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**ROLE OF EARLY-AGE CONCRETE PROPERTIES AND CONSTRUCTION **LOADING ON SLAB SERVICEABILITY

Table of Contents

# ABSTRACT

The slab is modeled using a shell element in the commercial finite element software package ABAQUS/Standard. To idealize material behavior a user-defined subroutine (UMAT) is developed. Time-dependent creep and shrinkage effects in concrete material are also incorporated to the subroutine. Recently proposed creep and shrinkage models are implemented along with tension stiffening models in a general purpose computer program for analysis of concrete slabs under sustained time-dependent loading.

Laboratory tests on nine simply supported one-way reinforced concrete members subjected to sustained load was performed. Each specimen was subjected to immediate full live again after six months. Applied load and mid-span deflections were recorded under immediate live load and sustained load. The test results demonstrated the effect of shrinkage restraint provided by embedded bars on the flexural cracking of the specimens under applied load, as well as effects of early age loading on time-dependent response.

Results of an analytical study of reinforced concrete two-way slab systems are also presented. Numerical results which are obtained using the developed time-dependent concrete model were compared with available experimental results. The results show good correlations between analysis and tests in terms of load-deflection and deflection histories.

A parametric study is carried out in order to investigate the various factors affecting slab deflections.

# TABLE OF CONTENTS

TABLE OF CONTENTS…………………………………………………………………………………iv

LIST OF FIGURES ………………………………………………………………………………………..vii

LIST OF TABLES………………………………………………………………………………………….xiv

LIST OF SYMBOLS………………………………………………………………………………………xvi

ACKNOLEDGEMENTS…………………………………………………………………………………xxii

Chapter 1 INTRODUCTION…………………………………………………………………………..1

1.1 Background……………………………………………………………………………………….3

1.2 Objective and Scope…………………………………………………………………………..6

1.3 Literature Review ………………………………………………………………………………8

1.3.1 Material Properties for the Early Age Concrete…………………………….9

1.3.1.1 Compressive Strength ………………………………………………………9

1.3.1.2 Tensile Strength……………………………………………………………….13

1.3.2 Tension Stiffening …………………………………………………………………….14

1.3.3 Creep and Shrinkage of Concrete………………………………………………..15

1.3.4 Concrete Tensile Creep ……………………………………………………………..18

1.3.5 Factors Affecting Creep and Shrinkage ……………………………………….18

1.3.5.1 Cement …………………………………………………………………………..19

1.3.5.2 Aggregate ……………………………………………………………………….191.3.5.3 Admixture……………………………………………………………………….20

1.3.5.4 Water-to-Cement Ratio …………………………………………………….21

1.3.5.5 Time ………………………………………………………………………………22

1.3.5.6 Other Factors…………………………………………………………………..22

1.3.6 Analysis Approaches…………………………………………………………………23

1.3.7 Construction Loads……………………………………………………………………25

1.3.8 Experimental Studies…………………………………………………………………29

1.4 Thesis Layout…………………………………………………………………………………….32

Chapter 2 METHOD OF ANALYSIS………………………………………………………………34

2.1 Introduction……………………………………………………………………………………….34

2.2 Material Models…………………………………………………………………………………35

2.2.1 Concrete Elastic Model ……………………………………………………………..35

2.2.2 Tension Stiffening Models …………………………………………………………37

2.2.3 Equivalent Uniaxial Strain …………………………………………………………38

2.2.4 Cracking Algorithm…………………………………………………………………..40

2.2.5 Creep and Shrinkage Algorithm………………………………………………….44

2.2.6 Strength Development of Concrete ……………………………………………..47

2.2.7 Reinforcing and Post-Tensioning Steel………………………………………..49

2.3 Interface of Concrete Model in ABAQUS/Standard……………………………….50

2.4 Solution Method ………………………………………………………………………………..51

2.4.1 Modified Newton-Raphson Method…………………………………………….51

2.4.2 Convergence…………………………………………………………………………….53

Chapter 3 EXPERIMENTAL STUDY……………………………………………………………..66

3.1 Introduction……………………………………………………………………………………….66

3.2 Specimen Design and Preparation………………………………………………………..663.3 Material Properties……………………………………………………………………………..67

3.4 Test Setup and Procedure ……………………………………………………………………68

3.5 Immediate Deflection due to Application of Live Load…………………………..68

3.6 Long-Term Deflection under Sustained Load………………………………………..70

3.7 Summary…………………………………………………………………………………………..70

Chapter 4 VERIFICATION OF DEVELOPED MODEL……………………………………90

4.1 Introduction……………………………………………………………………………………….90

4.2 Scott and Beeby (2005) ………………………………………………………………………90

4.3 McNeice Corner Supported Slab (1971) ……………………………………………….92

4.4 Burns and Hemakom (1985)………………………………………………………………..934.5 Gilbert and Guo (2005)……………………………………………………………………….94

4.6 Analytical Investigation of One Way Slab Specimens…………………………….95 4.6.1 Calculation of Deflections Using Method Specified in Design

