Flexural Redistribution in Ultra-High Performance Concrete Lab Specimens

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A thesis presented to

the faculty of

the Russ College of Engineering and Technology of Ohio University

In partial fulfillment

of the requirements for the degree

Master of Science

Mohammad Reza Moallem

June 2010

This thesis titled

Flexural Redistribution in Ultra-High Performance Concrete Lab Specimens

MOHAMMAD REZA MOALLEM

has been approved for

the Department of Civil Engineering

and the Russ College of Engineering and Technology by

Eric P. Steinberg

Associate Professor of Civil Engineering

Dennis Irwin

Dean, Russ College of Engineering and Technology 3

ABSTRACT

MOALLEM, MOHAMMAD REZA., M.S., June 2010, Civil Engineering

Flexural Redistribution in Ultra-High Performance Concrete Lab Specimens (105 pp.)

Director of Thesis: Eric P. Steinberg

Ultra-High Performance Concrete (UHPC) is a new generation of cement based

construction materials which features superior mechanical and material properties. Its

compressive and flexural strengths are higher than 29 ksi and 7 ksi respectively. UHPC is

reinforced with steel fibers of 0.5 to 1.0 in long and 0.008 in thick. Its constituent

materials are extremely fine graded—smaller than 0.024 in. The improvement in micro-

structural level results in very low permeability in UHPC which leads to enhancement in

durability and resistance against all kinds of corrosion.

For further utilization of UHPC in the industry, special knowledge of its behavior

is needed. The minimum dimensions of structural members allowed by building code

requirements are set based on conventional concrete. Since UHPC’s constituent materials

are more expensive than those of conventional concrete, utilization of UHPC with current

minimum dimensions increases the cost drastically. Thus, development of new

specifications and new applications is needed.

Prior research at Ohio University has shown that the bond performance between

UHPC and prestressing strands are satisfactory. This research addresses the flexural

redistribution issue in UHPC. Four beams, with dimensions of approximately 50 in x 4 in

x 4in were tested. The tests were set up such that two concentrated loads were applied at

about the center of two spans supported at three points. The amount of moment 4 redistribution from the middle support into the spans were found to be approximately

14 percent, which is lower than the 20 percent in conventional concrete allowed by ACI

318 – 08 building code requirements.

Approved: ______

Eric P. Steinberg

Associate Professor of Civil Engineering

ACKNOWLEDGMENTS

It is a pleasure to thank those who made this thesis possible. I owe my deepest gratitude to my academic advisor Dr. Eric P. Steinberg, who has been a tremendous help to me in numerous ways. I would like to thank him for his guidance, assistance and support. I am grateful to my thesis committee members Dr. Shad Sargand, Dr. Hajrudin

Pasic, Dr. Ken Walsh, and Dr. Martin Mohlenkamp for their constructive and helpful inputs and comments. Dr. Sargand has made his support and advice available through my graduate studies at Ohio University.

I would like to thank the USAID, Ohio University, Washington State University,

Afghan Equality Alliances, and Kabul University for providing me with the chance to participate in Afghan Merit Scholars Program and attain my master’s degree. I am indebted to many of my colleagues and friends who supported me. Andrew Russ and

Issam Khoury deserve thanks for their help and assistance.

This thesis would not have been possible without my family’s support. Especially my mother, whose love, patience and encouragement have given me energy, enthusiasm, and motivation not only during my graduate study but throughout my life.

TABLE OF CONTENTS

Abstract ...... 3

Acknowledgments...... 5

List of Tables ...... 8

List of Figures ...... 9

Chapter 1 ...... 12

1. Introduction ...... 12 1.1. Ultra-High Performance Concrete (UHPC) ...... 12 1.1.1. History of UHPC ...... 12 1.1.2. Types of UHPC ...... 14 1.1.3. Applications of UHPC ...... 14 1.1.4. Material Properties of UHPC ...... 16 1.1.5. UHPC Constituent Materials ...... 18 1.1.5.1. Portland Cement ...... 18 1.1.5.2. Silica Fume ...... 18 1.1.5.3. Quartz Powder ...... 19 1.1.5.4. Super-plasticizer ...... 19 1.1.5.5. Steel Fibers ...... 19 1.1.5.6. Water and Fine Sand ...... 20 1.2. Flexural Redistribution ...... 21 1.2.1. Background ...... 21 1.2.2. Past Definitions of Moment Redistribution ...... 24 1.2.3. Moment Redistribution in ACI 318 – 08 ...... 27 1.2.4. Moment Redistribution in AASHTO LRFD Specifications ...... 27 1.2.5. Moment Redistribution in ENV 1992-1-1:1991Eurocode 2: Design of Concrete Structures ...... 28 1.2.6. Moment Redistribution in Other Codes ...... 30 1.3. Problem Statement and Objectives ...... 30 1.4. Thesis Outline ...... 31 Chapter 2 ...... 32 7

2. Background ...... 32 2.1. Literature Review: Past Work on UHPC ...... 32 2.2. Literature Review: Studies on Flexural Redistribution ...... 37 Chapter 3 ...... 40

3. Testing and Methodology ...... 40 3.1. Sample Preparation ...... 40 3.2. Apparatus Used...... 45 3.3. Test Setup ...... 45 3.4. Test Procedure ...... 47 3.5. Data Analysis ...... 48 Chapter 4 ...... 52

4. Results ...... 52 4.1. Beam 1 ...... 52 4.2. Beam 2 ...... 61 4.3. Beam 3 ...... 62 4.4. Beam 4 ...... 63 4.5. Moment Redistribution ...... 63 4.6. Ultimate Loads and Associated Moments ...... 65 Chapter 5 ...... 67

5. Discussion ...... 67 5.1. Stress and Strain Profiles ...... 67 5.2. Premature Failure in Beam 2 ...... 68 Chapter 6 ...... 80

6. Conclusions and Recommendations ...... 80 6.1. Conclusions ...... 80 6.2. Recommendations ...... 81 References ...... 83

Appendix A: Load Vs. Strain Curves ...... 86

Appendix B: Load Vs. Deflection Curves ...... 98

Appendix C: Moment Vs. Load Curves ...... 102 8

LIST OF TABLES

Table 1 Properties of UHPC as Opposed to High Strength Concrete (Lubbers 2003) --- 13

Table 2 Typical UHPC Constituent Materials Proportions (Graybeal 2006) ------20

Table 3 Past Definitions of Moment Redistribution (Rebentrost 2003) ------24

Table 4 Proportion of UHPC with and without Coarse Aggregates (Graybeal 2006) --- 35

Table 5 Mix Design for Tested UHPC Specimens (Lubbers 2003) ------40

Table 6 Dimensions of Tested Beams ------41

Table 7 Strain Gages (Vishay Micro-Measurements) ------43

Table 8 Moments in Beam 1 at Various Stages ------60

Table 9 Moments in Beam 2 at Various Stages ------61

Table 10 Moment in Beam 3 at Various Stages ------62

Table 11 Moment in Beam 4 at Various Stages ------63

Table 12 Cracking Moments and % Moment Redistributed ------64

Table 13 Redistribution of Moment at the Ultimate State------65

Table 14 Load Redistribution at the Ultimate Stage ------66

Table 15 Strain and Stress Distribution Profiles over the Section of the Beam ------67

LIST OF FIGURES

Figure 1 Sherbrooke Footbridge Cross Section ------15

Figure 2 Peace Footbridge Cross Section ------16

Figure 3 Moment Redistribution in a Continuous Beam (Rebentrost 2003) ------22

Figure 4 Optimum Mix Proportion of UHPC ------34

Figure 5 Deviation of Actual Moment from Elastic Moment (Lopes et al. 1997) ------39

Figure 6 Point Loads and Strain Gages Locations ------44

Figure 7 Test Set Up ------47

Figure 8 Irregularities in the Geometry of the Beams ------48

Figure 9 Stress-Strain Curve for UHPC (Steinberg 2009) ------49

Figure 10 Total Load vs. Strain at the Middle Support ------52

Figure 11 Total Load vs. Strain at the Middle Support ------53

Figure 12 Total Load vs. Strain in the Span------54

Figure 13 Total Load vs. Strain in the Span------55

Figure 14 Total Load vs. Strain in the Span------56

Figure 15 Total Load vs. Strain in the Span------57

Figure 16 Two Side by Side Beams Equivalent to the Specimen with a Yielded Middle

Support ------58

Figure 17 Two Side by Side Beams Equivalent to the Specimen when Cracking

Occurred in the Spans ------59

Figure 18 Failure Crack in Beam 2 ------69

Figure 19 Load vs. Strain Curve for Beam 2 Strain Gage 5 ------70 10

Figure 20 Load vs. Strain Curve for Beam 2 Strain Gage 6 ------71

Figure 21 Load vs. Strain Curve for Beam 2 Strain Gage 1 ------72

Figure 22 Load vs. Strain Curve for Beam 2 Strain Gage 2 ------73

Figure 23 Load vs. Strain Curve for Beam 2 Strain Gage 3 ------74

Figure 24 Load vs. Strain Curve for Beam 2 Strain Gage 4 ------75

Figure 25 Beam 2 After Testing ------76

Figure 26 Cross-section of Beam 2 Compared to Beam 3 ------77

Figure 27 Beam 2's Cross-Section Compared to Beam 3 ------78

Figure A. 1 Load vs. Strain: Beam 3 Strain Gage 1 ...... 86

Figure A. 2 Load vs. Strain: Beam 3 Strain Gage 2 ...... 87

Figure A. 3 Load vs. Strain: Beam 3 Strain Gage 3 ...... 88

Figure A. 4 Load vs. Strain: Beam 3 Strain Gage 4 ...... 89

Figure A. 5 Load vs. Strain: Beam 3 Strain Gage 5 ...... 90

Figure A. 6 Load vs. Strain: Beam 3 Strain Gage 6 ...... 91

Figure A. 7 Load vs. Strain: Beam 4 Strain Gage 1 ...... 92

Figure A. 8 Load vs. Strain: Beam 4 Strain Gage 2 ...... 93

Figure A. 9 Load vs. Strain: Beam 4 Strain Gage 3 ...... 94

Figure A. 10 Load vs. Strain: Beam 4 Strain Gage 4 ...... 95

Figure A. 11 Load vs. Strain: Beam 4 Strain Gage 5 ...... 96

Figure A. 12 Load vs. Strain: Beam 4 Strain Gage 6 ...... 97

Figure B. 1 Load vs. Deflection: Beam 1 ...... 98

Figure B. 2 Load vs. Deflection: Beam 2 ...... 99

Figure B. 3 Load vs. Deflection: Beam 3 ...... 100

Figure B. 4 Load vs. Deflection: Beam 4 ...... 101

Figure C. 1 Moment vs. Load: Beam 1 ...... 102

Figure C. 2 Moment vs. Load: Beam 2 ...... 103

Figure C. 3 Moment vs. Load: Beam 3 ...... 104

Figure C. 4 Moment vs. Load: Beam 4 ...... 105

CHAPTER 1

1. Introduction

1.1. Ultra-High Performance Concrete (UHPC)

1.1.1. History of UHPC

Ultra-High Performance Concrete (UHPC), also referred to as Ultra-High

Performance Fiber Reinforced Concrete (UHPFRC), is a new generation of cement-based materials that was developed in France in the 1990s. At that time, High-Performance

