FRP STRENGTHENING OF RC BEAMS IN FLEXURE ... FAILURE MODES AND DESIGN

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FRP STRENGTHENING OF RC BEAMS IN FLEXURE AND SHEAR:
FAILURE MODES AND DESIGN
by
Erdem Karaca
B.S., Civil Engineering
Bogazici University (1999)
Submitted to the Department of Civil and Environmental Engineering
in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Civil and Environmental Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
February 2002
MAR 0 6 2002
D 2002 Massachusetts Institute of Technology
All rights reserved
LIBRARIES
BARKER
Signature of Author
Department of Civil an 'E vironmental, ngineering
Fe ruary 1, 2002
Certified by
Oral Buyukozturk
Engineering
Environmental
Professor of Civil and
Thesis Supervisor
Accepted by
A c Oral Buyukozturk
Professor of Civil and Environmental Engineering
Chairman, Departmental Committee on Graduate Studies
FRP Strengthening of RC Beam in Flexure and Shear:
Failure Modes and Design
by
Erdem Karaca
Submitted to the Department of Civil and Environmental Engineering
On February 1, 2002, in partial fulfillment of the requirements for the degree of
Master of Science in Civil and Environmental Engineering
Abstract
Maintenance and rehabilitation of reinforced concrete (RC) structures is becoming a major
concern in the construction industry. The costs associated with the renewal and retrofit of these
structures forced the government and private organizations to search for new techniques and new
materials to increase their safety and extend their service lives. Use of externally bonded fiber
reinforced plastic (FRP) composites is recognized as an effective technique in repair and
rehabilitation of concrete structures due to high specific strength, corrosion resistance, and
reduced weight of these materials, and ease of application. The main objectives of this study are
first to experimentally study the failure behavior and capacity of precracked RC beams
strengthened in flexure and then to develop the associated design criteria and guidelines.
The experimental study investigates the capacity and failure modes of precracked RC beams that
have shear capacities slightly over their unstrengthened flexural capacities and effect of external
shear strengthening on their behavior. It is observed in the experimental tests that provision of
flexural FRP strengthening might adversely affect the shear resistance of the beams strengthened
only in flexure and shear failures might take place at load levels lower than their theoretical shear
capacities. It has been found that the provision of external FRP shear strengthening in form of Uwraps prevents shear and also debonding failures by providing anchorage to the flexural FRP
plate. However, when shear strengthening is not provided over the whole shear critical region,
shear failures might occur in unstrengthened beam sections. It is also shown that, when the
external strengthening systems is properly designed to prevent debonding and shear failures, the
ductility of the strengthened beams may be as high as those of the corresponding unstrengthened
beams.
A fracture-energy based analytical model for delamination of FRP laminates from RC beams is
developed. The delamination loads predicted by the model are compared and found to agree with
the failure loads of the test specimens that failed by delamination in the compiled experimental
database. The developed delamination model is then incorporated into a comprehensive design
procedure that deals with the design of RC beams strengthened in flexure. The details of the
design procedure are presented and demonstrated through worked examples.
Thesis Supervisor: Oral Buyukozturk
Title: Professor of Civil and Environmental Engineering
2
Acknowledgements
I would like to express my deepest gratitude to my thesis supervisor Professor Oral Buyukozturk
first of all for providing me the opportunity to work with him and then for his support and
guidance throughout the course of this study. This work could not have been completed without
his tolerance and patience.
Partial support provided by Mid-America Earthquake Center through the project "Innovative
Materials for Bridge Rehabilitation" and by National Science Foundation through the project
"Failure Behavior of FRP Bonded Concrete Affected by Interface Fracture" is gratefully
acknowledged.
I am grateful to Prof. Ali Rana Atilgan for being a source of inspiration to pursue my academic
career in this field and for his guidance and encouragement.
I would like to thank Steven Rudolph for his help during the experimental study.
Thanks are also extended to all my friends and co-workers at MIT for their friendship and
support, especially to Oguz Gunes, who has been more than a close friend and co-worker. I will
definitely miss his companionship during the rest of my studies.
Finally, I would like to thank my parents and my fianc6e for their love, encouragement, and
support throughout my education.
3
Table of Contents
A bstract..........................................................................................................................................2
A cknowledgem ents........................................................................................................................3
Table of Contents ..........................................................................................................................
4
List of Figures................................................................................................................................7
List of Tables..................................................................................................................................9
N otation........................................................................................................................................10
1
Introduction .........................................................................................................................
