thesis master doc - university of...

An Experimental Investigation of Bond in Reinforced Concrete

Joshua S. Martin

A thesis

submitted in partial fulfillment of the

requirements for the degree of

Master of Science in Civil Engineering

University of Washington

2006

Program Authorized to Offer Degree:

Civil and Environmental Engineering

University of Washington

Graduate School

This is to certify that I have examined this copy of a master’s thesis by

Joshua S. Martin

and have found that it is complete and satisfactory in all respects,

and that any and all revisions required by the final

examining committee have been made.

Committee Members:

_________________________________________________

John F. Stanton

_________________________________________________

Laura N. Lowes

_________________________________________________

Dorothy A. Reed

Date __________________________

In presenting this thesis in partial fulfillment of the requirements for a master’s degree at

the University of Washington, I agree that the Library shall make its copies freely

available for inspection. I further agree that extensive copying of this thesis is allowable

only for scholarly purposes, consistent with “fair use” as prescribed in the U.S. Copyright

Law. Any other reproduction for any purposes or by any means shall not be allowed

without my written permission.

Signature ______________________________

Date __________________________________

i

TABLE OF CONTENTS

Page

List of Figures .................................................................................................................... iv

List of Tables ..................................................................................................................... ix

List of Variables................................................................................................................. xi

Chapter 1 - Introduction ....................................................................................................1

1.1 Background ........................................................................................1

1.2 X-Ray Tomography............................................................................3

1.3 Objectives and Scope of Research .....................................................3

1.4 Overview of Report ............................................................................4

Chapter 2 - Previous Work................................................................................................6

2.1 Introduction ........................................................................................6

2.1.1 Tepfers ........................................................................................6

2.1.2 Eligehausen, et. al. ......................................................................8

2.1.3 Malvar .........................................................................................9

2.1.4 Previous Works Conclusions ....................................................11

Chapter 3 - Test Matrix ...................................................................................................12

3.1 Specimens.........................................................................................12

3.1.1 Pull-Out Specimens...................................................................12

3.1.2 Uniform Tension Specimens.....................................................13

3.1.3 Parameters That Determine Bond Specimen Response ............14

3.1.4 Test Matrix ................................................................................16

Chapter 4 - Material Test Results....................................................................................22

4.1 Introduction ......................................................................................22

4.2 Compressive Strength ......................................................................23

4.3 Tensile Strength................................................................................24

4.3.1 Split-Cylinder Tension Test ......................................................24

4.3.2 Modulus of Rupture Test ..........................................................26

4.4 Elastic Modulus................................................................................27

4.5 Tape Strength ...................................................................................29

ii

4.6 Wire Strength ...................................................................................30

4.7 Fracture Energy ................................................................................32

4.7.1 Introduction...............................................................................32

4.7.2 Specimens .................................................................................32

4.7.3 Counter-Weight System............................................................34

4.7.4 Construction ..............................................................................35

4.7.5 Test Set-Up ...............................................................................36

4.7.6 Instrumentation .........................................................................38

4.7.7 Test Procedure...........................................................................40

4.7.8 Results .......................................................................................43

4.7.9 Analysis and Discussion of Results ..........................................48

4.7.10 Evaluation of Test Procedures ..................................................52

Chapter 5 - Tests on Embedded Bars ..............................................................................54

5.1 Test Set-Up.......................................................................................54

5.1.1 Pull-Out Test Set-Up.................................................................54

5.1.2 Uniform Tension Test Set-Up...................................................59

5.2 Test Procedure..................................................................................61

5.2.1 Pull-Out Test Procedure............................................................61

5.2.2 Uniform Tension .......................................................................64

5.3 Bond Test Results.............................................................................65

5.3.1 Measured Data ..........................................................................65

5.3.2 Observations..............................................................................80

5.3.3 Errors and Complications..........................................................81

Chapter 6 - Analysis of Embedded Bar Test Results ......................................................86

6.1 Correction of Measured Data ...........................................................86

6.2 Comparison with Eligehausen’s Analytical Bond Model ................87

6.3 Comparison with ACI models..........................................................98

6.4 Thick Walled Cylinder Model........................................................105

6.4.1 Pre-Cracking Stress State........................................................106

6.4.2 Effective Lug Angle at Peak Load..........................................112

Chapter 7 - Conclusion..................................................................................................116

iii

7.1 Summary ........................................................................................116

7.2 Conclusions ....................................................................................117

7.3 Recommendations ..........................................................................121

7.3.1 Impact on Current Practice .....................................................121

7.3.2 Further Research .....................................................................121

Bibliography ....................................................................................................................124

Appendix A - Load-Displacement Curves.................................................................126

Appendix B – Uniform Tension Specimen Photographs...........................................161

iv

LIST OF FIGURES

Figure Number Page

1.1: Schematic of internal forces within a reinforced concrete specimen ...........................2

2.1: Bond Capacity as a Function of Cover Thickness........................................................8

2.2: Malvar’s Bond Test Set-Up ........................................................................................10

2.3: Bond Stress vs. Slip Curves for Five of Malvar’s Tests.............................................11

3.1: Pull-Out Specimen Design..........................................................................................13

3.2: Uniform Tension Specimen Design............................................................................14

4.1: Failure mode in a split tension specimen....................................................................25

4.2: Compressometer for Elastic Modulus Test.................................................................28

4.3: Tape Strength Test ......................................................................................................30

4.4: Wire Strength Test ......................................................................................................31

4.5: Fracture Energy Specimen Diagram...........................................................................33

4.6: Beam Diagram with Counter-Weights and Bending Moment Diagram.....................35

4.7: Center-Point Loading Apparatus for Flexural Testing (ASTM C293).......................36

4.8: S-Type Load Cell........................................................................................................38

4.9: Bending Stress vs. Displacement for FR-63-A-2 .......................................................45

4.10: Stress-Displacement Plots for FR-42 Specimens .....................................................46



5.1: Series SA Test Set-Up ................................................................................................55

5.2: Potentiometer Locations for Series SA.......................................................................56

5.3: Mobile Pull-Out Test Apparatus: Picture and Schematic...........................................57

5.4: Rebar Chuck ...............................................................................................................58

5.5: Crack Displacement Potentiometer Locations............................................................60

v

5.6: Crack clamps...............................................................................................................61

5.7: Load-Displacement Curve for Specimen SA-0612-06-06-FS-A................................67

5.8: Load-Displacement Curve for Specimen SA-0612-06-03-FG-A...............................68

5.9: Load-Displacement Curve for Specimen SB-0612-08-06-TA-A...............................70

5.10: Load-Displacement Curve for Specimen SD-0816-06-01-TA-A.............................73

5.11: Load-Displacement Curve for Specimen SD-0612-08-03-TA-C.............................74

5.12: Load-Displacement Curve for Specimen SE-0612-08-03-W26-A...........................76

5.13: Load-Displacement Curve for Specimen SE-0612-08-03-WDBL-A.......................76

5.14: Uniform Tension Specimen Crack Patterns..............................................................79

6.1: Analytical Models Relating Bond Stress and Slip......................................................89

6.2: Pull-Through Specimen: Measured and Predicted Behavior......................................90

6.3: Specimens with High Confinement: Measured and Predicted Behavior....................91

6.4: Specimens with Moderate Confinement: Measured and Predicted Behavior ............92

6.5: Specimens with Low Confinement: Measured and Predicted Behavior ....................94

6.6: Comparison of Data with Equation 6.13…………………………………………...101

6.7: Bond Stress Distribution Using Raynor’s (2006) Linear Model ..............................108

6.8: Specimen Stress State at Splitting ............................................................................109

6.9: Mohr’s Circle for Peak Stress Analysis....................................................................110

6.10: Wedge Model for Rebar Lugs ................................................................................112

A.1: Load-Displacement Curve for Specimen SA-0612-06-06-FS-A.............................126

A.2: Load-Displacement Curve for Specimen SA-0612-06-03-AL-A............................127

A.3: Load-Displacement Curve for Specimen SA-0612-06-06-FG-A............................127

A.4: : Load-Displacement Curve for Specimen SA-0612-06-03-FG-A..........................128




vi

A.8: Load-Displacement Curve for Specimen SB-0612-08-06-NO-A............................130

A.9: Load-Displacement Curve for Specimen SB-0612-08-06-NO-B............................130

A.10: Load-Displacement Curve for Specimen SB-0612-08-06-NO-C..........................131

A.11: Load-Displacement Curve for Specimen SB-0612-08-06-TA-A..........................131

A.12: Load-Displacement Curve for Specimen SB-0612-08-06-TA-B ..........................132

A.13: Load-Displacement Curve for Specimen SB-0612-08-06-TA-C ..........................132

A.14: Load-Displacement Curve for Specimen SB-0612-08-06-TA-D..........................133

A.15: Load-Displacement Curve for Specimen SB-0612-08-06-TA-E ..........................133

A.16: Load-Displacement Curve for Specimen SB-0612-08-06-TA-F...........................134

A.17: Load-Displacement Curve for Specimen SC-0612-06-03-TA-A..........................134










A.27: Load-Displacement Curve for Specimen SD-0612-08-03-TA-A..........................139

A.28: Load-Displacement Curve for Specimen SD-0612-08-03-TA-B..........................140

A.29: Load-Displacement Curve for Specimen SD-0612-08-03-TA-C..........................140

A.30: Load-Displacement Curve for Specimen SD-0612-08-03-TA-D..........................141




vii













A.46: Load-Displacement Curve for Specimen SE-0612-08-03-W26-A........................149

A.47: Load-Displacement Curve for Specimen SE-0612-08-03-W26-B........................149






A.53: Load-Displacement Curve for Specimen SE-0612-08-03-W125-A......................152

A.54: Load-Displacement Curve for Specimen SE-0612-08-03-W125-B......................153

A.55: Load-Displacement Curve for Specimen SE-0612-08-03-WDBL-A....................153

A.56: Load-Displacement Curve for Specimen SE-0612-08-03-WDBL-B....................154

A.57: Load-Displacement Curve for Specimen SF-0612-08-03-WDBL-A....................154

A.58: Load-Displacement Curve for Specimen SF-0612-08-03-WDBL-B ....................155

A.59: Load-Displacement Curve for Specimen SF-0612-08-03-WDBL-C ....................155

viii

A.60: Load-Displacement Curve for Specimen SF-0612-08-03-W74-B ........................156

A.61: Load-Displacement Curve for Specimen SF-0612-08-03-W74-C ........................156

A.62: Load-Displacement Curve for Specimen SF-0612-08-03-W59-A........................157

A.63: Load-Displacement Curve for Specimen SF-0612-08-03-W59-C ........................157

A.64: Load-Displacement Curve for Specimen SF-0612-08-01-NO-A..........................158

A.65: Load-Displacement Curve for Specimen SF-0612-08-01-NO-B ..........................158

A.66: Load-Displacement Curve for Specimen SF-0612-08-01-NO-C ..........................159

A.67: Load-Displacement Curve for Specimen SF-0612-08-03-FI-A ............................159

A.68: Load-Displacement Curve for Specimen SF-0612-08-03-FI-B ............................160

A.69: Load-Displacement Curve for Specimen SF-0612-08-03-FI-C ............................160

B.1: Uniform Tension Specimen UV Photo 1 .................................................................161

B.2 Uniform Tension Specimen UV Photo 2 ..................................................................161





ix

LIST OF TABLES

Table Number Page

3.1: Pull-Out Test Parameters ............................................................................................16

3.2: Bond Specimen Details...............................................................................................18

4.1: Concrete Mix Design ..................................................................................................23

4.2: Compression Test Results...........................................................................................24

4.3: Split-Cylinder Tension Test Results ...........................................................................26

4.4: Modulus of Rupture Test Results ...............................................................................26

4.5: Elastic Modulus Test Results......................................................................................28

4.6: Wire Strengths ............................................................................................................31

4.7: Fracture Energy Specimen Dimensions......................................................................33

4.8: Fracture Energy Test Results......................................................................................44

4.9: Average Fracture Energy Results by Specimen Size..................................................50

4.10: Measured vs. Predicted GF........................................................................................51

5.1: Series 1 Specimen Alterations ....................................................................................63

5.2: Series SA Test Results................................................................................................66

5.3: Series SB Test Results ................................................................................................69

5.4: Series SC Test Results ................................................................................................71

5.5: Series SD Test Results................................................................................................72

5.6: Series SE Test Results ................................................................................................75

5.7: Series SF Test Results.................................................................................................77

6.1: Bond Model Constants................................................................................................88

6.2: Statistics for Series SF Specimen Results...................................................................97

6.3: ACI Equation Parameters .........................................................................................100

6.4: Confinement and Post-Cracking Bond Stresses for Series SE and SF .....................103

x

6.5: Select Tests From Eligehausen’s Study (1983) ........................................................104

6.6: Inputs for Linear Bond Model ..................................................................................108

6.7: Effective Lug Angles ................................................................................................115

xi

LIST OF VARIABLES

α = lug face angle relative to the longitudinal axis of the bar;

αo = aggregate shape factor;

αr = reinforcement location factor;

a = interior radius of the thick-walled cylinder;

Ab = cross-sectional area of the rebar;

Ac = cross-sectional area of the concrete cylinder;

Atr = total area of transverse reinforcement;

β = bar coating factor;

b = exterior radius of the thick-walled cylinder;

br = width of rupture beam;

c = amount of cover on the rebar;

δconc = axial deformation of the concrete;

δmeas = measured displacement of the bar;

δsteel = axial deformation of the bar;

d = depth of rupture beam;

D = diameter of the concrete cylinder;

da = maximum aggregate size;

db = nominal diameter of the bar;

Ec = elastic modulus of concrete;

Es = elastic modulus of steel;

F = frictional force acting on the lug;

f’c = compressive strength of concrete;

fr = modulus of rupture;

ft = tensile strength of the concrete;

xii

fy = the yield strength of the rebar;

fyt = yield strength of transverse reinforcement;

γ = reinforcement size factor;

k = bond stiffness;

Ktr = transverse reinforcement index;

λ = lightweight aggregate concrete factor;

L = length of concrete cylinder;

Lb = bonded length of bar;

Lu = unbonded length of bar between the bonded region and the potentiometer;

µ = coefficient of friction between steel and concrete;

n = number of bars or wires being developed along the plane of splitting;

N = force acting normal to the lug face;

P = applied load;

pi = internal pressure acting on the thick-walled cylinder;

po = external pressure acting on the thick-walled cylinder;

Py = load at which the rebar yields and the specimen fails;

Q = radial force acting on the bar by the concrete;

r = radius of interest in the thick-walled cylinder;

s = maximum center-to-center spacing of transverse reinforcement;

s1 = first slip value in Eligehausen’s bond equation;

s2 = second slip value in Eligehausen’s bond equation;

s3 = third slip value in Eligehausen’s bond equation;

τ = bond stress;

τ1 = first bond stress value in Eligehausen’s bond equation;

τ3 = second bond stress value in Eligehausen’s bond equation;

xiii

τu = maximum bond stress;

σr = radial stress;

σt = hoop stress;

w/c = water-cement ratio of the concrete;

z = distance from the beginning of the bonded region of the bar.

xiv

ACKNOWLEDGEMENTS

This research was sponsored by the National Science Foundation.

The author would like to recognize John Stanton and Laura Lowes for their influential

guidance and support throughout the project.

xv

DEDICATION

To my Grandparents; Jack and Sawako Martin and Jack and Marybelle Sceva.

1

CHAPTER 1 - INTRODUCTION

1.1 Background

Reinforced concrete is one of the most widely used composite materials in civil

engineering. A composite material is defined as a solid material that results when two or

more different materials are combined to form a new material with properties superior to

those of the individual components. Component materials are chosen so that the

strengths of each are enhanced and the weaknesses of each are avoided. Reinforced

concrete is composed of a concrete matrix surrounding strategically placed steel bars.

Plain concrete is very strong in compression but weak and brittle in tension, whereas steel

is very strong and ductile under tensile loads. In reinforced concrete members, concrete

forms the body of the member and provides stiffness and resistance to compression loads.

The steel reinforcing bars (rebar) are placed where tensile loads are expected, so that

once the concrete cracks, the steel is present to resist the tension.

In most composite members, including reinforced concrete, composite action

requires that loads be transferred from one material to another through bond. This

interface where bond occurs has the potential to be the weakest part of the member. In

uncracked reinforced concrete, the shear forces that are transferred across this interface

between the steel and the concrete can be seen as orthogonal compression and tension

fields, where the compression fields begin in a band around the lugs and expand outward

at approximately 45º angles to form cones of compression, as shown in Figure 1.1. This

type of stress field tends to cause three possible types of damage: conical pull-out cracks,

radial splitting and crushing around the lugs on the rebar. Each of these types of damage

can lead to bond failure and, consequently, failure of the member.

2

Figure 1.1: Schematic of internal forces within a reinforced concrete specimen

(Tepfers, 1979)

Due to the large effect that bond has on the behavior of the member as a whole, it

is important to have a clear understanding of its behavior. However, a number of issues

limit researchers’ ability to measure and study bond in real members. The primary

difficulty is that bond is internal to the member and cannot be observed directly from the

outside. Furthermore, any remote sensors placed at the interface prove to be invasive.

For example, contact devices, such as strain gauges, are ideal for taking measurements at

a particular location. However, the adhesives and waterproofing required for their

application effectively destroy the bond action they are intended to observe. Non-local

(external) devices, such as load cells, only record average or integral values and are not

capable of detecting small variations within a member, which is vital in such non-uniform

fields. In light of these difficulties, a new non-destructive and non-invasive sensor or

measurement technique is necessary to advance the state of the art in bond research. The

splitting failure of the concrete around the steel is a very brittle process and is therefore

sensitive to the peak stresses experienced within the member. Prediction of such splitting

and the consequent bond failure require prediction of the highly non-uniform distribution

of the stress fields along the bond interface and, in particular, of the peak stresses.

3

1.2 X-Ray Tomography

X-ray tomography has the ability to observe the local state of the bond interface in

composite materials without adversely affecting the environment it is observing. Thus, it

is holds great potential for overcoming the obstacles inherent in measuring bond behavior

in reinforced concrete. X-ray tomography is a process that utilizes high-energy radiation

from a linear accelerator, radiation detectors and computer reconstruction software to

produce highly detailed three-dimensional images of solid objects. These three-

dimensional images will allow researchers to observe the state of the bond zone in

reinforced concrete members, both at rest and under load. Researchers will then be able

to observe the initiation and progression of bond zone damage like never before.

1.3 Objectives and Scope of Research

This project is composed of three distinct parallel studies; an experimental

program, a finite element analysis, and an x-ray tomography image analysis. The overall

objectives of the project are to:

• Gain a better understanding of bond in reinforced concrete,

• Refine existing models on bond behavior, and

• Develop a new method for monitoring bond test specimens using x-ray

tomography.

The goals of the experimental program, which is the portion presented in this

thesis, are to:

• Conduct experiments to shed light on the conditions that promote different

types of bond failures (i.e. splitting, pull-through, etc.)

• Investigate the effect of various specimen parameters, such as dimension,

bar size, bonded length and confinement, on bond behavior,

4

• Prepare several series of bond specimens, and a mobile test apparatus, for

the x-ray tomography portion of the project,

• Produce specimens with different types and levels of bond-related

damage, and

• Conduct materials tests, including fracture energy tests, to provide

materials data for the x-rayed specimens and for use in the finite element

model.

The goals of the finite element analysis are to:

• Predict the bond behavior for the tests conducted in the experimental

program and

• Refine existing models on bond behavior for use in design.

The goals of the x-ray tomography analysis are to:

• Quantify bond zone damage using x-ray tomography,

• Quantify the fracture volume of the damaged specimens,

• Use image registration to determine strain and displacement fields.

The experimental program presented in this thesis was a stand-alone study aimed

at gaining a better understanding of bond in reinforced concrete experimentally. At the

same time, this program supported the parallel projects by designing test specimens and

testing apparatus, supplying materials properties data, and conducting bond tests. For

these reasons, all of the work conducted in this project is presented in this report.

1.4 Overview of Report

This report follows the development of the experimental program researching

bond in reinforced concrete. Chapter 2 details previous work conducted on the behavior

of bond in reinforced concrete. Chapter 3 describes the test specimens developed for this

study, including specimen design, specific parameters of interest, and the test matrix.

5

Chapter 4 contains the materials tests conducted during this study. Both standard ASTM

materials tests and fracture energy tests modified from RILEM standards are included in

this chapter. Chapter 5 details the tests conducted on the bond specimens described in

Chapter 3. Test set-ups, procedures and results are all discussed in this chapter. Chapter

6 contains an analysis of the measured results, including comparisons to existing models

and analyses seeking to gain an understanding of the bond behavior. Conclusions and

insights developed during this study are presented in Chapter 7.

6

CHAPTER 2 - PREVIOUS WORK

2.1 Introduction

Over the past 30 years, several studies have been conducted on bond in reinforced

concrete. Tepfers (1979) analyzed the stress state in the concrete due to bond forces and

used a concrete ring model to determine the cracking resistance of the concrete cover.

Eligehausen (1983) conducted an experimental program in order to develop a model for

the relationship between bond stress and slip in reinforced concrete. Malvar (1992)

investigated the effect of confinement on the bond stress-slip behavior. Together, these

studies have helped lay a foundation of solid research into bond behavior in reinforced

concrete.

2.1.1 Tepfers

Engineers have long known that a relationship exists between applied bond forces

in a reinforced concrete member and the resultant radial forces that cause the concrete

cover to split. Tepfers (1979) used a concrete ring model, as shown in Figure 1.1, to

determine the peak bond stress in a specimen when the cover cracks. These peak bond

stresses were calculated for three separate stages of behavior; an elastic stage, a plastic

stage, and a partially cracked elastic stage. In theory, these stages bound the actual

concrete behavior.