Concrete (HPC) was considered to be the strongest and stiffest cement based material with a compression strength of approximately 10 ksi (70 MPa) and a flexural strength of about 1.5 ksi (10 MPa) (www.fhwa.dot.gov/BRIDGE/hpcwhat.htm). Now, given the improvements on a microscopic scale, Ultra-High Performance Concrete (UHPC) can attain compression strengths higher than 29 ksi (200 MPa) and flexural strengths of about

7 ksi (50 MPa).

UHPC possesses higher strength than conventional and high strength concretes.

Replacing conventional concrete with UHPC results in smaller structural members.

Construction of smaller members is associated with less cost in transportation, formwork, labor, maintenance, etc. High strength of UHPC helps sustainability through the construction of slim and durable designs. UHPC’s high durability, which mainly initiates from its resistance against all kinds of corrosion, increases the design life of a project and reduces the maintenance cost. For instance, UHPC has an extremely low permeability against chloride penetration, which can be counted as one of the effective factors 13 improving durability. Other properties of UHPC which results in its high durability comprise lower total porosity, lower micro-porosity, lower water absorption, and lower chloride ion diffusion. Table 1 provides a comparison between properties of UHPC and high strength concrete (HPC).

Table 1 Properties of UHPC as Opposed to High Strength Concrete (Lubbers 2003) Material Characteristic UHPC Compared with HPC Compressive Strength 2 – 3 times greater Flexural Strength 2 – 6 times greater Elastic Modulus 1.5 times greater Total Porosity 4 – 6 times lower Micro-porosity 10 – 50 times lower Permeability 50 times lower Water Absorption 7 times lower Chlorine Ion Diffusion 25 times lower Abrasive Wear 2.5 times lower Corrosion Velocity 8 times lower

In order to fully utilize UHPC in industry, design specifications need to be

developed. Since the mechanical and material properties of UHPC are very different than that of conventional and high performance concrete, special knowledge is required for

utilization of UHPC in structures. The name “concrete” can even mislead designers as

according to Tang (2004) “it is not really concrete anymore.”

On the other hand, structural members are required to have a minimum dimension

to be workable. Given the relatively higher cost of UHPC constituents, switching from 14 normal concrete to UHPC with the same minimum values of dimensions increases the cost drastically. The existing minimum values are set based on conventional concrete, which is much less expensive. Therefore development of new applications will assist further utilization of UHPC.

1.1.2. Types of UHPC

Ductal®, the most common brand of UHPC, was patented by three French companies based on more than 10 years of research on UHPC. The companies are

LAFARGE, a construction material manufacturer, BOUYGUES, an industrial and structural contractor, and RHODIA, a chemical company. Due to reduced water-to- cementitious materials ratio, the creep coefficient for Ductal® is lower than 0.8 while that for normal concrete is 3 to 4. This reduces the prestress losses and makes Ductal more suitable for prestressing applications.

Ceracem®, marketed by BSI (Béton Spécial Industriel), and BCV® (Béton

Composite Vicat) are other types of UHPC in the market. Ceracem® has a unique rheological behavior. It is a self-leveling viscous fluid and vibration is not needed to work the concrete into the forms. BSI UHPC was employed in construction of Bourg-les-

Valence Bridges. BCV® is another brand of UHPC which has been developed by the

Vinci group and Vicat, a cement manufacturer.

1.1.3. Applications of UHPC

Some of the applications of UHPC include the Sherbrooke footbridge, constructed in July 1997 in Quebec Canada. The precast, prestressed bridge is for pedestrians and bicycles and spans 190 ft (60 meters) over Magog River (Blais and Couture 1999). The 15

bridge’s slab, made of Ductal® is just 1 inches (3 cm) thick. Figure 1 shows a cross section of the Sherbrooke footbridge (www.lafargenorthamerica.com).

Figure 1 Sherbrooke Footbridge Cross Section

Another major UHPC project is the Peace footbridge in Seoul, South Korea. The

footbridge was built by France as a symbol of cooperation between the two countries.

Completed in 2002, the Peace footbridge spans 400 ft (120 meters) with a slab thickness

of 1 inches (3 cm). The bridge utilizes 240 tons (220 tonnes) of Ductal®, along with

13.2 tons (12 tonnes) of prestressing reinforcement steel and no passive reinforcement.

Figure 2 shows a cross section of the bridge (www.lafargenorthamerica.com).

Figure 2 Peace Footbridge Cross Section

Other applications of UHPC are provided below:

• UHPC bridge on Valence bypass—built by Service d’Etudes Techniques des

Routes et Autoroutes (SETRA) and the Center d’Etudes Techniques de

I’Equipment (CETE) of Lyon, France

• A footbridge in Sakata Mirai, Japan

• The toll-gate of Millau Viaduct, France

• The Mars Hill bridge in Wapello County Iowa State, USA

• The Cat Point Creek bridge in Richmond County Virginia State, USA

• A bridge in Buchanan County Iowa State, USA, and

• Highway bridge over Torisaki River in Hokkaido, Japan.

1.1.4. Material Properties of UHPC

Permeability is an important issue in concrete members. Since UHPC is fiber reinforced, the cracking mechanism in UHPC is different than that in conventional reinforced concrete. In UHPC, the addition of steel fibers alters the “cracking 17 mechanism” from “few large width cracks” to “many small width cracks” (Graybeal

2006). This difference reduces the permeability of UHPC. Also permeability is inversely proportional to the volume percentage of steel fibers. This is because more fibers cause more distribution of the cracks (Rapoport et al).

In addition to high compressive strength, abrasion resistance, and low permeability, plain UHPC members show a brittle behavior. The addition of fibers helps change the load-displacement behavior, thus improving the ductility of the member.

Cracks propagate in a direction perpendicular to longitudinal axis. An optimum alignment of the steel fibers would be along the longitudinal axis of the beam in order to bridge the cracks. Fibers tend to align in the direction of flow; hence, the mix is recommended to be poured from one end of the mold to flow towards another end.

Longer flow distance as well as the fiber length helps better alignment, which improves tensile behavior, while obstruction of flow has a negative effect on alignment of fibers and consequently affecting tensile behavior of UHPC (Pansuk et al. 2008).

UHPC contains extremely low amount of water, 4.4 percent by weight.

Conventional concrete, on the other hand, contains 10 to 15 percent water. Consequently, the amount of shrinkage and creep in UHPC is much lower than that in conventional concrete. Although creep in UHPC is smaller than creep in conventional concrete at the same values of stress, higher strength concretes are more likely to undergo higher stresses. Therefore, it is hard to judge if UHPC has less creep.

1.1.5. UHPC Constituent Materials

1.1.5.1. Portland Cement

First patented in 1824 by Joseph Aspdin, Portland cement is the most common type of cement which is widely used in construction industry. Calcium, silicon, iron, and aluminum constitute Portland cement

(www.cement.org/basics/concretebasics_history.asp). Its average grain size ranges between 3.9*10-4 to 5.9*10-4 in (10 to 15 μm).

1.1.5.2. Silica Fume

Silica fume is a byproduct in production of silicon and ferrosilicon alloys. It is also collected as a byproduct in production of other silicon alloys such as ferrochromium, ferromanganese, ferromagnesium, and calcium silicon. This byproduct used to be discharged into the environment before the mid 1970s.

Silica fume has very fine particles, approximately 100 times smaller than the average cement particle, and has a large surface area spanning between 60,000 ft2/lb and

150,000 ft2/lb. Advantages of using silica fume in a concrete mix include enhancing

compressive strength, bond strength, and abrasion resistance while reducing permeability

and thus improving resistance against the corrosion of reinforcement. Possessing very

small particle size, silica fume fills the voids remaining between cement and quartz

powder particles. Consequently the permeability is reduced drastically and resistance

against chemical penetration is increased

(www.fhwa.dot.gov/infrastructure/materialsgrp/silica.htm).

1.1.5.3. Quartz Powder

Quartz powder is also referred to as quartz flour and ground quartz. It has an average diameter of 3.9*10-4 to 5.9*10-4 in (10 – 15 μm), approximately the same granular size as cement particles. Since quartz powder is a reactive material it acts as an excellent paste-aggregate interface. For cases which heat–treatment is employed, quartz powder demonstrates even higher reactivity. Other advantages of it include extreme hardness and availability. In spite of superior properties of quartz powder some UHPC mixes, such as HDR mix, do not include it in the matrix. HDR mix was developed by

HDR Inc., an engineering and consulting company based in Nebraska. Unlike other mixes, HDR mix does not include quartz powder besides quartz sand (Lubbers 2003).

1.1.5.4. Super-plasticizer

In order to obtain higher strength, the amount of water is decreased in UHPC.