1.1
Repair and Strengthening of Concrete Structures ......................................................
12
1.2
U se of FRP Com posites in Repair and Strengthening ...............................................
13
1.3
History of Research on Use of FRP Composites for Reinforced Concrete Beam
Retro fit ......................................................................................................................................
2
14
1.4
Research Needs .........................................................................................................
16
1.5
Research Objectives and Approach............................................................................
18
1.6
Thesis Organization...................................................................................................
19
Materials and Structural Behavior of FRP Retrofitted Beams ..................................
21
FRP Retrofitting System s.........................................................................................
2.1
2.1.1 Fiber Reinforced Plastic Composites ....................................................................
2.1.2 Adhesives ..................................................................................................................
2.2
Structural Behavior of RC Beam s Strengthened in Flexure......................................
2.3
Failure M odes of RC Beam s Strengthened in Flexure..............................................
2.3.1
Flexural Failures.....................................................................................................
2.3.2
2.3.3
2.3.4
3
12
Shear Failures ............................................................................................................
D ebonding Failures ................................................................................................
Estimation of Stress Concentrations and Modeling Debonding Failures .............
22
22
30
31
35
36
38
39
44
2.4
Behavior of RC Beams Strengthened in Flexure and Shear ....................................
49
2.5
Experim ental D atabase..............................................................................................
51
2.6
Sum m ary and Research Needs ..................................................................................
58
Experim ental Study.............................................................................................................61
62
3.1
D esign and Details of Test Specim ens ......................................................................
3.2
M aterials........................................................................................................................64
3.3
Specim en Preparation................................................................................................
65
3.4
Instrum entation and Test Procedure.........................................................................
67
4
3.5
Test Results ...................................................................................................................
3.5.1
3.5.2
3.5.3
3.6
4
5
6
Summ ary of Experimental Results...........................................................................
69
73
78
79
3.7
Discussion of Shear Resistance Mechanisms in Strengthened RC Beams ................
3.7.1 RC Beam s W ith Shear Reinforcement..................................................................
3.7.2 RC Beam s Strengthened in Flexure ......................................................................
86
86
88
3.8
Contribution of Results to The Experimental Database...........................................
95
3.9
Concluding Rem arks ..................................................................................................
96
Review and Evaluation of Debonding Models and Design Guidelines.........................102
4.1
Plate End Shear M odels ..............................................................................................
103
4.2
Interfacial Stress Based M odels ..................................................................................
106
4.3
Evaluation of ACI 440F Guidelines for Flexural Strengthening ................................
4.3.1 ACI 440F Draft Guidelines for Flexural Strengthening..........................................
4.3.2 Evaluation of Safety ................................................................................................
114
114
116
4.4
Concluding Rem arks ...................................................................................................
120
Fracture Energy Based Plate End Delamination Model ...............................................
123
5.1
Fracture Energy Based M odel for Plate-End Delam ination........................................
5.1.1 Delam ination Criteria and M odel............................................................................
5.1.2 Evaluation of Fracture Energy Dissipated ..............................................................
5.1.3 Comparison of with Experimental Results..............................................................
124
126
128
131
5.2
135
Concluding Rem arks ...................................................................................................
Design for Flexural Strengthening...................................................................................136
6.1
Phases of the Design Procedure ..................................................................................
6.1.1 Phase I: Selection of Retrofit M aterials ..................................................................
6.1.2 Phase II: Flexural Design with Section Analysis ....................................................
6.1.3 Phase III: Evaluation of Shear Capacity .................................................................
6.1.4 Phase IV : Design for Delamination Failures...........................................................
6.1.5 Phase V : Serviceability Check ................................................................................
138
138
138
149
150
151
6.2
W orked Exam ples .......................................................................................................
6.2.1 W orked Exam ple I: .................................................................................................
6.2.2 W orked Exam ple II: ................................................................................................
158
158
161
Concluding Rem arks ...................................................................................................
164
6.3
7
Test Results of Beam s in Set I .............................................................................
Test Results of Beam s in Set II.............................................................................
Test Results of Beam s in Set III...........................................................................
69
Sum m ary, Conclusions, and Future W ork .....................................................................
165
7.1
Research Needs ...........................................................................................................
166
7.2
Objectives....................................................................................................................
167
7.3
Sum m ary .....................................................................................................................
167
5
7.3.1
7.3.2
7.3.3
7.3.4
7.3.5
M aterials and Structural Behavior of FRP Beam s ..................................................
Experimental Study and Discussion of Observed Failure Modes...........................
