength (psi)
20000
23.0000 24.0000 25.0000 26.0000 27.0000 28.0000 29.0000
Shrinkage Coefficients x10A-6
Figure 6-10: Shrinakge Coefficients for Ultra High-Strength Concrete due to
Compressive Strength between 13,000 psi to 19,000 psi
67


7. Comparison of Results
7.1 Creep Coefficients Normal versus Ultra High-Strength
Analytically changing the compressive strength of the concrete affects the
modulus of elasticity. Creep coefficients do not depend on the modulus of
elasticity or the compressive strength which is why normal strength concrete and
ultra high-strength concrete have the same creep coefficients. This is shown in
Table 7-1.
Table 7-1: Creep Coefficients Normal versus Ultra High-Strength
. ^ '*7 , Normal Strength Ultra High- Strength
Time being considered Creep Coefficient Creep Coefficient
ti (days) 28(t) 28(t)
28 0.8859 0.8859
60 1.0996 1.0996
90 1.1890 1.1890
180 1.3394 1.3394
365 1.5072 1.5072
When creep coefficients were analytically analyzed at 60 days of age for various
compressive strength between 3,000 psi (21 MPa) and 19,000 psi (131 MPa) they
remained constant. This is demonstrated in Table 7-2.
68


Table 7-2: Creep Coefficients Due to Compressive Strengths between 3,000
psi and 19,000 psi ______________________
Compressive Creep
Strength Coefficient
fc (psi) 28(t)
3000 1.0996
4000 1.0996
5000 1.0996
6000 1.0996
7000 1.0996
8000 1.0996
9000 1.0996
10000 1.0996
11000 1.0996
12000 1.0996
. 13000 1.0996
14000 1.0996
15000 1.0996
16000 1.0996
17000 1.0996
18000 1.0996
19000 1.0996
GL2000 method estimation of creep coefficients was compared to the ACI
method (Videla, 2008) used to estimate the creep coefficients. This comparison
proves that the GL2000 method provides higher analytical estimates of creep
coefficients than the ACI method this is illustrated in Table 7-3 and Figure 7-1.
This difference is due to the ACI estimation of creep equation not considering the
volume to surface ratio as the GL2000 method does.
69


Table 7-3: Creep Coef: flcients GL2000 Method versus ACI Cree p Estimation
iiC:51 Normal Strength Ultra High-Strength ACI Method
Time being considered Creep Coefficient Creep Coefficient Creep Coefficient
ti (days) 028(t) 028(t) 28(t)
28 0.8859 0.8859 0.5645
60 1.0996 1.0996 0.8593
90 1.1890 1.1890 0.9882
180 1.3394 1.3394 1.1759
365 1.5072 1.5072 1.3287
Figure 7-1: Creep Coefficients GL2000 Method versus ACI Creep
Estimation
70


7.2 Elastic Compliance Coefficients Normal versus Ultra High-Strength
Elastic compliance coefficients are dependent upon the modulus of elasticity and
on the compressive strength which in turn is why normal strength concrete and
ultra high-strength concrete have different elastic compliance coefficients. This is
demonstrated in Table 7-3.
The elastic strain decreases by 35% when the compressive strength is analytically
increased from 4,000 psi (28 MPa) (normal strength) to 17,000 psi (117 MPa)
(ultra high-strength). This is directly related to the modulus of elasticity which
also increases by 35% when the compressive strength analytically increases to
17,000 psi (117 MPa) from 4,000 psi (28 MPa).
Table 7-4: Elastic Compliance Coefficients Normal versus Ultra High-
Strength________________________________________________________________
Elastic Compliance Coefficients
is rhtt Normal - -?'< 1 Strength Ultra High- Strength
Strength Development to Cement Type Pe 0.9330 0.9330
Concrete Strength at time to fcmto (psi) 4439 16886
Elastic Modulus at time to Ecmto (psi) 3964629 6058237
Elastic Strain 1/Ecmto (1/psi) 2.5223E-07 1.6506E-07
When elastic compliance coefficients were analytically analyzed at 60 days of age
for various compressive strengths between 3,000 psi (21 MPa) and 19,000 psi
(131 MPa) they decreased. This is illustrated in Table 7-4 and Figure 7-1.
71