Consequently, workability is reduced. The addition of a super-plasticizer can help

compensate for the workability, but the percentage of liquid portion is still much lower as

opposed to that in conventional concrete. As shown in Table 2, super-plasticizer is about

1.2 percent of the UHPC mixture which added to water at 4.4 percent, represents less

than 6 percent of the mix.

1.1.5.5. Steel Fibers

In a UHPC matrix, mild steel reinforcement is replaced by steel fibers to achieve

the tensile strength and ductility needed. However, fiber reinforcement is not the only

means of addressing the tensile strength and ductility issue. Another measure is to

enclose the UHPC in steel plates (Tue et al. 2004). Steel fibers are the largest component 20 of UHPC, as the aggregate size is limited to 0.024 in (600 μm). Non-metallic fibers are also one of the options (Rebentrost and Wight 2008). Organic fibers replace metallic fibers in Ductal®-FO for reinforcement. Ductal®-FO, one type of Ductal®, is suitable for architectural applications such as wall panels, furniture, canopies, etc. Steel fibers used in this research are 1.0 in (25.4 mm) long and 0.008 in (200 μm) thick.

1.1.5.6. Water and Fine Sand

The lower water-to-cementitious materials ratio, the higher the concrete strength as long as there is sufficient water for the hydration process. UHPC is not an exception and its strength is inversely proportional to water-to-cementitious materials ratio provided that the mix can hydrate the cement.

Table 2 provides information about constituent materials proportion in UHPC.

Table 2 Typical UHPC Constituent Materials Proportions (Graybeal 2006) Material Amount (lb/yd3) Percent by Weight (%)

Portland Cement 1,200 28.5

Fine Sand 1,720 40.8

Silica Fume 390 9.3

Ground Quartz 355 8.4

Super-plasticizer 51.8 1.2

Accelerator 50.5 1.2

Steel Fibers 263 6.2

Water 184 4.4

As expected, sand forms the largest portion of UHPC with about 41 percent by weight. To obtain a highly homogeneous matrix as well as minimum void, UHPC contains finely graded sand. The fine sand utilized is between 0.006 in (150 μm) to 0.024 in (600 μm) large.

1.2. Flexural Redistribution

1.2.1. Background

Linear elastic analysis can be utilized for predicting the bending moment in a beam up to a point where the elastic limit of any constituent material is not exceeded.

Beyond the material’s elastic limit, the bending moment diagram deviates from that determined by linear elastic analysis. This deviation is caused by time-effects (creep effect) or subsequent cracking. The bending moment diagram approaches the diagram obtained using plastic analysis under increasing loads. For values of moment greater than yield moment, My, inelastic deformation takes place in steel and the stiffness is considerably reduced. However, hysteresis associated with residual strain can be formed

before My, if a cyclic load is applied.

In a continuous beam, if the beam reacts elastically, the load-displacement

characteristics and change of support reactions with respect to the load applied show a

linear behavior. Thus, redistribution of moment deals with loads greater than the amount

which causes first yield in the member. In other words, moment redistribution is “a term

that describes the behavior of an indeterminate member after first yielding occurs at some

cross-section of the member” (Bondy 2003). Normally first yielding is expected to occur 22

at a section with highest stress compared to other sections all over the span. The bending

moment determined by means of linear elastic analysis, thus, is different than actual

bending moment after the elastic limit of material is exceeded. The difference between

the two is referred to as redistribution of moment.

Figure 3 shows a typical continuous beam with a couple of concentrated loads on the middle of both spans along with moments plotted against load.

Figure 3 Moment Redistribution in a Continuous Beam (Rebentrost 2003)

Maximum moments are usually concentrated over short segments of the beam

causing yielding and plastic hinge formation. Plastic hinges are short segments of the

member which rotate by increasing load but can transmit a small amount of increased

moment up to failure. After a plastic hinge is formed at a particular location, increased 23 moment at the section due to increased load is very small. Therefore, increased moment due to increased load redistributes to other sections that are still in the elastic range.

Subsequently, the moment in another section reaches the ultimate moment of resistance causing the formation of another plastic hinge. The process of plastic hinge formation continues until a plastic mechanism is formed. At this stage, the member is no longer able to support additional load and fails.

The moment redistribution is presented by a percent. It means that redistribution of moment can be full, partial, or none. A full redistribution is the case that enough plastic hinges are formed and a plastic mechanism is produced. In other words, if the number of plastic hinges formed is more than the degree of static indeterminacy a full redistribution of moments is said to have taken place. When failure occurs with maximum positive and maximum negative moments equal to those in the elastic case, no redistribution has taken place.

On the other hand, if both sections reach their ultimate capacity (Mu), full redistribution is attained. Figure 3 illustrates a two span beam with a concentrated load in the middle of each span along with hogging and sagging moments plotted against load. In this case hogging moment is higher than sagging moment and the beam will first crack at the middle support section. When yielding occurs at the middle support section, moment starts to redistribute into the spans.

If the beam fails before moment at the middle support is reached the ultimate capacity, Mu, the redistribution is said to be partial as shown in Figure 3 (Bondy 2003). In 24 this case plastic hinges have not formed in the maximum positive moment sections and the only plastic hinge formed would be the maximum negative moment section.

There are three degrees of freedom in such a set up and as mentioned earlier, if the number of plastic hinges formed is less than degrees of freedom the redistribution is partial. Stages (1), (2), and (3) correspond to none, partial, and full redistribution respectively.

1.2.2. Past Definitions of Moment Redistribution

There are several definitions for moment redistribution in a continuous beam.

Some of the definitions used in the literature are presented in Table 3.

Table 3 Past Definitions of Moment Redistribution (Rebentrost 2003) Reference Definitions of Moment Redistribution

Wult = actual ultimate load

Bennett Wel = ultimate load assuming structure behaves elastically (1955) Wpl = ultimate load assuming full plastic redistribution Trichy and Wu = ultimate load Rakosnik W = plastic failure load (1977) pl

Cohn M = actual moment ∆ (1986) Mel = elastic moment due to ultimate load

Campbell Mie = inelastic moment component ∆ (1983) M2 = secondary moment due to prestress 25

Arenas = load factor, = collapse (1985) LF, = plastic LF PAR = Plastic Adaptation Ratio r = redistribution factor

PAR1 = modified plastic adoption Moucessian ratio (1988) r = 1 wel wpl wnl = loads based on linear elastic, plastic and nonlinear analysis, respectively

β = possible redistribution Scholz βmax = maximum % of MR required for wpl (1990) 1 Md = , Mel = elastic moment, M2 = secondary moment due to prestress,

and Mu = ultimate moment M = actual moment Rebentrost Mel = elastic moment (2003) βp= moment redistribution expressed as %

= Moment capacity Bondy % 100 1 M = elastic moment at the section (2003) e under consideration

Bennett (1955) defined moment redistribution as the ratio between (Wult - Wel) and (Wpl - Wel), which later on Trichy and Rakonsnik (1977) simplified it as the ratio

between Wu/Wpl. In Trichy and Rakosnik’s definition, Wu/Wpl =1 corresponds to full

redistribution of moment. In the third definition by Cohn (1986), ∆ 0 corresponds to zero moment redistribution. Cohn (1986) quantified the redistribution of 26 moment as the difference between actual moment in the section and the moment obtained by means of linear-elastic analysis. Campbell (1983), on the other hand, took into account the effect of secondary moment due to prestressing on moment redistribution.

The definition of Plastic Adaptation Ratio (PAR), proposed by Arenas (1985), was first named ‘Coeficiente de Adaptacion Plastica’ (CAP) by Sallan (1984). PAR ranges anywhere between 0, for zero redistribution of moment, and 1.0 for full moment redistribution. Arenas argued that an advantage of PAR is being independent of member’s geometry and dead load to live load ratio. γ in this relationship represents safety factors. Three years later Moucessian (1988) quantified the flexural redistribution with a slightly different approach. He introduced the index PAR1 which was proposed first by Bennett (1955). Bennett called it ‘the redistribution factor’ represented by ‘r.’

Unlike PAR, PAR1 does not take a safety factor γ into account.

Scholz (1990) suggested the maximum percent of moment redistribution required for plastic loading to be considered. Similar to what Cohn (1986) had proposed,

Rebentrost (2003) calculated the redistribution from the difference between actual moment and the maximum elastic moment in the member. Finally, Bondy (2003) quantified the moment redistributed as the difference between elastic moment and factored moment capacity divided by elastic moment.

The definition of moment redistribution adopted in the current research is similar to the one proposed by Cohn (1986) and Rebentrost (2003). First ΔM, the difference between actual moment and maximum elastic moment, is calculated. The result is divided by elastic moment and multiplied by 100 to obtain the value as a percentage. 27

1.2.3. Moment Redistribution in ACI 318 – 08

In the previous editions of ACI 318 specifications a maximum amount of 20 percent of negative moment at the support was allowed to be redistributed into the span.

The decrease in factored negative moment causes an increase in positive moment regions.

In the ACI 318 – 08 redistribution of moment is bound to 20 percent for both the positive and negative moments. ACI 318 – 08 articles dealing with flexural redistribution are as follow:

8.4.1 – Except where approximate values for moments are used, it shall be

permitted to decrease factored moments calculated by elastic theory at

sections of maximum negative or maximum positive moment in any span

of continuous flexural members for any assumed loading arrangement by

not more than 1000εt percent, with a maximum of 20 percent.

8.4.2 – Redistribution of moments shall be made only when εt is equal to

or greater than 0.0075 at the section at which moment is reduced.

8.4.3 – The reduced moment shall be used for calculating redistributed

moments at all other sections within spans. Static equilibrium shall be

maintained after redistribution of moments for each loading arrangements

(ACI 318 – 08).

1.2.4. Moment Redistribution in AASHTO LRFD Specifications

AASHTO LRFD Specifications do not probe into the flexural redistribution topic.

