EFFECT OF BEAM SIZE AND FRP THICKNESS ON
INTERFACIAL SHEAR STRESS CONCENTRATION AND
FAILURE MODE IN FRP-STRENGTHENED BEAMS

LEONG KOK SANG

NATIONAL UNIVERSITY OF SINGAPORE
2003


Founded 1905

EFFECT OF BEAM SIZE AND FRP THICKNESS ON
INTERFACIAL SHEAR STRESS CONCENTRATION AND
FAILURE MODE IN FRP-STRENGTHENED BEAMS

LEONG KOK SANG
(B.Eng. (Hons.). UTM)

A THESIS SUBMITTED
FOR THE DEGREE OF MASTER OF ENGINEERING
DEPARTMENT OF CIVIL ENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE
2003


ACKNOWLEDGEMENTS

I would like to express my heartfelt gratitude and thanks to my supervisor,
Assistant Professor Mohamed Maalej, for his invaluable guidance, encouragement
and support throughout the research years.

I wish to thank the National University of Singapore for providing the
financial support and facilities to carry out the present research work.
Special thanks are extended to my family, and friends especially Ms. S.C. Lee
and Mr. Y.S. Liew for their continuous support and encouragement. Furthermore, I
would like to acknowledge the assistance of Mr. Michael Chen, a third year MIT
student, with the laboratory work during his three-month attachment with National
University of Singapore.
Finally I would like to thank the technical staff of the Concrete Technology
and Structural Engineering Laboratory of the National University of Singapore, for
their kind help with the experimental work.

January, 2004

Leong Kok Sang

i


TABLE OF CONTENTS

ACKNOWLEDGEMENTS .............................................................................................. i
TABLE OF CONTENTS ................................................................................................. ii
SUMMARY ...................................................................................................................... iv
NOMENCLATURE......................................................................................................... vi
LIST OF FIGURES ......................................................................................................... ix
LIST OF TABLES ......................................................................................................... xiii

CHAPTER ONE:
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1

Objective and Scopes of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2
Outline of Thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
2
3

CHAPTER TWO: LITERATURE REVIEW
2.1

2.2

2.3
2.4

Failure Modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Flexural Failure by FRP Rupture and Concrete crushing. . . . . . . . . .
2.1.2 Shear Failure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.3 Concrete Cover Separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.4 Plate-End Interfacial Debonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.5 Intermediate Flexural Crack-Induced Debonding . . . . . . . . . . . . . . . . .
2.1.6 Intermediate Flexural Shear Crack-Induced Debonding… … . .
Interfacial Shear Stress Concentration ………………………………..…
2.2.1 Taljsten’s Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Smith and Teng’s Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experimental Measurement of Interfacial Shear Stresses. . . . . . . . . . . . . . . . .
Strength Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Plate-End Interfacial Debonding ………………... . . . . . . . . . . . . . . . .
2.4.1.1 Ziraba et al.’s Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.1.2 Varastehpour and Hamelin’s Model. . . . . . . . . . . . . . . . . . . . . .
2.4.2 Concrete Cover Separation ……………….. . . . . . . . . . . . . . . . . . . . . . .
2.4.2.1 Saadatmanesh and Malek’s Model. . . . . . . . . . . . . . . . . . . . . .
2.4.2.2 Jansze’s Model.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 Intermediate Flexural Crack-Induced Debonding… … … … … . .
2.4.4 Intermediate Flexural Shear Crack-Induced Debonding… . . … . .

4
5
5
5
5
6
6
7
7
9
11
12
13
13
14
16
16
16
17
18

ii



CHAPTER THREE: EXPERIMENTAL INVESTIGATION
3.1
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2
Specimen Reinforcing Details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3
Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4
Casting Scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5
CFRP Application. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6
Instrumentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7
Testing Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8
Results and Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.81 Effects of Strengthening. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.82 Failure Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.83 Interfacial Shear Stresses … . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23
23
24
24
25
25
25

26
26
28
30
31

CHAPTER FOUR: FINITE ELEMENT ANALYSIS
4.1
4.2
4.3
4.4
4.5

4.6

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Elements Designation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Analysis Procedures… … … … … … . . … … . … . . … … … … … … . … .
Material Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results of Series A, B and C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Load-Deflection Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2 CFRP Strain Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.3 Interfacial Shear Stresses… . … … … . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.4 Effect of Cracking on Interfacial Shear Stress Distribution in the
Adhesive Layer… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51
51
51