Table 7-5: Elastic Compliance Coefficients Due to Compressive Strengths
between 3,000 psi and 19,000 psi ___________________
Compressive Strength Elastic Strain
fc (psi) 1/Ecmto (1/psi)
3000 2.8024E-07
4000 2.5223E-07
5000 2.3148E-07
6000 2.1528E-07
7000 2.0217E-07
8000 1.9126E-07
9000 1.8199E-07
10000 1.7398E-07
11000 1.6698E-07
12000 1.6078E-07
13000 1.8182E-07
14000 1.7664E-07
15000 1.7221E-07
16000 1.6839E-07
17000 1.6506E-07
18000 1.6216E-07
19000 1.5961E-07
72


20000
18000
16000
14000
Q.
C
B> 12000
g>
^ 10000
s
8 8000
a.
E
Q 6000
4000
2000 --------------------------------------------------------
0.00E+00 5.00E-08 1.00E-07 1 50E-07 2.00E-07 2.50E-07 3.00E-07
Elastic Strain (1/psi)
Figure 7-2: Elastic Compliance Coefficients Due to Compressive Strengths
between 3,000 psi and 19,000 psi
Data series represented by the gray line are results from normal-strength modulus
of elasticity equation 2.5 and data using ultra high-strength modulus of elasticity
equation 2.6 are represented by the black line. The jump between the data series is
due to elastic compliance depending on modulus of elasticity the use of the
different modulus of elasticity equations causes this.
7.3 Shrinkage Coefficients Normal versus Ultra High-Strength
Analytically changing the compressive strength of the concrete affects the
modulus of elasticity. Shrinkage coefficients depend on the compressive strength
Normal Strength
- Ultra-High Strength
73


which is why normal strength and ultra high-strength concrete have different
shrinkage coefficients. This is demonstrated in Table 7-5 and Figure 7-2.
The shrinkage coefficients decrease by 49% when the compressive strength is
increased from 4,000 psi (28 MPa) (normal strength) to 17,000 psi (117 MPa)
(ultra high-strength).
Table 7-6; Shrinkage Coefficients Normal versus Ultra High-Strength
ir' -pW-fv:;&!='-V: " Normal Strength Ultra High-Strength
Time being considered Shrinkage Strain at time i Shrinkage Strain at time i
ti (days) esi'wx10a-6 ESiwx10A-6
28 31.0672 15.9289
60 49.2529 25.2532
90 61.5168 31.5412
180 88.3042 45.2758
365 125.5615 64.3785
74


140
Figure 7-3: Shrinkage Coefficients Normal versus Ultra High-Strength
When shrinkage coefficients were analytically analyzed at 60 days of age for
various compressive strengths between 3,000 psi (21 MPa) and 19,000 psi (131
MPa) they decreased. This is illustrated in Table 7-6 and Figure 7-3.
75


Table 7-7: Shrinkage Coefficients Due to Compressive Strengths between
3,000 psi and 19,000 psi__________________________
Compressive Strength Shrinkage Strain at time i
fc (psi) £siwx10A-6
3000 55.6143
4000 49.2529
5000 44.6705
6000 41.1676
7000 38.3775
8000 36.0873
9000 34.1636
10000 32.5180
11000 31.0894
12000 29.8338
13000 28.7191
14000 27.7207
15000 26.8196
16000 26.0011
17000 25.2532
18000 24.5663
19000 23.9326
76


20000
0 ^------------1-----------!-----------r-----------'-----------r--------,
0.0000 10.0000 20.0000 30.0000 40.0000 50.0000 60.0000
Shrinkage Coefficients x10A-6
Figure 7-4: Shrinkage Coefficients Due to Compressive Strengths between
3,000 psi and 19,000 psi
GL2000 method estimation of shrinkage coefficients was compared to the ACI
method (Videla, 2008) used to estimate the shrinkage coefficients. This
comparison proves that the ACI method analytically estimates lower shrinkage
coefficients for normal strength concrete at younger ages when compared to the
GL2000 method this is illustrated in Table 7-8 and Figure 7-5. This is due to the
equation not considering the properties that the GL2000 method considers. Such
as cement type and concrete compressive strength at 28 days.
77


Table 7-8: Shrinkage Coefficients GL2000 Method versus ACI Shrinkage
Estimation
Normal Strength Ultra High- Strength ACI Method
Time being considered Shrinkage Strain at time i Shrinkage Strain at time i Shrinkage Strain at time i
ti (days) Esiwx10A-6 esiwx10A-6 £siwx10A-6
28 31.0672 15.9289 11.7896
60 49.2529 25.2532 28.8068
90 61.5168 31.5412 43.8044
180 88.3042 45.2758 83.9960
365 125.5615 64.3785 149.2630
<
o
X
u>
c
0)
o
ifc
o
O
0)
D)
ro
W
160.0000
140.0000
120.0000
100.0000
80.0000
60.0000
40.0000
20.0000
0 0000