In the uncracked elastic stage, the concrete is regarded as a thick-walled cylinder

with an internally applied pressure. The compression and tension fields within the

concrete caused by this pressure are assumed to form an angle of 45°. The principal

stresses are assumed to be equal in magnitude until the principal tensile stress at any

point exceeds the tensile strength, ft, of the concrete, at which point the cover completely

cracks. The bond at failure of the concrete cover can be calculated by Equation 2.1.

7

22

22

22

22

+

+

−

+

⋅=DDc

DDcftuτ (2.1)

The bond stress at failure in the plastic stage is considered the upper limit for

resistance using this concrete ring model. Again, the concrete cover is regarded as a

thick-walled cylinder with an applied internal pressure. However, in this phase, the

cylinder is assumed to distribute the stress throughout the cylinder until the hoop stress,

σt, at every point has reached the tensile capacity of the concrete. Only then does the

concrete crack. In this case, the bond stress at failure can be calculated by Equation 2.2.

Dcftu

⋅⋅=2τ (2.2)

In the partially cracked elastic stage, the thick-walled cylinder is again assumed to

be elastic. A crack will initiate at the inside surface of the cylinder once the principal

tensile stress exceeds the tensile strength of the concrete. However, as opposed to the

elastic stage, once the crack initiates it will only propagate as far out as the hoop stress

exceeds the peak tensile stress. This model implies that the cracks can propagate out to

any point in the cylinder and be stable. The peak bond stress is reached at the same time

that the cracks propagate to the outside edge of the cylinder. The peak bond stress for

this stage can be calculated using Equation 2.3.

DDcftu 664.1

2/+⋅=τ (2.3)

Figure 2.1 shows the peak bond capacity of a cylinder for all three phases based

on the relative dimensions of the concrete cylinder.

8

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6c/D

τ u/f t

Uncracked Elastic

Uncracked Plastic

Partially Cracked Elastic

Figure 2.1: Bond Capacity as a Function of Cover Thickness

The uncracked elastic and uncracked plastic stages (lower and upper bounds,

respectively) can be averaged to determine the maximum bond stress in a specimen at the

time of a splitting failure. The partially cracked elastic stage gives failure stresses that

are just lower than the average of the upper and lower bounds.

Tepfers compared his models to experimentally determined peak bond stresses

and confirmed that most of the data points landed between the uncracked plastic stage

and the partially cracked elastic stage.

2.1.2 Eligehausen, et. al.

Eligehausen, Popov and Bertero (1983) conducted bond tests on 125 reinforced

concrete specimens. The bars in these specimens were bonded for a short length (five

times the bar diameter) in the middle of concrete blocks containing various amounts of

9

transverse reinforcement. As the bars were subjected to various displacements, the force

required to do so was recorded. Subsequently, the data was presented as bond stress-slip

curves. These curves represent the amount of force necessary to cause the bar to slip by a

desired amount. After conducting 125 tests, Eligehausen compiled the data and created a

simplified model that models the bond stress-slip behavior of a specimen subjected

monotonic loading. Eligehausen’s research has been the seminal study on bond behavior

for over twenty years. His model is actually compared to the data collected in this project

and is presented in Section 6.2.

2.1.3 Malvar

Malvar (1992) also conducted tests on reinforced concrete specimens. However,

what sets his work apart is his focus on the role of radial stress and deformation in the

bond stress-slip behavior. Malvar’s tests used various amounts of active confinement to

investigate the effect it has on the pre- and post-peak bond stress behaviors. Figure 2.2

shows a schematic of Malvar’s test set-up. Like Eligehausen’ts tests, Malvar’s test

specimens used relatively short bonded lengths to investigate the bond stress-slip

relationship.

10

Figure 2.2: Malvar’s Bond Test Set-Up

From his tests, Malvar was able to conclude that the amount of confinement has a

definite effect on the bond stress-slip relationship in the post-crack region. Figure 2.3

shows data for five of his test specimens. This plot clearly shows an increase in the post-

cracking bond stress relating to an increase in confining pressure. What is not so clear is

the effect the confinement has on the pre-cracking behavior. Malvar suspects that there

maybe an effect in this region, but due to the scatter in his data, he is unable to establish

the exact relationship. However, he is also able to determine that the confinement limits

the amount of radial deformation in the specimen.

11

Figure 2.3: Bond Stress vs. Slip Curves for Five of Malvar’s Tests

2.1.4 Previous Works Conclusions

Tepfers (1979) was able to show that splitting failure in pull-out specimens can be

predicted using Timoshenko’s (1930) thick-walled cylinder formulas as an approximation

for the concrete cover. The results corresponded closely with experimental data. From

experimental data, Eligehausen (1983) was able to develop a bond stress-slip model that

has been the primary prediction model used for bond over the last twenty years. In fact,

it is used in this report as a comparison for the data measured during this project. Malvar

(1992) determined that non-local factors, confinement in particular, can have a large

effect on the bond behavior in the post-cracking region of the load history, and possibly

in the pre-cracking region as well.

12

CHAPTER 3 - TEST MATRIX

3.1 Specimens

In total, seven test series were conducted on steel bars embedded in concrete

specimens. During the course of this investigation, two different types of specimens

were tested which will be referred to as pull-out and uniform tension specimens. The

specimen designs needed to fit the requirements for the x-ray imaging portion of the

project, which dictate that the specimens be axi-symmetrical and tested without

obstructing the sides of the specimen, through which the x-rays would need to penetrate.

3.1.1 Pull-Out Specimens

Six of the test series used the pull-out specimen design. Each pull-out specimen

consisted of a concrete cylinder with rebar embedded along its axis and protruding from

one end. These are called “pull-out” specimens because the specimen is tested by pulling

on the protruding bar until failure, as shown in Figure 3.1. In most, but not all cases, the

bar was deliberately debonded over part of its length to avoid premature failure by

yielding.

13

Figure 3.1: Pull-Out Specimen Design

3.1.2 Uniform Tension Specimens

Series SG consisted of two uniform tension specimens, identical in every respect

except rebar size. These specimens were 4 inches in diameter and 24 inches in length.

The rebar ran along the axis of the cylinder and protruded from both ends. These

specimens were meant to simulate approximately how rebar and concrete behave in the

tension areas of flexural members by applying (uniform) tension to both ends until the

concrete cracks reach a desired width. In the absence of special devices, predicting

exactly where concrete will fail is difficult. Therefore, crack initiators were inserted into

the specimen during casting so that, as the cracks formed, displacement readings could be

taken across them. The crack initiators consisted of ¼” wire loops with a diameter of

3.25”. These were inserted into the specimen every 4” along the length, with a total of 5

14

crack initiators per specimen. Figure 3.2 shows the design of the uniform tension

specimens.

Figure 3.2: Uniform Tension Specimen Design

3.1.3 Parameters That Determine Bond Specimen Response

The following section details the parameters studied in this project and the range

over which each was varied within the study.

3.1.3.1 Concrete Cylinder Dimensions

The diameters of the specimens in this study ranged from 4 inches to 10 inches.

With a few exceptions, the height of every specimen was twice the diameter, resulting in

similar geometries throughout the test series. The exceptions are specimen S1-1014-10-

14-FG-A, the height of which was constrained to only 14 inches due to lack of molds (a

10” diameter bucket was used instead) and the uniform tension specimens in Series F.

3.1.3.2 Bar Size

Bar nos. 4, 6, 8 and 10 were used in this study. The nominal diameters of each of

these bars are 0.5”, 0.75”, 1.0” and 1.128” respectively.

15

3.1.3.3 Bonded Length

In each specimen, the rebar was embedded over the full length of the cylinder, but

the length over which it was bonded varied, ranging from 1” to 16”. Partial debonding

was achieved by cutting a PVC tube, slightly larger in diameter than the rebar, to a

specified length and either taping or gluing it to the rebar prior to casting. In this way,

the portion of rebar within the PVC tubing was able to elongate and move relative to the

concrete without inducing any unwanted stresses.

3.1.3.4 Concrete Confinement

Several different types of confinement were used in this study. The purpose of

the confinement was twofold; to hold the specimens together once failure had occurred

and to create cracks which propagated in a controlled manner. Series SA utilized three

types of confinement, fiberglass jackets, steel spirals and aluminum jackets. Each of

these provided too much confinement for the specimens, resulting in failure by pull-

through or bar fracture rather than concrete splitting. New types of confinement were

therefore tested in the next series of tests.

Series SB used both a clear duct tape and fiber-reinforced strapping tape. It was

hoped that the much lower confinement forces provided by these tapes would allow

failure by splitting, but would still prevent the specimen from falling apart directly after

splitting. The strapping tape was applied both in 2 and 4 layers to determine which

provided the best crack control. The four layers of strapping tape provided the most post-

cracking confinement of the series and were used thereafter in Series SC and SD.

Though the strapping tape provided some post-cracking confinement, it was not

enough to stop the cracks propagating right across the cylinder as soon as they initiated.

A confining medium that would arrest crack development and allow controllable

propagation of those cracks was desired. For this reason, steel wire spirals were cast into

16

the specimens of Series SE and SF. High (> 300 ksi) and low (~85 ksi) strength of

various diameters were used in order to determine which allowed for the best crack

control in the post-peak region of the load history. The use of a wide range of steel

strengths allowed elastic and yielding confinement to be studied at approximately the

same confining stress. The specific types of confinement for each specimen are detailed

in Table 3.2.

3.1.4 Test Matrix

Each series of tests consisted of a different number of specimens with different

physical parameters, such as cylinder size, rebar size, rebar embedded length, and

concrete confinement type. Table 3.1 lists the primary test parameter for each series and

Table 3.2 lists the specific details for each specimen.

Table 3.1: Pull-Out Test Parameters

Series Geometry Confinement Comments

SA Varied Varied Preliminary Test Series

SB Constant Varied Various amounts of tape confinements

SC Varied Constant Investigated geometry effects on bond

SD Varied Constant Investigated line between splitting & pull-through

SE Constant Varied Various wire spiral confinements

SF Varied Varied Various wire spiral confinements, pull-through specimens and fiber-reinforced specimens

So that the reader can identify a particular specimen without referencing the table,

the specimen names all have the following form:

(Series Label)-(Specimen Dimension)-(Rebar Size)-(Bonded Length)-

(Confinement Type)-(Identifier)

17

where:

• the first set of numbers indicate the test series to which specimen belongs

(e.g. SA = Series A)

• the second set indicate the diameter and height of the specimen, in inches

(e.g. 0612 = 6”x12”)

• the third indicates the rebar size, in eights of an inch (e.g. 06 = no. 6 bar)

• the fourth indicates the rebar bonded length (e.g. 03 = 3 inches)

• the fifth indicates the confinement type, such as a fiberglass jacket or wire

spiral (e.g. FG = Fiberglass)

• the last set distinctly identifies individual specimens the names of which

would otherwise be identical (e.g. A, B, or C)

The following specimen name is an example of this naming convention.

SA-0612-06-03-FG-A

18

Table 3.2: Bond Specimen Details

Specimen Diameter

(in) Height

(in)

Rebar Size (no.)

Rebar Bonded Length

(in) Confinement Type SA-0612-06-06-FS-A 6 12 6 6 Fiberglass and Steel Spiral SA-0612-06-03-AL-A 6 12 6 3 Aluminum jacket (2" thick) SA-0612-06-06-FG-A 6 12 6 6 Fiberglass SA-0612-06-03-FG-A 6 12 6 3 Fiberglass SA-0612-06-12-FG-A 6 12 6 12 Fiberglass SA-0816-08-16-FG-A 8 16 8 16 Fiberglass SA-1014-10-14-FG-A 10 14 10 14 Fiberglass SB-0612-08-06-NO-A 6 12 8 6 None SB-0612-08-06-NO-B 6 12 8 6 None SB-0612-08-06-NO-C 6 12 8 6 None SB-0612-08-06-TA-A 6 12 8 6 Clear Duct Tape (4 Lyrs) SB-0612-08-06-TA-B 6 12 8 6 Clear Duct Tape (4 Lyrs) SB-0612-08-06-TA-C 6 12 8 6 Strapping Tape w/ Fiber (2 Lyrs) SB-0612-08-06-TA-D 6 12 8 6 Strapping Tape w/ Fiber (2 Lyrs) SB-0612-08-06-TA-E 6 12 8 6 Strapping Tape w/ Fiber (4 Lyrs) SB-0612-08-06-TA-F 6 12 8 6 Strapping Tape w/ Fiber (4 Lyrs) SC-0612-06-03-TA-A 6 12 6 3 Strapping Tape w/ Fiber (4 Lyrs) SC-0612-06-06-TA-A 6 12 6 6 Strapping Tape w/ Fiber (4 Lyrs) SC-0612-08-03-TA-A 6 12 8 3 Strapping Tape w/ Fiber (4 Lyrs) SC-0612-08-06-TA-A 6 12 8 6 Strapping Tape w/ Fiber (4 Lyrs) SC-0816-06-03-TA-A 8 16 6 3 Strapping Tape w/ Fiber (4 Lyrs) SC-0816-06-06-TA-A 8 16 6 6 Strapping Tape w/ Fiber (4 Lyrs) SC-0816-08-03-TA-A 8 16 8 3 Strapping Tape w/ Fiber (4 Lyrs) SC-0816-08-06-TA-A 8 16 8 6 Strapping Tape w/ Fiber (4 Lyrs) SC-1020-06-03-TA-A 10 20 6 3 Strapping Tape w/ Fiber (4 Lyrs) SC-1020-06-06-TA-A 10 20 6 6 Strapping Tape w/ Fiber (4 Lyrs) SC-1020-08-03-TA-A 10 20 8 3 Strapping Tape w/ Fiber (4 Lyrs) SC-1020-08-06-TA-A 10 20 8 6 Strapping Tape w/ Fiber (4 Lyrs) SD-0612-08-03-TA-A 6 12 8 3 Strapping Tape w/ Fiber (4 Lyrs) SD-0612-08-03-TA-B 6 12 8 3 Strapping Tape w/ Fiber (4 Lyrs) SD-0612-08-03-TA-C 6 12 8 3 Strapping Tape w/ Fiber (4 Lyrs) SD-0612-08-03-TA-D 6 12 8 3 Strapping Tape w/ Fiber (4 Lyrs) SD-0408-06-01-TA-A 4 8 6 1 Strapping Tape w/ Fiber (4 Lyrs) SD-0408-06-02-TA-A 4 8 6 2 Strapping Tape w/ Fiber (4 Lyrs) SD-0408-06-03-TA-A 4 8 6 3 Strapping Tape w/ Fiber (4 Lyrs) SD-0612-06-01-TA-A 6 12 6 1 Strapping Tape w/ Fiber (4 Lyrs) SD-0612-06-02-TA-A 6 12 6 2 Strapping Tape w/ Fiber (4 Lyrs) SD-0612-06-03-TA-A 6 12 6 3 Strapping Tape w/ Fiber (4 Lyrs) SD-0816-06-01-TA-A 8 16 6 1 Strapping Tape w/ Fiber (4 Lyrs) SD-0816-06-02-TA-A 8 16 6 2 Strapping Tape w/ Fiber (4 Lyrs) SD-0816-06-03-TA-A 8 16 6 3 Strapping Tape w/ Fiber (4 Lyrs)

19

Table 3.1 continued

Specimen Diameter

(in) Height

(in)

Rebar Size (no.)

Rebar Bonded Length

(in) Confinement Type

SD-0408-04-01-TA-A 4 8 4 1 Strapping Tape w/ Fiber (4 Lyrs)SD-0408-04-02-TA-A 4 8 4 2 Strapping Tape w/ Fiber (4 Lyrs)SD-0408-04-03-TA-A 4 8 4 3 Strapping Tape w/ Fiber (4 Lyrs)SD-0816-08-01-TA-A 8 16 8 1 Strapping Tape w/ Fiber (4 Lyrs)SD-0816-08-02-TA-A 8 16 8 2 Strapping Tape w/ Fiber (4 Lyrs)SD-0816-08-03-TA-A 8 16 8 3 Strapping Tape w/ Fiber (4 Lyrs)

SE-0612-08-03-W26-A 6 12 8 3 Wire (.026" diameter, 355 ksi) SE-0612-08-03-W26-B 6 12 8 3 Wire (.026" diameter, 355 ksi) SE-0612-08-03-W41-A 6 12 8 3 Wire (.041" diameter, 330 ksi) SE-0612-08-03-W41-B 6 12 8 3 Wire (.041" diameter, 330 ksi) SE-0612-08-03-W59-A 6 12 8 3 Wire (.059" diameter, 312 ksi) SE-0612-08-03-W59-B 6 12 8 3 Wire (.059" diameter, 312 ksi) SE-0612-08-03-W74-A 6 12 8 3 Wire (.074" diameter, 84 ksi) SE-0612-08-03-W74-B 6 12 8 3 Wire (.074" diameter, 84 ksi)

SE-0612-08-03-W125-A 6 12 8 3 Wire (.125" diameter, 84 ksi) SE-0612-08-03-W125-B 6 12 8 3 Wire (.125" diameter, 84 ksi)

SE-0612-08-03-WDBL-A 6 12 8 3 Wire (.125"+.074" diam., 84 ksi)SE-0612-08-03-WDBL-B 6 12 8 3 Wire (.125"+.074" diam., 84 ksi)

SF-0612-08-03-WDBL-A 6 12 8 3 Wire (.125"+.074" diam., 84 ksi)SF-0612-08-03-WDBL-B 6 12 8 3 Wire (.125"+.074" diam., 84 ksi)SF-0612-08-03-WDBL-C 6 12 8 3 Wire (.125"+.074" diam., 84 ksi)SF-0612-08-03-W74-A 6 12 8 3 Wire (.074" diameter, 84 ksi) SF-0612-08-03-W74-B 6 12 8 3 Wire (.074" diameter, 84 ksi) SF-0612-08-03-W74-C 6 12 8 3 Wire (.074" diameter, 84 ksi) SF-0612-08-03-W59-A 6 12 8 3 Wire (.059" diameter, 312 ksi) SF-0612-08-03-W59-B 6 12 8 3 Wire (.059" diameter, 312 ksi) SF-0612-08-03-W59-C 6 12 8 3 Wire (.059" diameter, 312 ksi) SF-0612-08-01-NO-A 6 12 8 1 None SF-0612-08-01-NO-B 6 12 8 1 None SF-0612-08-01-NO-C 6 12 8 1 None SF-0612-08-03-FI-A 6 12 8 3 None – Fiber reinforced SF-0612-08-03-FI-B 6 12 8 3 None –Fiber reinforced SF-0612-08-03-FI-C 6 12 8 3 None – Fiber reinforced

SG-0424-06-24-NO-A 4 24 6 24 None SG-0424-08-24-NO-A 4 24 8 24 None

20

Series Identification

Series SA consisted of seven pull-out specimens, each with variations in

dimension, bar size, bonded length and confinement type. This was the first series of

tests and was viewed as a preliminary investigation to determine the parameters that

would be useful to investigate further.

Series SB consisted of nine pull-out specimens, which were all 6”x12” specimens

with a #8 bar bonded for 6” (SB-0612-08-06…) and were used to explore the effects of

several different external confinement types. The confinements for these specimens

consisted of duct tape and fiber-reinforced strapping tape, which were then compared to

control specimens without confinement.

For Series SC, the strapping tape was used exclusively, allowing an investigation

into the other parameters (i.e. specimen dimensions, rebar size and bonded length). One

pull-out specimen was made for each combination of cylinder diameter (6, 8, or 10 inch),

bar size (6 or 8), and bonded length (3 or 6 inches).

Series SD consisted of nineteen pull-out specimens, all confined with strapping

tape. Again, the parameters that were tested were specimen dimension, rebar size and

bonded length. However, this series differed from Series SC in that it was more focused

on finding the boundary between a pull-through failure and a splitting failure. The

specimens tested in this series had diameters of 4”, 6” and 8” with rebar sizes 4, 6, and 8,

and bonded lengths of 1”, 2” and 3”. Specifically, this series was meant to investigate

how bonded length and the ratio of specimen diameter to rebar size affected the type of

failure observed.

Series SE consisted of 12 pull-out specimens, each 6”x12” with a number 8 rebar

bonded for 3 inches. However, this series of tests used wire spiral embedded in the

specimen as confinement. This series was intended to determine whether a yielding or an

21

elastic confining medium would allow controlled propagation of cracking during testing.

This control over the propagation of cracking was desirable because it would allow a

more complete series of images, with a larger number of crack dimensions, to be

produced in the x-ray tomography portion of this project. Both high and low strength

steel wires were used in this series, with a wide range of wire sizes. Two of each

specimen type were constructed and tested to determine the repeatability of the test

results.

Series SF consisted of 15 pull-out specimens, many of which were similar to

those in Series SE. Nine of the specimens contained wire confinement and were intended

to produce slower and more controllable cracking patterns during testing, as with Series

SE. Three specimens had only 1 inch of bonded length and were intended to fail by

crushing the concrete in front of the rebar lugs. Three specimens had no confinement but

were made with polypropylene fiber reinforcement embedded in the cement matrix.

These were included to see if these types of fibers would slow the cracking during testing

so that images could be taken between loading stages.

Series SG consisted of 2 uniform tension specimens as discussed in Section 3.1.2.

Overall, seven series of tests, consisting of seventy-six specimens, were

conducted over the course of this study. The effects on the bond behavior of parameters

such as dimension, bar size, bonded length and confinement type, were explored in the

six series of pull-out tests. The uniform tension tests were intended to approximately

simulate the tension region in a flexural member.

22

CHAPTER 4 - MATERIAL TEST RESULTS

4.1 Introduction

Chapter 4 details the material properties tests conducted on the concrete used for

the test specimens in this study. Materials testing was conducted both for the purpose of

investigating bond behavior and for supporting the finite element analysis portion of the

project. Material properties tests included compression tests, split-cylinder tension tests,

modulus of rupture tests, elastic modulus tests and fracture energy tests for concrete, as

well as simple strength tests on strapping tape and reinforcing wire. In general, the tests

were performed in accordance with the standards set by the America Society for Testing

and Materials (ASTM), or RILEM (fracture energy test only). A few simple strength

tests were conducted on tape and wire and did not follow any standard test

methodologies.