52
53
53
54
54
55
57

CHAPTER FIVE: STRENGTHENING OF RC BEAMS
INCORPARATING A DUCTILE LAYER OF ENGINEERED
CEMENTITIUOS COMPOSITE
5.1
5.2
5.3

5.4

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experimental Investigation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1
Test Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Finite Element Investigation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1
Load-Deflection Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2
CFRP Strain Distribution.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.3
Interfacial Shear Stresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


82
83
84
85
86
86
87
87

CHAPTER SIX: CONCLUSIONS AND RECOMMENDATIONS
Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Recommendations for Further Studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

100
101

REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

102

6.1
6.2

iii


SUMMARY

Epoxy-bonding of fibre reinforced polymers (FRP) has emerged as a new
structural strengthening technology in response to the increasing need for repair and

strengthening of reinforced concrete structures. Because of its excellent strength- and
stiffness-to-weight properties, corrosion resistance, and the benefit of minimal labor
and downtime, FRP has become a very attractive construction material and has been
shown to be quite promising for the strengthening of concrete structures. Although
epoxy bonding of FRP has many advantages, most of the failure modes of FRPstrengthened beams occur in a brittle manner with little or no indication given of
failure. The most commonly reported failure modes include ripping of the concrete
cover and interfacial debonding. These failure modes occur mainly due to interfacial
shear and normal stress concentrations at FRP-cut off points and at flexural cracks
along the beam. Although there are various analytical solutions proposed to evaluate
the state of stress at and near the FRP cut-off points as well as the maximum carbon
fibre reinforced polymer (CFRP) tensile stress for intermediate crack-induced
debonding, there is a lack of definite laboratory tests and numerical analyses
supporting the validity of the proposed model.
The main objective of this study is, therefore, to investigate the interfacial
shear stress concentration at the CFRP cut-off regions as well as the failure mode of
CFRP-strengthened beams as a function of beam size and FRP thickness. Because
most structures tested in the laboratory are often scaled-down versions of actual
structures (for practical handling), it would be interesting to know whether the results
obtained in the laboratory are influenced by the difference in scale.

iv


The scope of the research work is divided into three parts: 1) a laboratory
investigation involving seventeen simply-supported RC beams to study the interfacial
shear stress concentration at the CFRP cut-off regions as well as the failure mode of
CFRP-strengthened beams; 2) a finite element investigation to verify the experimental
results; and 3) an investigation of the performance of FRP-strengthened beams
incorporating Engineered Cementitious Composites (ECC) as a ductile layer around
the main flexural reinforcement.

The studies showed that increasing the size of the beam and/or the thickness of
the CFRP leads to increased interfacial shear stress concentration in CFRPstrengthened beams as well as reduced CFRP failure strain. The non-linear FE
analysis was found to predict the response of the beam fairly well. Finally, the results
showed that ECC can indeed delay debonding of the FRP and result in the effective
use of the FRP materials

Keywords: CFRP; strengthened beams; interfacial shear stress; failure mode;
debonding; ECC.

v


NOMENCLATURE
a

Distance from support to CFRP cut-off point

A, B

Coefficients of curve fitting of ε=A×(1-e-Bx);

Ac

Cross sectional area of concrete

Afrp

Cross sectional area of FRP

b


Distance from CFRP cut-off point to loading point

bc

Width of concrete beam

bfrp

Width of FRP sheet

Bm

Modified shear span

C

Coefficient of friction

d

Effective depth of concrete beam

dfrp

Distance from top of beam to centre of FRP

dmax

Maximum aggregate size


Ea

Elastic modulus of adhesive

Ec

Elastic modulus of concrete

Eelastic

Elastic energy of beam

Efrp

Elastic modulus of FRP

Etol

Total energy of beam

f c'

Cylinder strength of concrete

fcu

Cube strength of concrete

fct


Tensile strength of concrete

Ga

Shear modulus of adhesive

hc

Depth of beam

I

Second moment of area

Itr

Second moment of area of transformed cracked FRP section

vi


Itr,conc

Second moment of area of transformed cracked concrete section

Kn

Normal stiffness


Ks

Shear stiffness

l

Distance from middle of FRP-beam to CFRP cut-off point

L

Span of beam

Lbd

Bond length

Le

Effectives stress transfer (bond) length

Mo

Bending moment

P

Point load

Pult


Ultimate load;