The only article concerning the subject is article 5.7.3.5 which bounds the redistribution of moment within the same limits as in ACI 318 – 08. 28

5.7.3.5 – In lieu of more refined analysis, where bonded reinforcement

that satisfies the provision of Article 5.11 is provided at the internal

supports of continuous reinforced concrete beams, negative moments

determined by elastic theory at strength limit states may be increased or

decreased by not more than 1000εt percent, with a maximum of 20

percent. Redistribution of negative moments shall be made only when εt is

equal to or greater than 0.0075 at the section at which moment is reduced.

Positive moments shall be adjusted to account for the changes in

negative moments to maintain equilibrium of loads and force effects

(AASHTO LRFD Specifications 2007).

1.2.5. Moment Redistribution in ENV 1992-1-1:1991Eurocode 2: Design of

Concrete Structures

ENV 1992-1-1:1991Eurocode 2: Design of concrete structures is a set of rules for concrete structural design. Eurocode 2: Design of concrete structures addresses the moment redistribution with taking into account factors such as ratio of adjacent spans and the frame being sway or non-sway. The following is the main article concerning the moment redistribution issue in concrete structures:

2.5.3.4.2 Linear analysis with or without redistribution

(3) In continuous beams where the ratio of adjacent spans is less than 2, in

beams in non-sway frames and in elements subject predominantly to

flexure, an explicit check on the rotation capacity of critical zones may be

omitted provided that the conditions a) and b) given below are satisfied. 29

a. for concrete grades not greater than C 35/45

δ ≥ 0.44 + 1.25 x/d

for concrete grades greater than C 35/45

δ ≥ 0.56 + 1.25 x/d

b. For high ductility steel, δ ≥ 0.7

For normal ductility steel, δ ≥ 0.85 where:

δ = the ratio of the redistributed moment to the moment before

redistribution

x = the neutral axis depth at the ultimate limit state after

redistribution

d = the effective depth.

(4) In general, no redistribution is permitted in sway frames.

(5) In elements as defined in (3), where no redistribution has been carried out, the ratio of x/d should not exceed

x/d = 0.45 for concrete Grades C12/15 to C35/45

x/d = 0.35 for concrete Grade C40/50 and greater at the critical

section unless special detailing provisions (e.g. confinement) are

made.

(6) Redistribution should not be carried out in circumstances where the rotation capacity cannot be defined with confidence (e.g. in the corners of prestressed frames) (Eurocode 2: Design of concrete structures). 30

The letter C represents the grade of concrete in Eurocode 2: Design of concrete structures. For instance, grade C35 has a 28-days-strength of 5.1 ksi (35

MPa), minimum cement content of 18.7 lb/ft3 (300 kg/m3), maximum aggregate

size of 0.79 in (20 mm), and maximum water to cement ratio of 0.6.

1.2.6. Moment Redistribution in Other Codes

ODOT (Ohio Department of Transportation) as well as International

Building Code (IBC 2009) do not allow moment redistribution (S5.7.3.5).

1.3. Problem Statement and Objectives

Utilization of prestressed concrete members in structures is common and is growing rapidly in bridges. UHPC, which possesses outstanding compressive strength and durability, makes an excellent choice for prestressing applications. One of the obstacles ahead of transition from conventional concrete to UHPC in prestressing is limited technical knowledge about behavior of UHPC. Research conducted in the field is very limited and new specifications need to be developed to pave the way to more applications of UHPC and to use its superior mechanical and material properties.

The objective of this thesis was to investigate redistribution of moment in UHPC lab specimens. Since UHPC is a relatively new construction material, analysis and study of its ductility are of high importance. With UHPC’s superior properties taken into account, knowledge of its behavior can lead to better designs of structures. Thus, the flexural redistribution and post-crack behavior of UHPC lab specimens are studied in this thesis.

1.4. Thesis Outline

The scope of this research covers investigation of moment redistribution in UHPC lab specimens. The first chapter of this thesis provides general information about historical background, properties, types, applications, and constituents of UHPC followed by a look into redistribution of moment. Chapter 2 comprises a review of past work done in both UHPC and flexural redistribution fields. A compendious review of the literature is presented.

Chapter 3 provides details about sample preparation, apparatus used, experiment set up, test procedure, and how the data was analyzed. Results of the investigation are presented in Chapter 4 and discussed in Chapter 5. The last chapter comprises the conclusions along with recommendations for further investigation of the topic.

CHAPTER 2

2. Background

2.1. Literature Review: Past Work on UHPC

Tang (2004) studied the effects of material properties on the shape of structures it is used for. Romans utilizing a mixture of stone, lime, sand, and water invented one of the ancient types of concrete. At the time, many remarkable structures have been built in today’s Europe and Middle East with the use of Roman concrete. Romans invented the arch, vault, and dome as well. Arches made of Roman concrete can span over 165 ft (50 meters) while girders made of stone, common before Romans; can hardly span more than

17 ft (5 meters).

Unlike old construction materials, which possessed high compression strength, the next generation of materials came with higher tensile strength. Consequently the overall figure of structures changed. For instance, cold drawn steel wires made long span suspension bridges possible. Also, steel strands possessing high tensile strength were used in prestressed beams allowing application of longer spans.

Since a concrete structural member ought to have minimum dimensions to be workable, directly replacing conventional concrete with UHPC is not economical. Thus,

Tang (2004) concludes that in order to fully utilize the superior characteristics of UHPC new application geometries need to be developed.

After over 10 years of laboratory research and experience from implemented projects, the first recommendations for UHPC were published in 2002 (Resplendino

2004). The recommendations, consisting of three parts, were in English and French 33 languages. The first part of the recommendations deal with characterization of UHPC.

Analysis and design of UHPC structure constitutes the second part, and the third part of the recommendations cover durability of UHPC.

Researchers at Luleå University studied effects of energetically modified cement

(EMC) on the hardening time and durability of UHPC. Their findings show that one day old UHPC with EMC represents 100 percent higher strength compared to that with conventional cement. Also EMC concrete demonstrated lower porosity (Elfgren et al.

2004).

Talebinejad et al. (2004) investigated the optimum proportions of constituents and the effect of curing temperature on a Reactive Powder Concrete (RPC) with ultimate compressive strength greater than 29 ksi (200 MPa). Besides other factors, the effect of the cement factor was studied as well. They found that highest compressive strength can be attained with a cement factor of 100 lb/ft3 (1700 kg/m3) to 125 lb/ft3 (2000 kg/m3); however, beyond 125 lb/ft3 (2000 kg/m3) ultimate compressive strength of the concrete

decreases. This reduction occurs because in a mix with a very high cement factor,

acceptable grading and compaction cannot be achieved. In case of cement factor lower

than 100 lb/ft3 (1700 kg/m3) fine aggregates form a major part of the mix and

compressive strength of fine aggregate is way less than that of UHPC. Other optimum

values found in this research include curing temperature of higher than 390 oF (200 oC), silica fume content of 30 – 35 percent of the cement weight, and water-to-cementitious materials ratio of 15 percent by volume. A water-to-cementitious materials ratio of lower than 10 percent by volume (about 4.4 percent by weight), super-plasticizers not included, 34 leads to insufficient workability. In such a case, the amount of water is not enough to hydrate the cement and the mix is said to be ‘starved’.

Park et al. (2008) also conducted research on UHPC matrix in Korea Institute of

Construction Technology. An optimum proportion of materials was aimed to be found.

Water, sand, silica fume, filling powder and steel fibers were the varying parameters in this research. The optimum proportion of materials found in the investigation is summarized and illustrated in Figure 4. Maximum compressive strength was reached when 70 percent of the aggregate was 0.012 to 0.020 in (0.3 to 0.5 mm) and the remaining 30 percent was 0.007 to 0.012 in (0.17 to 0.3 mm) in size.

Figure 4 Optimum Mix Proportion of UHPC

The amount of water in the two researches is significantly different. In the first study, a water ratio of less than 15 percent by volume is recommended while Park et al.

(2008) found 25 percent water to be optimum. 35

Researchers at University of Leipzig, Germany, conducted comparative investigations on UHPC with and without coarse aggregates. Coarse aggregate used in this study was a crushed basalt stone with grain size ranging from 0.08 to 0.2 in (2 to 5 mm) while the largest particle size of reactive powder concrete, the UHPC without coarse aggregates, was 0.024 in (0.6 mm). Table 4 shows proportion of both mixes used in the tests and the compressive strengths achieved.

Table 4 Proportion of UHPC with and without Coarse Aggregates (Graybeal 2006) UHPC 2 Materials UHPC 1 (RPC) (with coarse aggregates) Cement CEM 1 42.5 R (c) 1.0 1.0 Water to cement ratio (w/c) 0.268 0.302 Water to binder ratio (w/b) 0.206 0.232 Volumetric water to 0.431 0.487 powder ratio Quartz sand 1.532 0.811 Basalt split 0.0 1.830 Paste volume fraction 60 % 50 % o fc,cyl.100*200 ( ksi, 28d/68 F) 21.8 – 23.2 21.8 – 23.9 o fc,cyl.100*200 ( ksi, 90d/68 F) 23.9 – 26.1 23.9 – 25.4

The cementitious materials volume fraction in UHPC 2 is about 20 percent lower

than that in UHPC 1 for a specific compressive strength and workability. Hence, the cement content in UHPC 2 decreases to 34.3 lb/ft3 (550 kg/m3) from 43.7 lb/ft3 – 62.4

lb/ft3 (700 kg/m3 - 1000 kg/m3) in UHPC 1. Besides, utilizing coarse aggregates of size 36

0.08 to 0.2 in (2 – 5 mm) reduces mixing time and autogenous shrinkage as well (Ma et al. 2004).

Jayakumar (2004) carried out experiments to look into the effects of cement replacement with different percentages of Condensed Silica Fume (CSF) on characteristics of UHPC. For 28 days of age, he achieved compressive strength of 11.1 ksi (76.5 MPa) by replacement of 7.5 percent Ordinary Portland Cement (OPC) with CSF and compressive strength of 8.81 ksi (60.75 MPa)by replacement of 5 percent Portland

Pozzolana Cement (PPC) with CSF. Likewise, for 90 days of age, compressive strengths recorded for replacement of 7.5 percent OPC with CSF and 5 percent PPC with CSF were

12.95 ksi (89.25 MPa) and 11 ksi (75.75 MPa), respectively. The ratio of water to cementitious materials was kept at 0.32.