Series SA was a preliminary set of tests conducted on specimens cast before the

main test program started and no material properties were available for them. Also, since

the modulus of rupture and fracture energy tests were a complex series of tests in

themselves and were cast from separate concrete batches, standard material properties

pertaining to those concrete batches are presented. A preliminary set of specimens was

created for the fracture energy tests in order to set up and evaluate the effectiveness of the

fracture energy testing apparatus. No material tests were conducted on the preliminary

series of fracture energy tests, as these were initially intended only to evaluate the test

apparatus. Values for Series SB and SC are combined because both series were cast

using the same batch of concrete.

23

4.2 Compressive Strength

Compression tests were conducted in accordance with ASTM C 39 (2002). This

test method consists of applying a compressive axial load to a concrete cylinder (6-inch

diameter and 12-inch height for these particular tests) until failure. The compressive

strength of the concrete is calculated by dividing the final failure load of the concrete by

the cross-sectional area of the specimen, as shown in Equation 4.1.

cc A

Pf =' (4.1)

where P is the maximum applied load and Ac is the cross-sectional area of the cylinder.

For most specimens, the mix design was the same and is given in Table 4.1. The

exceptions were Series SA (mix design not recorded) and the preliminary Fracture

Energy tests, which used the quantities given in Table 4.1, but used 7/8” crushed

aggregate in place of 3/4" rounded river aggregate. The substitution was made because

of a temporary shortage of the correct material.

Table 4.1: Concrete Mix Design

Component Weight (lbs/yd3) % of Mix (by weight) Cement (Type I) 517 12.63

Water 257 6.28 Gravel (3/4 in.) 1800 43.97 Building Sand 1520 37.13

Table 4.2 details the compressive strengths for the concrete used in each test

series. Two compression tests were conducted for each series, except for Series SA,

Series SD, and the Modulus of Rupture series. Series SA consisted of existing specimens

for which control specimens were not available. Three compression tests were conducted

for Series SD. Only one compression test was conducted for the modulus of rupture

series due to miscalculations during the concrete batch preparations.

24

Table 4.2: Compression Test Results

Test Series Test Type f’c (psi)

Series SA Pull-Out n/a Series SB and SC Pull-Out 6143.4

Series SD Pull-Out 6893.2 Series SE Pull-Out 6787.1 Series SF Pull-Out 5642.6 Series SG Uniform Tension 7929.5

Modulus of Rupture Material 5227.4 Fracture Energy (Type A/B) Material 6971.0

Fracture Energy (Type C) Material 5722.0 Average 6414.5

4.3 Tensile Strength

Two types of tests were conducted in order to gain an understanding of the tensile

strength of the concrete used in the tests on embedded bars. The split-cylinder tension

test was conducted on every test series except Series SA, while the Modulus of Rupture

test was an independent test series, albeit closely correlated with Series SD.

4.3.1 Split-Cylinder Tension Test

The split-cylinder tension tests were performed in accordance with ASTM C 496.

This test consists of applying a compressive load along the length of a cylindrical

concrete specimen until failure. This compressive load induces tensile stress within the

cylinder, causing it to fail in tension over the diameter of the cylinder, as illustrated in

Figure 4.1.

25

Figure 4.1: Failure mode in a split tension specimen.

The tensile strength, ft, is then calculated using Equation 4.2.

LDPft π

2= (4.2)

where P is the maximum applied load, L is the length of the specimen and D is the

diameter of the specimen.

Table 4.3 details the split cylinder tensile strengths for the concrete used in each

test series. In design, the split cylinder strength is often taken as cf '6 ⋅ . Values of

ct ff ' obtained from the tests are also given in Table 4.3, the average being 7.35.

26

Table 4.3: Split-Cylinder Tension Test Results

Test Series Test Type ft (psi) ft/√(f’c)

Series SA Pull-Out n/a n/a Series SB and SC Pull-Out 567.7 7.2

Series SD Pull-Out 653.4 7.9 Series SE Pull-Out 591.5 7.2 Series SF Pull-Out 528.9 7.0 Series SG Uniform Tension 626.0 7.0

Modulus of Rupture Material 624.2 8.6 Fracture Energy (Types A/B) Material 647.2 7.8

Fracture Energy (Type C) Material 526.5 7.0 Average 595.7 7.35

4.3.2 Modulus of Rupture Test

The modulus of rupture tests were conducted in accordance with ASTM C 78.

This test consists of applying point loads at the third-points along the length of a

6”x6”x21” concrete beam with an 18” span length. The failure load is recorded and the

modulus of rupture of the concrete is calculated by Equation 4.3.

2dbPLfr

r = (4.3)

where fr is the modulus of rupture of the concrete, P is the maximum applied load, L is

the length of the beam, br is the width of the beam and d is the depth of the beam.

Table 4.4 shows the failure load and modulus of rupture for the two specimens

tested in this series. In design, the modulus of rupture is often taken as cf '5.7 ⋅ .

Values of cr ff ' obtained from the tests are given in Table 4.4. The average value of

10.35 is significantly higher than the code-advocated 7.5.

Table 4.4: Modulus of Rupture Test Results

Test Specimen fr (psi) fr/ √f’c

Rupture-1 741.7 10.3 Rupture-2 750.0 10.4 Average 745.9 10.35

27

4.4 Elastic Modulus

The elastic modulus tests were performed in general accordance with ASTM C

469. This test consists of applying a compressive axial load to a concrete cylinder (6-

inch diameter and 12-inch height for these particular tests) up to approximately 40% of

the compressive strength of the concrete. ASTM specifies only to record data when the

longitudinal strain reaches 50 micro-strain and when the load reaches 40% of the

compressive strength, after which it is possible to calculate the chord modulus of

elasticity. In this case, a data acquisition system was used to collect data regularly until

loading was stopped at 40% of the compressive strength. The slope of the resulting

stress-strain curve was taken as the modulus of elasticity, Ec, of the concrete. This test

requires a compressometer, which is a device that attaches to a concrete cylinder and

allows for the measurement of axial displacement in the specimen (Figure 4.2).

28

Figure 4.2: Compressometer for Elastic Modulus Test

Table 4.5 shows the results of the elastic modulus tests conducted in this project.

Due to the delicacy and time requirements of this test, many of the test series in this study

do not have valid data for the modulus of elasticity. Series SE was the first test series to

produce adequate elasticity data. In design, the modulus of elasticity (Young’s

Modulus) is often taken as cf '57000 ⋅ . Values of cc fE ' obtained from the tests are

also given in Table 4.4. Keep in mind that there is often have quite a bit of scatter

associated with experimental values for Ec.

Table 4.5: Elastic Modulus Test Results

Test Series Test Type Ec (ksi) Ec√f’c Series SA n/a n/a n/a

Series SB and SC n/a n/a n/a Series SD n/a n/a n/a Series SE Pull-Out 4910.6 59600 Series SF Pull-Out 4317 57500 Series SG Uniform Tension 5282.8 59300

Modulus of Rupture Material n/a n/a Fracture Energy (Types A/B) Material 5409.0 64800

Fracture Energy (Type C) Material 5315.0 70300 Average 5046.9 62300

A few difficulties were encountered while conducting the elastic modulus tests.

They are associated with the need to measure very small displacements (approximately

0.0001”) with a high level of accuracy. Initially, the modulus of elasticity tests were

conducted using half-inch Duncan Potentiometers, which are contact devices used for

measuring displacement. Because a potentiometer is a contact device, the slider

experiences a small amount of friction, and may stick at the start of any motion.

Consequently, the stress-strain curves for Series SE and the fracture energy elastic

modulus tests were not linear, as expected, but rather wavy. However, fitting a linear

29

trendline to these non-linear data did result in elastic modulus values that compared well

with the value computed using the equation given in ACI 318-02 (ACI, 2002), which is:

cc fE '57000= psi (4.4)

For Series SF and SG, a Linear Voltage Displacement Transducer (LVDT) was

used. The LVDT is not a contact device and provided data that was much more linear.

However, for these tests, the LVDT consistently showed a load offset before recording

any change in displacement, in both the ascending and descending directions. It was

discovered afterwards that a spring used with the LVDT caused this offset. Despite the

load offset, the slopes of the ascending and descending stress-strain data are consistent

and result in essentially identical elastic modulus values.

The values of Ec obtained from the testing agree well with those predicted using

Equation 4.4. The fact that the measured values are all slightly higher than the prediction

of Equation 4.4 is consistent with many other tests using similar local aggregates, which

are particularly stiff and hard. However, the experimental difficulties experienced

suggest that they should not be used for purposes where reliance on great accuracy is

necessary.

4.5 Tape Strength

Bond specimens in Series SC and SD all utilized the same amount of

confinement; four layers of strapping tape applied to the outside of the specimen after

curing. Simple strength tests were conducted on the strapping tape to determine how

much load a layer of tape could hold.

The tape was tested simply by looping it around two smooth metal bars, keeping

one bar fixed and applying a tensile load to the other bar, as illustrated in Figure 4.3.

30

Figure 4.3: Tape Strength Test

The tensile load was applied by attaching a bucket to the lower bar and adding

weights until the tape broke. The bucket and weights were then weighed on a digital

scale to determine the load at which the tape broke. This failure load was approximately

100 pounds. The tape is 1” wide, so a rough estimate of the tape strength is

approximately 50 lbs per inch width.

4.6 Wire Strength

Specimens in Series SE and SF used wire spiral reinforcement rather than tape as

confinement. For some of the analyses presented in Chapter 6, the wire strength was

vital for determining the confining pressure applied to the specimen. The method used

for determining the strength of the wire was similar to the Tape Strength test. The wire

was wrapped around two bars, as shown in Figure 4.4, and tension was applied until the

wire broke. In this test, the bars were attached to a 120 kip Baldwin universal testing

31

machine and the load was recorded using Labview software on an HP data acquisition

system.

Figure 4.4: Wire Strength Test

Table 4.6 gives the diameters, cross-sectional areas and peak strengths of the five

types of wires tested. Two tests were conducted for each wire type. The three wire types

with the smallest diameters were high-strength solid steel wires, while the two with larger

diameters were low-strength solid steel wire.

Table 4.6: Wire Strengths

Wire Diameter (in)

Wire Area (in2)

Average Ultimate Strength (ksi)

0.026 0.0005 370 0.041 0.0013 328 0.059 0.0027 354 0.074 0.0043 83 0.125 0.0123 84

32

4.7 Fracture Energy

4.7.1 Introduction

The research presented here was part of a larger research effort that included the

use of nonlinear finite element analysis to predict the behavior of bond in reinforced

concrete specimens. In order for this technique to be effective, all the material models

used must simulate accurately the real behavior. The finite element analysis program

DIANA was used for that portion of the project. To represent the concrete it uses a

smeared-crack model, which requires the user the input several material properties,

including tensile strength, elastic modulus and fracture energy. This section details the

test methods used to obtain the fracture energy of the concrete used in the embedded bar

specimens. Because fracture of concrete is a brittle event, the test is usually conducted in

a special test frame equipped with a high-speed, closed-loop servo-controlled system. No

such frame was available in the University of Washington laboratory. Thus, the test

specimen geometry was modified with counterweights (Section 4.7.3), thereby allowing a

conventional non-servo-controlled test machine to be used.

4.7.2 Specimens

The important variables considered in the selection of fracture energy specimens

were size, shape and concrete material properties. In this study, three series of tests were

conducted, with the intention of exploring the effects of geometry and aggregate shape.

An illustration of a typical fracture energy specimen is shown in Figure 4.5 while the

dimensions of the three specimen types are listed in Table 4.7. The specimen name

consists of the letters “FR” (for fracture) and two digits, which represent the width and

depth (in inches) of the throat region. For example, specimen FR-63 has a throat that is

6” wide and 3” deep.

33

Figure 4.5: Fracture Energy Specimen Diagram

Table 4.7: Fracture Energy Specimen Dimensions

Specimen Type Length (in) Span (in) Depth (in) Width (in) Notch Depth (in) FR-42 21 18 3 4 1 FR-63 21 18 4.5 6 1.5 FR-33 21 18 6 3 3

RILEM (1985) recommends test specimens of several different sizes depending

on the aggregate size. They are not all geometrically similar, and have span-to-total-

depth ratios between 4 and 8, with notch depths approximately half the beam depth. The

choice of dimensions for the specimens used in this study was influenced by the desire to

use existing steel beam molds and the need for specimens to fit existing testing

equipment. The span-to-depth ratios varied between 3 and 6, and therefore lay within

the range proposed by RILEM. Specimen Types FR-42 and FR-63 have notches that are

1/3 the beam depth as opposed to the 1/2 ratio proposed by RILEM, however, the cross-

sectional area of the fracture regions of the specimens are within the recommended range

34

(8-18 square inches, compared to RILEM’s specimens, which range from 7.8-62 square

inches).

In order to complete these tests as quickly and efficiently as possible, existing

beam molds were used for the casting of the concrete specimens. The existing molds are

for beams with a length of 21 inches, a width of 6 inches and depth of 6 inches. These

molds were modified using plywood blockouts to create the three specimen sizes used in

the fracture energy tests.

Specimen Types FR-42 and FR-63 were designed for the purpose of investigating

any possible size effect. All dimensions of Specimen Type FR-63 are 1.5 times those of

Type FR-42, except for length and span, which are fixed due to concrete molds and test

setup. Type FR-33 was designed to investigate the difference in notch depth-to-beam

depth ratio (1/2 vs. 1/3). The cross-sectional areas of the throats of Types FR-42 and FR-

33 were designed to be similar (8 in2 vs. 9 in2) in order to study the effect of the aspect

ration of the throat region.

Due to test machine availability and other scheduling limitations, testing did not

begin until 54 days after casting for specimens type A and B, whereas testing for

specimen type C began 41 days after casting. In the analysis of the data the strengths at

the times of testing were used.

4.7.3 Counter-Weight System

To enable the use of an open-loop testing machine, the specimens were modified

to account for the brittle nature of the test. The specimens were supported, as prescribed

by RILEM, by two supports; a roller that was free to rotate about an axis and a pivot that

was free to rotate about any axis. However, if the specimen were to be tested exactly as

prescribed, without a high-speed, closed-loop servo-controlled testing machine, the

specimen would fail suddenly as soon as cracking occurred, because of the self-weight of

35

the specimen. To counteract this behavior, counterweights were applied to the ends of

the beam, effectively creating a small negative moment at the midpoint of the beam.

Because of this negative moment, the beam would resist collapsing under the applied

load, even when completely cracked. Figure 4.6 shows a diagram of the counter-weights

applied to a specimen, along with a bending moment diagram showing the negative

moment at the crack location. The moment at the center of the beam, and the magnitude

of counterweight required, was pre-calculated to produce equalizing force at midspan

equal to 1/200 of the peak load experienced by the specimen during testing. This residual

load was then accounted for in the analysis of the test data.

Figure 4.6: Beam Diagram with Counter-Weights and Bending Moment Diagram

4.7.4 Construction

The beams were made in standard ASTM 6”x6”x21” steel molds, into which

plywood blockouts were inserted to achieve the desired dimensions. The plywood was

sealed to prevent moisture absorption. Forms were removed after a few days. At all times

prior to testing, the specimens were stored at room temperature in sealed plastic bags that

contained moist towels.

To form the notch at mid-span, RILEM recommends saw-cutting but allows

casting. Casting was chosen here because of the potential risk of premature cracking

during saw-cutting and handling. In order to prevent shrinkage cracking during curing,

36

the notch was created using a flexible form composed of a 1/4 inch thick piece of foam,

sandwiched inside a folded piece of sheet metal and wrapped in plastic wrap. The root of

the notch was formed by foam covered by plastic wrap protruding from between the

metal plates; this produced a rounded end to the notch and prevented stress cracks from

forming during the curing process. Notch widths ranged from 1/4 – 3/8 inch (6 – 9 mm).

After the concrete was poured into the forms, plastic wrap was placed over the

forms until the concrete had set. Once set, the forms were placed within two plastic bags

along with wet towels, to prevent moisture loss. After a few days, the specimens were

removed from the steel molds and returned to the plastic bags until the day of testing,

again with wet towels to prevent moisture loss. The specimens were cured at room

temperature.

4.7.5 Test Set-Up

The laboratory apparatus used for the fracture energy tests was adapted from a

standard center-point loading flexural strength test setup (ASTM C293) and is illustrated

in Figure 4.7.

Figure 4.7: Center-Point Loading Apparatus for Flexural Testing (ASTM C293)

37

The specimen rested notch downwards on two simple supports of which one was

a roller and the other was a ball. The load was applied to a single roller at mid-span via a

concentrated load at its mid-width. This arrangement was adopted to avoid introducing

torsion into the specimen. Plywood blocking was applied to the interior edges of the

rotating supports so that they could rotate outwards (i.e. away from the center of the

specimen), but not rotate inwards. This ensures that the load remains in the center of the

specimen by restricting rigid body translation.

After setting the specimen on the supports, concrete blocks were attached to the

ends of the specimen to act as counterweights. The blocks were attached by thin steel

sheets anchored at the top of both the specimen and the counterweights with ¼ inch

concrete anchors. Steel weights were placed on top of the concrete weights when

additional load was necessary. The purpose of the counterweights was to produce a small,

negative mid-span moment under dead load. With the counterweights, the specimen

remained in contact with the loading head even after cracking had occurred, thereby

allowing the descending branch of the load –deflection curve to be followed.

The load was applied to the specimen using a 300 kip Baldwin testing machine.

The load was transferred from the test machine to the specimen through a load train

composed of threaded steel bars and a 3 kip load cell. The load cell was necessary to

measure the load with sufficient accuracy. For the preliminary specimens with angular

aggregate, a ¾ inch diameter threaded rod was attached to the test machine using two ¾

inch plates and several bolts, and the load cell was attached to the other end of the bar.

Another short ¾ inch diameter bar with a rounded tip was attached to the bottom of the

load cell for contacting the loading roller.

In any test machine, but especially an open loop one, a flexible load train will lead

to loss of some data on the descending part of the load-deflection curve, as the system

38

jumps to a position of stable equilibrium. A jump was observed in the first specimens to

be tested (FR-42-R1 and FR-42-R-2). Consequently, in order to stiffen up the load train

for subsequent specimens, the threaded rod and plates were increased to 2” diameter and

3” thick respectively. This change reduced, but did not eliminate the jump. Most of the

remaining flexibility in the load train was found to lie in the load cell. There was little

that could be done about this remaining flexibility because sensitivity and stiffness are

mutually exclusive characteristics of load cells.

4.7.6 Instrumentation

The instrumentation used for these tests consisted of a load cell, displacement

measurement gauges and a data collection system.

The load cell used in these series of tests was a 3 kip S-type load cell made by

Interface MFG, shown in Figure 4.8. It has screw thread on each end, used for attaching

it to the load train and transferring the load to the specimen. The geometry and

sensitivity of this load cell makes it inherently quite flexible.

Figure 4.8: S-Type Load Cell

39

Four Duncan potentiometers were used to measure the displacement of the

specimen during testing. The potentiometers were placed under the specimen and

attached to either a wood or aluminum block for stability. The potentiometers were

placed such that there were two on each side of the notch, one near each edge of the

specimen. The potentiometers were located within ½ inch of the notch.

Three different potentiometer blocks were used during this series of tests, each

having the same purpose. The successive changes were made with the goal of improving

accuracy. The first block was a wooden block with holes in which the potentiometers

were glued. The second was similar, but composed of aluminum. The third was an

inverted T-shaped beam, with the potentiometers glued to the sides of the up-turned stem

of the T.

RILEM (1985) suggests the use of a beam-like apparatus for supporting the

displacements sensors. This apparatus is composed of steel or aluminum channel

sections. It is supported on top of the specimen above the supports and extends to the

bottom of the specimen near the notch, where the displacement sensors are located

(locations shown in Figure 4.5). This arrangement is intended to ensure that settlement of

the supports is excluded from the displacement measurements. This apparatus was not

utilized because the deflections expected due to the flexibility of the channel sections

were estimated and deemed to be larger in magnitude than possible settlements of the

supports. Therefore, the potentiometers and potentiometer block were simply placed on

the steel slab on which the simple supports rested.

Two different data collection systems were used during this test series.

Datalogger software running on HP hardware was initially used for Specimen Types FR-

42 and FR-63. Labview software run on National Instruments hardware was then

purchased for use with Specimen Type FR-33. Labview is able to collect data at shorter

40

time intervals than Datalogger, which improved the measurement capabilities of the

system during the rapidly descending portion of the load-displacement curve.

4.7.7 Test Procedure

The following test procedure description details the testing process from the time

that the specimens were removed from curing bags until testing was complete.

On the day of testing, a specimen was removed from the plastic bags and placed

in a tub of water, to prevent drying. The water level almost, but not quite, covered the

specimen. While the specimen sat nearly submersed, two ¼ inch holes were drilled in it,

using a diamond tipped drill bit to prevent vibrations. The holes were drilled in the top

(face opposite the notch) along the centerline of the specimen, approximately 1.5 inches

from each end. These holes allow the counterweights to be attached just prior to testing.

Once these holes had been drilled, the specimen was turned so that the bottom

face was exposed. At this point the metal support plates were attached, as well as the

contact plates for the displacement potentiometers. The support plates measured

approximately 2 inches wide and extend the entire width of the beam. Specimen Types

FR-42 and FR-63 used 1/16 inch thick aluminum plates while Specimen Type C used ¼

inch thick machined steel plates. These plates were attached to the bottom of the

specimen with l/2 inch layer of hydrostone and were centered approximately 1.5 inches

from each end of the specimen. In order to pour the hydrostone, a dam of clay needed to

be placed around the area where the support plates were located. The dam allowed the

hydrostone to completely contact the support plate. Once the dam was in place and the

hydrostone was poured, the support plates were placed on top of the wet hydrostone and

are held in place by the clay on the sides of the specimen. The support plates were

pressed down until they were in complete contact with the hydrostone. It took the

hydrostone approximately 30 minutes to set. During this time, it was important to keep

41

the rest of the specimen wet, thus the tub of water and a damp towel were placed over

exposed portions of the specimen.