R2

Correlation coefficient of curve fitting;

ta

Thickness of adhesive

tfrp

Thickness of FRP

Vo

Shear force

xtr,frp

Neutral axis of transformed cracked FRP section

xtr,conc

Neutral axis of transformed cracked concrete section

yc, yfrp

Distance from the bottom of concrete and top of FRP to their respective centroid


Zc

Section modulus of concrete

ε

Strain in the FRP plate;

εs

Maximum tensile strain

εpfail

Strain in the FRP at midspan at failure;

εpu

FRP tensile rupture strain;

εu

Limiting strain of concrete

α

Effective shear area multiplier

vii



τ

Shear stress

σy

Normal stress

σdb

Debonding stress

φ

Friction angle

σ1

Principal stress

σx

Longitudinal stress caused by bending moment

βp

Ratio of bonded plate width to the concrete member

ρp


CFRP reinforcement ratio, Ap/Ac

∆

Deflection of the beam at midspan;

∆y

Deflection of the beam at midspan at the yielding of steel reinforcement

∆fail

Deflection of the beam at midspan at failure load

ψ

Dilantancy angle of concrete in Drucker-Prager plasticity model

µ∆

Deflection ductility index

µe

Energy ductility index

viii



LIST OF FIGURES
Page
Figure 2.1(a)

Failure mode in FRP-strengthened beams i. FRP rupture ii.
Concrete crushing iii. Shear failure iv. Concrete cover
ripping v. Plate-end interfacial debonding

19

(After Teng et al. 2002a)
Figure 2.1(b)

Failure mode in FRP-strengthened beams vi. Intermediate
flexural crack-induced debonding v. Intermediate flexural
shear crack-induced debonding (After Teng et al. 2002a)

Figure 2.2

Type A partial cover separation
(After Garden and Hollaway 1998)

Figure 2.3

20

20

Type B partial cover separation
(After Garden and Hollaway 1998)


21

Figure 2.4

FRP-strengthened beam

21

Figure 2.5

Load cases

22

Figure 3.1

Specimen reinforcing details

38

Figure 3.2

Section details for Series A, B and C beams

39

Figure 3.3

Reinforcement of Series A, B and C


39

Figure 3.4

Series A, B and C beams

40

Figure 3.5

Typical Series A beams test setup

40

Figure 3.6

Typical Series B beams test setup

41

Figure 3.7

Typical Series C beams test setup

41

Figure 3.8

Notched beam specimen


42

Figure 3.9

Load-midspan deflection for Series A beams

43

Figure 3.10

Load-midspan deflection for Series B beams

43

Figure 3.11

Load-midspan deflection for Series C beams

44

ix


Figure 3.12

Approximate calculation of equivalent elastic energy release
at failure

Figure 3.13


Comparison of measured and predicted CFRP debonding
strains

Figure 3.14(a)

50

Typical finite element idealization of the (a) RC beams (b)
FRP-strengthened beams

Figure 4.2

49

Variation of peak interfacial shear stress with respect to
beam depth for Group 1 and 2 beams at peak load

Figure 4.1

48

Experimentally-measured interfacial shear stress
distributions in Series C

Figure 3.19

47

Experimentally-measured interfacial shear stress

distributions of Series B

Figure 3.18

46

Experimentally-measured interfacial shear stress
distributions of Series A

Figure 3.17

45

Load versus CFRP strain at midspan for Group 2
(ρρ=0.212%) beams

Figure 3.16

45

Nominal bending stress at peak load as a function of beam
depth

Figure 3.15

45

Nominal bending moment at peak load as a function of beam
depth


Figure 3.14(b)

44

61

Modified Hognestad compressive stress-strain curve of
concrete

62

Figure 4.3

Material properties

62

Figure 4.4

Load-deflection response of control beams in Series A iff

63

Figure 4.5

Load-deflection response of control beams in Series B

63

Figure 4.6


Load-deflection response of control beams in Series C

64

Figure 4.7

Load-deflection response of FRP-strengthened beams in
Series A

65

x


Figure 4.8

Figure 4.9

Load-deflection response of FRP-strengthened beams in
Series B

66

Load-deflection response of FRP-strengthened beams in

67

Series C
Figure 4.10


CFRP strain distribution in Series A at peak load

68

Figure 4.11

CFRP strain distribution in Series B at peak load

69

Figure 4.12

CFRP strain distribution in Series C at peak load Load-d

70

Figure 4.13

Interfacial shear stress distribution in the CFRP cut-off
region for Series A at peak load