Code ………………………………………………………………………………………….96

4.6.2 Prediction of Cracking Loads……………………………………………………..98

4.6.3 Results of Analysis: Instantaneous Deflections …………………………….99

4.6.4 Results of Analysis: Long-Term Deflections………………………………..100

4.7 Finite Element Analysis using Developed Concrete Model……………………..102

4.7.1 Finite Element Model………………………………………………………………..1024.7.2 Immediate Deflections……………………………………………………………….103

4.7.3 Long-Term Deflections ……………………………………………………………..104

4.8 Summary…………………………………………………………………………………………..106

Chapter 5 PARAMETRIC STUDY BASED ON THE DEVELOPED MATERIAL MODEL ………………………………………………………………………………148

5.1 Introduction……………………………………………………………………………………….148

5.2 Slab Design……………………………………………………………………………………….149

5.3 Finite Element Model…………………………………………………………………………150

5.4 Parameters…………………………………………………………………………………………151

5.4.1 Load-Time History Model………………………………………………………….152

5.4.2 Slab Thickness………………………………………………………………………….155

5.4.3 Column Stiffness ………………………………………………………………………155

5.4.4 Separation of Creep and Shrinkage Effect ……………………………………156

5.4.5 Elastic and Nonlinear Analysis …………………………………………………..157

5.4.6 Extraordinary Superimposed Loading………………………………………….157

5.4.7 Age of Application of Loading……………………………………………………158

5.5 Long-Term Multiplier…………………………………………………………………………159

5.6 Moment Variation………………………………………………………………………………160

5.7 Summary…………………………………………………………………………………………..162

Chapter 6 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS…………..197

6.1 Summary…………………………………………………………………………………………..1976.2 Conclusions……………………………………………………………………………………….199

6.3 Recommendations………………………………………………………………………………201

Bibliography ………………………………………………………………………………………………….202

**Chapter 1 **

** **

# INTRODUCTION

The design of reinforced and prestressed concrete slab requires a limitation of deflection and camber. In order to provide the limitation, it is necessary to perform extensive experiments and develop accurate analysis methods. Because nonlinear properties of concrete as well as time-dependent effects make the analysis difficult, practical modeling methods are essential for analysis.

During construction of multistory buildings, shoring and reshoring processes are employed and construction loads are applied to the slab. The construction load affects floor and roof slab deflection because the strength of concrete and age of loading vary according to the construction methods and cycles used. Also, the slab experiences construction loading due to material storage and construction equipment which may also cause cracking at early age of concrete. An early loss of stiffness may cause a high short term deflection. In addition, it is well known that creep and shrinkage effects increase long-term deflections. The loading history including construction loads is an important factor which can increase cracking in the concrete slab (ACI Committee 347, 2005; Hurd, 1995).

Concrete shows different material behavior under compression and tension. Under certain levels of loading, cracks are formed in the concrete slabs. These cracks are the major factor causing nonlinear material behavior of concrete. In addition, time-dependent material behavior, creep and shrinkage, are also the major sources of nonlinear behavior of concrete. Nonlinear analysis, therefore, needs to be used to express real behavior of concrete and reinforcement as closely as possible (Phuvoravan and Sotelino, 2005).

The calculation of deflections for two-way slab is complicated even if behavior of concrete slab is linear elastic. In order to analyze the concrete slab, classical mechanics based on plate and shell theory, numerical methods such as finite difference method (FDM) and finite element method (FEM) have been developed. Among these methods, the finite element method may be the most popular application in a complex concrete slab system. Although classical plate and shell theory has provided theoretical background for developing other methods, it has limitations in analyzing the plate and shell when there are complicated shape of slab, composite materials, loading conditions, and boundary conditions. On the other hand, as a result of development of micro computer, numerical method has become more popular. The Finite Element Method has been described in detail by Chapelle and Bathe (2003), Ugural (1981), and Szilard (1974).

When performing the finite element analysis of concrete slabs, it is necessary to incorporate nonlinear material properties of concrete and reinforcement into the model. In addition, proper finite element types should be chosen according to the problem. Under service load, the most important aspect in concrete material model is a tensile cracking. Tension stiffening models usually have been introduced to model the stiffness provided by concrete between cracks. In these models, the concrete cracking is treated as a gradual reduction of tensile stiffness with increasing load (e.g. Scanlon, 1972; Fields and

Bischoff, 2004; Link et al, 1989).

In the analysis, the tension stiffening effect is normally applied when calculating the short-term deflection. When the concrete structure is subjected to time-dependent condition, the tension stiffening model needs to be changed into a function of time. This research introduces a long-term loss of tension stiffening in finite element analysis. In the level of material model, it is not easy to combine both concrete and reinforce with the instantaneous and time-dependent material model. Also, proper numerical solution method is necessary. An important aspect of early age concrete is the development of compressive and tensile strengths with time. It is reported that shrinkage can cause cracks, so that the concrete cracking moment can be reduced by shrinkage caused during curing (Bischoff, 2005, Gilbert, 1992, Scanlon and Murray, 1982). Also, the creep and shrinkage effect can be increased if the loading starts at early age. Long-term loss of tension stiffening also needs to be considered when modeling time-dependent effects.

Experimental studies for early age creep showed that the creep is significantly high (Altoubat and Lang, 2001; Kovler, 1995; Bissonnette and Pigeon, 1995). Therefore, an analytical model explaining the shrinkage effect during curing needs to be developed.

## 1.1 Background

Many modeling approaches have been developed in order to analyze concrete slabs. Smeared crack models and discrete crack models have been developed. Discrete model approach considers a crack as geometrical discontinuity. The crack occurs following predefined path by using nodal separation in the finite element analysis. This method changes the connectivity of nodes continuously. But nodal separation and predefined crack path are not the nature of finite element method. These weaknesses have been modified by using graphic-aided algorithms. Discrete model is more proper to idealize the local effect such as punching shear and column-slab connection in the concrete slab modeling. On the other hand, the smeared approach considers a cracked concrete as a cracked solid continuum. Smeared crack models use a concept of oriented damaged elasticity in terms of stress-strain relations. Researchers have suggested smeared model and proved its accuracy. Especially, in order to calculate the loaddeflection response of concrete slab, a smeared model has provided good results (e.g.

Rots and Blaauwendraad, 1989).

Although commercial finite element program such as ABAQUS (2002) provides a plasticity concrete models based on plasticity theory, the calculation procedure for creep and shrinkage have not been implemented with the cracking algorithm for concrete. In order to calculate the short-term deflections, smeared model and damaged-plasticity material model for concrete are provided in ABAQUS. Smeared crack model uses a concept of oriented damaged elasticity in terms of stress-strain relations. The inelastic compressive stress-strain relation is used to express the isotropic compressive inelasticity and the tension stiffening effect and tensile stress-strain relation are adopted to account for tensile cracking. Damaged-plasticity model for concrete was proposed by Lubliner et al (1989). This model uses fracture-energy-based scalar damaged variables to represent a damage of concrete. Also, the model introduces elastic and inelastic stiffness degradation variables which are used to make an inelastic constitutive model of concrete. However, ABAQUS does not provide a procedure to calculate the creep and shrinkage under cracked condition. Therefore, it is crucial to combine the procedures to calculate the short and long-term behavior of concrete slabs together.