While the hydrostone is setting, the contact plates may be attached. The contact

plates for the displacement gauges were 1/16 inch aluminum plates and were attached the

bottom of the specimen directly alongside to the notch using hot glue.

Once the hydrostone had set and the hot glue had dried, the specimen was

carefully taken from the tub and wrapped in moist towels. The specimen was then taken

to the test machine, where it was set upon the simple supports of the test apparatus. The

support plates were the only portion of the specimen to be in contact with the test rig. It

was important that the simple supports were centered on the support plates and that the

wooden blocks used to prevent rigid body translation were in place. With a pen, a mark

was made on the centerline of the specimen where the load was to be applied. This

ensured that the roller used to transfer the load to the specimen was correctly centered

over the notch. Once the roller was in place, the test rig was carefully maneuvered so

that it was directly beneath the load train attached to the test machine.

It was then necessary to attach the counterweights. This portion of the process

had the potential to damage the specimen if done incorrectly. Blocks were situated to

support the counterweights until they were attached to the specimen. Once the holes in

the counterweight plate and the specimen were lined up, a concrete anchor was installed

to connect them. The type of anchor used in these tests was a ¼ inch plastic sleeve with a

nail in the top. The sleeve was inserted into the hole drilled earlier and the nail was

tapped into place so that the sleeve expanded and anchored into the hole. The nail was

tapped lightly yet firmly to ensure that it adequately anchored into the specimen. The

nail was almost directly on top of the specimen supports, so light tapping caused almost

no stress at the notch, however, care should was still taken not to jar the specimen during

42

this process. Once the counterweights were attached, the counter-weight support blocks

were removed and the specimen was re-checked for alignment on the supports and under

the load train.

When the specimen was in the correct position, the potentiometers were installed.

The potentiometers were positioned in the potentiometer block so that they were

approximately 0.5 inches from the notch and 0.5 inches from the edges of the specimen.

The potentiometer block was slid underneath the specimen, taking care not to disturb the

specimen from its alignment. Once the potentiometers had been properly situated so that

they were touching the contact plates and equidistant from the edges of the specimen, the

potentiometer block was secured to the test rig with hot glue.

From the time the specimen was removed from the tub of water to the time it was

ready to test, it was covered in moist towels and prevented from drying by adding more

water occasionally. This prevented any possible shrinkage cracks from forming in the

notch region.

Once everything was in place, the data acquisition system was checked to ensure

that the load cell and potentiometers were properly functioning. This was done by

pressing on the load cell and lightly depressing the potentiometers. The moist towels

were then removed. The instrumentation was zeroed in this initial configuration to

ensure accurate readings. An initial set of photos of the test specimen and set up were

taken for documentation purposes.

The data acquisition system was set to take at least 20 reading per second per

channel and the test machine was run so that the loading rate was approximately 3 lbs/sec

initially. For specimens as flexible as these, the test machine really imposes a fixed

displacement, rather than load, rate if the controls are left unattended. This allowed the

measurement of the early descending portion of the curve to be measured properly.

43

Once the load had reached its maximum value and began to drop, the loading rate

was reduced in order to further improve data collection in the post-peak region.

However, once the load stopped dropping rapidly and began to level off, the loading rate

was increased so that the number of data points in the end of the data set was not

prohibitively large.

4.7.8 Results

Table 4.8 lists fracture energy values, as well as other material parameters, for the

twelve test specimens included in this study. The first four test specimens listed in Table

4 were originally intended merely to fine-tune and evaluate the test set up to be used in

the subsequent tests, and no material testing was done for these specimens. These

specimens exhibited somewhat different fracture response than the subsequent

specimens, which is attributed to the use of angular crushed aggregate, versus rounded

aggregate, in the concrete mix for these specimens. Thus, fracture energy data for these

specimens is included in Table 4. Following the initial four tests, two specimens with 4”

x 2” throats and two specimens with 6” x 3” throats were tested in close succession.

Approximately three months later, four additional specimens with 3” x 3” throats were

tested.

44

Table 4.8: Fracture Energy Test Results

Specimen b (in) dthroat Ec (ksi) f’c (psi) f’t (psi) σmax (ksi)

GF (lb/in)

FR-42-A-1 4 2 NA NA NA 0.45 0.69 FR-42-A-2 4 2 NA NA NA 0.56 0.49 FR-42-R-1 4 2 5410 697 647 0.73 0.65 FR-42-R-2 4 2 5410 697 647 0.84 0.60

Average 0.65 0.61 FR-63-A-1 6 3 NA NA NA 0.51 0.53 FR-63-A-2 6 3 NA NA NA 0.50 0.41 FR-63-R-1 6 3 5410 697 647 0.59 0.72 FR-63-R-2 6 3 5410 697 647 0.64 0.67

Average 0..56 0.58 FR-33-R-1 3 3 5320 572 527 0.71 0.79 FR-33-R-2 3 3 5320 572 527 0.71 0.67 FR-33-R-3 3 3 5320 572 527 0.53 0.63 FR-33-R-4 3 3 5320 572 527 0.55 0.48

Average 0.63 0.64

4.7.8.1 Fracture-Energy Test Observations

The observed behavior was essentially the same in each fracture test. Prior to

cracking, the deflections were too small to be seen with the naked eye. In order to

facilitate observation of cracking, the sides of the specimen were sprayed lightly with

water, but in no case was a crack observed before the data acquisition system revealed

that the peak load had been passed. The first crack to appear was hairline in thickness,

and occurred without any audible sound. In most specimens a single crack formed but in

specimens FR-42-R-2, FR-63-R-1, and FR-33-R-2 the crack bifurcated into several

branches. Shortly after the crack formed, it propagated up to approximately 0.5” from the

top face of the beam in the span of about 15-20 seconds. Thereafter, its length remained

visibly unchanged until the end of the test. When the load was removed, the specimens

generally remained in one piece until they were moved, at which point they separated

into two pieces.

In general, most of the tests were conducted at a loading rate of approximately

200 lb/min for the initial loading sequence. As the specimen was approaching near

45

cracking, the specimens’ rates of displacement increased dramatically until the specimen

cracked, at which point it proceeded too quickly for the data acquisition system to keep

up. Often, on the unloading portion of the curve after cracking had occurred, gaps

between data points reached up to 0.007 inches, as shown in Figure 4.9. When the load

began to plateau after failure, the data acquisition system caught back up with the test

machine and resumed regular data acquisition. Specimen FR-33-R-4 experienced a

higher than normal loading rate during testing due to a testing error. This caused the test

to proceed very quickly and may have influenced the behavior of the specimen.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.000 0.010 0.020 0.030 0.040 0.050 0.060

Displacement (Inches)

Ben

dign

Str

ess, σ b

(ksi

)

Figure 4.9: Bending Stress vs. Displacement for FR-63-A-2

46

4.7.8.2 Measured Response

Figures 4.10, 4.11 and 4.12 show normalized load versus deflection histories for

all of the test specimens; Table 4.8 lists fracture energy and maximum tensile stress for

each specimen.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040Displacement (Inches)

Ben

ding

Str

ess, σ b

(ksi

)

FR-42-A-1FR-42-A-2FR-42-R-1FR-42-R-2

Figure 4.10: Stress-Displacement Plots for FR-42 Specimens

47

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70


Ben

ding

Str

ess, σ b

(ksi

)FR-63-A-1FR-63-A-2FR-63-R-1FR-63-R-2


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80


Ben

ding

Str

ess, σ b

(ksi

)

FR-33-R-1FR-33-R-2FR-33-R-3FR-33-R-4


48

Prior to reporting the stress-deflection curve, the origin of the curve was shifted

and load data were normalized. First, the value of the “residual load”, i.e. the load

corresponding to the counterweight, was subtracted from all load readings. The values lay

in the range between -1.7 and 8.9 lbs. This correction was slightly different for every

specimen, and was determined by weighing each specimen and the counterweights. If the

computed residual load was negative, the load was not adjusted. Second, a linear

trendline was superimposed on the linear portion of the ascending curve for each

specimen. It was projected backwards to zero load, and that point was used as the new

origin. This procedure was necessary to eliminate any initial non-linearity in the curve,

which was attributed to settling in at the supports and initial stick-slip in the

potentiometers. Finally, the load data were normalized to express load in terms of applied

bending stress, computed using the conventional methods of mechanics of materials. This

facilitates comparison of the data from different tests.

The fracture energy, GF, was computed from the area under the complete load-

deflection curve divided by the cross-sectional throat area. Here the load data were

adjusted for un-balanced self-weight but not normalized. Because for some specimens the

corrected load never dropped to exactly zero, even at deflections of approximately 0.25”,

a definition was needed for the upper limit of deflection to be used in the integration.

This value was set arbitrarily to the displacement at which specimens achieved a strength

loss of 95% from the peak.

4.7.9 Analysis and Discussion of Results

4.7.9.1 Peak load

The nominal peak bending stresses, computed from the peak loads using

principles of mechanics of materials and the throat cross-sections, are shown in Table 4.8

49

for individual specimens and in Table 4.9 for each specimen size (rounded aggregate

only). These are not the true peak stresses, because they ignore the stress concentration

effect of the notch.

FR-42 and FR-33 specimens have throats with similar cross-sectional areas

(Athroat), but different aspect ratios (b/dthroat). As shown in Table 4.9, the average values

of σmax/ft for these two specimen types differ by 0.03 (2.5%) and the average values of GF

differ by 0.018 lb/in (2.8%). This indicates that the strength and fracture energy of the

specimen are largely independent of the aspect ratio.

FR-42 and FR-63 specimens have throats with similar aspect ratios, but different

cross-sectional areas. The average values of σmax/ft for these two specimen types differ

by 0.27 (28%) and the average values of GF differ by 0.095 lb/in (13%). This indicates

that the strength of the specimen (in terms of nominal peak stresses) drops as the cross-

sectional area increases, while the fracture energy increases with cross-sectional area.

The fact that these two parameters show opposite tendencies is surprising and lays their

reliability open to question.

Recall that the term GF, commonly called the fracture energy, is in reality a

fracture energy density, and is the energy required to cause fracture per unit area of

surface. At the simplest level, it might therefore be expected to be a constant material

property, similar to compressive or tension strength. However, Bazant (2002) and others

have argued that GF does in fact vary slightly with area, thereby leading to a “size effect”

that causes large specimens to fail by fracture at lower nominal stresses than do their

smaller counterparts. This finding fuels much of the ongoing debate (e.g. Bazant, Kani,

Collins) over size effects in shear failure. The finding from these tests that GF increases

with area is therefore in disagreement with the preponderance of previous evidence.

50

Table 4.9: Average Fracture Energy Results by Specimen Size (Rounded Aggregate Only)

Throat Dimensions b/dthroat

Athroat (in2) ft (psi) σmax (psi) σmax/ft GF (lb/in) COVGF

4x2 2 8 647 787 1.22 0.625 0.057 6x3 2 18 647 616 0.95 0.720 0.049 3x3 1 9 527 626 1.19 0.643 0.199

4.7.9.2 Fracture energy

Bazant (2002) presents two equations, Equations 4.5 and 4.6, for predicting the

fracture energy of concrete. Equation 4.5 was proposed by Bazant and Equation 4.6 was

recommended by the Comité Euro-International du Béton (C.E.B.).

Bazant: ( ) 30.022.046.0

27.111

051.0'

5.2−

⋅

+⋅

⋅⋅= c

wdfG ac

oF α N/m (4.5)

C.E.B.: ( )7.0

2

10'

265.00469.0

⋅+⋅−⋅= c

aaFf

ddG N/m (4.6)

where αo is an aggregate shape factor (αo = 1 for rounded aggregate, αo = 1.44 for angular

aggregate), f’c is the compressive strength of the concrete (MPa), da is the maximum

aggregate size (mm), and w/c is the water-cement ratio of the concrete. Table 4.10 shows

the results of these equations, converted from N/m to lb/in, compared to each specimen

with rounded aggregate (compressive strength is not available for angular aggregate

specimens).

The fracture energy values for specimens with rounded aggregate range from 0.60

- 0.79 lb/in (the smaller fracture energy value for FR-33-R-4 may be attributed to the

large gaps in the displacement history caused by the high loading rate it experienced

during the test). These values are slightly higher than the expected range of fracture

energy values given in Table 4.10. These higher-than-expected values may be related to

the physical properties of the local aggregate available near the University of

51

Washington, which are particularly stiff and hard. The values predicted for specimens

with rounded aggregate differ from the measured values by an average of 20%.

Table 4.10: Measured vs. Predicted GF

Specimen f’c (psi) Measured GF (lb/in)

Bazant GF (lb/in)

C.E.B. GF (lb/in)

FR-42-R-1 7000 0.65 0.51 0.58 FR-42-R-2 7000 0.60 0.51 0.58 FR-63-R-1 7000 0.72 0.51 0.58 FR-63-R-2 7000 0.67 0.51 0.58 FR-33-R-1 5700 0.79 0.46 0.50 FR-33-R-2 5700 0.67 0.46 0.50 FR-33-R-3 5700 0.63 0.46 0.50 FR-33-R-4 5700 0.48 0.46 0.50

4.7.9.3 Initial stiffness

Difficulties were experienced in obtaining good initial stiffness values. Part of the

problem was caused by the fact that the specimens appeared to twist slightly in the initial

stages of loading. This caused two of the instruments to record a positive displacement

and two to record a negative one. Averaging both pairs did not always produce a linear

curve. Furthermore, the displacements to be measured are so small (about 0.001” at peak

load) that the characteristics of the instruments might affect the results. It is believed that

some of the error was caused by slight friction at the contacts, and consequent initial

sticking in the sliders, in the potentiometers. The effect is confined to the pre-peak range,

since after that the displacements increase, and the instrument resolution becomes less

important.

52

4.7.10 Evaluation of Test Procedures

The tests involved relatively delicate procedures, the details of which may

significantly affect the results, especially if an open-loop test machine is used. The most

important issues are reviewed here.

Counterweights were found to provide a feasible method of controlling the

progression of deformation and cracking. Attaching them presented no particular

problems. They allowed the complete load-displacement curve to be recorded, albeit

with a slight gap in the data collection soon after the peak load.

The technique allowed the test to be taken to quite large displacements (up to

0.125”) under stable conditions. This raised questions over how much of the curve to use

in evaluating GF. It is likely that the large displacement data may in fact be measured

more accurately in an open-loop machine using the counter-weight methods than in a

closed-loop machine without the counter-weights.

The data show that the data gap occurs because the system jumps from an

unstable to a stable equilibrium configuration. The instability is caused by the fact that

the secant unloading stiffness of the specimen is greater in absolute value than the

stiffness of the load train. The latter was dominated in these tests by the flexibility of the

load cell, which is an inevitable consequence of using a sensitive (low-capacity) device.

However, the missing data had little impact on the value of the value of GF obtained from

the data.

Measuring the displacements by placing sensors directly below the specimen,

rather than on an instrumentation rig as recommended by RILEM, did not impose any

perceptible penalties. Non-contact displacement sensors, such as LVDTs, appear

preferable to potentiometers, if accurate measurement of very small displacements is

necessary.

53

Forming, rather than saw-cutting, the notch led to peak load readings that were

similar for nominally identical specimens, implying that any random errors introduced by

the forming procedure are minor.

The GF values were also consistent with published values for similar concretes,

suggesting that testing with an open loop machine is viable and produced reliable results.

Note that the procedure was sufficiently sensitive to detect easily the difference in GF

caused by changing only the angularity of the aggregate in the concrete mix.

54

CHAPTER 5 - TESTS ON EMBEDDED BARS

5.1 Test Set-Up

The test set-up for this study evolved as the study progressed. This section

describes the types of testing equipment and instrumentation used with each series.

5.1.1 Pull-Out Test Set-Up

The testing apparatus for the pull-out tests underwent several changes during the

course of this study. Initially, load was applied by one of the large testing machines in

the lab, as a matter of convenience. Later, as the needs of related portions of this project

became clearer, a smaller and more portable testing apparatus was developed. Also, the

instrumentation changed during the course of this study.

Series A was the first set of tests conducted in this study. At this point in the

study, it was unclear exactly which types of specimens would be tested in the future, so

an existing 300 kip Baldwin testing machine was used, as shown in Figure 5.1. The

Baldwin consists of a loading platform and an upper cross-head, which are linked and

move up or down as needed, and a lower cross-head (between the other two), which is

fixed and provides the resistance necessary to load a specimen in tension or compression.

For this set of tests, a pull-out specimen was placed upside down on top of the upper

cross-head. The rebar protruded through a hole in the upper cross-head and was gripped

by the second cross-head. The specimen was then tested by raising the upper cross-head

and holding the lower cross-head fixed.

55

Figure 5.1: Series SA Test Set-Up

Several precautions were taken in order to ensure that the specimen was in full

contact with the cross-head and would not rock or rotate when loaded. First, a layer of

hydrostone was poured on the top surface of the specimen. This was applied when the

rebar was in a vertical position so that the rebar would protrude normally to the

hydrostone surface. Second, a machined steel plate was placed atop the cross-head so

that the loading surface would be flat. A layer of grease was applied between the

specimen and the plate on the cross-head to minimize the lateral friction and thereby to

prevent unwanted confinement.

The data acquisition system (DAQ) used in this test series was an HP data

acquisition system coupled with a program called Datalogger. These allowed different

types of inputs of be read by the computer and stored in a data file. The digital load

sensor from the Baldwin output data directly to the HP unit. Two Duncan potentiometers

were used to measure the displacement of the rebar relative to the concrete of the

specimen, placed as shown in Figure 5.2. One potentiometer was placed at each end of

56

the specimen. At the front end of the specimen (loaded end), the potentiometer was

glued onto the bar and put in contact with the bottom of the cross-head on which the

specimen rested. At the back (dead) end, concrete was chipped away so that the end of

the rebar was exposed. A potentiometer was then glued to the concrete and put in contact

with the bar. These potentiometers were then attached to the data acquisition system to

record bar displacements.

Figure 5.2: Potentiometer Locations for Series SA

By the time Series B was ready to test, it had become apparent that a mobile test

set-up would be required. Figure 5.3 shows the test apparatus used for Series SB through

SE. The Baldwin was replaced by a center-hole load cell and a center-hole ram, which is

57

powered by a hydraulic hand pump. As shown in Figure 5.3, each component of the test

apparatus was separated by a metal spacer to ensure proper placement and even contact.

Figure 5.3: Mobile Pull-Out Test Apparatus: Picture and Schematic

58

A bar grip, similar to a prestressing strand chuck and consisting of conical wedge

grips and a steel collar, was placed on the end of the rebar so that as the ram extended,

the rebar was placed in tension (see Figure 5.4).

Figure 5.4: Rebar Chuck

The load cell was connected to the data acquisition system in order to record the

load history of the test. This set-up requires the specimen to support itself by resting

upright on its back end, making it difficult to place a potentiometer in that position. For

this reason, only one potentiometer was used for the subsequent pull-out tests. It was

located inside the load cell, about 2 inches from the front end of the specimen, as shown

in Figure 5.3. The potentiometer body was glued onto the rebar and the plunger was put

in contact with the steel plate on which the load cell rests.

A different data acquisition system was used for Series SE and all tests thereafter.

The new system, based on National Instruments hardware and LabView software,

operates slightly differently and more efficiently than the HP system. LabView is able to

take many more readings per second than the HP system, and is also able to take readings

for all sensors simultaneously, as opposed to the HP system which took readings

sequentially. This eliminated the need to adjust for small time lag differences in the data

59

file and allowed for precise readings to be taken during periods of rapid strength loss,

which were exhibited by most of the specimens. Overall, switching data acquisition

systems improved the quality of the data collected from all types of tests, including the

pull-out tests.

5.1.2 Uniform Tension Test Set-Up

The uniform tension tests were only performed at the University of Washington,

so the 300 kip Baldwin test machine was used to apply load to these types specimens.

The load on the specimen was measured using the Baldwin test machine and the

displacements were measured using Duncan potentiometers. The LabView data

acquisition system was used, as described in the previous section.

The uniform tension specimens in Series F each contained five crack initiator

spaced every 4 inches along the specimen, as shown in Figure 3.2. Therefore, ten

potentiometers were used to measure the displacements, with two arranged on opposite

sides of each initiator location, as shown in Figure 5.5.

60

Figure 5.5: Crack Displacement Potentiometer Locations

In order to get as much information as possible from only two specimens, this

series of tests utilized some metal clamps intended to immobilize and preserve the state

of particular cracks at any point in the load history. Figure 5.6 shows the clamps used on

the uniform tension specimens. This allowed some cracks to be preserved as they were in

early stages of the test while others were subjected to the full range of loading. This

procedure provided a range of crack sizes within the same specimen.

61

Figure 5.6: Crack clamps

5.2 Test Procedure

The following section details the test procedure used for testing the various

embedded bar specimens. These procedures include all events from the time the

specimens were removed from the curing room until testing was completed. Unless

otherwise noted, all specimens were tested in the same manner.

5.2.1 Pull-Out Test Procedure

Preparation of the pull-out specimens consisted of leveling the front loading

surface and applying external confinement, such as strapping tape, when required. Once

62

removed from the curing room, the pull-out specimens were placed upon a table with the

rebar extending vertically above the specimen. Shims and a magnetic level were used to

ensure that the rebar was vertical. A strip of duct tape was then placed around the

perimeter of the specimen with about 1/2"-3/4” inches extending above the front surface,

effectively creating a dam around the top of the specimen. Wet hydrostone was then

poured onto the top of the specimen. The hydrostone was mixed so that it had very low

viscosity and was self-leveling. This procedure ensured that the rebar was normal to the

plane of the front loading surface of the specimen.

Once the hydrostone had cured, confinement was added when necessary.