Figure 4.14

Interfacial shear stress distribution in the CFRP cut-off
region for Series B at peak load

Figure 4.15

72


Interfacial shear stress distribution in the CFRP cut-off
region for Series C at peak load

Figure 4.16

71

73

Variation of peak shear stresses with respect to beam depth
for group 1 and 2 beams

74

Figure 4.17

Location of elements with lower tensile strength

75

Figure 4.18

Interfacial shear stress distribution in the adhesive layer in
the CFRP cut-off region

Figure 4.19

Shear stress distribution in FRP strengthened RC flexural
members (After Buyukozturk et. al 2004)


Figure 4.20

77

Numerical crack symbols and interfacial shear stress
distribution in the adhesive layer at load P=32 and 40 kN

Figure 4.22

76

Numerical crack symbols and interfacial shear stress
distribution in the adhesive layer at load P= 8, 16 and 24 kN

Figure 4.21

75

78

Evolution of crack patterns and interfacial shear stress
distribution in the adhesive layer of beam A5 at load P=32,
40 and 48 kN

79

xi



Figure 4.23

Evolution of crack patterns and interfacial shear stress
distribution in the adhesive layer of beam A5 at load P=56,
64 and 72 kN

Figure 4.24

80

Evolution of crack patterns and interfacial shear stress
distribution in the adhesive layer of beam A5 at load P=80
and 86 kN

81

Figure 5.1

Specimen reinforcing details

93

Figure 5.2

Tensile stress-strain curve of ECC test

93

Figure 5.3


Load-deflection responses of beams ECC-1, ECC-2, A1 and

94

A3
Figure 5.4

Debonding of CFRP sheets in beam ECC-2 (a) Debonding of
CFRP (b) CFRP sheets after debonding (c) Bottom surface
of beam ECC-2 after debonding

Figure 5.5

Middle section cracking behaviour of control beams ECC-1
and A1, respectively MiA1-A2 control beams

Figure 5.6

95

96

Cracking patterns of beams ECC-2 and A3 (a) Cracking
patterns of beam ECC-2 around the loading point.(b)
Cracking patterns of beam A3 around the loading point

Figure 5.7

96


Simplified multi-linear tension softening curve for numerical
modelling

97

Figure 5.8

Load-deflection response of control beams

97

Figure 5.9

Load-deflection response of CFRP strengthened beams

98

Figure 5.10

CFRP strain distribution of beam ECC-2 at peak load

98

Figure 5.11

Interfacial shear stress distribution in the CFRP cut-off

Figure 5.12

region at peak load of beam ECC-2Ll beams


99

Flexural-shear crack at CFRP cut-off point of beam ECC-2L

99

xii


LIST OF TABLE
Page
Table 3.1

Description of specimens

33

Table 3.2

Material properties

33

Table 3.3

Material properties of CFRP provided by manufacturer

33


Table 3.4

Location of strain gauges on the CFRP sheets along half of the
beam

34

Table 3.5

Summary of results

35

Table 3.6

Ductility index of FRP-strengthened beam

36

Table 3.7

Curve fitting results

37

Table 4.1

Material model for concrete in Series A and B

59


Table 4.2

Material model for concrete in Series C

60

Table 4.3

Material model for CFRP, adhesive and steel reinforcement

60

Table 5.1

ECC and concrete mix proportions

89

Table 5.2

Material properties of ECC and concrete

89

Table 5.3

Summary of test results

89


Table 5.4

Material model for concrete

90

Table 5.5

Material model for ECC

91

Table 5.6

Material model for CFRP, adhesive and steel reinforcement

92

xiii


CHAPTER ONE
INTRODUCTION

Statistics have shown that a great number of structures may need to be
strengthened or rehabilitated due to changes in utilization, damages (e.g. fire,
accident), deterioration (e.g. corrosion of steel) or even construction defects. For
instance, in the United States, Canada and United Kingdom, it is estimated that about
243,000 infrastructures are in need of remedial action at a cost of at least $ 296 billion