Graybeal (2006) completed a large number of tests at FHWA to characterize the material properties of UHPC. The technical report, published after testing over 1,000 specimens, presents results which include mainly strength and durability based characteristics of UHPC.

Steinberg and Lubbers (2003) investigated bond performance between UHPC and

1/2” diameter prestressing strands. They used three development lengths of 24 in (61 cm), 18 in (46 cm), and 12 in (30.5 cm) in their tests. In all tests, strand rupture occurred before noticeable slip out of UHPC blocks. However, small amount of displacements were detected at the dead ends of the strands. Given the shortest development length in the experiments was 12 inches (30.5 cm), it was concluded that the bond between UHPC and prestressing strands will develop in 12 inches (30.5 cm) of embedment. 37

2.2. Literature Review: Studies on Flexural Redistribution

With a special focus on the 2002 edition of ACI 318 specifications, Bondy (2003) investigated plastic redistribution of moment in statically indeterminate prestressed concrete beams. He discusses the secondary moments and its relevance to redistribution of moment as well. ACI 318-02 specifications allows 1000εt percent but not greater than

20 percent of the maximum negative moments to be redistributed to the positive moment

regions. Examples are presented as well to help understand the concept of moment

redistribution and secondary moment. With an emphasis on the secondary moment, the

author suggests ACI 318-02’s bounds for moment redistribution need to be modified for

positive moment sections. He proposes a limit of 30 percent decrease for positive

moment and increase in negative moment. However, the 2008 edition of ACI 318 allows

20 percent of moment redistribution for both positive and negative moments.

Unlike others, who deal with flexural redistribution as an Ultimate Limit State

(ULS) incident, Scott and Whittle (2005) studied redistribution of moment at Service

Limit State (SLS). After testing 33 two span beams, they found out that a noticeable

amount of moment redistribution occur at service limit state. The real stiffness existing at

the service limit state differs from what has been assumed while calculating moment for

ultimate limit state. It is because of changes in layout of reinforcement along the member.

Their findings also showed that arrangement of reinforcement (e.g. large bars versus

small bars) was not an important factor of moment redistribution.

Kodur and Campbell (1997) developed a new approach to quantify the

redistribution of moments in continuous prestressed concrete beams. The approach 38 stemmed from the relationship between percentage of redistributed moment and moment ratio which played a noticeable role in redistribution of moment. In order to develop the approach, a nonlinear finite element analysis was utilized. Expression of moment redistribution in terms of moment ratio ensured that the effects of overall structural properties of the member are taken into account not only its cross-sectional characteristics. The definition of moment redistribution in this study was more complicated compared to other definitions in the literature. Finally in addition to having different perspective to the topic, the investigation points out factors affecting the redistribution of moment.

Lopes et al. (1997) studied the moment redistribution by conducting full scale tests on 7 beams. They used precast segments, made continuous by means of cast in-place slabs. This type of structural member, in which the precast section was prestressed and after erection the segments were post tensioned, is widely used in the industry. The amount of redistribution was presented in curves in which measured and calculated values of bending moment were plotted against load. The experimental conditions were almost identical to what is widely used in the industry as the test specimens were full scale, 20.3 ft (6.2 meters) in length, and two precast segments were made continuous by means of cast in-situ slabs. Therefore, the findings were close to reality and more reliable.

Figure 5 shows the result of first beam Lopes et al. (1997) tested. Actual moment deviates from the elastic moment at about the cracking point. The other six beams showed about the same post crack behavior. 39

Figure 5 Deviation of Actual Moment from Elastic Moment (Lopes et al. 1997)

CHAPTER 3

3. Testing and Methodology

3.1. Sample Preparation

The UHPC used in the samples for the experiments of this thesis was Ductal®, manufactured by Lafarge North America Inc. The test beams were cut from larger UHPC samples used in other research. Table 5 provides information about the mix design of the

UHPC block. The premix packages included Portland cement, silica fume, quartz powder and sand.

Table 5 Mix Design for Tested UHPC Specimens (Lubbers 2003) Percent by Mix Component Weight (lbs/yd3) Weight (%)

Premix 3693.4 87.2 Water 227.3 5.4

3000NS 51.71 1.2 Superplasticizer Steel Fibers 262.6 6.2

The beams were cut by a hand-held concrete saw. The geometry of the beams was

irregular from the sawing process as well as the casting process for the original samples.

The irregularity in the beams’ geometry caused the data to be slightly affected.

In order to study the redistribution of flexure in ultra-high performance concrete, four beams were tested. Table 6 presents the dimensions of the beams. 41

Table 6 Dimensions of Tested Beams Beam No. Beam Length Span Length (in) Depth ± 0.1 Width ± 0.1 (in) (in) (in) 1 47.1 22.5 3.75 3.60 2 47.0 22.5 3.00 2.90 3 48.0 22.5 4.00 3.31 4 47.0 22.5 3.56 3.50

One of the simple ways to study the redistribution of moment in a member is to set up a continuous system with two equal spans. This way the beam will undergo a

maximum negative moment at the middle support and two maximum positive moments at

the point of the two concentrated loads applied within the spans. Thus, the beams in this

test were supported at three points: two at both ends and one at the middle of the beams

along with two point loads at a distance of 11.5 inches from the middle support into the

span. This will create a negative moment approximately 20 to 30 percent larger than the

positive moment produced in the spans under the load. Considering the redistribution of

moment in conventional concrete is within the range of 20 to 30 percent, the distance of

concentrated loads from the middle support were calculated such that the negative

moment became larger than the positive moments by 20 to 30 percent.

The point of keeping maximum positive moment within a specific range of

maximum negative moment was to possibly obtain full redistribution. It was presumed

that the redistribution of moment in UHPC would be somewhere within the range of that

in conventional concrete. Therefore, a minimal difference would be expected between the

maximum positive and maximum negative moments in the beam under the failure load. 42

The negative moment will start to redistribute when it reaches a cracking moment capacity and when the extra 20 to 30 percent moment redistributes, the maximum positive moment will be not very different from the moment at which the middle support cracked. Thus, plastic hinges will form in the spans as well as the middle support section.

Since this set up has three degrees of freedom, three plastic hinges need to be formed in order to obtain a full redistribution of moment.

Samples were cut from a relatively large block of UHPC. A hand-held grinding machine was used to grind rough spots on the beams and make it even where the strain gages were going to be installed. The dust was brushed off the samples with a wire brush, rinsed with water and dried with a heat gun to improve the strain gage bond.

The following procedure was followed to install the strain gages:

− A small amount of epoxy was applied over the spot and left for 24 hours. Then

the dried epoxy was sanded off with sand paper. This filled the small pores on the

surface for better adhesion.

− The surface was cleaned with a CSM degreaser.

− The surface was dry-abraded with a 100 grit paper first and then with a 300 grit

sand paper.

− Neutralizer was applied.

− The gage was put on a piece of tape and placed carefully on the previously

marked spot aligning the triangle marks on the gage with the marks on the beam. 43

− The tape was peeled back with the gage on it, and a small amount of adhesive was

applied on the gage. The tape was reapplied and aligned with the marks. A firm

pressure was applied on the gage for optimum bond.

− After a while the tape was slowly removed.

− Proper wires were selected and soldered to the strain gages.

Six strain gages per beam were used to record the strains during testing. The strain gages were product of Vishay, a manufacturer of discrete semiconductors and passive components. The strain gages used in the first and second beams were type N2A

– 06 – 10CBE – 350 and the ones used in the third and fourth beams were type N2A – 06

– 20CBW – 350 which basically are the same. Both types of strain gages had a strain range of ±3% and a temperature range of –100° to +200°F. The only difference between the two types of strain gages was in their size. The latter’s overall grid length was two inches while the first one has a grid of one inch long. Both types were constantan foil gages with a thin, laminated, polyimide-film backing. Table 7 shows the properties of the strain gages.

Table 7 Strain Gages (Vishay Micro-Measurements) Pattern Gage Gage Gage Overall Grid Matrix Matrix

series resistance length pattern length width length width

10CBE N2A 350 Ω 1.0 in 1.250 in 0.250 in 1.36 in 0.33 in

20CBW N2A 350 Ω 2.0 in 2.250 in 0.188 in 2.46 in 0.32 in

Strain gages were installed about one-half an inch along the side of the beam from

the extreme compression fiber to avoid concentrated loads and support reaction effects on

the gage grids (see Figure 6). This way when the cracks initiated in the tension fiber, the

strain gages were not damaged. Also, strain gages were installed on both sides of the

beam in case out-of-plane bending occurred.

Figure 6 is the AutoCAD drawing of the beam with the top, front and side views

of the beam. Dimensions, location of the point loads, reactions, and strain gages are

shown as well.

Figure 6 Point Loads and Strain Gages Locations

Yielding of fibers on the tension edge will be associated with neutral axis shift

and finally there will be a situation that one half of the strain gage grid is in tension and the other half in compression. Tensile strain across the gage would lead to cracking and failure of the gage. At this point the strain recorded would be zero. However, at this time 45 the beam has likely failed because the strain gage is very far from the extreme tension fiber. When the crack propagates this high, the fibers will likely have been pulled out or fractured at the outermost tension fibers. Regardless, a fair amount of strains can be recorded after beam cracks as well as before cracking initiates in the member.