Fiberglass confinement was applied by laying a sheet of fiberglass weave on a table,

applying the adhesive to both the weave and the specimen and rolling the specimen up

with the fiberglass. Tape was applied by either rolling the specimen on a table while

holding constant tension on the roll of tape or by inserting the specimen into a lathe and

applying the tape as the specimen turned. In both cases, the tape was always applied so

that each loop of tape overlapped the previous one, effectively using two layers of tape

once the specimen was completely covered. Specimen SA-0612-06-06-FS-A was

initially tested with the complete fiberglass jacket. However, this first test showed that

the fiberglass was much too strong and would fracture the rebar instead of breaking the

concrete. The fiberglass jackets were subsequently slit to certain degrees as shown in

Table 5.1.

63

Table 5.1: Series 1 Specimen Alterations

Specimen Jacket Slit Split Tension Load (kips)

SA-0612-06-06-FS-A No Slit n/a SA-0612-06-03-AL-A n/a n/a SA-0612-06-06-FG-A Full Slit n/a SA-0612-06-03-FG-A Full Slit n/a SA-0612-06-12-FG-A Full slit, except for ¾” at back end 65 SA-0816-08-16-FG-A Full slit, except 1" at ends and middle 123 SA-1014-10-14-FG-A No Slit 149

For Series SA, the test procedures differed from those used for the rest of the pull-

out specimens, due the test set-up used. Once the fiberglass on Series SA specimens was

dry (about a day), they were ready for testing. Each specimen had a coat of grease

applied to the hydrostone surface and placed atop the top cross-head of the Baldwin test

machine, with the rebar extending downwards through the center of the cross-head

(Figure 5.1). The potentiometers were attached with hot glue and the rebar was secured

in the grips of the lower cross-head. Once the specimen was secure, the load and

displacement sensors were set to zero and load was gradually applied until failure of the

concrete occurred.

Testing for Series SA proceeded in the order as listed in Table 5.1. Once

Specimen SA-0612-06-03-FG-A was tested, it was apparent that due to the strength of

the fiberglass confinement the failure mode of the remaining specimens in the series

would be by fracture of the rebar and not bond. For this reason, the last three specimens

were weakened prior to testing by loading them laterally, in a method similar to a split-

cylinder tension test, to create diametric cracks. Maximum lateral loads applied to the

specimen are given in Table 5.1. The cylinders were then tested for pull-out in the same

way as the previous specimens had been. Specimen SA-1014-10-14-FG-A was not tested

to failure, but rather until the potentiometer at the front end of the specimen indicated a

0.1 inch displacement. Loading was stopped there so that the specimen could be imaged

64

to determine if the small cracks within the specimen could be detected through x-ray

tomography.

All pull-out test series aside from Series A used the mobile test apparatus

described in Section 5.1.1 and shown in Figure 5.3. Once each of the specimens in Series

SB through SE was hydrostoned and had confinement applied (where needed), they were

ready to test. Each specimen was placed on a steel plate resting on the floor of the

structures lab (Figure 5.3). The plate has a hole in its center to allow the specimen to sit

flat with the rebar protruding from the back end. Grease was then applied to the

hydrostone on the front end of the specimen, where the hydrostone had been applied.

Another steel plate with a hole in its center was placed over the rebar and on top of the

hydrostoned surface. The potentiometer was then hot-glued to the rebar above this steel

plate and put in contact with it to measure bar displacement. Once the potentiometer was

secure, the center-hole load cell was placed over the bar and set upon the steel plate

followed by an aluminum spacer plate and the center-hole ram. Finally, two washers and

the chuck were applied, followed by a spring and a C-clamp to make sure the chuck got a

good grip in the early stages of loading. The hydraulic hand-pump was then attached to

the ram and the potentiometer and the load cell were set to zero. Load was gradually

applied via the hand-pump until failure of the specimen or until it became clear that the

specimen would fail by breaking the rebar.

5.2.2 Uniform Tension

Once each uniform tension specimen in Series F had been removed from the

curing room and molds, it was secured in the Baldwin test machine by placing the rebar

protruding from each end into the grips in the upper and lower cross-heads. Once the

specimen was secure, the potentiometers were applied with hot glue. The sensors were

set to zero and the load was gradually applied. When the load had reached a particular

65

value (approximately 27 kips), loading was paused and the clamps were attached to the

cracks that had opened at the lower 3 crack initiators. The bolts on the clamps were

tightened to approximately 45 ft-lbs. This torque had been pre-calculated to cause the

clamp to grip the concrete tightly enough to prevent further opening of the radial cracks.

Loading was resumed after the clamps had been attached and continued until crack sizes

were deemed to be sufficient.

5.3 Bond Test Results

In this section, both the measured data and observations made during the test are

reported. In addition, an analysis of the results follows the data presentation along with

an analysis of the two different types of tests conducted in this study.

5.3.1 Measured Data

The data collected from the pull-out tests consists of load and displacement data

(referring to the distance the rebar pulls out of the concrete cylinder). These data are

presented both as numerical results and as load-displacement curves, which allows most

of the important events (such as splitting, rebar pull-through, rebar yielding, etc.) to be

observed. The numerical results presented include the peak load that specimens

experienced during testing, the displacement at peak load and average bond stress along

the bonded length of the bar at peak load. When possible, the elastic deformation of the

bar at failure and the amount of slip the rebar experienced relative to the concrete are also

presented. However, in cases where the rebar yielded, it was not possible to derive the

latter values because the plastic strain for a given load could not be computed with

sufficient accuracy. Load-displacement curves, which have been corrected for any initial

non-linearity caused by the testing apparatus, are presented in Appendix B. This section

66

includes numerical results for each test series, along with individual stress-strain plots

that exhibit certain interesting characteristics.

Pull-Out Test Data

Series SA (Preliminary)

The results for Series SA reflect the variety of specimen properties present in the

set. Each specimen had some unique combination of dimension, rebar size, bonded

length and confinement type. Table 5.2 shows the numerical data results for Series SA.

Table 5.2: Series SA Test Results

Specimen Peak Load (kips)

Disp @ Peak Load

(in)

Slip @ Peak Load (in)

Ave. Peak Bond Stress

(ksi)

First Major Event

SA-0612-06-06-FS-A 41.1 unknown unknown 2.91 Bar Yielding SA-0612-06-03-AL-A 26.4 0.081 0.041 3.74 Pull-Through SA-0612-06-06-FG-A 40.6 unknown unknown 2.87 Bar Yielding SA-0612-06-03-FG-A 30.6 0.200 unknown 4.32 Bar Yielding SA-0612-06-12-FG-A 12.2 0.039 0.024 0.43 Splitting SA-0816-08-16-FG-A 55.4 0.150 unknown 1.10 Bar Yielding SA-1014-10-14-FG-A 87.9 0.075 unknown 1.60 Bar Yielding

Specimens SA-0612-06-06-FS-A and SA-0612-06-06-FG-A both experienced

problems with the potentiometers used to measure displacement of the rebar, as discussed

in Section 5.3.3. Therefore, the displacement experienced by the rebar when the peak

load was achieved is not known. Also, for five of the specimens, the rebar yielded prior

to failure, preventing calculation of the deformation of the bar and the slip of the bar

relative to the concrete. Load-deflection curves for all specimens are given in Appendix

A

Figure 5.7 is an example of a specimen whose rebar yielded during testing. From

the data, it is possible to distinguish elastic deformation of the bar from bar slip until the

bar begins to yield. After that, because of the design of the specimen, it is not possible to

67

distinguish the plastic deformation of the bar from the bar slip. This plot also illustrates

what happens when the potentiometer reaches its displacement limit. Its stem ceases to

be in contact with the specimen and continues to read the maximum amount of

displacement, even though the actual displacement of the bar continues to increase with

increasing load. This results in a vertical line of data points which only serve to record

what load the specimen experienced.

0

5

10

15

20

25

30

35

40

45

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45


Loa

d (K

ips)

Figure 5.7: Load-Displacement Curve for Specimen SA-0612-06-06-FS-A

Figure 5.8 illustrates a sudden, brittle failure of the specimen. This generally

indicates a splitting fracture, however, there are exceptions (discussed later). The gap in

the recorded data after specimen SA-0612-06-03-FG-A had reached its maximum load

indicates that the displacement of the rebar occurred between readings taken by the DAQ,

further implying that either the rebar fractured (which did not happen in any of the tests)

68

or that the concrete failed suddenly, which happened in this test. This particular

specimen was completely unloaded and then reloaded after the concrete failed, which is

represented on the chart between 0.20 and 0.27 inches of displacement.

0

5

10

15

20

25

30

35

0.00 0.05 0.10 0.15 0.20 0.25 0.30


Loa

d (K

ips)

Figure 5.8: Load-Displacement Curve for Specimen SA-0612-06-03-FG-A

Series SA implies that the maximum bond stress in a reinforced concrete

specimen is higher than suggested by ACI, because the specimens in this series needed

considerable weakening before the concrete failed by splitting or pull-through.

Series SB (Confinement)

Series SB contained specimens that were identical in size, rebar size and bonded

length. Results for this series are summarized in Table 5.3. The distinguishing factor

between the specimens was the type of confinement used for each. Three had no

confinement at all, while the others used varying amounts and types of tape applied to the

69

exterior of the specimen. The similarities between the specimens are apparent in the

results of these pull-out tests. With a few exceptions, these specimens tended to reach a

peak load of approximately 54 kips (+/- 3 kips). The exceptions (SB-0612-08-06-NO-B,

SB-0612-08-06-NO-C, and SB-0612-08-06-TA-F) were all from the same batch of

concrete, which is believed to have had a slightly higher water-cement ratio than the rest

of the concrete used in this series (further discussion in Section 5.3.3) and failed at 41.5

kips (±2.5 kips). As the water-cement ratio of a concrete mix inversely affects the

strength of the concrete, it is not surprising that these three specimens failed at lower

loads than the rest of the series.

Table 5.3: Series SB Test Results


Disp @ Peak Load (in)

Slip @ Peak

Load (in)

Ave. Peak Bond Stress (ksi)

Residual Strength

(kips)

First Major Event

SB-0612-08-06-NO-A 51.1 0.036 0.006 2.71 0.036 Splitting SB-0612-08-06-NO-B 41.9 0.038 0.014 2.22 0.038 Splitting SB-0612-08-06-NO-C 39.4 0.040 0.017 2.09 0.040 Splitting SB-0612-08-06-TA-A 54.1 0.050 0.019 2.87 0.050 Splitting SB-0612-08-06-TA-B 56.4 0.112 unknown 2.99 0.112 Bar Yielding SB-0612-08-06-TA-C 54.1 0.044 0.013 2.87 0.044 Splitting SB-0612-08-06-TA-D 55.6 0.054 0.022 2.95 0.054 Splitting SB-0612-08-06-TA-E 57.2 0.059 unknown 3.03 0.059 Bar Yielding SB-0612-08-06-TA-F 44.1 0.039 0.013 2.34 0.039 Splitting

In Table 5.3, the slip at the front of the bonded region was obtained by subtracting

from the measured displacement the bar elongation and concrete compression calculated

using the specimen geometry. The average bond stress at peak was computed using

Equation 5.1.

bbave Ld

P⋅⋅

=π

τ (5.1)

70

Load Displacement Curve for Specimen SB-0612-08-06-TA-F

0

5

10

15

20

25

30

35

40

45

50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4


Loa

d (k

ips)

Figure 5.9: Load-Displacement Curve for Specimen SB-0612-08-06-TA-A

Regardless of the peak load, these specimens all failed in similar manners. They

deformed nearly linearly with load, at which point either the bar yielded or the concrete

failed by splitting. For the two whose rebar yielded (SB-0612-08-06-TA-B and SB-

0612-08-06-TA-C), the load increased only slightly after yielding before the concrete

finally failed by splitting. In any case, once the concrete split, the load dropped sharply

and the displacement of the bar increased dramatically. The residual strength remaining

in the specimen after failure varied according to the type of confinement. Specimens

with no confinement broke apart and had no residual strength after failure. Specimens

with duct tape confinement had very little residual strength, while specimens with four

layers of fiber-reinforced strapping tape had the most (about 12 kips). Confinement types

are listed in Table 3.2. Figure 5.9 is an example of a typical Series SB pull-out test,

71

showing the linear loading up to failure, at which point dramatic changes in load and

displacement are evident. This figure also shows the residual strength of the specimen

after failure, attributed to the tape confinement.

Series SC (Geometry)

In Series SC, the same confinement was used for each specimen (four layers of

fiber-reinforced strapping tape), but the specimen dimensions, rebar sizes, and bonded

lengths varied. This variety led to a multitude of different results, as summarized in

Table 5.4. Each specimen with an “unknown” displacement entry yielded during testing.

The specimens with “n/a” entries were not tested (see Section 5.3.3 for details).

Table 5.4: Series SC Test Results



Slip @ Peak Load

(in)


(ksi)

First Major Event

SC-0612-06-03-TA-A 36.1 0.212 unknown 5.11 Bar Yielding SC-0612-06-06-TA-A 46.5 0.499 unknown 3.29 Bar Yielding SC-0612-08-03-TA-A 46.3 0.049 0.020 4.91 Splitting SC-0612-08-06-TA-A 41.4 0.035 0.011 2.20 Splitting SC-0816-06-03-TA-A 41.1 0.215 unknown 5.82 Bar Yielding SC-0816-06-06-TA-A 45.0 0.271 unknown 3.19 Bar Yielding SC-0816-08-03-TA-A 50.5 0.081 0.042 5.36 Splitting SC-0816-08-06-TA-A 63.7 0.070 0.023 3.38 Splitting SC-1020-06-03-TA-A 36.9 0.392 unknown 5.22 Bar Yielding SC-1020-06-06-TA-A n/a n/a n/a n/a n/a SC-1020-08-03-TA-A 56.7 0.150 unknown 6.01 Bar Yielding SC-1020-08-06-TA-A n/a n/a n/a n/a n/a

No single specimen in this series exhibits “typical” behavior for this series.

Individual load-displacement curves are presented in Appendix A.

Series SD (Geometry)

Series SD also contained specimens with a variety of dimensions, rebar size, and

bonded length while keeping the confinement type the same. However, for this series

72

smaller specimens were used along with smaller bonded lengths, which avoided many of

the problems encountered in Series SC. Still, seven of the specimens yielded prior to

failure, which prevented calculation of rebar slip relative to the concrete. Table 5.5

contains the numerical results for Series SD. Individual load-displacement curves are

presented in Appendix A.

Overall, the Series SD specimens had similar failure types. The majority of the

specimens failed by splitting, but two failed by pull-through without splitting (specimens

SD-0816-06-01-TA-A and SD-0816-08-01-TA-A). Each of the pull-through failures had

only 1 inch of bonded length. Figure 5.10 shows an example of one of the pull-through

failures. Instead of the sudden jump present in the data of a splitting failure, the pull-

through failure data shows a gradual reduction of the load as the rebar displacement (and

presumably the slip) is increased.

Table 5.5: Series SD Test Results


Disp @ Peak Load

(in)

Slip @ Peak Load

(in)


(ksi)

First Major Event

SD-0612-08-03-TA-A 34.1 0.041 0.020 3.62 Splitting SD-0612-08-03-TA-B 35.2 0.040 0.018 3.73 Splitting SD-0612-08-03-TA-C 45.4 0.050 0.022 4.81 Splitting SD-0612-08-03-TA-D 38.0 0.048 0.025 4.03 Splitting SD-0408-06-01-TA-A 16.5 0.036 0.023 7.00 Splitting SD-0408-06-02-TA-A 23.4 0.034 0.015 4.97 Splitting SD-0408-06-03-TA-A 27.3 0.036 0.015 3.87 Splitting SD-0612-06-01-TA-A 14.8 0.056 0.040 6.27 Splitting SD-0612-06-02-TA-A 23.1 0.065 0.041 4.90 Splitting SD-0612-06-03-TA-A 30.5 0.103 unknown 4.31 Bar Yielding SD-0816-06-01-TA-A 16.2 0.063 0.041 6.86 Pull-Through SD-0816-06-02-TA-A 32.2 0.139 unknown 6.83 Bar Yielding SD-0816-06-03-TA-A 43.2 0.478 unknown 6.11 Bar Yielding SD-0408-04-01-TA-A 10.7 0.057 0.040 6.81 Splitting SD-0408-04-02-TA-A 19.0 0.193 unknown 6.05 Bar Yielding SD-0408-04-03-TA-A 20.4 0.067 unknown 4.33 Splitting SD-0816-08-01-TA-A 22.1 0.065 0.047 7.05 Pull-Through SD-0816-08-02-TA-A 33.4 0.003 unknown 5.32 Splitting SD-0816-08-03-TA-A 60.1 0.164 unknown 6.38 Bar Yielding

73

0

5

10

15

20

25

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45


Loa

d (K

ips)

Figure 5.10: Load-Displacement Curve for Specimen SD-0816-06-01-TA-A

The rest of the specimens failed by splitting and exhibited characteristics similar

to those in Series SB. They deformed somewhat linearly with load, at which point the

concrete split, with or without the bar yielding. Figure 5.11 illustrates a typical Series SD

splitting failure.

74

0

5

10

15

20

25

30

35

40

45

50

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70


Loa

d (K

ips)

Figure 5.11: Load-Displacement Curve for Specimen SD-0612-08-03-TA-C

Series SE (Wire Confinement)

Series SE used a different type of confinement than the previous series. This was

due to the fact that the tape confinement did not arrest the crack development enough to

allow imaging of the cracks at different stages. Therefore, Series SE utilized wire spiral

reinforcement embedded within the concrete as a confining medium with the goal of

generating specimens with finer cracks for use in the parallel x-ray tomography study.

Other than the amount of confinement, each of the Series SE specimens was identical in

dimension, rebar size, and bonded length. Table 5.6 contains the numerical results for

this series.

75

Table 5.6: Series SE Test Results



Slip @ Peak Load (in)


(ksi)

Residual Strength

(kips)

First Major Event

SE-0612-08-03-W26-A 38.0 0.040 0.017 4.03 6.9 Splitting SE-0612-08-03-W26-B 36.3 0.036 0.014 3.85 7.1 Splitting SE-0612-08-03-W41-A 36.3 0.033 0.011 3.85 6.9 Splitting SE-0612-08-03-W41-B 34.8 0.037 0.015 3.69 15.6 Splitting SE-0612-08-03-W59-A 36.2 0.041 0.018 3.84 15.6 Splitting SE-0612-08-03-W59-B 34.8 0.035 0.014 3.70 20.3 Splitting SE-0612-08-03-W74-A 47.3 0.048 0.019 5.02 18.2 Splitting SE-0612-08-03-W74-B n/a n/a n/a n/a n/a n/a

SE-0612-08-03-W125-A 43.1 0.044 0.018 4.57 22.1 Splitting SE-0612-08-03-W125-B 38.6 0.050 0.026 4.10 unknown Splitting

SE-0612-08-03-WDBL-A 40.6 0.053 0.028 4.31 27.4 Splitting SE-0612-08-03-WDBL-B 45.4 0.057 0.029 4.82 unknown Splitting

All the specimens reached similar peak loads at similar rebar displacement levels.

The displacement for specimen SE-0612-08-03-W74-A seems particularly large, which

may have been due to a potentiometer malfunction. Like Series SB and SD, specimens in

Series SE deformed nearly linearly with load up to a peak load, at which point the

concrete split. None of the rebars in this series yielded. However, what distinguishes this

series are the residual strengths of the specimens after failure, measured at 0.2 inches of

displacement. Figure 5.12 and Figure 5.13 illustrate the effect of the confinement on the

residual. Figure 5.12 shows a stress-strain curve for a specimen with the smallest wire

used for confinement (0.026” diameter). This specimen acted like those in previous series

that were confined only with tape. Figure 5.13 shows a load-deflection curve for the

specimen with the heaviest confinement (one 0.125” diameter wire and one 0.074”

diameter wire). For this specimen, the concrete cylinder split at the peak load; however,

this was followed by gradual strength loss as the cracks widened.

76

0

5

10

15

20

25

30

35

40

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70


Loa

d (K

ips)

Figure 5.12: Load-Displacement Curve for Specimen SE-0612-08-03-W26-A

0

5

10

15

20

25

30

35

40

45

0.00 0.10 0.20 0.30 0.40 0.50 0.60


Loa

d (K

ips)

Figure 5.13: Load-Displacement Curve for Specimen SE-0612-08-03-WDBL-A

77

Series SF (Confinement)

Series SF used either wire confinement, as in Series SE, or no confinement at all.

As with Series SE, the goal was to create fine cracks by controlling their propagation.

Each of the specimens in this series is identical in dimension and rebar size. Three

different confinement ratios were used for nine of the specimens. Three specimens had

only 1 inch of bonded length and three contained polypropylene fibers (FI) embedded in

the concrete matrix in order to arrest crack development (approximately 3 lb of fiber per

cubic yard of concrete). Table 5.7 contains the numerical results for this series. Five

types of specimens were made, each with three copies made of each type (A, B, and C).

Table 5.7: Series SF Test Results



Slip @ Peak Load

(in)

Ave. Peak Bond Stress (ksi)

Residual Strength

(kips)

First Major Event

SF-0612-08-03-WDBL-A 30.4 0.057 0.038 3.23 20 Splitting SF-0612-08-03-WDBL-B 31.2 0.062 0.042 3.31 22 Splitting SF-0612-08-03-WDBL-C 34.0 0.043 0.021 3.61 22 Splitting SF-0612-08-03-W74-A n/a n/a n/a n/a n/a n/a SF-0612-08-03-W74-B 30.9 0.063 0.043 3.28 9 Splitting SF-0612-08-03-W74-C 31.0 0.039 0.019 3.29 10 Splitting SF-0612-08-03-W59-A 25.8 0.026 0.009 2.73 11 Splitting SF-0612-08-03-W59-B n/a n/a n/a n/a n/a n/a SF-0612-08-03-W59-C 30.7 0.042 0.022 3.26 15 Splitting SF-0612-08-01-NO-A 12.7 0.050 0.041 4.05 2 Splitting SF-0612-08-01-NO-B 12.8 0.063 0.054 4.06 3 Splitting SF-0612-08-01-NO-C 15.6 0.055 0.045 4.96 3 Splitting SF-0612-08-03-FI-A 25.5 0.049 0.033 2.71 3 Splitting SF-0612-08-03-FI-B 31.0 0.050 0.030 3.29 4 Splitting SF-0612-08-03-FI-C 32.1 0.044 0.024 3.40 3 Splitting

Series SF was tested in three stages. First, one specimen (the A specimen) of

each type was tested at the University of Washington in order to verify the expected

behavior. The remaining specimens were taken to Texas (Sprague, 2006) to image for

the x-ray tomography portion of this project. In Texas, a second specimen of each type

78

(the C specimen) was tested and imaged, with the remaining specimen of each type

available in case of mishap. Fortunately, each of the C-specimens was successfully

imaged without incident. Once the imaging was completed, the remaining specimens

(the B specimens) were tested, without imaging, in order to obtain another data set for

analysis.