The inelastic stress-strain relation is used to express the isotropic compressive inelasticity and the tension stiffening effect. Tensile stress-strain relation is adopted to account for tensile cracking. The tension stiffening effect is especially important aspect of tensile behavior of reinforced concrete. It is because concrete can carry tension between cracks in a reinforced concrete. Scanlon (1971) first introduced the tension stiffening model in finite element analysis. Tensile stress between cracks in concrete member is considered as an average tensile stress of concrete. A number of tension stiffening models have been proposed (e.g. Fields and Bischoff, 2004; Massicotte et al,

1990; Damjanic and Owen, 1984; Lin and Scordelis, 1975; Scanlon and Murray, 1974). According to Bischoff (2001), the tension stiffening can be reduced due to shrinkage effect. He addressed that test results can be affected by shrinkage significantly. It is because reinforcement has compressive stress and concrete has tensile stress as a result of member shortening caused by shrinkage prior to loading. Fields and Bischoff (2004) proposed a tension stiffening equation including shrinkage effect. Ostergaard et al (2001) performed test, and presented result that tensile creep of concrete is much higher when loading is applied at early age. It is also controversial that the decay of tension stiffening exists for some time after loading as like the results of Scott and Beeby’s test (2005).

The advantages of smeared model include its efficiency in prediction of loaddeflection response of the concrete slab and simplicity of implementation. Layered model approaches introduced to embody the smeared model. It allows the stress-strain variation through thickness and makes possible reinforcement modeled as smeared layer between concrete layers. It is also an advantage that flexural and membrane action of concrete slab can be expressed as two dimensional plane stress behavior. Thus, the concrete slab can be idealized as two-dimensional plane finite elements. This shortens the run-time and makes it easy to develop a material model. Material model is treated as a two-dimensional biaxial stress-strain relation (Scanlon, 1971; Scanlon and Murray, 1974; Lin and

Scordelis, 1975, Gilbert and Warner, 1978).

Noh et al (2003) presented a finite element analysis using the reinforced concrete shell element. For the concrete material model an orthotropic model was used. The concrete model is based on the elastic-plastic damage model for the cyclic and monotonic loading. Layered shell element based on Reissner-Mindlin shell theory was adopted with the orthotropic concrete model and a bilinear elastic-plastic reinforcement model.

Phuvoravan and Sotelino (2005) suggested a new finite element for the nonlinear analysis of reinforced concrete slabs. The developed model was implemented in

ABAQUS using user-defined element (UEL) and user-defined material model (UMAT). The concrete slab was idealized with four node shell element based on Kirchhoff shell theory and the reinforcement was modeled with two node beam element. The difference between existing layered model and proposed method was that the reinforcement was considered as beam element and connected shell element with rigid link. For the concrete material model, orthotropic model was adopted and uniaxial stress-strain relation was used for reinforcement model.

## 1.2 Objective and Scope

The objective of this study is to develop analytical methods to investigate the influence of material properties, construction sequence, and time-dependent effect on the performance of concrete flat slab systems. Emphasis will be placed on implementation of material constitutive model, cracking, and deflection of slabs under service load conditions. In order to investigate the early age effect of concrete, an experimental program was performed for one-way reinforced concrete slab. Results of this study will be used to provide recommendations for improved design of concrete slab systems. This objective will be achieved within the following scope:

- Literature review to determine current state-of-the-knowledge including timedependent effects, nonlinearity and early age effect of concrete slabs.
- Evaluations of existing creep, shrinkage, and cracking models obtained from the literature for implementation in the analytical model.
- Implementation of selected models in a general purpose program

(ABAQUS/Standard) through user-defined subroutine.

- Performing the experimental program to investigate the early age effect of concrete.
- Validation of the analytical model using available experimental data.
- Parametric studies to examine the influence of material model parameters, environmental condition, and construction sequences on slab performance.
- Development of conclusions and recommendations for design and construction of concrete slab system.

## 1.3 Literature Review

In order to investigate the structural behavior of concrete slabs, a proper analytical approach must be chosen and evaluated. Several analytical approaches have been suggested such as equivalent frame method, classical plate and shell theory, and numerical analysis. In addition, numerous experimental studies are focused on the structural behavior of concrete slabs: short-term load-deflection response; creep and shrinkage effect of concrete; long-term deflection history; effect of construction sequence and evaluation of construction loads (Ofosu-Asamoah and Gardner, 1997; Rosowsky et al,

1994; Stivaros and Halvorsen, 1990; Jokinen and Scanlon, 1987).

Loading at early age occurs in multistory concrete building construction. The fleshly poured concrete slab is supported by a system of shores and reshores. During shoring and reshoring process construction loads are transferred into previously cast floors which may not have attained the specified concrete strength. These loads also can be higher than the design service loads. If the construction loads are not evaluated before the design based on the understanding of the concrete properties at early age, there may be structural failures or serviceability failures (Hurd, 1995).

The characteristics of the early age concrete are that strengths are still under development and show low strengths in compression, and tension. A low elastic modulus and stiffness of loading at early age can cause larger long-term deflections and cracking than concrete slabs loaded at matured strength and stiffness. Time-dependent creep and shrinkage of concrete can affect significantly long-term deflections.

This chapter presents the literature review to obtain the state-of-art knowledge of material model for the early age concrete, analytical approaches, experimental studies, and construction loading of the concrete slabs.

### 1.3.1 Material Properties for the Early Age Concrete

The strengths of early age concrete are mainly dependent on the rate of strength development. The early age of concrete may be defined before 28 days after concrete pouring. Because many construction sequences impose significant construction loads on the concrete structure even though the concrete strength does not reach its maximum specified strength, it is essential to know the properties of early age concrete. For simplicity it may be assume that the strengths of concrete such as flexural strength, shear, tensile is proportional to the concrete compressive strength at loading age (ACI Committee 347, 2005).

Cracking and deflections are primarily related to the tensile strength, elastic modulus and tension stiffening at that age. Prediction of proper concrete strengths at the loading age is essential in calculation of slab deflections. Time-dependent properties at early age are also important factors in prediction of the long-term deflections.