3.2. Apparatus Used

The primary equipment used for the testing is summarized below:

• Material Test System (MTS 810) Loading machine ( Model No.: 661.22C-01,

Serial No.: 263, Capacity: 250,000 N 55,000 lbf)

• MEGADAC Data acquisition system (Model: 5414AC, Serial: SO6253, Version:

7.0.4, ADC Type: ADC5616, Total RAM: 268435456, and Acquisition RAM:

268435456)

• N2A – 06 – 20CBW – 350 and N2A – 06 – 10CBE – 350 Vishay micro-

measurements strain gages

• Hand-held grinding machine

3.3. Test Setup

In order to investigate the redistribution of flexure in beams they need to be statically indeterminate, thus the test beams were supported near the two ends and in the middle. Two concentrated loads were applied at a distance of 11.0 inches from the middle support and 11.5 inches from both end supports. The distances were chosen so that the negative moment at the middle support falls in the range of 20 to 30 percent larger than 46 the maximum positive moment produced within the two spans. In other words, hogging moment exceeds sagging moment by 20 to 30 percent of sagging moment.

A small frame was built for suitably exerting point loads on the beam. The frame was built such that it could be fastened to the top portion of the MTS load cell. The bottom portion of the MTS test frame contained a hydraulic cylinder which moved upward and exerted the load at two points within the spans of the test sample. The only reason that the test was set up upside down, reactions at the top and point loads at the bottom, was that the frame was built in such a way that it could be fastened to the top portion of the load cell. The bottom portion of the MTS loading machine also moved upward while applying load and the top portion was in a static position.

After strain gages were checked for bond, the beams were set in the loading machine as shown in Figure 7. The beams were set in a way that the three concentrated reactions were applied from the top, one on each end and one in the middle. Two concentrated loads were exerted from the bottom of the beam at a distance of 11.5 in from the end supports. To make sure the loads were concentrated short steel rods were put under the frame as illustrated in Figure 7. 47

Short Steel Rods

Figure 7 Test Set Up

3.4. Test Procedure

Load was increased manually and the MEGADAC data acquisition system was set to record data at a rate of 1,000 scans/second. Depending on the size and strength of each beam, the test duration and total number of scans were different for each test.

Two strains gages were installed along the beam at points of maximum positive and negative moments, one on each side of the beam. For instance strain gages 5 (SG5) was mounted on one side of the beam at middle support (maximum negative moment) and strain gage 6 (SG6) was mounted on the other side of the beam at middle support.

Strains measured on both sides at each location were not always the same. This could 48 have been caused by slight out-of-plane bending and slightly different vertical positioning. As it can be seen from Figure 8, the beams had some irregularities in their geometry.

Figure 8 Irregularities in the Geometry of the Beams

3.5. Data Analysis

Like all other types of concrete, UHPC shows little tensile strength compared to compressive strength. Equation 1 provides the relationship between tensile and compressive strengths of UHPC.

Equation 1 (Graybeal 2006) 49

and are tensile and compressive strengths, respectively. x in Equation 1 equals to

0.046 for steam treated, 0.049 for untreated, and 0.052 for tempered steam treated. Figure

9 shows atypical stress-strain curve for UHPC.

Stress

COMPRESSION SIDE

strain

TENSION SIDE

Figure 9 Stress-Strain Curve for UHPC (Steinberg 2009)

In case of flexure, stress distribution profile is similar to stress-strain curve. Up to a specific distance from the neutral axis, stress increases with strain. After a maximum stress value is reached, the stress starts decreasing. The reason for this is that fibers with larger distance from the neutral axis undergo larger tensions. Near to the outermost tension side, fibers are either fractured or pulled out and stress value reduces to zero. 50

By looking at the beams after the test, it could be verified that the beams were without damage on the compression side. Thus, arguments can be made that the compressive strains were within the linear elastic range.

The total load was plotted against strain for each separate strain gage. Then the load was plotted against the average strain from the gages on both sides of the beam.

From the load vs. strain curves, the maximum elastic load, the load at which the specimen at the middle support cracked, the load at which the specimen cracked within the spans, and the ultimate load were determined. The values of load at the mentioned conditions were determined based on major change of slope in the load-strain curves. The load vs. strain curves are presented in Appendix A.

The support reactions, the maximum positive and negative elastic moments, and

% moment redistributed can be calculated by Equations 2 through 6. Equations 7 through

9 can be used to calculate the moment from strain. Finally, Equations 10 and 11 are utilized to compute the moments beyond the elastic limit.

Equation 2

Equation 3

Equation 4

Equation 5

– % Equation 6

Equation 7 51

Equation 8

Equation 9

Equation 10

Equation 11

Where

R1 = R3 = exterior support reaction in Equation 2

R1 = M/a in Equation 10 (The middle support yielded and Equation 2 cannot be used

because Equation 2 is valid within the elastic range of the material)

R2 = interior support reaction

a = distance between exterior support and concentrated load (11 in)

b = distance between concentrated load and middle support (11.5 in)

L = span length (22.5 in)

E = Young’s Modulus = 7,500,000 psi (Reeves 2004)

P = concentrated load 52

CHAPTER 4

4. Results

4.1. Beam 1

Figures 10 and 11 show the total load plotted against strain at the middle support

for Beam 1. The curve was linear up to a total load of 5,000 lb. At this load, the curve

deviated from linearity designating the onset of cracking. The fibers likely started to yield or slip and the strain value began to decrease when the total load reached 6,500 lb. As it

can be seen from Figures 10 and 11, the strain values on both sides of the beam showed

similar behavior.

Figure 10 Total Load vs. Strain at the Middle Support 53

The strain was approximately 300 με at one side of the beam and 200 με at the

opposite side of the beam when cracking occurred at the middle support section under a

total load of 5,000 lb.

Figure 11 Total Load vs. Strain at the Middle Support

As the neutral axis shifted towards the strain gage, the strain value started

decreasing. At a total load of about 10,000 lb the strain reduced to zero implying that the

neutral axis had reached the strain gage location. The strain gage was installed close to

extreme compression fiber. After the neutral axis moved above the strain gage, tensile strain was recorded. At this height of crack, most of the steel fibers in the extreme tension zone were already fractured or pulled out. 54

Since the strain values at proportional limit, cracking point, elastic limit, and yielding point was needed and plotting all the data points did not show these points clearly, the plots in Figures 10 and 11 were zoomed in and strains larger than 500 με were not shown. The ultimate load actually increased up to 18,000 lb.

The fibers started yielding/slipping at the middle support section at a load of

6,500 lb. The rate of increasing load and associated moment decreased significantly at the interior support section long before the total load of 18,000 lb was reached.

Figures 12 and 13 show the strains on both sides of the beam in one of the spans.

13,600

Figure 12 Total Load vs. Strain in the Span

Strain Gage 1 (SG1) recorded a very small amount of strain up to a load of 7,000 lb while strain on the opposite side of the beam, recorded by Strain Gage 2 (SG2), was increasing at a rate of 1 με/20 lb. This was likely caused by the out-of-plane bending due to the geometric irregularity of the beam. A load of 13,600 was reached before the spans cracked.

The ultimate total load in Beam 1 was 18,000 lb. This value for the other three tested specimens was lower. After cracking occurred in the span at a load of 13,600 lb, one side of the beam experienced a strain change (Δε) of about 400 με (from -200 με to -

600 με) while that on the opposite side of the beam was approximately 300 με ( from 200

με to -100 με) for loading up to the ultimate.

13,600

Figure 13 Total Load vs. Strain in the Span 56

Likewise, strain values on both sides of the Beam 1 in the other span were recorded by strain gages 3 and 4. Figures 14 and 15 show the total load plotted against the strain in this span. Similar to the other span of the beam, Strain Gage 3 recorded very small amount of strain up to a total load of about 7,000 lb. On the other hand, strain on the other side of the beam was increasing with a rate of 1 με/75 lb. The fact that strain values were different at each side of the beam, while the strain gages were located at the same height on both sides, can be justified by out-of-plane bending caused by geometric irregularities of the specimen.

13,600

Figure 14 Total Load vs. Strain in the Span 57

After cracking occurred in the span, a strain change (Δε) of -300 με (from -200 με to -500 με on one side and from −20 με to −320 με on the other side) was recorded up to the ultimate load. An average of the strain values from both sides of the beam was used for analysis and load-deflection curves presented in Appendix B.

13,600

Figure 15 Total Load vs. Strain in the Span

Moments in Beam 1 were calculated at different stages which are presented in

Table 8. The beam cracked at the middle support section at a total load of 6,500 lbs and cracking within the spans did not occur until a total load of 13,600 kip was reached.

Before yielding/slip of the fibers occurred at the middle support, Equations 2 and 3 of 58

Chapter 3 were used to calculate the interior and exterior reactions and Equations 4 and 5 were used to calculate the maximum positive and negative elastic moments. Yielding occurred at the interior support section at a bending moment of -1.134 kip-ft. Thus, the rate of increasing load and associated bending moment decreased at this section compared to that in elastic stage.

Then, specimen was dealt with as two side by side beams with a moment of -

1.134 kip-ft acting at one end. Figure 16 provides the drawing of the two side by side beams equivalent to the specimen associated with a yielded middle support section.

Figure 16 Two Side by Side Beams Equivalent to the Specimen with a

Yielded Middle Support

Given the concentrated load and yielding moment at one end were known, the exterior reaction was found by equating the moments about the interior support to zero.

Once the exterior reaction was found, Equation 11 was employed to calculate the positive moment in the span to be 0.969 kip-ft.

The exterior reaction found by the way illustrated in Figure 16 is different than the reaction R1 calculated by Equation 2. Equation 2 is valid within the elastic range of 59 the member. Beyond the elastic limit, the specimen’s behavior is no longer elastic and the exterior reaction R-ext.supp cannot be found by means of Equation 2. Figure 17 presents the

drawing of two side by side beams equivalent to the specimen when cracking happened in the spans.

Figure 17 Two Side by Side Beams Equivalent to the Specimen when Cracking Occurred in the Spans

Next stage was when yielding occurred in the spans. Cracking was assumed to

take place in the spans at the same amount of bending moment under which cracking

occurred at the middle support section. Hence, a positive bending moment of +1.134 kip-

ft was assumed in the span and exterior reaction R-ext.supp was found by Equation 10.

Equilibrium equations were applied to determine negative moment at the middle support

section.

Finally, bending moment corresponding to the ultimate load was calculated.