Like Series SB, SD, and SE, specimens in Series SF deformed somewhat linearly

with load, at which point the concrete split. None of the rebars in this series yielded.

This series was the most consistent series in the study in terms of repeatability of data.

Again, the residual strength left in the specimens increased in proportion to the amount of

confining wire embedded in the concrete. The specimens with 1 inch of bonded length

were intended to fail by pure pull-through (i.e. only crushing of the concrete in front of

the lugs and no splitting), as had been observed in other specimens with 1” bonded

lengths (i.e. Series SD). However, each of these failed with a slight radial crack (in the r-

z plane) coinciding with crushing of the concrete lugs. The polypropylene fibers did not

arrest crack development as much as had been hoped. Rather, the specimens split quite

suddenly and dramatically, though they did not fall apart after failure as other specimens

without confinement had done. The fibers kept the large sections of concrete together,

but did not serve to slow the propagation of the cracks at all.

Uniform Tension Test Data

These two specimens were tested in very similar manners. The specimens were

mounted into the 300 kip Baldwin universal testing machine and tension load was

applied. After about 10 kips of applied load, both specimens exhibited cracking over all

five of the embedded crack initiators. Unfortunately, the potentiometers applied to

measure crack growth did not function as expected, so those data are not available.

However, load data was obtained. Loading was paused at the yield plateau of the rebar

79

(approximately 26-27 kips) to remove the potentiometers from the lower three cracks and

install the clamps discussed in Section 5.1.2. The load was then further increased until

crack sizes were deemed large enough to be used by Sprague (2006) in his x-ray

tomography portion of the project.

After testing, one of the specimens, SG-0424-06-24-NO-A, was injected with

UV-sensitive epoxy and cut in half along its axis, as shown in Figure 5.14, to reveal the

crack pattern. The remainder of the images are presented in Appendix B. These cracks

clearly show the radial cracks caused by the crack initiators, as well as some conical

cracks near the radial ones, implying that the specimen may have been developing a pull-

out cone, as discussed by Goto (1971).

Figure 5.14: Uniform Tension Specimen Crack Patterns

80

5.3.2 Observations

Pull-Out Tests

In general, all of the pull-out specimens behaved similarly. As the initial few kips

of load was applied to the specimen, the test apparatus would settle. This settlement

consisted of the wedge grips slipping slightly before finding a grip on the rebar and the

metal plate compressing the grease and hydrostone on top of the specimen. After this

settlement, the loading sequence was standard for each specimen until the first major

event (FME) occurred (the first major event consists of either splitting, pull-through,

yielding, etc.). It was observed that the load tended to oscillate, rising when the hand

pump was stroked and falling a bit as the ram and pump lost a little pressure. This was

normal throughout the tests which used the mobile testing apparatus. The Baldwin

testing machine exerted continuous loading and did not exhibit this behavior.

In most cases, the specimens failed by splitting, at which time a popping noise

could be heard as the cracks opened up. If the concrete was confined, then the specimen

retained some residual bond strength and its grip on the bar. Specimens that were not

confined broke immediately into several pieces in dramatic manner.

Uniform Tension Tests

The uniform tension specimens were intentionally not loaded to failure because

they were designed to display the crack pattern expected near midspan of a beam. It was

observed that the cracks over the crack initiators opened simultaneously and not

sequentially from the center out, as had been expected. Once the clamps were applied,

the cracks over which they spanned did not open further. However, smaller cracks did

open between clamps, which produced a useful range of cracks sizes in one specimen.

81

5.3.3 Errors and Complications

This section describes the observations made during the testing process. These

observations may or may not be recorded in or supported by the recorded data, but were

observations made by the researchers during the time of testing.

Pull-Out Test

Series SA (Preliminary)

The observations in this test series are indicative of the issues inherent in

conducting tests for the first time. Two specimens (SA-0612-06-06-FS-A and SA-0612-

06-06-FG-A) experienced issues with the potentiometers used to measure the rebar

displacement at the front end of the specimen. The potentiometers used in this series

were ½” potentiometers and the displacements twice exceeded the limits of the device.

This resulted in a loss of displacement data after a particular point in the load histories of

these two specimens. Another issue that arose was in regards to the method used to level

the tops of the specimens. Apparently the rebar was not normal to the plane of the front

loading surface of the specimens. During the test of specimen SA-0612-06-12-FG-A it

was observed that, although the specimen was resting flat on the top of the test machine

cross-head, the rebar extended downward at an angle. When the rebar was gripped by the

lower crosshead and tension applied, the rebar straightened. This must have forced the

specimen to take the load only on one side of the loading surface. This was apparent in

the data, because while the cracks were growing very wide, the displacement measured

was not very large. After the test, it was clear that the rebar had remained bonded to one

half of the specimen while separating from the other half and allowing it to crack and

move away. This also allowed the potentiometer to read very small displacements while

the crack was very large.

82

When Specimen SA-0816-08-16-FG-A failed, it split wider on one side of the

specimen than the other. The reason for this was that the fiberglass reinforcement

applied to the outside of the cylinder overlapped for approximately an inch.

Unfortunately, when this specimen underwent the split tensile test prior to testing, one

end of the crack formed at this overlapping section of confinement. When the specimen

was then tested, the pre-existing crack opened wider, but opened wider on the side

opposite the double layer of fiberglass.

Series SB (Confinement)

Testing went a lot more smoothly and efficiently for Series SB than for Series SA.

The use of the new mobile testing rig made changing test specimens especially easy. The

whole mobile apparatus is simple and easy to use.

One of the batches of concrete used for this set of specimens was a lot more

workable than the other batches. The quantities of components (i.e. aggregate, cement,

water, etc.) were all pre-measured and should have resulted in identical batches.

However, this particular batch seemed much less viscous than the others and it seems

likely that more water may have been added to this particular batch than the rest. One

control specimen and three embedded bar specimens were cast using this “wet” mix (SB-

0612-08-06-NO-B, SB-0612-08-06-NO-C, and SB-0612-08-06-TA-F). It was observed

that these specimens generally failed at lower-than-expected loads (see Measured Data

section). In addition, specimen SB-0612-08-06-NO-B was not well consolidated, a fact

which may have had an impact on its failure load.

Series SC (Geometry)

Specimens in Series SB and Series SC were cast using the same batch of concrete.

One specimen from Series C (SC-0612-08-06-TA-A) was made from the “wet” batch as

83

described in the previous section. This specimen also failed at a lower-than-expected

value.

During the course of testing, a few specimens from Series SC were strong enough

to allow the rebar to reach higher than expected loads. Specimens SC-0612-06-06-TA-A

and SC-0816-06-06-TA-A were both loaded until the rebar reached a stress of over 100

ksi. These specimens were then unloaded due to safety concerns regarding the failure of

the rebar. Since these two specimens did not reach a failure load, specimen SC-1020-06-

06-TA-A was not tested at all, because its size and proportions suggest it would be

stronger than the previous two specimens. Specimen SC-0816-08-06-TA-A also did not

reach a failure load, but this was due to the load limit on the hydraulic ram used for this

testing rig. The hydraulic ram had a nominal capacity of 30 tons (60 kips) and this

specimen was loaded up to 63.7 kips. Loading was discontinued for safety reasons.

Consequently, specimen SC-1020-08-06-TA-A was not loaded at all, again, because its

size and proportions suggest it would be stronger than specimen SC-0816-08-06-TA-A.

Series SD (Geometry)

Specimen SD-0612-08-03-TA-D was not consolidated well, which resulted in

honey-combed areas on the exterior of the specimen. However, when compared to

similar tests, this does not seem to have affected the failure load of the specimen.

A potentiometer malfunctioned during the testing of specimen SD-0816-08-02-

TA-A, which resulted in bad displacement data. After the test, it was observed that the

hot glue used to attach the potentiometer to the rebar had also come in contact with the

moveable “stem” of the potentiometer, preventing it from moving and measuring

displacement data.

84

Series SE (Confinement)

The tests for Series SE proceeded quite smoothly and without any unusual

incidents. One observation made that was true in general for the whole series was that

the cracks tended to be smaller than cracks in previous series and opened more

progressively as the rebar was pulled from the specimen. However, these were not

gradual in the desired way. Ideally, the cracks would form in the center of the cylinder

adjacent to the bar and progress out towards the exterior slowly enough for x-ray images

to be taken at different phases. However, in practice these cracks immediately extended

to the exterior of the specimen near the back end of the cylinder once the peak load was

reached, and extended upwards toward the front. This type of confinement was a step

forward in terms of the x-ray portion of the project, but still did not produce ideal results.

The data for specimen SE-0612-08-03-W74-B was lost due to user error. The

data acquisition system was not turned on prior to testing.

Series SF (Confinement)

The tests conducted in Series SF had only a few difficulties. Data for specimen

SF-0612-08-03-W74-A was not collected due to mismanagement of the data acquisition

system software. Specimen SF-0612-08-03-W59-B measured valid data until the

concrete split, at which point the plunger of the potentiometer got caught on a spur of

steel on the rebar, causing all subsequent displacement values to be invalid. Also, all of

the specimens with one inch of bonded length failed by splitting as well as pull-through,

instead of pure pull-through, as was expected on the basis of previous testing.

85

Uniform Tension Test Observations

Series SG

These tests were expected to produce progressive series of cracks, beginning at

the centermost crack initiator and proceeding to the next set of initiators and so on. What

was observed was quite different. All five of the cracks began to open simultaneously.

This allowed the metal clamps to be used to arrest the development of some of the cracks

and further widen others (as described in Section 4.3). There was no dramatic point of

failure for this test, as with the pull-out specimens. Once the crack formed, it simply

widened as the load was increased.

86

CHAPTER 6 - ANALYSIS OF EMBEDDED BAR TEST RESULTS

Although the portion of the X-Ray Tomography project reported in this thesis was

mainly experimental and meant to support the imaging and analyses conducted by other

members of the project, an analysis of the data is presented here in order to gain insight

into behavior, determine trends and present models with which the behavior of the

specimens may be analyzed in the future. The data collected in this study is compared

with Eligehausen’s (1983) bond model in order to evaluate the validity of that model for

these reinforced concrete specimens. The data is also compared with the ACI bonded

length requirements to determine how well the code predicts the behavior of reinforced

concrete specimens. Finally, a thick-walled cylinder approximation of the concrete

specimens will be used to gain insight into their behavior. In particular the failure modes

and post-cracking residual stresses is compared to dominant theories about concrete and

bond behavior.

6.1 Correction of Measured Data

The measured load displacement data conveys an understanding of the general

behavior of the test specimens during the test procedure. However, due to the nature of

the test apparatus, the data does not represent the true behavior of the specimens during

the tests. Unexpected non-linear trends are present in the data at the beginning of most

tests, which implies that there was some sort of settlement in the testing apparatus early

in the loading process. This non-linearity was corrected simply by shifting the entire

curve until the linear ascending portion of the curve lined up with the origin. This

correction disregards any initial movement of the testing apparatus and presents the

purely the behavior of the specimen itself. The plots in Appendix A show these corrected

data.

87

6.2 Comparison with Eligehausen’s Analytical Bond Model

The results from the present test series were first compared with those obtained in

the seminal study by Eligehausen, Bertero and Popov (1983). They conducted tests on

deformed bars embedded in concrete and developed an analytical model to relate local

bond stress to slip under monotonic loading (Figure 6.1).

This model is a simplified envelope that simulates the relationship between bond

stress and slip observed experimentally in their study. It consists of an initial non-linear

ascending relationship followed by a plateau. After the plateau, the bond stress decreases

linearly until it reaches a second plateau, which corresponds to the bar lugs plowing

through previously crushed concrete. All of the test specimens in the Eligehausen study

had very short bonded lengths. Most also had relatively large amounts of confining

reinforcement; this resulted in most specimens exhibiting splitting followed by a pull-

through failure, with the effect of creating very fine cracks (< 0.004 inches). The

baseline Eligehausen model represents this behavior. Eligehausen investigated the effect

of confinement and provides an adjustment to his baseline model to account for this

parameter. In specimens with longer bond lengths and less confinement, splitting is the

prevalent mode of failure, as seen in the data of this study. Thus, integration of

Eligehausen’s model along the bar does not necessarily give the correct failure load if

splitting controls the behavior.

The following equations define the relationship between the bond stress (τ) and

the slip (s) for the different portions of the Eligehausen model.

88

1

11

α

ττ

=

ss for s ≤ s1 (6.1)

1ττ = for s1 ≤ s ≤ s2 (6.2)

( ) 1223

13 τττ

τ +−⋅−−

= ssss

for s2 ≤ s ≤ s3 (6.3)

3ττ = for s ≥ s3 (6.4)

where s1 through s3 are the slip values at critical events and τ1 and τ2 are the

corresponding bond stress values.

The value s1 is approximately 1.2 times the lug height of the rebar used in the

experiment, s2 is three times s1, and s3 is the clear spacing between lugs. The limits τ1

and τ3 are equal to cf '30 and cf '11 , respectively. The exponent α1 is a function that

depends on the lug bearing area, and is assumed to be approximately 0.4.

The values used by Eligehausen (converted to U.S. units) for each of the constants

used in his model are compared to those used in this project in Table 6.1.

Table 6.1: Bond Model Constants

Constant Eligehausen’s Data Present Study’s Data f'c 4350 psi (30 N/mm2) 6270 psi s1 0.04 inches (1 mm) 0.075 inches s2 0.12 inches (3 mm) 0.225 inches s3 0.41 inches (10.5 mm) 0.375 inches τ1 1960 psi (13.5 N/mm2) 2376 psi τ3 725 psi (5 N/mm2) 871 psi α1 0.4 0.4

In this study, the clear spacing between lugs varied depending on the size of rebar,

with No. 4, No. 6 and No. 8 bars having clear spacings of 0.25, 0.375 and 0.5 inches,

respectively. The lug heights were nearly constant at approximately 1/16 in., regardless

of bar size and an α of 0.4 was used for all bar sizes as well. Concrete strengths vary

from 5640 to 6900 psi. Figure 6.1 shows the bond-slip relationship defined by the model

89

for both Eligehausen’s data and the data collected in this project. For the latter, f’c, s3, τ1

and τ3 were taken as the average of each value range.

0

0.5

1

1.5

2

2.5

0.000 0.100 0.200 0.300 0.400 0.500 0.600

Slip (inches)

Bon

d St

ress

(psi

)

Eligehausen's Data

Present Study's Data

Figure 6.1: Analytical Models Relating Bond Stress and Slip

This model’s predictions are compared with the measured values for some of the

embedded bar tests conducted in this study. Specimens with different amounts of

confinement behaved in dramatically different manners. Several cases of specimens with

varying confinements are compared to the model to see how well the expected behaviors

line up with the observed behaviors. The recorded loads and displacements were

converted to bond stresses and slips by using Equations 6.5 and 6.6. The slip defined by

Equation 6.6 represents the value at the loaded end of the bonded region.

bb LdP

⋅⋅=

πτ (6.5)

90

bsumeas AE

PLslip ⋅−= δ (6.6)

where P is the measured load, Lb is the bonded length of the bar, Lu is the

unbonded length of the bar, Es is Young’s modulus for steel, Ab is the cross-sectional

area of the bar and δmeas is the measured displacement of the bar.

Figure 6.2 compares the measured results for Specimen SA-0612-06-03-AL-A,

the most heavily confined specimen in the whole program, with the predictions of the

model. Since the compressive strength for this particular specimen is unknown (see

Chapter 4), a value of 6000 psi was assumed.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0.000 0.100 0.200 0.300 0.400 0.500 0.600

Bar Slip (inches)

Bon

d St

ress

(ksi

)

PredictedSA-0612-06-03-AL-A

Figure 6.2: Pull-Through Specimen: Measured and Predicted Behavior

The model captures the global features of the behavior of this specimen, although

its predictions differ in detail. This specimen was confined in a heavy aluminum tube,

which caused the failure to be purely pull-through without any visible cracks in the r-z

91

plane. On the ascending part of the curve, the predicted curve is more nonlinear than the

measured one (α is too low). The s1 value is well predicted by the model, but the

predicted peak stress is about 20% too low. Thereafter, the measured curve descends

nearly linearly, rather than exhibiting the upper plateau of the model, with a slope

approximately the same as the predicted one in the descending region..

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0.000 0.100 0.200 0.300 0.400 0.500 0.600Bar Slip (inches)

Bon

d St

ress

(ksi

)

PredictedSG-0612-08-03-WDBL-ASG-0612-08-03-WDBL-BSG-0612-08-03-WDBL-C

Figure 6.3: Specimens with High Confinement: Measured and Predicted Behavior

Figure 6.3 shows the three nominally identical specimens in Series SF that

contained the maximum amount of confinement, which consisted of two steel wire spirals

with a total cross sectional area of approximately 0.1 in2 and yield strengths of

approximately 84 ksi. The pulsed appearance of the loading was caused by the use of a

hand pump, whereas specimen SA-0612-06-03-AL-A, shown in Figure 6.2 was tested in

a Baldwin universal test machine, which provided a continuous load. Each specimen

92

split at the peak load. However, the wire confinement was sufficient to prevent

significant opening of the cracks, so the lugs maintained good mechanical interlock with

the concrete and the bar pulled through with only a gradual reduction in resistance.

Subsequent displacement of the rebar served to slowly decrease the bond stress until a

final minimum frictional bond stress was attained. Apart from under-predicting the peak

bond stress by about 35 %, the model again predicts the behavior reasonably well. As

with specimen SA-0612-06-03-AL-A, the measured bond stress rose more linearly than

the model suggests, and the predicted s1 is about twice the measured value, but the

model’s descending curve and the residual plateau fit the data well for these well-

confined specimens.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0.000 0.100 0.200 0.300 0.400 0.500 0.600

Bar Slip (inches)

Bon

d St

ress

(ksi

)

Modified EligehausenSG-0612-08-03-W59-ASG-0612-08-03-W74-B

Figure 6.4: Specimens with Moderate Confinement: Measured and Predicted

Behavior

93

The two curves plotted in Figure 6.4 are from Series SF and contain small

amounts (0.0043 and 0.0027 in2) of reinforcing wire embedded as spirals within the

specimen to act as confinement. These specimens split at the peak load, but the wire

confinement was strong enough to provide some residual bond resistance after cracking

had occurred. The data show the bond stress-slip relationship to be fairly linear until the

concrete cracks, at which point the bond stress drops significantly. Once the measured

displacement reached about 0.6”, the cracks in these two specimens measured

approximately 0.07”. The initial ascending portions of the predicted curve and the

residual bond stresses at the end of the model correspond reasonably well with the

measured behavior. However, the peak plateau is not observed in the data and the

residual load drops only slightly after splitting. The discrepancy between the measured

and predicted results is probably due to the failure mode and the amount of confinement

in the specimens. The jump in the load after splitting is influenced by the energy stored in

the stretched bar. The amount of energy the confinement can absorb is proportional to

the size of the cracks and the jump in load in the post-peak region.

The following is an excerpt from Eligehausen’s report discussing the failure mode

of his specimens.

“In all tests, except those with an applied transverse

pressure, a splitting crack developed prior to failure in the plane of

the longitudinal axis of the bar. Its development could often be

noted from a low bang or could sometimes be detected from the

monitored load-slip relationship. …After developing this crack, the

load dropped rapidly if the concrete was not confined by

reinforcement. However, in the case of confined concrete, the load

94

could be increased further with a gradually decreasing bond

stiffness.”(Eligehausen, et al., 1983)

From this description of the failure mode, it is clear that Eligehausen’s model is

intended to replicate the behavior of confined specimens. The model does not account

for a rapid drop in load after failure, but rather shows a plateau where the confinement is

acting on the bonded region. It also does not account for such large crack widths, as the

cracks in Eligehausen’s specimens did not exceed 0.004”. The specimens in Figure 6.4

apparently do not have the amount of confinement necessary to be simulated by the

model, and actually correspond more closely with Eligehausen’s description of non-

confined specimens.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0.000 0.100 0.200 0.300 0.400 0.500 0.600

Bar Slip (inches)

Bon

d St

ress

(ksi

)

Modified EligehausenSD-0612-08-03-TA-ASD-0612-08-03-TA-BSD-0612-08-03-TA-CSD-0612-08-03-TA-D

Figure 6.5: Specimens with Low Confinement: Measured and Predicted Behavior

95

Figure 6.5 shows four minimally confined specimens from Series SD

superimposed on the results predicted by Eligehausen’s model. These specimens had a

compressive strength of 6900 psi and were confined solely with strapping tape, a medium

that provides at most 50 lb/inch width of confinement per layer of tape. For practical

purposes, these specimens have nearly zero confinement. However, these tests provide

strikingly similar results to those specimens that contain moderate confinement. This

shows the bond stress-slip relationship to be fairly linear until the concrete cracks, at

which point the bond stress drops dramatically, just as with the moderately confined

specimens. In the tape-confined specimens the drop is larger than in the wire-confined

ones. Hence the latter only managed to retain approximately 0.5 ksi more bond stress

after failure than these taped-wrapped specimens.