(Bonacci and Maalej 2001). The increasing demand for structural strengthening has
pointed to the need to develop a cost-effective structural strengthening technology.
The emergence of plate/sheet bonding technique using fibre reinforced polymers
(FRP) is in response to this challenge. FRP bonding technique has been established as
a simple and economically viable way of strengthening and repairing concrete
structures. The use of fibre-reinforced polymer presents a labor saving, aesthetically
pleasing and rapid field application of plate bonding. Moreover, FRP does not corrode
and creep, thereby offering long-term benefits. The application of FRP involves
buildings, bridges, chimneys, culverts and many others.
Although epoxy bonding of FRP has many advantages, most of the failure
modes of FRP-strengthened beams occur in a brittle manner with little or no
indication given of failure. The most commonly reported failure modes include
ripping of the concrete cover and interfacial debonding. These failure modes occur
mainly due to interfacial shear and normal stresses concentrations at FRP-cut off
points and at flexural cracks along the beam. Even though researchers have shown
that an anchorage system can be used to prevent plate debonding, the design is still
mainly based on intuition (Mukhopadhyaya and Swamy 2001). Moreover, the

1


inability to determine the optimum way of utilizing the FRP will only come at a
significant increase in cost.

1.1

Objective and Scopes of Research
Numerous researchers have studied interfacial stresses intensively over the

past few years. Several analytical models have been proposed to quantify these

stresses in order to predict the failure mode of FRP-strengthened beam. However,
there is a lack of definite laboratory tests and numerical analyses to support the
validity of the proposed models.
The main objective of this study is, therefore, to investigate the interfacial
shear stress concentration at the carbon fibre reinforced polymer (CFRP) cut-off
regions as well as the failure mode of CFRP-strengthened beams as a function of
beam size and FRP thickness. Because most structures tested in the laboratory are
often scaled-down versions of actual structures (for practical handling), it would be
interesting to know whether the results obtained in the laboratory are influenced by
the difference in scale.
The scope of the research work is divided into three parts:
1)

A laboratory investigation of the interfacial shear stress concentration at the
CFRP cut-off regions as well as the failure mode of CFRP-strengthened beams
as a function of beam size and FRP thickness

2)

A finite element investigation to verify the experimental results.

3)

An investigation of the performance of FRP-strengthened beams incorporating
Engineered Cementitious Composites (ECC) as a ductile layer around the
main flexural reinforcement.

2



1.2

Outline of Thesis

The present thesis is divided into six chapters.

Chapter one introduces the background, research scope and objectives of this study.

Chapter Two gives an introduction to previous and latest studies dealing with
interfacial shear stress concentration as well as failure mode of FRP-strengthened
beams. In particular, this chapter describes the various analytical interfacial stresses
and strength models available in the literature to date.

Chapter Three presents a detailed description of the experimental setup and procedure.
Analysis and discussion of the experimental results are also included.

Chapter Four presents the results of numerical simulations carried out to verify the
experiment results.

Chapter Five presents the results of an investigation where a ductile ECC layer is used
to replace the ordinary concrete around the main flexural reinforcement to delay the
debonding failure mode and increase the deflection capacity of the FRP-strengthened
beam.

Chapter Six summarizes the main findings of the study and provides some
recommendation for future works.

3



CHAPTER TWO
LITERATURE REVIEW

2.1

Failure Modes
Over the years, extensive research works have been carried out to study the

various failure modes of FRP-strengthened beams. This has given rise to many
classifications of failure modes (Chajes et al. 1994, Meier, 1995 Buyukozturk and
Hearing 1998, Chaallal et al. 1998, Garden and Hollaway 1998, Taljsten 2001 and
Teng et al. 2003). Overall, Teng et al. (2003) appear to provide the latest and most
comprehensive classification of failure modes. In their paper, they identified seven
types of failure modes in FRP-strengthened beams (Figure 2.1):
a)

Flexural failure by FRP rupture

b)

Flexural failure by concrete crushing

c)

Shear failure

d)

Concrete cover separation


e)

Plate-end interfacial debonding

f)

Intermediate flexural crack-induced interfacial debonding

g)

Intermediate flexural shear crack-induced interfacial debonding
Of all these failures, failure mode (d) and (e) were classified as plate-end

debonding while failure mode (f) and (g) were classified as intermediate crackinduced interfacial debonding. A mixture between these failure modes are also
possible such as concrete cover separation combined with plate-end interfacial
debonding and plate debonding at a shear crack section with extensive yielding of the
tension reinforcement (Taljsten 2001).