#### 1.3.1.1 Compressive Strength

A typical concrete stress-strain relationship depends on various properties including the strength of concrete, age of concrete, rate of loading, material properties of

cement and aggregate and size of specimen. The compressive stress of concrete shows an approximately linear increase with strain in the range of0.4 ~ 0.45 *f*_{c}^{‘ }. Once the strain of concrete exceeds the elastic range, the concrete stress increases nonlinearly and reaches the specified compressive strength *f*_{c}^{‘ }. After that, the stress decreases nonlinearly and that is referred to as the softening phenomenon. ACI 318 (2005) code specifies an ultimate strain of 0.003 for design. In the elastic range concrete is assumed to be an isotropic linear elastic model. The linear elastic model is valid with the response of concrete subject to both tensile stress below cracking and compressive stress in the range of0.4 ~ 0.45 *f*_{c}^{‘ }. Researchers have extensively investigated nonlinear stress-strain relations of concrete for decades using mathematical form (Carreira and Chu, 1985; Popovics, 1970; Hognestad et al, 1955).

The relations for early age concrete may not be investigated thoroughly.

Numerous attempts have been made to investigate the concrete properties at early age. The development of the compressive strength is varied under different curing temperature and curing conditions. Klieger (1958) performed experiment about the strength development under different curing condition. Experiment showed that the compressive strength can be stronger as the duration of the moist curing is longer. Also, as the initial temperature and curing temperature are increasing, the compressive strength is lower at 3 months and 1 year. The experiment shows that the development of the compressive strength showed a nonlinear increase of its value.

Gardner and Poon (1976) tested a series of concrete cylinders to investigate the compressive strength, tensile strength, and bond strength at early age. Experiment showed that the curing at high temperature increase the rate of strength at early age, but the final ultimate strength reached lower value.

Gardner (1990) performed experiment to investigate the effect of temperature on the early age concrete properties. Type I, III, and Type I/Fly ash concrete cylinder and prism specimens were used to get the compressive, split tensile strength and elastic modulus. The controlled temperature conditions were 0, 10, 20, and 30 degree in Celsius. According to experiment, the rate of strength development was related to water-cement ratio, cement type, and temperature. The development of strength at early age was retarded at low temperature (0 C) and curing temperature had little effect on the development of strength of Type III or Type I having 0.35 water-to-cement ratio. Also, experiment showed that the lower the curing temperature, the higher the rate of strength development at early age but the lower the strength at early age less than 14 days. In the research, the final ultimate strength seemed to reach at the expected strength at any curing temperature regardless of the type of cement. Empirical equations predicting tensile strength and elastic modulus were suggested as the relation of the power of compressive strength.

Oluokun (1991) and Oluokun et al (1991) investigated the relationships between the elastic modulus, Poisson’s ratio and the cylinder strength at early age. The results were obtained for ages from 6hrs to 28 days. It is concluded that the modulus of elasticity at appropriate age is proportional to the 0.5 power of the compressive strength. For the Poisson’ ratio the values was not only insensitive to both the age of concrete and the concrete mix, but also the value approximately taken as 0.19 did not change with compressive strength development.

Khan et al (1995) performed experiment about the early age compressive stressstrain characteristics of low (30 MPa), medium (50 MPa) and high-strength (70 MPa) concrete. The experiment showed that the stress-strain relation for all of the concrete started to be similar to the relation of 28 days after 24 hrs. Under different curing conditions, the rate of development of strength follows by the order of temperaturematched curing, sealed curing, and air-dried curing.

Schutter (1999) suggested the extended compressive stress-strain relation based on CEB-FIP Model Code 1990 for early age concrete. In the research modifications using the improved parameters were made. Once the compressive strength, tangent elastic modulus, and strain at the peak compressive strength for early age concrete were known, the CEB-FIP model produced the most accurate predictions compared with results from experiment.

Yi et al (2003) proposed time-dependent stress-strain relation for the compressive strength of concrete. The proposed model was not only verified against the experimental results, but also compared with existing empirical equations. The range of specified compressive strength from 30 MPa to 70 MPa with water-to-cement ratio from 0.89 to 0.30 was investigated. Total 8 different ages, 0.5, 0.75, 1, 2, 3, 7, 14, and 28 days, were compared with experiment results. Results showed that the proposed model can predict the compressive stress-strain relation accurately.

#### 1.3.1.2 Tensile Strength

Before cracking, tensile stress of concrete is assumed to be linear elastic. After cracking, the stress decreases according to the tension stiffening equation or softening equation. Tensile strength is expressed in terms of a specific test method. The direct tensile, the beam test for modulus of rupture, and split cylinder test are the three kinds of tests that are frequently have been used. The strain at the maximum tensile stress usually is assumed to increase up to the modulus of rupture while pure bending condition, and sometimes can be assumed to be linear or nonlinear decrease. The modulus of rupture or bending tensile strength *f** _{r }*, direct tensile strength,

*f*

*, of concrete is assumed as the maximum elastic tensile strength of concrete. Therefore, the tensile stress-strain relation in the elastic range can be assumed as linear elastic response.*

_{t }Gardner and Poon (1976) showed that the relation that the tensile strength and bond strength were proportional to the compressive strength. The 0.8 power of cylinder strength at the appropriate age was suggested. Also, there was no significant effect on the interrelationship of tensile strength or bond strength and compressive strength according to different curing at temperature, cement type.

Oluokun (1991) presented a prediction method for tensile strength from the compressive strength for normal weight concrete. In the research instead of using the 0.5 power relation used in ACI 318 for predicting the splitting tensile strength of concrete the

0.69 power relation is proposed.

Swaddiwudhipong et al (2003) performed the experiment about direct tensile test and showed the result of tensile strain of concrete at early age. The investigation concluded that the rate of development of tensile strength is lower than the compressive strength and the average tensile strain at maximum strength is relatively independent parameter. The average tensile strain at failure does not depend on strength, mix proportion and age of concrete.

### 1.3.2 Tension Stiffening

The tension stiffening effect is usually considered to represent the tensile strength of concrete after cracking in reinforced concrete. The effect contributes to overall stiffness in cracked reinforced concrete particularly at service load levels. After the concrete tensile stress reaches the maximum tensile strength, cracking will occur. Once cracked, the concrete is assumed not to carry any tension at the cracks. But the tension is transferred by reinforcement into the surrounding concrete. Consequently, the concrete tensile stress can be assumed as the average tensile stress. The average tensile stress in the concrete continues to decrease with increasing strain.