Considering the moment at the middle support section increased from -1.134 kip-ft to -

4.197 kip-ft, the same amount of increase in bending moment was assumed to take place

in the spans before failure. Similar to Figure 17, having the positive moment in the span, 60 the exterior reaction was calculated by equilibrium equations and negative moment at the middle support section was found to be close to zero defining failure. Although this value for other beams was larger, implying that the specimen’s flexural strength at the middle support and span section were not completely equivalent.

Table 8 Moments in Beam 1 at Various Stages Stage Middle Support Span 1 Span 2

Maximum Elastic Load (lb) 5,000 5,000 5,000

Load at Yield (lb) 6,500 13,600 13,600

Ultimate Load (lb) 18,000 18,000 18,000

Max. Elastic Moment (kip-ft) -0.872 0.745 0.745

Moment when Middle -1.134 0.970 0.970 Support Yields (kip-ft)

Moment when Spans Yield -4.197 1.134 1.134 (kip-ft)

Ultimate Moment (kip-ft) -0.040 4.197 4.197

Moments in the spans when cracking occurred at the middle support section was found

from strain too. Equations 7 through 9 were used for this purpose. In Tables 8 through 12

the moment values found from strain are used.

4.2. Beam 2

The maximum load that Beam 2 could resist was 6,360 lb. At a load of 4,900 lb, a crack initiated at the middle support and after the moment was redistributed from the middle support to the spans, the specimen cracked within the spans when load reached

5,830 lb. Unlike other specimens, strain in this beam was linear

The moments in Beam 2 under different loads are calculated following the same method as Beam 1 and the results are presented in Table 9.

Table 9 Moments in Beam 2 at Various Stages Stage Middle Support Span 1 Span 2

Maximum Elastic Load (lb) 4,900 4,900 4,900

Load at Yield (lb) 4,900 5,830 5,830

Ultimate Load (lb) 6,360 6,360 6,360

Max. Elastic Moment (kip-ft) -0.854 0.730 0.730

Moment when Middle -0.854 0.761 0.761 Support Yields (kip-ft)

Moment when Spans Yield -1.045 0.854 0.854 (kip-ft)

Ultimate Moment (kip-ft) -0.911 1.045 1.045

The ultimate moment at the middle support does not decrease as much as in Beam

1. The beam was supposed to crack at the maximum positive moment section, but a weak

section at a distance of about 5 in from the maximum positive moment section towards 62 the end of the beam resulted in a premature failure without the middle support section reaching its maximum capacity. Possible factors affecting abnormal failure in Beam 2 are discussed in Chapter 5.

4.3. Beam 3

Table 10 shows the loads and moments in Beam 3.

Table 10 Moment in Beam 3 at Various Stages Stage Middle Support Span 1 Span 2

Maximum Elastic Load (lb) 5,750 5,750 5,750

Load at Yield (lb) 8,300 15,200 15,200

Ultimate Load (lb) 17,500 17,500 17,500

Max. Elastic Moment (kip-ft) -1.003 0.857 0.857

Moment when Middle -1.447 1.269 1.269 Support Yields (kip-ft)

Moment when Spans Yield -4.324 1.447 1.447 (kip-ft)

Ultimate Moment (kip-ft) -0.458 4.324 4.324

Beam 3 was the deepest beam among the four test samples. As expected, the load

and moment in this beam were higher than those in the other beams. Up to 5,750 lb, the

beam’s behavior was elastic. The middle support cracked at a load of 8,300 lb which is

quite higher than 6,500 lb in Beam 1. 63

4.4. Beam 4

Beam 4 was dimensionally the smallest beam in this research. This beam showed linear behavior up to a load of 2,500 lb. When the load reached 4,200 lb, a big change in the trend of the strain was recorded. This indicated the crack initiation in the specimen at the middle support. Considering the relatively smaller size of Beam 4 compared to Beams

1 and 3, the ultimate total load reached in this specimen was 9,700 lb. The load and respective moment results for Beam 4 are presented in Table 11.

Table 11 Moment in Beam 4 at Various Stages Stage Middle Support Span 1 Span 2

Maximum Elastic Load (lb) 2,500 2,500 2,500

Load at Yield(lb) 4,200 8,000 8,000

Ultimate Load (lb) 9,700 9,700 9,700

Max. Elastic Moment (kip-ft) -0.436 0.373 0.373

Moment when Middle -0.732 0.765 0.765 Support Yield (kip-ft)

Moment when Spans Yield -2.336 0.732 0.732 (kip-ft)

Ultimate Moment (kip-ft) -0.130 2.336 2.336

4.5. Moment Redistribution

Table 12 provides the results for moments before and after redistribution in all

four specimens and the percent moment redistribution results. The first column of Table 64

12 provides the maximum positive moments in the spans when cracking occurred at the middle support. At this stage, the moment started to redistribute into the spans. This moment is referred to as moment before redistribution in Equation 6. The second column shows the maximum positive moments at which spans cracked. In other words, this is the moment after redistribution. From Equation 6, the percent moment redistributions are found as the ratio of the difference between moment after redistribution and moment before redistribution over moment before redistribution.

Table 12 Cracking Moments and % Moment Redistributed

+Moment when Cracking +Moment when

Occurs at Middle cracking Occurs within Redistribution Beam Support—Moment Before Spans—Moment After (%)

Redistribution (kip-ft) Redistribution (kip-ft)

Beam 1 0.970 1.134 16.91

Beam 2 0.761 0.854 12.22

Beam 3 1.269 1.447 14.03

Beam 4 0.633 0.732 15.64

Average = 14.70

The flexural redistribution was 12.22 percent for Beam 2. This value was 16.91 percent for Beam 1. The average redistributed moment was found to be 14.70%. Table 12 shows that in spite of smaller dimensions and a weak section, the moments before and 65 after redistribution in Beam 2 were higher than that in Beam 4 implying that Beam 4 was also weak.

4.6. Ultimate Loads and Associated Moments

Since ultimate load and moment are of importance in designing structures, the behavior of members in the ultimate stage need to be studied. As it is illustrated in

Figure 3 of Chapter 1, the amount of ultimate moment (Mu) is noticeably higher than cracking moment (Mcr). Table 13 provides moment when cracking occurred in the spans and ultimate moments along with the amount of redistributions.

Table 13 Redistribution of Moment at the Ultimate Stage Positive Moment when Ultimate Positive Redistribution Beam cracking Occurs Moment within the (%) within Spans (kip-ft) Spans (kip-ft)

Beam 1 1.134 4.197 270

Beam 2 0.854 1.045 22.4

Beam 3 1.447 4.324 200

Beam 4 0.732 2.336 220

In the current test, ultimate moment was recorded to be significantly higher than

cracking moment. Except for the Beam 2, this value was 200 percent or higher for the

tested specimens. 66

Table 14 shows the loads at ultimate stage as well as when cracking occurred in the spans. As it can be seen from the table, as high as 32.4 percent of load were distributed after cracking occurred in the span of Beam 1. This value was 15.1 percent and 21.2 percent for Beams 3 and 4 respectively. Beam 2 showed the lowest amount of load redistribution at the ultimate stage as a result of premature failure.

Table 14 Load Redistribution at the Ultimate Stage

Load when cracking Occurs Ultimate Load Redistribution Beam within the Spans (lb) (lb) (%)

Beam 1 13,600 18,000 32.4

Beam 2 5,830 6,360 9.0

Beam 3 15,200 17,500 15.1

Beam 4 8,000 9,700 21.2

From Tables 13 and 14 as well as moment-load curves provided in Appendix C, it can be perceived that the amount of increase in total load after cracking occurred in Beam

2 was less in comparison to that in other beams. As a result of a weak section, Beam 2 showed a poor post crack behavior.

CHAPTER 5

5. Discussion

5.1. Stress and Strain Profiles

Realizing the fact that by increasing the load, bending in the member causes the outermost fibers to be the first to fail either by pull out or fracture and some unavoidable irregularities of the beam geometry, the beam cross-section was assumed to remain plane before and after loads applied. Table 15 illustrates the three stages along with assumed strain and stress distribution profiles over the beam’s cross section.

Table 15 Strain and Stress Distribution Profiles over the Section of the Beam Strain distribution Stress distribution Stage over the section over the section

N.A. N.A. Elastic Range

N.A. N.A. Cracking

N.A. Fibers Fracture N.A. or Pull Out

The possible torsion effects are neglected in the analysis. Likewise, the assumption was made that all planes remain perpendicular to the longitudinal axis of the beam. Thus, the normal strain of any fiber is linearly proportional to its distance from the neutral axis.

As long as the load is within the elastic range, the strain distribution is linear with fiber’s distance from the neutral axis. Similarly, stress profile increases linearly over the depth of the beam (Table 15—Elastic Range). Maximum stress in this stage ranges between 1.0 ksi (steam treated) and 1.4 ksi (tempered-steam treated). Untreated UHPC showed a tensile cracking strength of 1.1 ksi which was higher than that of steam treated

UHPC. (Graybeal 2006).

Beyond the tensile cracking load, bending moment and stress keep increasing until outermost fibers start to fail either by pull out or fiber fracture. At this stage, stress increases to a value of about 1.6 ksi. However, UHPC can have a tensile strength of up to

2 ksi (Graybeal and Hartmann 2003).

The last stage of Table 15 shows the strain and stress profiles after fibers start to fail. The closer to the tension side the more fibers are either fractured or pulled out.

Therefore, the stress decreases towards the tension side of the flexure member.

5.2. Premature Failure in Beam 2

Figure 18 shows Beam 2 at the end of testing. The load-strain curves along with the abnormal failure of Beam 2 are discussed in this section.

Failure Crack Max. +M Section

Figure 18 Failure Crack in Beam 2

Strain Gages 5 and 6 were installed at the middle support section in all four specimens. Strain Gages 1 and 2 were installed in one of the spans and Strain Gages 3 and 4 in the other. Figures 19 and 20 show the load-strain curves of Beam 2 at the interior support section. 70

Figure 19 Load vs. Strain Curve for Beam 2 Strain Gage 5

Starting from a relatively small value, Strain Gages 5 and 6 started recording a linear change of strain with increasing load. All load-strain curves showed that compressive strain increased up to a point and started decreasing. Except for Strain Gages

3 and 6 strain in all of the other curves reduced to zero and continued to tensile strain.