4


2.1.1 Flexural Failure by FRP Rupture and Concrete Crushing
FRP-strengthened beams can fail by tensile rupture or concrete crushing. This
type of failure was less ductile compared to flexural failure of reinforced concrete
beam due to the brittleness of the bonded FRP (Teng et al. 2002a).

2.1.2

Shear Failure
Shear failure of FRP-strengthened beams can occur in a brittle manner. In


many FRP-strengthened structures, this failure can frequently be made critical by
flexural strengthening. Furthermore, research has shown that the addition of FRP at
the bottom of beam did not contribute much to an increase in shear strength
(Buyukozturk and Hearing 1998). This has called for great care and attention in the
design of FRP-strengthened beams to guard against possible shear failure.

2.1.3

Concrete Cover Separation
This type of failure mode had been widely reported by researchers (Sharif et

al. 1994, Nguyen et al. 2001, Maalej and Bian 2001). It occurs due to high interfacial
shear and normal stress concentrations at the cutoff point of the FRP plate/sheet.
These high stresses cause cracks to form in concrete near the FRP cut-off point and
subsequently along the level of the tension steel reinforcement before gradually
leading to separation of concrete cover (Teng et al. 2002a).

2.1.4 Plate-End Interfacial Debonding
Plate-end interfacial debonding refers to debonding between adhesive and
concrete that propagate from the end of plate towards the inner part of the beam.
Upon debonding, a thin layer of concrete generally remains attached to the plate.

5


Researchers related this type of failure to the high interfacial shear and normal
stresses near the end of plate. The debonding normally occurred at the layer of
concrete, which was the weakest element compared to adhesive (Teng et al. 2002a).


2.1.5

Intermediate Flexural Crack-Induced Debonding
This type of failure mode occurs when a major crack forms in the concrete.

The crack causes tensile stresses to transfer from the cracked concrete to the FRP. As
a result, high local interfacial stresses are induced near the crack between the FRP and
concrete. Upon subsequent loading, stresses at this crack increases and debonding of
FRP will take place once these stresses exceed a critical value. The debonding process
generally occurs in the concrete, adjacent to the adhesive-to-concrete interface and it
propagates from the crack towards one of the plate ends (Teng et al. 2002a).

2.1.6

Intermediate Flexural Shear Crack-Induced Debonding
This failure mode initiates when the peeling stresses due to relative vertical

displacement between the two faces of a crack is high enough (Meier 1995, Swamy
and Mukhopadhyaya 1999, Rahimi and Hutchinson 2001). Garden et al. (1998)
categorized this type of failure into two distinct modes, depending on their shear
span/depth ratio: partial cover separation of type A and partial cover separation of
type B. Type A failure mode was initiated by the vertical step between A and B as
shown in Figure 2.2 while Type B failure mode was initiated by the rotation of a
“triangular” piece of concrete near the loading position that causes displacement of
the plate (Figure 2.3). According to Teng et al. (2002a), the debonding propagation is
strongly influenced by the widening of the crack, as in the case of intermediate

6



flexural crack-induced debonding, rather than the relative movement of crack faces,
which is of only secondary importance.

2.2

Interfacial Shear Stress Concentration
Many researchers had come up with approximate analytical models to predict

interfacial stresses (Jones et al.,1998; Roberts 1989, Taljsten 1997, Malek et al. 1998
and Smith and Teng 2001). The model by Smith and Teng (2001) is the most recent
and performs relatively well. However, the model proposed by Taljsten (1997)
appears to be more simple and easy to apply. In this literature review, only the
approximate interfacial shear stress models of Taljsten (1997) and Smith and Teng
(2001) were presented.

2.2.1

Taljsten’s Model (1997)
Taljsten (1997) proposed an analytical model to calculate the interfacial

stresses in the adhesive layer. The model was based on the following assumptions:
bending stiffness of the strengthening plate was negligible as the bending stiffness of
beam was much greater than the stiffness of plate; stresses were constant across the
adhesive thickness; load is applied at a single point (Figure 2.4). The model for a
single point load can be applied to two point loads by superimposing the shear
stresses obtained from first and second point loads.
The equation for the shear stresses in the adhesive layer was given by:

τ = C1 cosh(λx) + C 2 sinh(λx) +


Ga P
(2l + a − b)
l+a
2λ t a E c Z c
2

2.1

7


where

λ2 =

Ga b frp ⎛ y c
1
1
⎜
+
+
⎜
t a ⎝ E c Z c E c Ac E frp A frp

⎞
⎟
⎟
⎠

Ga


Shear modulus of adhesive

P

Point load

ta

Thickness of adhesive

Ec

Elastic modulus of concrete

Zc

Section modulus of concrete

l

Distance from middle of FRP-beam to CFRP cut-off point

a

Distance from support to CFRP cut-off point

b

Distance from CFRP cut-off point to loading point


2.2

C1,C2 Constants
Ac

Cross sectional area of concrete

Afrp

Cross sectional area of FRP

yc

Distance from bottom of concrete beam to its centroid

Equation 2.1 was valid for a distance from cut-off point to loading point ( 0 ≤ x ≤ b )
since singularity exists under the point load. By considering only the case where λb is
greater than 5 and with appropriate boundary condition, Taljsten (1997) comes out
with a final expression for the shear stress:

τ max =

Ga P (2l + a − b) (aλe − λx + 1)
2t a E c Z c
l+a
λ2

2.3


However, this equation should be used only when close to the end, x = 0, to reduce the
simplification error. Then, the maximum shear stress at the cut-off point was given
by:

8


τ max =

Ga P (2l + a − b) (aλ + 1)
2t a E c Z c
l+a
λ2

2.4

If there were two point loads, P1 and P2, the total peak shear stresses were calculated
by adding the peak shear stresses caused by both of the point loads as follows:

τ max 1 =

Ga P1 (2l + a − b1 ) (aλ + 1)
2t a E c Z c
l+a
λ2

τ max 2 =

Ga P2 (2l + a − b2 ) (aλ + 1)
2t a E c Z c

l+a
λ2

2.5

2.6

and the total peak shear stress is equal to :

τ total = τ max 1 + τ max 2

2.2.2

2.7

Smith and Teng’s Model (2001)

Many of the available interfacial stress models did not consider the effects of
axial deformation or bending deformation of bonded plate which can be critical when
the bonded plate has significant flexural rigidity. Furthermore, some of the analytical
models suffered from limited loading conditions. To overcome these limitations,
Smith and Teng (2001) proposed a new model to determine interfacial shear and
normal stress concentrations of FRP-strengthened beams with the inclusion of axial
deformation and several load cases. Smith and Teng’s solution was applicable for
beams made with all kinds of bonded thin plate materials. In their model, they
assumed: linear elastic behaviour of concrete, FRP and adhesive; deformations were
due to bending, axial and shear; adhesive layer was subjected to constant stresses
across its thickness; no slip at the interface. The derivation below was expressed in
terms of adherends 1 and 2, where adherend 1 refers to the concrete beam and


9


adherend 2 refers to the FRP composite (Figure 2.4). There are a total of three load
cases being considered, namely uniformly distributed load, single point load and two
symmetric point loads as shown in Figure 2.5.

Uniformly distributed load
⎡ m2 a
⎤ qe − λx
⎛L
⎞
+ m1 q⎜ − a − x ⎟
( L − a ) − m1 ⎥
⎝2
⎠
⎣ 2
⎦ λ

τ ( x) = ⎢

2.8

Single point load
a< b ' : τ (x)
⎛ b' ⎞
⎛ b' ⎞
Pa⎜1 − ⎟e −λx + m1 P⎜1 − ⎟ − m1 cosh(λx)e − k for 0 ≤ x ≤ (b'− a )
λ
⎝ L⎠

⎝ L⎠

m2

=

b'
⎛ b' ⎞
Pa⎜1 − ⎟e −λx − m1 P − m1 P sinh(k )e −λk
λ
L
⎝ L⎠

m2

or =

2.9

for (b'− a ) ≤ x ≤ L p

a> b ' : τ (x)

b'
⎛ a⎞
Pb' ⎜1 − ⎟e −λx − m1 P
λ
L
⎝ L⎠


m2

=

for 0 ≤ x ≤ L p

2.10

Two symmetric point loads
a< b ' : τ ( x)
=

or =

m2

λ

m2

λ

Pae −λx + m1 P − m1 P cosh(λx)e − k

for 0 ≤ x ≤ (b'−a)
2.11

Pae −λx + m1 P sinh(k )e −λk

for (b'−a) ≤ x ≤ L p / 2


a> b ' : τ ( x)
=

m2

λ

Pb' e −λx

for 0 ≤ x ≤ L p

2.12

where

10