Eligehausen also suggests a similar model for specimens within a tension zone.

The general behavior of this model more closely represents the behavior of specimens

with little or no confinement, however, the peak bond stress predicted by the tension

model (11√f’c) is up to 80% lower than the peak bond stresses exhibited by unconfined

specimens in this study. Thus, the tension model is less accurate in its predictions than

the baseline model.

The foregoing test results can be evaluated both for consistency among each other

and for agreement with Eligehausen’s model.

First, the initial bond stiffness was established on the basis of the slip at the front

end of the bonded length (Equation 6.6), whereas the bond stress was taken as the

average value (Equation 6.5), which occurs in the interior of the bonded region. These

two values are not quite consistent because they are taken at different locations.

However they were used because, without knowing the local bond stress vs. slip law,

determining the true slip at the middle of the bonded length is not possible. (Note that the

96

measured values give only the average, and not the local, bond stress, and the front end,

rather than the local, slip). The error caused by this procedure can be estimated by

assuming a linear local bond stiffness, given approximately by the measured values. Use

of Raynor’s (2000) linear bond stress model then shows that the bond stress varies by

only less than 1% from the middle to the end of the bonded length, and that the slip at the

mid point differs only slightly from that at the front end. For a No. 8 bar bonded over 3”

length and subjected to an average bond stress of 3.25 ksi, the two slips differ by 0.00146

inches, or less than 1% of the front end slip. The error introduced by the approximation

is thus less than the probable experimental errors, and continued use of the measured

values is warranted.

The Series SF tests contained sets of three nominally identical specimens (two for

the W74 and W59 sets), and therefore provided an opportunity for evaluating the scatter

in results. The values chosen for evaluation are the initial bond stiffness, the peak

average bond stress, and the bond stresses at slips of 0.2” and 0.5”. The initial bond

stiffness was, for these purposes, taken as the secant value between 25% and 75% of the

peak stress. The initial stiffness is the hardest of these quantities to obtain accurately.

Not only are the relevant displacements very small (and therefore subject to instrumental

error) but also several sources of displacement other than the desired bar slip (e.g.

hydrostone compression) are inevitably included in the measurement.

For each group of three nominally identical tests, the mean and coefficient of

variation of the values are given in Table 6.2. The overall scatter is then indicated by the

mean and coefficient of variation of the individual coefficients of variation. These are

0.195 and 0.863 respectively, which is relatively good considering the size of the sample

set. They suggest that the data are consistent enough to allow important trends to be

discerned.

97

Table 6.2: Statistics for Series SF Specimen Results

Bond Stiffness, k

(ksi/in)

Peak Ave. Bond Stress, τmax (ksi)

τ @ 0.2 inches of slip

(ksi)

τ @ 0.5 inches of slip

(ksi) Specimen Sets

Mean COV Mean COV Mean COV Mean COVSF-0612-08-03-WDBL Specimens 188 0.420 3.38 0.059 2.12 0.041 1.18 0.257SF-0612-08-03-W74 Specimens 148 0.212 3.29 0.001 0.99 0.093 0.48 0.160SF-0612-08-03-W59 Specimens 264 0.722 3.00 0.124 1.38 0.141 0.76 0.099SF-0612-08-01-NO Specimens 126 0.078 4.36 0.120 0.89 0.208 0.34 0.104SF-0612-08-03-FI Specimens 117 0.358 3.14 0.119 0.29 0.195 0.12 0.393

Average 169 3.43 1.13 0.58

The primary differences between the results measured in the present tests and the

predictions of Eligehausen’s model (using material properties from the current study) are:

• The peak stresses predicted by the model were consistently lower than the

measured values for specimens with 3 inches of bonded length. The

difference ranged from 16.9% to 37.6%.

• The predicted initial (rising) part of the curve was much more nonlinear

for the predicted curve than the measured curve.

• The predicted slip values at peak load were typically larger than the

measured values, by a factor between 1.3 and 5.4.

• The measured bond stiffnesses (using the 25%-75% secant) ranged from

39 to 172 ksi/in of slip, varying by a factor between 1.3 and 5.7 from the

average stiffness (30 ksi/in of slip) of Eligehausen’s model.

• For the specimens with good confinement, the measured data exhibited a

gradual reduction in bond stress with increasing slip, rather than the

plateau predicted y the model. For specimens with poor confinement

(which the model should not be expected to replicate), a sharp and

significant drop in load was followed by a gradually decreasing bond

stress. The sharp drop in the load was caused by the release into the bond

zone of the elastic energy stored in the bar, after the concrete cracked.

98

6.3 Comparison with ACI models

The ACI code (ACI 318-02, 2002) provides an equation for the minimum

required development (bonded) length for rebar in reinforced concrete structures. It is

possible to manipulate this equation in such a way as to get a relationship between the

bond stress available in a bonded region and the amount of confinement present in the

specimen. This section compares the amount of bond stress measured in the tests

conducted in this project with the ACI equation.

If one assumes that the rebar has yielded when the maximum bond stress occurs,

then the following equations can be established.

bbuy dLP ⋅⋅⋅= πτ (6.7)

yby fAP ⋅= (6.8)

where Py is the yield load of the bar, τu is the maximum bond stress experienced

by the system, Lb is the bonded length of the bar, db is the bar diameter, Ab is the cross-

sectional area of the bar and fy is the yield strength of the bar.

From Equations 6.7 and 6.8, it is possible to solve for the bond stress, as shown in

Equation 6.9.

b

byu L

df⋅=

4τ (6.9)

The ACI equation (Equation 6.10) for the minimum required bonded length (ACI,

Section 12.2.3) can be rearranged in the form of Equations 6.11 and 6.12.

99

b

b

tr

r

c

yb d

dKcf

fL ⋅

+⋅⋅⋅

⋅⋅=λγβα

'403 (6.10)

λγβα ⋅⋅⋅

+

⋅⋅=r

b

tr

y

c

b

b dKc

ff

Ld '

340 (6.11)

nsfA

K yttrtr ⋅⋅

⋅=

1500 (6.12)

where Lb is the bonded length, fy is the yield strength of the bar, f’c is the concrete

compressive strength, c is the amount of cover measured from the center of the bar, db is

the diameter of the bar, Atr is the area of the transverse reinforcement, fyt is the yield

strength of the transverse reinforcement, s is the transverse reinforcement spacing, n is

the number of bars being developed, αr is the reinforcement location factor, β is the bar

coating factor, γ is the reinforcement size factor, and λ is the lightweight aggregate

concrete factor.

Combining Equations 6.9 and 6.11 gives, the bond stress as:

+⋅

⋅⋅⋅⋅=

b

tr

r

cu d

Kcfλγβα

τ'

310 (6.13)

The bond stress, as shown in Equation 6.13, is a function of concrete and steel

properties, as well as the amount of cover and confinement active in the bonded region.

The term in parentheses represents the strength of confining materials (concrete cover

and steel). The fact that they are added suggests that both act simultaneously. This is

perhaps surprising, in that the steel stress is small prior to cracking, and the concrete

tensile strength is small after cracking. If one assumes that the amount of cover and

material properties remain constant, as is true with Series SE and SF of this study, then

100

the bond stress is simply a function of the amount of confinement in the specimen. Table

6.3 shows the values of the parameters used to compare Equation 6.13 to the data

collected in Series SE and SF. Two values (0.0 and 3.0 inches) were used for c,

representing both the full amount of cover and no cover at all (i.e. after cracking of the

cover). The cover likely provides less and less benefit as the concrete cracks and the

cracks grow wider. These values bracket the possible effects of the cover on the bond

stress and are presented as a shaded region in the plot of the data in Figure 6.6.

Table 6.3: ACI Equation Parameters

Parameter Value f'c 5640 psi αr 1.0 β 1.0 γ 1.0 λ 1.0 db 1.0 inches c 0.0, 3.0 inches s 1.0 inches n 1.0

101

y =

2.04

x +

0.67

R2 =

0.7

7y

= 1.

62x

+ 0.

39R

2 = 0

.78

y =

1.25

x +

0.21

R2 =

0.8

3

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Con

finin

g Pr

essu

re, f

' l (k

si)

Bond Stress (ksi)

0.20

in. d

isp.

0.35

in. d

isp.

0.50

in. d

isp.

Elig

ehau

sen

AC

IA

CI w

/out

cov

erA

CI 2

.5 m

axLi

near

(0.2

0 in

. dis

p.)

Line

ar (0

.35

in. d

isp.

)Li

near

(0.5

0 in

. dis

p.)

Lim

it on

(c+K

tr)/d

b in

Equ

atio

n 6.

12

Figu

re 6

.6: C

ompa

riso

n of

Dat

a w

ith E

quat

ion

6.13

102

The post-cracking bond stress was calculated for each SE and SF specimen at

displacements of 0.2, 0.35, and 0.5 inches (except for specimens for which data were not

collected or specimens that were not subjected to such large displacements). These bond

stresses were then plotted versus the amount of confinement present in the specimen

(specifically the confining pressure, f’l, which was computed assuming that the steel was

at yield). Only the confining material in the bonded length was assumed to be active in

promoting “frictional” bond after cracking. Since the compressive strengths of the

concrete used in the two series of tests were different, the bond stresses plotted were

converted to correspond with a compressive strength of 5640 psi using Equation 6.14.

ctruepsif fc '

5640)5640'( ⋅== ττ (6.14)

A compressive strength of 5640 psi, which corresponds with Series SF, was

chosen because Series SF produced the most consistent results in terms of load and

displacement histories for identical specimens. Table 6.4 shows the amounts of

confinement and residual bond stresses at each displacement for all applicable specimens

in Series SE and SF.

103

Table 6.4: Confinement and Post-Cracking Bond Stresses for Series SE and SF

Specimen Atr

(in2) fyt

(ksi)Atr*fyt (kips)

f'l (psi)

τ @ 0.20 in.

τ @ 0.35in.

τ @ 0.50 in.

SF-0612-08-03-WDBL-A 0.0168 84 8.42 802 2.09 1.46 1.08 SF-0612-08-03-WDBL-B 0.0168 84 8.42 802 2.29 1.80 1.22 SF-0612-08-03-WDBL-C 0.0168 84 8.42 802 2.33 1.79 1.48

SF-0612-08-03-W74-B 0.0043 83 2.14 204 0.97 0.74 0.38 SF-0612-08-03-W74-C 0.0043 83 2.14 204 1.08 0.66 0.52 SF-0612-08-03-W59-A 0.0027 354 5.80 553 1.19 0.86 0.71 SF-0612-08-03-W59-C 0.0027 354 5.80 553 1.58 1.20 0.89 SF-0612-08-01-NO-A 0.0000 0 0.00 0 0.70 0.61 0.35 SF-0612-08-01-NO-B 0.0000 0 0.00 0 1.05 0.66 0.39 SF-0612-08-01-NO-C 0.0000 0 0.00 0 0.99 0.54 0.29 SF-0612-08-03-FI-A 0.0000 0 0.00 0 0.31 0.16 0.07 SF-0612-08-03-FI-B 0.0000 0 0.00 0 0.44 0.26 0.17 SF-0612-08-03-FI-C 0.0000 0 0.00 0 0.28 0.16 0.13

SE-0612-08-03-W26-A 0.0005 370 1.18 112 0.69 0.55 0.33 SE-0612-08-03-W26-B 0.0005 370 1.18 112 0.63 0.50 0.36 SE-0612-08-03-W41-A 0.0013 328 2.60 247 1.14 0.47 0.15 SE-0612-08-03-W41-B 0.0013 328 2.60 247 1.52 0.90 0.47 SE-0612-08-03-W59-A 0.0027 354 5.80 553 1.49 0.98 0.68 SE-0612-08-03-W59-B 0.0027 354 5.80 553 2.03 1.24 0.84 SE-0612-08-03-W74-A 0.0043 83 2.14 204 1.71 1.01 0.60

SE-0612-08-03-W125-A 0.0123 84 4.10 391 2.14 1.67 1.10 SE-0612-08-03-WDBL-A 0.0168 84 8.42 802 2.65 2.06 1.31

Additionally, a few of Eligehausen’s test results have been included in this

comparison. Table 6.5 shows the properties of these tests, again corrected for the

differences in f’c with Equation 6.14. The f’l values for Eligehausen’s data represent a

range of confinements based on observations of response. The reinforcement present in

his specimens did not necessarily yield, as was assumed for Series SE and SF in this

study.

104

Table 6.5: Select Tests From Eligehausen’s Study (1983)

Specimen f'c τtrue (ksi) τ 5640 (ksi) S3 (in) f'l (ksi) 1.4 4400 0.06 0.07 0.08 0.00 1.3 4500 0.76 0.85 0.41 0.11 6.2 4500 0.81 0.91 0.41 0.11 6.3 4500 0.84 0.94 0.41 0.11 6.4 4500 0.88 0.99 0.41 0.11

Series 2, lower bound 4500 0.71 0.79 0.41 0.11 Series 2, upper bound 4500 0.71 0.79 0.41 0.46

6.1, lower bound 4500 0.76 0.85 0.41 0.11 6.1, upper bound 4500 0.76 0.85 0.41 0.46

Figure 6.6 shows a good agreement between the bond equation derived from ACI

and the data from Series SE and SF. The trendline fit to the data corresponding with a

displacement of 0.2 inches is nearly the same in magnitude and slope as the upper bound

of the Equation 6.13, which accounts for all 3.0 inches of cover and the spiral acting

together as confinement on the specimens. These data points were taken almost

immediately after cracking so the crack widths were at their smallest (non-zero) value of

the load history. The result implies that they were still fine enough that some tension

could be carried across them.

Similarly, the trendline corresponding with a displacement of 0.5 inches is similar

in magnitude and slope to the lower bound of the Equation 6.13, which assumes the

concrete has cracked sufficiently so that the cover is no longer effective and the spiral

provides all of the confining pressure. The crack sizes at this slip value are most likely

quite large. For example, the crack sizes for specimens SF-0612-08-03-W59-C and SF-

0612-08-03-W74-C were measured from x-ray images taken of these specimens

(Sprague, 2006) and measured 0.073 and 0.071 inches, respectively. These are over 17

times as large as the cracks observed by Eligehausen, which did not exceed 0.004 inches

in width (Eligehausen, et. al., 1983). The crack width is also approximately the same as

the lug height, suggesting that, not only is there no tension strength across the crack, but

also the lugs have lost approximately half of their mechanical interlock with the

105

surrounding concrete. Therefore the data taken at displacements of 0.5 inches might be

expected to correspond closely with the Equation 6.13 if cover is disregarded.

As a validation of this comparison, a few of Eligehausen’s tests were included in

Figure 6.6. The majority of his data falls entirely within the bounds set by the Equation

6.13, with the exceptions exceeding these bounds by only 0.06 ksi, at most.

ACI sets an upper limit of 2.5 for the value of ( ) btr dKc + . This limit, shown in

Figure 6.6, falls below the majority of the data collected both in this study and by

Eligehausen, suggesting that ACI is quite conservative in its predictions for the bond

stress capacity of well-confined reinforced concrete.

In general, the bond equation used by ACI correlates well with the observed

behavior of test specimens. It seems that the concrete and spiral can both provide

confinement at the same time, as ACI implies, although this is contrary to traditional

theory that presumes reinforcement is not active until after concrete is cracked.

However, the limit which ACI places on the value for ( ) btr dKc + seems to be quite

conservative in terms of the actual bond stress capacity of reinforced concrete.

6.4 Thick Walled Cylinder Model

This section seeks to gain some insight into the behavior of the embedded bar

tests by assuming the concrete acts as a thick-walled cylinder. In particular, there is a

need to understand the radial stresses induced by bond that lead to r-z-plane splits in the

concrete.

Timoshenko (1930) has derived the governing equations for the stresses and

displacements observed in a thick-walled cylinder subjected to uniformly distributed

internal and external pressures, as shown in the following equations.

106

( )( )222

22

22

22

abrbapp

abpbpa oioi

r −−

−−−

=σ (6.15)

( )( )222

22

22

22

abrbapp

abpbpa oioi

t −−

+−−

=σ (6.16)

where σr is the radial stress, σt is the hoop stress, a is the interior radius of the

cylinder, b is the exterior radius of the cylinder, r is the radius of the point of interest, pi

is any internal pressure acting on the cylinder and po is any external pressure acting on

the cylinder. These equations are the basis of the following analyses.

6.4.1 Pre-Cracking Stress State

This analysis addresses the state of the internal stresses within the concrete just

prior to failure by comparing the maximum bond stress and radial stress in the concrete.

At this point in the load history the concrete is still uncracked. In order to create a simple

model, the concrete is assumed to be a thick-walled cylinder with a pressure applied to

the inside of the cylinder. Furthermore the system, including the stresses, is assumed to

be prismatic. The pressure is caused by the wedging action of the rebar lugs pushing

radially outwards on the concrete as the rebar is pulled in tension. In this case, there is no

external pressure applied to the system, which allows equations 6.15 and 6.16 to be

simplified as follows:

−

−= 2

2

22

2

1rb

abpa i

rσ (6.17)

+

−= 2

2

22

2

1rb

abpa i

tσ (6.18)

107

Equations 6.17 and 6.18 can then be combined to express the radial stress as a

function of the hoop stress.

22

22

brbr

tr +−

⋅= σσ (6.19)

Inspection of Equation 6.19 shows that the highest hoop stress will occur on the

inside surface of the cylinder (r = a). If the concrete fails when σt reaches the tensile

capacity of the concrete, then it is possible to solve for the maximum radial stress at

failure. If the tensile strength is taken as 530 psi, as was true for Series SF, and the inner

and outer radii of the cylinder are set at 0.5 and 3.0 inches, respectively, then Equation

6.19 can be used to obtain the highest radial stress occurring within one of the Series SF

specimens. Using these values, the maximum radial stress is σr = 501 psi.

Raynor (2006) has proposed a linear model for bond stress distribution along the

length of an embedded bar (Equation 6.20).

( )

⋅⋅⋅

⋅⋅⋅−

⋅⋅⋅

⋅

⋅

=

bs

bb

bs

bb

bs

b

b

AEdk

L

AEdk

zL

AEdk

dP

zπ

π

ππ

τ

sinh

cosh)( max (6.20)

where τ(z) is the bond stress along the bonded region of the bar, Ab is the area of

the rebar, db is the bar diameter, Es is Young’s Modulus for steel, k is the bond stiffness

(bond stress per unit slip), Pmax is the peak load reached by the specimen, z is the distance

from the beginning of the bonded region of the bar, and Lb is the bonded length of the

embedded bar.

Table 6.6 shows the values used in Equation 6.20 for the analysis of this system.

Most of the specimens in Series SF with a 3 inch bonded length failed at loads between

30 and 35 kips. Therefore, Pmax was set at 32 kips for this analysis, which corresponds to

108

a average longitudinal stress in the concrete, σz, of 1132 psi. Also the measured stiffness

of the bond stress-slip relationship varied among tests, so upper and lower bounds (k2 and

k1) of this value were used.

Table 6.6: Inputs for Linear Bond Model

Variable Value Pmax 32 kips db 1.0 inches E 29000 ksi A 0.79 in2

L 3.0 inches k1 78 ksi/in k2 208 ksi/in

Figure 6.7 shows the bond stress distribution for both the upper and lower bounds

on bond stiffness.

3.15

3.25

3.35

3.45

3.55

3.65

3.75

0 0.5 1 1.5 2 2.5 3Length Along Bonded Region (inches)

Bon

d St

ress

(ksi

)

k1k2k_ave

Figure 6.7: Bond Stress Distribution Using Raynor’s (2006) Linear Model

109

Regardless of whether the bond stiffness is taken at its maximum or minimum

value, the bond stress is relatively constant along the bond length of the bar. If the

average value for k is used (kave=143 ksi/in), then the maximum bond stress at failure for

a Series SF specimen is approximately 3590 psi. The longitudinal stress in the specimen

is obtained assuming that the load is uniformly distributed over the cross-sectional area of

the cylinder. Assuming 32 kips are acting on a 6” diameter cylinder, σz = -1100 psi. The

orientations of the active stresses in the specimen are illustrated in Figure 6.8.

Figure 6.8: Specimen Stress State at Splitting

The stresses in the concrete in the r-z plane adjacent to the bar may be plotted on

a Mohr’s circle, as shown in Figure 6.9.

110

Figure 6.9: Mohr’s Circle for Peak Stress Analysis

The Mohr’s circle indicates that the maximum tensile stress in the concrete is

2790 psi at an orientation of 42.5° from the rebar. This conflicts with the damage

patterns observed in the tested specimens. Mohr’s circle indicates that the concrete

should crack much earlier than it did, with conical cracks running at approximately 42.5°

to the rebar. Instead, the observed damage is that the concrete failed in hoop tension

when the hoop stress reached the tensile strength, creating cracks in the r-z plane.

The reason for this discrepancy probably lies in the assumptions underlying the

model. The primary ones are that the stresses are prismatic (i.e. the stress state is at the

111

same at all points along the bonded length), and that the longitudinal stress in the

concrete is uniform over the radius. The second assumption is probably the most

seriously in error. If the longitudinal stress is higher near the bar, as would be expected,

then the Mohr’s circle gets pushed to the left and the maximum principal tension on the

42.5 degree plane (or cone) drops. The simple model breaks down because of these

assumptions. The fact that the predicted tensile stress across the potential conical crack is

2790 psi, about 5.3 times the estimated tension strength of the concrete, suggests that the

local stress state around the bar is much more complex than that assumed in the simple

thick-walled cylinder analysis. In order to for this problem to be addressed, a 3-

dimensional analysis is required, which is impractical given the time constraints on this

project. However, such an analysis would be valuable and is a potential area of future

research.

One issue that arose during the completion of this analysis dealt with the

computation of k. In this analysis the elastic strain of the rebar was taken into account

when adjusting for the slip measurement, but the elastic compression of the concrete was

not. If one were to use Equation 6.21 to relate the relative elongations of the steel and

concrete, then the result would show that the concrete would contract 1/8 the length that

the steel expands.

