Citation |

- Permanent Link:
- http://digital.auraria.edu/AA00003024/00001
## 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:
- 2010
- 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 )
## Auraria Membership |

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 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) 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 = 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,, Â£^,= >.>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 'Â£) 0254 158 .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 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) 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) 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) . \ 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) 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) 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) Â£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) 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) 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) 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 Â£ 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 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) 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 Â£ b> c s? 12000 - CO 0) > 10000 - Q. Â£ 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 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 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) 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 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) Â£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 Â£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 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 |