The tension stiffening effect was first introduced in finite element analysis by

Scanlon (1971) and various tension stiffening models have been proposed. Lin and Scordelis (1975) proposed a bilinear type concrete tension stress-strain model to explain the tension stiffening effect. Damjanic and Owen (1984) also suggested a bilinear type tension stiffening effect but with sudden drop of tensile stress immediately after concrete cracking. Fields and Bischoff (2004) proposed tension stiffening equation including shrinkage before loading. Shrinkage reduced the tension stiffening effect of high strength reinforced concrete tension member according to experiment. This is because the member is initially shortened due to shrinkage. As result, compressive stress is caused in reinforcing steel in opposite to concrete. The tensile stress in concrete reduces the axial force causing cracks. They explained the shrinkage effect on tension stiffening as the equation fitting experimental data. The tension stiffening equation includes a term for shrinkage strain.

Scott and Beeby (2005) investigated long-term tension stiffening effects by laboratory tests. Time-dependent strain variation of concrete and reinforcement due to creep was investigated. It is reported that concrete tension stiffening was decayed significantly during experiment. According to tests, decay of tension stiffening may affect deflection history.

### 1.3.3 Creep and Shrinkage of Concrete

Time-dependent deformations can be divided into stress-dependent and stressindependent. Shrinkage is a stress-independent deformation of concrete, and caused by the loss of moisture of concrete or defined as the time-dependent volume or strain change of concrete specimen not subjected to an external stress at a constant temperature after hardening of concrete. On the other hand, creep refers to time- and stress-dependent variation of strains in hardened concrete subjected to a constant sustained stress. Creep and shrinkage, as a matter of fact, are interdependent processes. Although they are affecting each other on their processes, they are treated as independent and assumed to be additive as independent processes for simplicity. This is because the process between creep and shrinkage is very complicated and hard to identify the process independently (Bazant, 1988).

Creep and shrinkage is an inelastic behavior of concrete. This phenomenon is caused by combining complex physical and chemical actions in concrete member. Shrinkage may be defined as drying shrinkage, autogenous shrinkage, carbonation shrinkage, and plastic shrinkage. Drying Shrinkage refers to general meaning of shrinkage phenomenon in concrete (Pickett, 1946). This shrinkage is caused by the loss of moisture from concrete under drying condition. Strain of drying shrinkage is partially irreversible. Reversibly, the swelling can occur when concrete is saturated again. However, the swelling is not only insignificant but insufficient to completely compensate for shrinkage. Autogenous (hydration or chemical) shrinkage occurs when water is removed internally by chemical combination during hydration in a moisture-sealed state. Autogenous shrinkage is quite small for ordinary normal concrete but it is significant for high-performance concretes. Carbonation shrinkage occurs when concrete is carbonated in a low, relative humidity environment. Plastic (capillary) shrinkage occurs when water is lost from concrete while it is in the plastic state (** fib**, 1999).

Creep of concrete may be divided into two types; basic creep and drying creep. Basic creep is the time-dependent deformation that occurs when concrete is loaded in a sealed condition so that moisture cannot escape (ACI Committee 209, 1992). Drying creep occurs when concrete is loaded in allowing drying. Drying creep is the additional creep in excess of basic creep and can be considered as stress-induced shrinkage. According to the concept of drying and basic creep, there are existing differences between inside and outside of concrete. But both creep strains are considered as one creep strain and assumed to have the same creep strain rate when doing analysis. Transitional creep strains are used as another nomenclature about creep strain, and those are related to environmental condition. Transitional creep strains can be divided into three components; transitional hygral creep, transitional chemical creep, and transitional thermal creep. Transitional hygral creep refers to wetting creep and drying creep. Transitional chemical creep strain occurs when concrete is under significant chemical reactions. Transitional chemical creep strain is caused by hydration, carbonation of cement paste. Transitional Thermal Creep Strain occurs when temperature is changed under loading (Bazant, 1988; ACI Committee 209, 2005).

Many different theories have been suggested to explain observed behavior of creep and shrinkage mechanism. Creep and shrinkage mechanisms could be distinguished between real and apparent mechanism. Real mechanism could be considered as physical and chemical properties of materials. This mechanism is independent of size and shape effect. On the other hand, apparent mechanism is caused by other effect such as composite action between aggregate and cement paste, moisture gradients, thermal effect caused by hydration. Creep of concrete is an extremely complex phenomenon, mostly because concrete is such a complex composite material. Extensive testing has been performed on numerous varieties of concrete, but the creep mechanism is still not fully understood today. However, the effects of certain factors have been concluded based on trends observed in creep testing (Bazant, 1988).

### 1.3.4 Concrete Tensile Creep

Concepts of creep mechanism are usually regarded as compression phenomenon.

Also, tensile creep of concrete can be considered to be as large as the compression creep (Bazant, 1988; Gilbert, 1988). Experimental studies of tensile creep have been reported by researchers (Ostergaard et al, 2001; Altoubat and Lange, 2001; Kovler, 1999; Kovler; 1996; Kovler, 1995). It is reported that tensile creep is affected by many factors such as curing condition, drying condition, loading condition, and stress levels. Although tensile creep has similar characteristics as compressive creep has, there may be differences between compression and tensile creep according to the development of micro cracking. Tensile creep models are not suggested in the design code up to now and compression creep models are prevalent in the analysis.

### 1.3.5 Factors Affecting Creep and Shrinkage

Concrete is made of cement, aggregates, water and admixtures. There are numerous interacting factors affecting creep and shrinkage. The interaction among these factors is very complicated and difficult to be understood because of complex chemical and physical interactions. The factors are discussed and categorized to understand the effect of each factor affecting creep and shrinkage. The factors may be categorized into internal and external factors. Internal factors can include materials and mix-proportions. External factors consist of stress level, environmental condition and geometry of the concrete member, and structure type.