125.0≈

⋅

⋅

=

steel

concrete

steel

concrete

LEA

LEA

δδ

(6.21)

Although this amount of contraction would not be very high, it would be a

valuable refinement for this calculation.

112

6.4.2 Effective Lug Angle at Peak Load

The pull-out specimens tested in this study typically exhibited a combination of

failure modes. A few pieces of the concrete specimens were removed from the bar after

testing, with the results showing that both splitting and pull-through occurred, to different

extents, at the same time. In an attempt to determine how much crushing occurs ahead of

the lug prior to splitting of the concrete, this analysis looks at the effective lug angle of

the bar using the thick-walled cylinder approximation used in the previous section.

If one considers the lugs on a piece of rebar as it is pulled through concrete, the

lug can be approximated as a simple wedge applying radial load to the concrete as it is

pulled out, as shown in Figure 6.10. The net force then acting on the bar by the concrete

perpendicular to its axis, Q, can be split into its components N and F, the normal and

frictional forces on the bar. If α is the angle the lug makes with the axis of the bar, then

Equations 6.22 and 6.23 can be derived.

Figure 6.10: Wedge Model for Rebar Lugs

113

)sin()cos( αα ⋅−⋅= FNQ (6.22)

)sin( φα +⋅= QP (6.23)

where

)(tan 1 µφ −= (6.24)

and µ = 0.6 is the coefficient of friction between steel and concrete, N is the force

acting normal to the lug face, F is the frictional force acting on the lug, Q is the radial

force acting on the bar by the concrete, and α is the lug face angle relative to the

longitudinal axis of the bar. If Equation 6.23 yields Equation 6.25 when P is converted

into bond stress.

)sin( φατ +⋅⋅

=bo Lb

Q (6.25)

where bo is the circumference of the bar and Lb is the bonded length of the bar.

The radial stress can be computed from this as Equation 6.26.

)cot( φατσ +⋅=r (6.26)

Using Equations 6.26 and 6.19 along with the Goalseek function in Microsoft

Excel, it is possible to solve for the effective lug angle, α, at the time of failure of the

concrete. The concrete tensile strength (Section 4.3.1) is used for the hoop stress in

Equation 6.19 and the peak load is used to calculate τ at the point of failure. Using this

method, the effective lug angle for all specimens tested in Series SB, SC, SD, SE and SF

were computed and are presented in Table 6.7. These results show that the mean for the

effective lug angle, α, is 49.8° (α + φ = 80.8°), with a coefficient of variation of .04.

Therefore, the angle of the resultant compressive stress in the concrete (i.e. the sum of the

radial and longitudinal stresses) is 90°-(α + φ ) = 9.2°.

This result shows an high degree of correlation for the effective lug angle between

specimens which varied quite a bit in dimension, bonded length, bar size, and

114

confinement type and amount. This shows that for almost any specimen with any

combination of these variables, the peak bond stress at failure can be computed.

For example, a specimen with an 11-inch diameter, 4 inches of bonded No. 7 bar,

compressive strength of 6000 psi and tensile strength of 450 psi will fail by splitting with

a maximum bond stress of 2.9 ksi. However, the same model predicts that if the same

specimen were to have a tensile strength of 700 psi, the bond stress required to cause

splitting is 4.5 ksi. This much bond stress is much higher than any values attained in this

study, even the specimens which failed by pull-through and not splitting, implying that

this specimen would fail by pull-through before enough load was attained to cause

splitting.

The model presented here, based on a thick-walled cylinder approximation of the

concrete specimens, does a good job of predicting both the failure mode and bond stress

at failure of specimens of any type, even specimens with parameter values not tested in

this study.

115

Table 6.7: Effective Lug Angles

Specimen # Alpha (Degrees)

Specimen # Alpha (Degrees)

SB-0612-08-06-NO-A 47.1 SE-0612-08-03-W26-A 50.0 SB-0612-08-06-NO-B 44.6 SE-0612-08-03-W26-B 49.6 SB-0612-08-06-NO-C 43.7 SE-0612-08-03-W41-A 49.6 SB-0612-08-06-TA-A 47.7 SE-0612-08-03-W41-B 49.2 SB-0612-08-06-TA-B 48.1 SE-0612-08-03-W59-A 49.6 SB-0612-08-06-TA-C 47.7 SE-0612-08-03-W59-B 49.3 SB-0612-08-06-TA-D 48.0 SE-0612-08-03-W74-A 51.8 SB-0612-08-06-TA-E 48.3 SE-0612-08-03-W125-A 51.1 SB-0612-08-06-TA-F 45.2 SE-0612-08-03-W125-B 50.2 SC-0612-06-03-TA-A 52.3 SE-0612-08-03-WDBL-A 50.6 SC-0612-06-06-TA-A 49.0 SE-0612-08-03-WDBL-B 51.5 SC-0612-08-03-TA-A 51.9 SF-0612-08-03-WDBL-A 48.1 SC-0612-08-06-TA-A 44.4 SF-0612-08-03-WDBL-B 48.3 SC-0816-06-03-TA-A 53.1 SF-0612-08-03-WDBL-C 49.2 SC-0816-06-06-TA-A 48.6 SF-0612-08-03-W74-B 48.2 SC-0816-08-03-TA-A 52.4 SF-0612-08-03-W74-C 48.2 SC-0816-08-06-TA-A 49.2 SF-0612-08-03-W59-A 47.0 SC-1020-06-03-TA-A 52.4 SF-0612-08-03-W59-C 48.8 SC-1020-08-03-TA-A 53.1 SF-0612-08-01-NO-A 49.3 SD-0612-08-03-TA-A 48.1 SF-0612-08-01-NO-B 49.4 SD-0612-08-03-TA-B 48.4 SF-0612-08-01-NO-C 51.0 SD-0612-08-03-TA-C 50.7 SF-0612-08-03-PF-A 48.7 SD-0612-08-03-TA-D 49.1 SF-0612-08-03-PF-B 50.5 SD-0408-06-01-TA-A 52.6 SF-0612-08-03-PF-C 50.8 SD-0408-06-02-TA-A 50.9 SD-0408-06-03-TA-A 49.1 SD-0612-06-01-TA-A 51.9 SD-0612-06-02-TA-A 50.7 SD-0612-06-03-TA-A 49.9 SD-0816-06-01-TA-A 52.6 SD-0816-06-02-TA-A 53.0 SD-0816-06-03-TA-A 52.5 SD-0408-04-01-TA-A 52.8 SD-0408-04-02-TA-A 52.5 SD-0408-04-03-TA-A 50.1 SD-0816-08-01-TA-A 52.4 SD-0816-08-02-TA-A 51.1 SD-0816-08-03-TA-A 52.6

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CHAPTER 7 - CONCLUSION

7.1 Summary

Tests were conducted on deformed steel bars embedded in concrete in order to

gain a better understanding of bond in reinforced concrete. These tests formed a part of a

larger project investigating the use of x-ray tomography as a method for observing and

measuring the localized bond behavior within a specimen without destroying the bond

interface in the process. The program consisted of seventy-four pull-out specimens in six

series and two uniform tension specimens.

The pull-out tests were used to investigate some fundamental aspects of bond.

These included the impacts of specimen size, rebar size, bonded length and confinement

type on the failure mode of the concrete (splitting or pull-through), the peak stress

applied at the bond interface at the point of failure, and the residual bond strength

remaining in the specimen after the first major event had occurred. They used cylindrical

specimens that contained a piece of rebar embedded within the concrete matrix, bonded

for a specified length and protruded from one end. Tension was applied to the bar by

reacting against the end of the cylinder in order to apply stress across the bonded region

of the bar. Specimen sizes ranged from 4” to 10” in diameter (with heights generally

twice the diameter) with rebar sizes between No. 4 and No. 10 bars. Bonded lengths

were varied between 1” and 16”. A range of confinement types, including external

jackets made from aluminum tubing, fiberglass, or tape and internal wire spirals or fibers,

were used.

The two uniform tension specimens were intended to simulate more accurately

the conditions present in the constant moment region near midspan of a beam, where

“flexural bond” is the prevalent action. Each specimen was a 24” long and 4” diameter

cylinder, with a bar embedded along its axis. The two specimens were nominally

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identical apart from their rebar sizes, which were a No. 6 bar and a No. 8 bar. The bar

was gripped at each end and subjected to tensile load to cause a constant tension force

along the system. After the concrete cracked, bond stresses were induced adjacent to the

cracks.

Materials testing was also conducted. In addition to conventional compression

and tension tests, twelve fracture energy tests were conducted on notched beam

specimens. The primary purpose was to establish the fracture energy of the concrete used

in the bond tests, because that value was needed for the detailed Finite Element studies

that formed another part of the overall project. Such tests are normally carried out in a

fast-feedback closed loop testing machine, in order to capture the data as the crack

propagates through the plain concrete specimen. No such machine was available, so the

RILEM test method was adapted for use in an open loop machine (i.e. without servo

controls). Specimens with different sizes and shapes were used to explore some of the

effects of the geometry of the test specimen.

7.2 Conclusions

The results of this study have led to several significant observations about

behavior of bond. Of key importance are the following:

• In all the pullout specimens, behavior was essentially linear to approximately

90% of the peak load.

• The First Major Event (FME), which occurred approximately at peak load,

signaled the change from elastic behavior. It consisted of either bar yielding,

bar pull-through, or concrete splitting. The behavior that occurred was

controlled largely by the confinement of the concrete and the geometry of the

specimen, and in particular the bonded length. Response between the FME

and failure was characterized by one or more of these behaviors.

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• In specimens with very short bonded lengths relative to cylinder diameter (e.g.

1” bond in an 8” diameter cylinder), the system failed by the bar pulling

through the concrete, with no evidence of cracking. The bar lugs crushed the

concrete immediately in front of them as they pulled through the cylinder.

After the peak load, the resistance fell slowly with increasing displacement,

and failure was relatively ductile.

• In all other specimens, the concrete split. For the X-ray tomography part of

the overall project, test conditions were sought in which the splitting cracks

would propagate in a controlled way as the load increased. These conditions

were never achieved. When splitting cracks formed, they always propagated

immediately to the outer edge of the cylinder.

• In specimens with heavy confinement, the FME consisted of the concrete

splitting, after which the load dropped gradually as the bar then pulled through

in a ductile manner, while the confinement reinforcement inhibited the cracks

from opening.

• In specimens with little or moderate confinement reinforcement, the FME

consisted of the concrete splitting, after which bar jumped forward and the

load dropped sharply, followed by pull-through behavior at a small “residual”

resistance.

• In specimens with no confinement, reinforcement, behavior was extremely

brittle. The FME consisted of the concrete splitting, after which the load fell

immediately to zero as the pieces of the cylinder fell apart.

• The results were compared with predictions from Eligehausen’s bond model.

The model predicted an initial bond stiffness that was nonlinear and smaller

than the observed linear one, it under-predicted the peak load in all cases (by

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between 17% and 38%), and it predicted a plateau after the peak load that was

not observed in any of the tests.

• The dependence of bond stress on confinement was compared with the

relationship implied by the development length equations in ACI 318-05.

Good overall agreement was found, except that, in the tests, no evidence was

found of the upper bound imposed by ACI on the term (c+Ktr)/db.

• A simple elastic model, using a thick-walled cylinder analogy, predicted that

first cracking on a conical surface projecting from the lugs on the bar would

precede longitudinal splitting. This behavior was not observed in the tests.

The assumptions underlying the model must therefore be incorrect, and

determination of the stress distribution immediately preceding cracking

requires the use of a 3-D (or at least axi-symmetric) Finite Element model.

• A second simple model was created to predict whether splitting or pull-

through would control in an unconfined specimen. It treated the bar and lug

system as a conical wedge, and was able to predict the bond stress active in

the specimen at the time of splitting. If this bond stress is higher than the

maximum bond strength of the system, the model predicts that the FME will

be pull-through and not splitting.

• In each of the two Uniform Tension Tests, a bar bedded in a concrete cylinder

was subjected to a pull test. The specimen was subsequently injected with

epoxy that was sensitive to UV light and cut longitudinally to allow inspection

of the crack pattern. The crack pattern was dominated by planar cracks in the

radial plane and by slip at the bar surface. Almost no evidence was seen of

the conical “comb-like” cracks described by Goto (1971).Fracture energy tests

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that produce valid results are feasible without the use of high-speed, closed-

loop servo test systems.

Fracture energy tests were an integral part of this project. Several notable

observations were made during the process of conducting these tests.

• The fracture energy of concrete can be established without the use of a closed

loop testing machine provided that a counterweight system, similar to the one

developed here, is used to prevent sudden collapse immediately following first

cracking.

• Stiffness in the load train is important if gaps in the data, caused by sudden

jumps in the load-deflection response, are to be avoided. In these tests,

flexibility of the load cell was found to be the critical link.

• The counterweight system allowed stable readings of load and deflection to be

taken to large displacements. It was found that significant energy exists in the

long “tail” of the curve, and this fact raises questions over the region of the

curve to be used for establishing fracture energy.

• The tests were few, but, within that limitation, they showed that the aspect

ratio of the fracture surface had almost no effect on the measured value of GF,

but that GF dropped with an increase in area. Furthermore, tests on concretes

that were identical except for the coarse aggregate showed that the use of

angular aggregate led to a decrease in fracture energy.

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7.3 Recommendations

7.3.1 Impact on Current Practice

This study has produced several results that may be immediately applicable in

practice. First, in the area of materials testing, this study shows the high-speed, closed-

loop servo systems are not necessary for valid fracture energy testing, as is commonly

proposed. The methods used in this study were developed for use with open-loop

facilities. The fracture energy values obtained agree well with published values for

comparable concrete, leading to the conclusion that this test may be conducted in almost

any lab.

Secondly, although the ACI bond equation adequately predicts the bond behavior

of a specimen according to the amount of confinement acting on it, limitations placed on

cover and confinement counteract the accuracy of this model. The limit of

( ) btr dKc + ≤ 2.5 seems to be quite conservative in terms of the actual bond stress

capacity of reinforced concrete. This limit leads to major under-estimation of the peak

bond stresses within a reinforced concrete member.

7.3.2 Further Research

This study considered the effect of quite a few parameters, such as specimen size,

rebar size, bonded length and confinement, on the behavior of bond in reinforced

concrete specimens. However, this was far from exhaustive and the following are a few

recommendations for further experimental research:

• Location of the bonded zone. This study only looked at bonded zones at

the back (unloaded) end of the specimen. If the bond zone were moved, it

is possible that the concrete cover would have more of a confining effect,

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which would effect the fine line between splitting and pull-through, as

well as peak bond stresses and residual stresses. It is recommended that

similar specimen be tested with bonded regions in the middle, rather than

the end, of the specimen.

• Investigation of splices. This study only included specimens with single

bars embedded in them. This could be expanded to include splices of

varying lengths and types.

• Cyclical loading. The specimens in this study were loaded monotonically.

Cyclical loading may have an effect on the bond behavior and is worth

investigating.

• Active confinement. The confinement applied to the specimens tested in

this study was passive confinement. Active confinement applied as

needed in order to further control crack propagation is an area of research

that was not addressed in this study.

In terms of analysis, there is much that could be done to follow up and expand

upon what has been presented in this report. The following investigations may lead to a

better understanding of bond behavior:

• 3-D finite element analysis. In addition to the experimental program and

the x-ray image analysis, this project was originally intended to have a

research track focused on finite element modeling of the system and

prediction of the responses observed in the experimental program. As of

yet, this has not been completed and holds great potential for modeling the

true behavior of bond in reinforced concrete.

123

• Thick-walled cylinder analysis. The thick-walled cylinder approximation

used in Section 6.4.1 did not produce meaningful results due to 3-D

assumptions being placed into a 2-D model. Expanding this analysis into

three dimensions would allow for more accurate and meaningful results.

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BIBLIOGRAPHY

ACI 318-02. Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (ACI 318R-02). Farmington Hills, MI: ACI, 2002.

ASTM C 39, "Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens." Annual Book of ASTM Standards, Vol. 04.02 (2002).

ASTM C 78-02, "Standard Test Method for Flexural Strength of Concrete (Using Simple Beam with Third-Point Loading)." Annual Book of ASTM Standards, Vol. 04.02 (2002).

ASTM C 293, “Standard Test Method for Flexural Strength of Concrete (Using Simple Beam With Center-Point Loading).” Annual Book of ASTM Standards, Vol. 04.02 (2002).

ASTM C 469-02, "Standard Test Method for Static Modulus of Elasticity and Poisson's Ratio of Concrete in Compression." Annual Book of ASTM Standards, Vol. 04.02 (2002).

ASTM C 496, "Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens." Annual Book of ASTM Standards, Vol. 04.02 (2002).

Bazant, Z.P., and Becq-Giraudon, E. “Statistical prediction of fracture parameters of concrete and implications for choice of testing standard.” Cement and Concrete Research, 32 (2002): pp. 529-556.

Eligehausen R., Bertero V., and Popov E. “Local Bond Stress-Slip Relationships of Deformed Bars Under Generalized Excitations.” Earthquake Engineering Research Center, Report no. 83-23, University of California, Berkeley, CA, 1983.

Goto, Y., “Cracks Formed in Concrete Around Tension Bars.” ACI Journal Proceedings, Vol. 68, No. 4, April 1971.

Lowes, L.N., Moehle, J.P., and Govindjee, S. “Concrete-Steel Bond Model for Use in Finite Element Modeling of Reinforced Concrete Structures.” ACI Structural Journal, July-August (2004).

Malvar, L.J. “Bond of Reinforcement under Controlled Confinement.” ACI Materials Journal, 89, no. 6 (1992): pp.593-601.

Raynor, D.J. “Bond Assessment of Hybrid Frame Continuity Reinforcement.” MSCE Thesis, University of Washington, Seattle, WA, 2000.

Sprague, T.S. “An X-Ray Tomography Investigation of Bond in Reinforced Concrete.” MSCE Thesis, University of Washington, Seattle, WA, 2006

Tepfers, R. “Cracking of concrete cover along anchored deformed reinforcing bars.” Magazine of Concrete Research, 31, No. 106 (1979): pp. 3-12.

125

Timoshenko, S. Strength of Materials, Part II; Advanced Theory and Problems. New York: Van Nostrand Reinhold Company, 1930.

126

APPENDIX A - LOAD-DISPLACEMENT CURVES

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Figure A.2: Load-Displacement Curve for Specimen SA-0612-06-03-AL-A

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Figure A.3: Load-Displacement Curve for Specimen SA-0612-06-06-FG-A

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Figure A.4: : Load-Displacement Curve for Specimen SA-0612-06-03-FG-A

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Figure A.8: Load-Displacement Curve for Specimen SB-0612-08-06-NO-A

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Figure A.9: Load-Displacement Curve for Specimen SB-0612-08-06-NO-B

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Figure A.10: Load-Displacement Curve for Specimen SB-0612-08-06-NO-C

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Figure A.11: Load-Displacement Curve for Specimen SB-0612-08-06-TA-A

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Figure A.12: Load-Displacement Curve for Specimen SB-0612-08-06-TA-B

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Figure A.13: Load-Displacement Curve for Specimen SB-0612-08-06-TA-C

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Figure A.14: Load-Displacement Curve for Specimen SB-0612-08-06-TA-D

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Figure A.15: Load-Displacement Curve for Specimen SB-0612-08-06-TA-E

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Figure A.16: Load-Displacement Curve for Specimen SB-0612-08-06-TA-F

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Figure A.17: Load-Displacement Curve for Specimen SC-0612-06-03-TA-A

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Figure A.27: Load-Displacement Curve for Specimen SD-0612-08-03-TA-A

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Figure A.28: Load-Displacement Curve for Specimen SD-0612-08-03-TA-B

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Figure A.29: Load-Displacement Curve for Specimen SD-0612-08-03-TA-C

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Figure A.30: Load-Displacement Curve for Specimen SD-0612-08-03-TA-D

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Figure A.46: Load-Displacement Curve for Specimen SE-0612-08-03-W26-A

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Figure A.47: Load-Displacement Curve for Specimen SE-0612-08-03-W26-B

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151

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152

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0.00 0.10 0.20 0.30 0.40 0.50 0.60


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153

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Figure A.55: Load-Displacement Curve for Specimen SE-0612-08-03-WDBL-A

154

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0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08


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Figure A.56: Load-Displacement Curve for Specimen SE-0612-08-03-WDBL-B

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0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70


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Figure A.57: Load-Displacement Curve for Specimen SF-0612-08-03-WDBL-A

155

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Figure A.58: Load-Displacement Curve for Specimen SF-0612-08-03-WDBL-B

0

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0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70


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Figure A.59: Load-Displacement Curve for Specimen SF-0612-08-03-WDBL-C

156

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0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70


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Figure A.60: Load-Displacement Curve for Specimen SF-0612-08-03-W74-B

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Figure A.61: Load-Displacement Curve for Specimen SF-0612-08-03-W74-C

157

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0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70


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Figure A.62: Load-Displacement Curve for Specimen SF-0612-08-03-W59-A

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Figure A.63: Load-Displacement Curve for Specimen SF-0612-08-03-W59-C

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Figure A.64: Load-Displacement Curve for Specimen SF-0612-08-01-NO-A

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Figure A.65: Load-Displacement Curve for Specimen SF-0612-08-01-NO-B

159

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Figure A.66: Load-Displacement Curve for Specimen SF-0612-08-01-NO-C

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Figure A.67: Load-Displacement Curve for Specimen SF-0612-08-03-FI-A

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Figure A.68: Load-Displacement Curve for Specimen SF-0612-08-03-FI-B

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Figure A.69: Load-Displacement Curve for Specimen SF-0612-08-03-FI-C

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APPENDIX B – UNIFORM TENSION SPECIMEN PHOTOGRAPHS

Figure B.1: Uniform Tension Specimen UV Photo 1

Figure B.2 Uniform Tension Specimen UV Photo 2

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