50 100 150 200 250 300 350 400
Normal GL2000
Ultra High GL2000
* ACI
Time (days)
Figure 7-5: Shrinkage Coefficients GL2000 Method versus ACI Shrinkage
Estimation
78


8. Conclusions and Recommendations
8.1 Conclusion
This thesis analytically evaluated creep and shrinkage as a function of two
different strength types. This thesis consists of comparisons between normal
strength and ultra high-strength concrete.
The normal strength concrete parameters used in this study are as follows: a
compressive strength of 4,000 psi (28 MPa), an average compressive strength of
5,100 psi (35 MPa), cure period of 7 days, age of concrete at loading 14 days,
relative humidity of 70%, a volume to surface ratio of 10 inches (254 mm),
strength gain factor of 0.335, a shrinkage constant of 1, and a modulus of
elasticity of 4,213,543 psi (29,051 MPa).
The ultra high-strength concrete parameters used in this study are as follows: a
compressive strength of 17,000 psi (117 MPa), an average compressive strength
of 19,400 psi (134 MPa), cure period of 7 days, age of concrete at loading 14
days, relative humidity of 70%, a volume to surface ratio of 10 inches (254 mm),
strength gain factor of 0.335, a shrinkage constant of 1, and a modulus of
elasticity of 6,322,216 psi (43,590 MPa).
79


The scope of this research was to analytically compare normal strength concrete
to ultra high-strength concrete with respect to creep, elastic compliance, and
shrinkage coefficients. The normal strength concrete with a compressive strength
of 4,000 psi (28 MPa) was analytically compared to ultra high-strength concrete
with a compressive strength of 17,000 psi (117 MPa). This research found that
the creep coefficient remained constant due to the fact that creep coefficient is
independent of compressive strength and modulus of elasticity. The elastic
compliance coefficients were reduced by as much as 35% and the shrinkage
coefficients were reduced by as much as 41%.
The factors that influence creep coefficients are as follows: age of loading, curing
time, volume to surface ratio, and ambient relative humidity. The factors that do
not influence creep coefficients are cement type and compressive strength.
The factors that influence elastic compliance coefficients are as follows: age of
loading, cement type, and compressive strength. The factors that do not influence
elastic compliance coefficients are curing time, volume to surface ratio, and
ambient relative humidity.
The factors that influence shrinkage coefficients are as follows: curing time,
volume to surface ratio, ambient relative humidity, cement type, and compressive
80


strength. The factor that does not influence shrinkage coefficients is age of
loading
8.2 Recommendations
This study recommends the use of ultra high-strength concrete in structures. The
use of ultra high-strength concrete has many benefits. First, the analytical
approach used in this study found that ultra high-strength concrete experiences
less shortening than normal strength concrete. Second, ultra high-strength uses
slender members and creates more floor space. Third, ultra high-strength
concrete is more cost effective as less material is needed. Fourth, with ultra high-
strength concretes there will be less of a need for reinforcement which will also
decrease cost. And lastly, ultra high-strength concrete will have a longer life
span.
Experimental testing of normal and ultra high-strength concrete is recommended
to examine creep, elastic compliance and shrinkage coefficients to verify the
computational results that are presented in this study.
81


Appendix A
Hand Calculation
A.1 Hand Calculation for Normal Strength Concrete
Age of concrete ti 28 days
Age of concrete at loading to 14 days
Age of concrete cured tc 7 days
Relative Humidity h 0.7
Volume-Surface Ratio v/s 10 in
Cement Type s 0.335
Concrete compressive strength fcm28 5100 psi
A.1.1 Creep Strain for Normal Strength Concrete
14-7
,0.5
14 7 + 77x (l0):
2 x (28 -14)3
0.5
- 0.9848
028(/) = (0.9848)
(28-14)3 +14
+
f 7 l 0.5 ( 28-14 ^
ll4j [28-14 + 7,
0.5
2.5(l-(l .086 x0.7)2]
28-14
+
28-14 + 77x(4)2
A.1.2 Elastic Strain for Normal Strength Concrete
P=e
= 0.933
fcm28 = 1.1 x 4000 + 700 = 5100
f =0.9332 X 5100 = 4439.5
J cnUfi
E = 500,000 + 52,000^4439^5 =3.96x106
ME =l/3.96xl06 = 0.252x10"
= 0.881
82