#### 1.3.5.1 Cement

Portland cement is usually referred to general meaning of hydraulic cement. Cement binds aggregates and provides adhesive property. Cement has effect on strength of concrete and produces heat of hydration. Since the rate of hydration is connected to development of strength and removal of moisture in concrete, creep and shrinkage are also affected by cement characteristics. Cement content affects degree of hydration, and volume change occurs due to hydration of cement paste. Also, cement content affects compressive strength of concrete. The modulus of elasticity has relationship with strength of concrete. This means that creep strain is affected by the modulus of elasticity of concrete (Mehta and Monteiro, 1992).

#### 1.3.5.2 Aggregate

The aggregate as well as cement in concrete mixture occupies most of volume. About 60 to 80 percent of volume is filled up with the aggregate. The strength of concrete and dimensional stability and durability of concrete can be affected by the aggregate. For instance, size, shape, surface texture, and composition of coarse and fine aggregate are known to affect concrete strength (Mehta and Monteiro, 1992).

The size of aggregate has influence on the proportions of concrete mix. If the ratio of water to cement is constant, the larger aggregate in mixture, the less compressive strength of concrete. This is because the large aggregates have smaller surface area than the small aggregates. As a result, the bond between cement and aggregates is weaker than the small aggregates (Popovics, 1998).

The shape and surface texture of aggregates has effect on the strength of concrete at early age. The shape of aggregates refers to geometrical properties such as rounded, angular, elongated, and flaky. Rough textured aggregate may help formation of strong bond between the cement paste and aggregates, but rough texture or flat shape requires more water to produce workability (PCA, 1968).

#### 1.3.5.3 Admixture

Admixtures are ingredient of concrete mixture and added to the batch before or during mixing as well as water, cement, and aggregates. It is difficult to classify admixtures because there are so many kinds of admixtures and some admixtures have more than two kinds of effects. However, those can be classified according to chemical composition and functions on concrete mixture. Mehta and Monteiro (1992) classified admixture according to their composition, mechanism of action, applications, surfaceactive chemicals, set-controlling chemicals, and mineral admixtures.

Air-entraining and water-reducing admixtures can be categorized as surfaceactive chemicals. Air-entraining admixtures are used to improve durability under the weather cycle of freezing and thawing. Those improve workability of concrete mixtures. Lager amount of air-entraining admixtures can cause delaying in cement hydration and decrease of concrete strength. Water-reducing admixtures are used to reduce the water requirement in concrete mixture. An increase in strength can be achieved by reducing water under condition that cement and slump are constant. In spite of reduction in water content, it is reported that there is significant drying shrinkage in concrete made of some water-reducing admixtures. Accelerating and retarding admixture can be included in setcontrolling admixtures. Those admixtures control the setting time of concrete and the rate of strength development at early age. An accelerating admixture is used to accelerate the setting time and the strength development. Most accelerating admixtures have the effect on drying shrinkage and those are increase the drying shrinkage. Calcium chloride is the most common accelerating admixture. On the other hand, it is reported that retarding admixtures reduce the strength of concrete at early age but shrinkage may not be predictable (PCA, 1968).

Mineral admixtures refers to pozzolanic and/or cememtitious admixtures. These admixtures can be obtained from the nature or by-product of the industry. Also, these admixtures have tendency to increase the volume of fine pores in hydrated cement. Creep and drying shrinkage in concrete are associated with the water held by small pores. If concrete has higher pore refinement, the higher drying shrinkage and creep occur (Mehta and Monteiro, 1992).

#### 1.3.5.4 Water-to-Cement Ratio

Creep and shrinkage effect are directly not influenced by water and cement content. Water and cement are influencing each other when mixing concrete proportions. Also, the variation in water and cement content in concrete mixture affects other proportions. It is difficult to understand what the contribution of each factor is in creep and shrinkage. For constant water-to-cement ratio, as cement content increases, creep and shrinkage has tendency to increase (Mehta and Monteiro, 1992).

#### 1.3.5.5 Time

Creep and shrinkage effect is the function of time and takes place over long period. Water movement taken place by capillary tension effect from small pores of hydrated cement paste to the atmosphere and/or other small pores is the time-dependent process. 75 to 80 percents of total amount of creep and shrinkage occurs within one year

(Mehta and Monteiro, 1992)

#### 1.3.5.6 Other Factors

Curing condition greatly affects creep and shrinkage effect of concrete.

Depending on curing method and curing history, creep and shrinkage can be varied. There is significant difference between value obtained in practice under varying humidity and that obtained in laboratory at constant humidity. For stress level, there is proportionality between creep strain and stress level. This relation may be valid when stress level is in the range of elasticity of concrete. In regard to the atmospheric humidity, while humidity increases, it makes the relative rate of moisture flow from the interior to the exterior surface of concrete slow down. For a same condition of exposure, it is reported that the increased humidity in the air reduces the shrinkage and creep. Geometry and structure type of concrete member can affect creep and shrinkage. Because there is resistance to water movement from the interior to the exterior of concrete, the rate of water movement can be governed by the total length of path traveled by water (Mehta and Monteiro, 1992).

### 1.3.6 Analysis Approaches

In the numerical analysis of reinforced concrete slab a finite element analysis is usually used. This numerical approach usually provides reasonable accuracy of solution. In the finite element method, the plate or slab is idealized into a finite number of elements using triangular or rectangular in shape. Finite elements are connected at their nodes at which the compatibility and equilibrium conditions are satisfied. For the nonhomogeneous material such as reinforced concrete slab, layered model is adopted with nonlinear material behavior of concrete (AAlami, 2005; .Wang et al, 2004; Ghosh and Dey, 1992).

Scanlon and Murray (1974) presented a finite element model in order to simulate the time-dependent reinforced concrete slab deflections. A layered model was adopted to idealize a concrete slab. Time-dependent creep and shrinkage strains were considered as initial strains. For the concrete model, an orthotropic material model was used. In addition, tension stiffening model was introduced in the finite element analysis.

Gilbert and Warner (1979) also used a layered finite element model with an orthotropic concrete model to calculate the short-term deflection of slab. In the study, different tension stiffening models were compared. In order to simulate concrete model, modified stress-strain diagram for tension steel was used as well as tension stiffening model using stress-strain diagram for concrete.