Considering the increasing trend of loading, the only factor that can reduce strain is a decrease in cross-section due to cracking, fiber fracture or pull out, followed by neutral axis shift and redistribution of load. Since the strain gages were installed in the compression zone, the neutral axis shifted towards strain gage after specimen cracked and reinforcement at outermost fiber yielded, pulled-out, or fractured. This caused the 71 distance from the neutral axis to the strain gage to decrease and strain gage recorded smaller strain. Further propagation of the crack shifted the neutral axis further. Strains increased to a maximum negative value and decreased as more fibers failed. Some strain gages recorded positive strain values while being installed in the initial compression zone. When the neural axis passed the strain gage location, the strain gage was no longer in a compression zone and the strain recorded was positive.

Crack in middle support section

Figure 20 Load vs. Strain Curve for Beam 2 Strain Gage 6

Figures 21 and 22 show the total load plotted against strain in the span of Beam 2.

The point at which cracking occurred in the span is marked in Figure 21 and

Figure 22. At this point strain started decreasing. The total load at this stage was

5,830 lb which is very close to the ultimate load 6,360 lb. The amount of increase in the total load along with decrease in compressive strain, shown with a dashed line in Figures

21 and 22, after cracking took place in the span was much smaller than that in other specimens. This was because the specimen failed before it was expected to fail.

Crack in the span

Figure 21 Load vs. Strain Curve for Beam 2 Strain Gage 1

Crack in the span (Strain decreasing)

Figure 22 Load vs. Strain Curve for Beam 2 Strain Gage 2

Figures 23 and 24 show the total load plotted against strain in the other span of

the Beam 2. The overall trend that strain recorded by Strain Gage 3 followed was different than that of other strain gages in the test but the change in strain at the load of

4,900 lb matches with that in Strain Gage 4 which was installed at the same section on the opposite side of the specimen. The Strain Gage 3 kept recording compressive strain and the strain did not decrease at any stage of loading. It could have happened because the cracking occurred at the opposite side of section. By inspection of the specimen after the test, the crack width was noticed to be wider at the other side of the beam. The load- strain curve for Strain Gage 4 is shown in Figure 24. 74

Figure 23 Load vs. Strain Curve for Beam 2 Strain Gage 3

Strain Gage 3 recorded a rapid change in strain. Δε on this side of the beam was approximately 1400 με which is more than 14 times larger than Δε in the other side of the specimen.

The cracking occurred at the interior support section at a load of 4,900 lb. The difference between the load at which negative moment section cracked (4,900 lb) and the load at which positive moment section cracked (5,830 lb) was small compared to that in other specimens. The difference was about 20 percent more than the first cracking load while in other specimens this difference was greater than 80 percent. 75

Figure 24 Load vs. Strain Curve for Beam 2 Strain Gage 4

Beam 2 cracked at a section five inches from the concentrated load (maximum positive moment location) towards the exterior end. Figures 18 and 25 show the location of crack in Beam 2. Although the failure section was within a distance from the section at which the Strain Gages 3 and 4 were installed, the neutral axis will shift no matter if the section with strain gage is still in its elastic range.

Figure 25 Beam 2 After Testing

The specimen was expected to crack at maximum moment sections. The following factors may have caused Beam 2 to crack at a section with a significantly smaller moment than the maximum positive moment in the span:

− The beam’s cross section was slightly reduced at the section in which the beam

failed.

− Beam 2 is the specimen on the right side of the picture in Figure 26. As it can be

seen, a large portion of Beam 2’s cross section in the upper right of the section

shows a lighter colorization. This may be due to poor hydration or curing of the

sample, leading to a plane of weakness.

Beam 3 Beam 2

Lighter Colorization

Figure 26 Cross-section of Beam 2 Compared to Beam 3

− The failure section might have had higher material impurities compared to those

in the rest of the beam.

− Beam 2, the one at the right on Figure 26 and Figure 27, had more void spaces

than the other beams. Being more porous at the failure section made the section

weaker and could have caused a premature crack.

− Less steel fibers may have been aligned in the direction of beam’s longitudinal

axis at the section during the pouring of UHPC. However, this was not visible by

close inspection.

Beam 3 Beam 2

Figure 27 Beam 2's Cross-Section Compared to Beam 3

− Since the specimens were cut from larger UHPC samples used in other research,

different points of the initial sample might have different proportions of

constituting materials, different amount of reinforcing steel fibers, and different

water-to-cementitious materials ratio. However, this could not be verified with

visual inspection.

− Very small cracks, not detectable by visual inspection, might have been in the

sample before testing. 79

− Close visual inspection of the sections showed that the density of fibers at the

failure section, especially in the tension zones, of Beam 2 was less compared to

that in the other beams.

CHAPTER 6

6. Conclusions and Recommendations

6.1. Conclusions

Ultra-High Performance Concrete (UHPC) is a new generation of cement-based construction materials which possesses tremendously high strength. Researchers working on UHPC agree on the need for developing new specifications in order to further utilize its high strength. Some researchers even think “it is not really concrete anymore” (Tang

2004).

UHPC demonstrates superior mechanical and material properties which make it a perfect option for prestressing applications. For further utilization of UHPC, in structures in general and in prestressed members in particular, special knowledge of its behavior needs to be attained. One of the crucial issues regarding a structural member is ductility.

In order to address the ductility issue, as well as enhancing tensile strength, mild steel rebar are replaced with steel fibers in UHPC. The fibers are part of the material matrix and included with other constituents when mixing.

As it would be expected, post-crack behavior of UHPC is different from that of conventional concrete. Specifically, flexural redistribution differs in UHPC considering the steel fiber reinforcement is distributed all over the section. When a member undergoes flexure, cracking initiates at the outermost tension fibers and propagates towards neutral axis. At some point, some steel fibers have already failed either by pull- out or fracture, some are in their plastic range, and the steel fibers that are close to the neutral axis are still in their elastic range. 81

Four beams with approximate dimensions of 45 in x 4 in x 4 in were tested in this research. Beams were cut from a large block of UHPC—approximately 50 in x 50 in x 50 in. A Material Testing System (MTS 810) loading machine, a MEGADAC data acquisition system, and Vishay Micro-Measurements strain gages were used in the tests.

Six strain gages were installed on each beam to record the strains.

The load was plotted against strain for each beam. Moments were determined under different loading stages. Knowing the elastic and plastic moments, the percent of moment redistributed was calculated.

The amount of bending moment redistributed was found to be about 14 percent.

This value is less than 20 percent in conventional concrete with mild steel reinforcement

(ACI 318 – 08, articles 8.4.1 – 8.4.3).

Within the limitations of this research, it can be concluded that if new specifications are developed for UHPC or current specifications are modified to address the flexural redistribution in UHPC, no more than 14 percent redistribution should be allowed.

6.2. Recommendations

UHPC does not show ideal post crack properties. The post cracking behavior of

UHPC is one of main concerns. More investigation of plastic behavior of the product will help its further utilization in industry.

UHPC is mainly employed in bridge constructions and consequently exposed to large temperature changes. The temperature change in the current tests was negligible. 82

Since temperature change is one of the factors which has a large effect on a structure’s durability and service, UHPC’s reaction to temperature change should be studied.

As mentioned in Chapter 1, the addition of more steel fibers change the cracking mechanism of UHPC from a few large cracks to many tiny cracks (Graybeal 2006). In the current research the beams underwent few large cracks. A parametric study of the optimum steel fiber proportion is recommended.

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APPENDIX A: LOAD VS. STRAIN CURVES

Figure A. 1 Load vs. Strain: Beam 3 Strain Gage 1 87

Figure A. 2 Load vs. Strain: Beam 3 Strain Gage 2

Figure A. 3 Load vs. Strain: Beam 3 Strain Gage 3 89

Figure A. 4 Load vs. Strain: Beam 3 Strain Gage 4

Figure A. 5 Load vs. Strain: Beam 3 Strain Gage 5

Figure A. 6 Load vs. Strain: Beam 3 Strain Gage 6

Figure A. 7 Load vs. Strain: Beam 4 Strain Gage 1

Figure A. 8 Load vs. Strain: Beam 4 Strain Gage 2

Figure A. 9 Load vs. Strain: Beam 4 Strain Gage 3

Figure A. 10 Load vs. Strain: Beam 4 Strain Gage 4

Figure A. 11 Load vs. Strain: Beam 4 Strain Gage 5

Figure A. 12 Load vs. Strain: Beam 4 Strain Gage 6

APPENDIX B: LOAD VS. DEFLECTION CURVES

Figure B. 1 Load vs. Deflection: Beam 1 99

Figure B. 2 Load vs. Deflection: Beam 2

100

Figure B. 3 Load vs. Deflection: Beam 3 101

Figure B. 4 Load vs. Deflection: Beam 4

102

APPENDIX C: MOMENT VS. LOAD CURVES

Beam 1 4.5

3.5

3 ft) ‐ 2.5 Span (kip

Moment 1.5 Interior Support

0.5

0 0 5000 10000 15000 Load (lb)

Figure C. 1 Moment vs. Load: Beam 1

103

Beam 2 1.2

0.8 ft) ‐ (kip 0.6 Span

Moment Interior 0.4 Support

0.2

0 0 2000 4000 6000 8000 Load (lb)

Figure C. 2 Moment vs. Load: Beam 2

104

Beam 3 5

4.5

3.5 ft) ‐ 3 Span (kip 2.5 Interior 2 Support Moment 1.5

0.5

0 0 5000 10000 15000 20000 Load (lb)

Figure C. 3 Moment vs. Load: Beam 3

105

Beam 4

2.5

Span ft) ‐ 1.5 (kip

Interior

1 Support Moment

0.5

0 0 2000 4000 6000 8000 10000 12000

Load (lb)

Figure C. 4 Moment vs. Load: Beam 4