Scanlon and Murray (1982) presented methods for calculating deflections of twoway slabs. In order to take into account restraint stresses due to shrinkage and thermal effects reducing a modulus of rupture was used instead of using code specified modulus of rupture. In calculation of deflections of two-way slabs the equivalent frame method and the finite element analysis were presented. Reduction of flexural stiffness due to cracking was accounted for using effective moment of inertia. Calculation of long-term deflection could be determined by ACI 209 model.

Graham and Scanlon (1985) investigated the effect of construction loading on deflection of flat plate slabs using finite element method. Two-way slabs were modeled using equivalent frame method. For the material model of concrete the modified linear elastic material properties proposed by Scanlon and Murray (1982) were used. The reduced flexural stiffness to express a degree of cracking was obtained from a momentcurvature relationship. The long-term deflections and time-dependent strength of concrete were calculated by the recommendation of ACI 209 Committee. Construction loading from three levels of shoring process was adopted to investigate the deflection of slab. The comparison of model results with field measurement showed that the analysis method using equivalent frame method with iterative reduced stiffness of slab could produce a good agreement and the deflection due to construction loads could exceed the deflections due to service loads. Although the analysis method could predict the deflections of twoway slab, the modeling method could not consider the deformation of in-plane and the member forces.

Gardner and Scanlon (1990) addressed that the design estimation of the long-term deflection of reinforce concrete two-way slab could be different from the field measured deflections. The reasons of causing discrepancy between calculated and measured deflections could be explained by numerous effects. The construction loads and schedules could cause early cracks and reduction of flexural stiffness. Creep and shrinkage could be varied according to environmental conditions and concrete mix and the restraint stresses could be produced by shrinkage. Also, the analysis method could have errors because the numerical model could not express the practical problems thoroughly.

### 1.3.7 Construction Loads

During construction of multistory building with reinforced concrete floor slabs, shoring and reshoring operations are carried out. The construction is started by setting up the shoring on the previously cast floors. The second step is to pour fresh concrete on next floor. The same procedures are practically continued two or three times leaving the previously installed shore system according to the number of shoring and reshoring process such as three levels of shores, two levels of shoring and one level of reshoring, one level of shoring and two levels of reshoring, and so on. During shoring and reshoring process the weight of freshly poured concrete is transferred by shoring into the previously cast floors. The construction load may exceed the design loads and the load is usually expressed as load ratio of construction load to self-weight of slab. It is known that the distribution of construction loads depends primarily on the shoring/reshoring and the number of supporting floors.

Grundy and Kabalia (1964) developed a simplified method to estimate the construction loads in a multistory building. The method is developed based on several assumptions: elastic behavior of slabs, completely rigid foundation supporting the slabs, and infinitely rigid shores compared with the slab in vertical displacement. In the research constant flexural stiffness of slab as well as a flexural stiffness increasing with time was investigated. The flexural stiffness was assumed to be proportional to the modulus of elasticity. For the three levels of shores the maximum load ratio was 2.36, while the load ratio was converged for upper levels and the value was 2.0 in both constant flexural stiffness and increasing flexural stiffness with time.

Agarwal and Gardner (1974) performed the field tests to determine the actual construction load ratio of multistory flat slab building. The obtained load ratios were compared with the theoretical load ratios. During building construction three levels of shore and four levels of reshores were used for the first building and three levels of shores were used for the second building. They reported the comparisons field measurement with load ratios by the simplified method by Grundy and Kabalia (1964). The predicted load ratios were calculated from the one level of shoring and multi levels of reshoring was used. Results showed that the reshoring process could reduce the maximum load of supporting slabs significantly. The factored construction load ratio with number of shores and reshores were suggested. The results showed the accuracy of load ratios by the simplified method within 10 to 15 percent. Also, the research suggested the construction ultimate loads on the slabs as simplified mathematical equation.

Lasisi and Ng (1979) presented a modification of Grundy and Kabalia simplified method. Analysis included the construction live load assuming 50 psf and 10% of selfweight for the weight of shoring and reshoring. Because the construction live load could be produced by construction workers and equipments, the peak loads could be produced by self-weight of slab, formwork, and construction live loads together.

Sbarounis (1984) included the effects of cracking on the previously cast floors and reported the maximum load ratios could be reduced up to approximately 10 percent.

This was because the cracking occurred during construction changed the stiffness of previously cast slabs and produced different load distribution between these slabs. The analysis results implied that the cracking during construction might not only cause greater immediate deflections than predicted from the design, but also the long-term deflection could be greater.

Gardner (1985) considered the effect of early age strength of concrete in order to check the safety of structure during construction. The factored construction loads were compared with the slab strength at certain construction age. The factored construction loads were calculated from simplified method suggested by Grundy and Kabalia (1964) and extended by Agarwal and Gardner (1974). The obtained factored construction loads were compared with the design loads multiplied by the ratio of strength development of concrete at the age of loading. When the factored construction loads is greater than the design loads, the construction method using shoring and reshoring could not be used. This method may be useful when deciding the number of shoring and reshoring process and construction cycles at the design stage.

Liu et al (1985) developed a three-dimensional finite element model to investigate the load ratios. In the research the effects of time-dependent material properties of concrete, foundation rigidity, column axial stiffness, aspect ratio of slab were considered. The more realistic approaches could be initiated using a finite element model. However, the model had a limitation that the behavior slabs were considered as linear elastic. Also, the effects of cracking and time-dependent creep and shrinkage were not considered in the analysis. In spite of limitations the finite element model could be used in the situation of various boundary conditions, obtaining slab moments and shore loads, and investigating the influence of shore stiffness. The analysis results showed that the Grundy and Kabalia method needed to be corrected about 5 to 10% conservatively.

Fu and Gardner (1986) compared construction loads of one level of shoring and two levels of reshoring (1S2R), one level of shoring and two levels of preshoring (1S2P), and three levels of shoring (3S). The load ratios were calculated based on Grundy and Kabalia’s simplified method and the construction cycle were assumed to be a 7-day casting cycle with stripping after 5 days.

Gardner and Muscati (1989) suggested an algorithm that analyzes the construction sequences of shoring and reshoring process. To determine the design ultimate construction loads a simplified method by Grundy and Kabalia and extended by Agawal and Gardner was used. The empirical equations of the strength of concrete with time were incorporated in the algorithm. The safety of structure during construction could be checked by that the ultimate construction loads calculated by the simplified method did not exceed the design loads.

SEI/ASCE 37-02 (2002) defined minimum design load requirements during construction for building and other construction. The loads specified involved final loads, construction loads, material loads, lateral earth pressure, and environmental loads. The additive load combinations which are not defined in ACI 318 were suggested and the most critical load combination should be used. The standard provided the combined uniformly distributed loads for the combined material, personnel, equipment, and other applicable construction loads on the working surface according to the operational class in traditional design. The range of construction live loads varied from 20 psf to 70 psf.

ACI Committee 347 (2005) recommended that construction loads on formwork be designed for minimum live load of 50 psf as weights of workers, runaways, screeds, and other equipment. The minimum live loads of 75 psf are recommended when the motorized carts are used. Also combined design loads for dead and live loads should be 100 psf and 125 psf when motorized carts are used. For the load factors and strengths of concrete, ACI 209 and ACI 318 were recommended. Also, it is recommended that construction loads can be distributed by simplified method.

Stivaros (2005) addressed the estimation of construction load distribution, strength requirement of early age concrete, and serviceability problems during construction of multistory buildings. Although Grundy and Kabalia’s simplified method could be used to calculate the load ratio, caution should be taken because the axial stiffness of shoring and reshoring could not be ignored in the load distribution. Also, it is addressed that the time-dependent development of strength needed to be taken into account and the consideration of load factors not covered in ACI 318-05 for the construction loads were needed. Finally, the requirement of minimum thickness in current ACI 318-05 could not be used as safety against excessive deflections and cracking because the large construction loads could be imposed to the slab at early age.

### 1.3.8 Experimental Studies

In the construction of multistory building the previously cast slabs experience the construction load transferred by shoring and reshoring process. The construction schedules can be shorter due to competitive bids. As the schedules are shorter, relatively large loads can be applied to immature slabs. The loading at early age stage of construction may cause large immediate and long-term deflections. However, there are a few experimental researches of long-term deflections considering construction loads.

Washa and Fluck (1952) presented the effect of compressive reinforcement on the long-term behavior of simply supported reinforced concrete beams. Five different beam sizes with three different conditions of reinforcement were investigated. As results, the compressive reinforcement reduced the long-term deflections due to creep and shrinkage significantly.

Heiman (1974) measured long-term deflections for approximately 8 years of reinforced concrete buildings. The long-term deflections at mid-spans of interior panels were measured after construction was completed.

Bakoss et al (1982) tested simply supported and two spans continuous reinforced concrete beams. The instantaneous and long-term deflections were measured and compared with values predicted by the design codes and finite element analysis. The specified compressive strength 30 MPa of normal weight concrete was cast. The creep coefficient and shrinkage strain were recorded and compared with values specified in the design codes-British, European, American, and Australian. The cross-section of beam was 100mm wide 150 mm deep and 12mm diameter deformed rebars were use. The span lengths of simply supported and each span length of continuous beams were 3750 mm and 3500 mm respectively. The two simply supported beams were subjected to sustained load consisting of two point loads, applied at the third points of the span at 28 days after casting. The two continuous beams were loaded at 23 days after casting. A point load loaded at the mid-point of each of the two equal spans.

Gardner and Fu (1987) investigated the effect of early age construction loads on the long-term deflections of reinforced concrete flat slabs. In order to simulate the construction loads the approximately twice the slab dead load. Shrinkage strains were obtained from 3 x 4 x 15 in and 3 x 2.5 x 15 in prisms. Creep tests were conducted on both compression and flexure. Concrete cylinders were loaded in accordance with ASTM in compression. Plain, two singly reinforced, and two doubly reinforced concrete beams were manufactured to investigate the creep under flexure. The deflections were measured using dial gages and steel scales.

Gilbert and Guo (2005) investigated immediate and long-term deflections of seven large-scale of reinforced two-way flat slab structures. Two spans in each orthogonal direction continuous two-way slabs were cast. A plan dimension of each slab was 6.2m by 7.2m and two 3m continuous spans in each orthogonal direction. The thickness of each slab was 90mm. Each slab was supported on nine columns and each column size was 200 by 200 by 1250 mm. In order to investigate parameters influencing the long-term deflections, concrete properties, reinforcing spacing and reinforcement ratios, slab thickness, boundary conditions, and loading history were varied. Slabs were loaded at 14 and 15 days after casting. Material properties such as compressive strength, flexural tensile strength, elastic modulus, the creep coefficient, and shrinkage strain were measured. Time-dependent crack patterns, immediate and long-term deflections were measured for three years. Results showed that time-dependent cracking significantly affected the serviceability of flat slabs. The measured long-term deflections were approximately 5 to 9 times the initial short-term deflections. It was conclude that the current ACI 318 Building Code could not account for this effect appropriately for deflection calculation and control.

## 1.4 Thesis Layout

The research carried out is presented in 6 chapters. Chapter 1 introduces the background of the research and presents the objectives and scope. In addition, literatures are reviewed to get the state-of-art knowledge of time-dependent effect of concrete, concrete material model, construction loads in multistory building, analysis of concrete slab systems and experimental approaches.

In chapter 2, analytical modeling of reinforced concrete slabs is presented. Userdefined material subroutine and layered shell element in ABAQUS/Standard are introduced. An orthotropic time-dependent concrete model is explained.

Chapter 3 presents the experimental program in order to investigate the loading at early age on concrete one-way slabs. Procedure and test setup are explained.

Instantaneous and time-dependent deflections are shown.

In chapter 4, verification of developed material model is presented using the results of experimental programs as well as pre-existing results in the literature.

Chapter 5 deals with parametric study for a flat plate system. Loading history is considered according to shoring/reshoring method in multistory building. Also, long-term multiplier and moment diagram of slab based on parametric study are described in this chapter.

Finally, chapter 6 presents the conclusion, summary, and recommendations.