Review and Evaluation of Debonding Models and Design Guidelines ..................
Fracture Energy Based Plate End Delam ination M odel..........................................
Design For Flexural Strengthening .........................................................................
167
168
169
170
171
7.4
Conclusions .................................................................................................................
172
7.5
Future Work ................................................................................................................
173
References ..................................................................................................................................
174
Appendix I: Experimental Database .......................................................................................
181
6
List of Figures
Figure 2-1: Comparison of Typical Tensile Modulus of FRP Composites with Other
C onstruction M aterials...........................................................................................
27
Figure 2-2: Typical Load Deflection Behavior of Plated and Unplated RC Beams ................ 32
Figure 2-3: Failure Modes of FRP Strengthened Beams.........................................................
35
Figure 2-4: Stresses in FRP Strengthened Beams ....................................................................
40
Figure 2-5: Theoretical Shear Demand/Shear Capacity versus Actual Shear Demand/Shear
C ap ac ity ......................................................................................................................
54
Figure 2-6: Strengthening Ratio versus Actual Shear Demand/Calculated Shear Capacity ........ 54
Figure 2-7: Change of Strengthening Ratio with Steel Reinforcement Ratio ..........................
56
Figure 2-8: Strengthening Ratio versus Steel to Balanced Stiffness Ratio ..............................
56
Figure 2-9: Strengthening Ratio versus FRP to Balanced Stiffness Ratio ...............................
57
Figure 2-10: Strengthening Ratio versus FRP to Steel Stiffness Ratio ....................................
57
Figure 2-11: Change of Strengthening Ratio with Unplated Length to Shear Span Ratio.....58
Figure 3-1: D etails of Test B eam s...........................................................................................
62
Figure 3-2: Precracking Load-Deflection Curves for Beams F-I and F-II-2............................66
F igu re 3- 3 : T est S et u p .................................................................................................................
68
Figure 3-4: Locations and Designations of Strain Gages ........................................................
68
Figure 3-5: Load-Deflection Curves of Test Beams in Set I....................................................
69
Figure 3-6: Failure M ode of Beam F-I....................................................................................
70
Figure 3-7: Measured FRP Strains Along Beam F-I ...............................................................
70
Figure 3-8: Failure Mode of Beam FS-HU-I...........................................................................
71
Figure 3-9: Failure M ode of Beam FS-FU-I .............................................................................
72
Figure 3-10: Load-Deflection Curves of Test Beams in Set II................................................
73
Figure 3-11: Failure M ode of Beam F-II..................................................................................
74
Figure 3-12: Failure M ode of Beam F-II-2 .............................................................................
75
Figure 3-13: Measured FRP Strains Along Beam F-II-2 ........................................................
75
Figure 3-14: Failure Mode of Beam FS-HU-II ........................................................................
76
Figure 3-15: Failure Mode of Beam FS-FU-II........................................................................
77
Figure 3-16: Load-Deflection Curves of Test Beams in Set III ...............................................
78
Figure 3-17: Failure mode of Beam FS-HU-III.......................................................................
80
Figure 3-18: Measured FRP Strains Along Beam FS-HU-III..................................................80
Figure 3-19: Failure Mode of Beam FS-FU-III.........................................................................81
Figure 3-20: Measured FRP Strains along Beam FS-FU-III....................................................81
Figure 3-21: Shear Resistance Mechanisms in a RC Beam With Shear Reinforcement..........87
Figure 3-22: Shear Resistance Mechanisms in a RC Beam With Shear Reinforcement..........88
Figure 3-23: Plate End Shear in a RC Beam Strengthened in Flexure ....................................
90
Figure 3-24: Shear Resistance Mechanisms in a RC Beam Strengthened in Flexure away from
4
P late E n d s...................................................................................................................9
Figure 3-25: Theoretical Flexural Capacity/Shear Capacity versus Shear Demand/Shear
97
C ap acity ......................................................................................................................
97
Figure 3-26: Strengthening Ratio versus Shear Demand/Shear Capacity ................................
Figure 3-27: Change of Strengthening Ratio with Steel Reinforcement Ratio ......................... 98
7
Figure 3-28: Strengthening Ratio versus Steel to Balanced Stiffness Ratio ............................
98
Figure 3-29: Strengthening Ratio versus FRP to Balanced Stiffness Ratio .............................
99
Figure 4-1: Comparison of Failure Loads Predicted by Jansze's Model with Experimental
R e su lts ......................................................................................................................
104
Figure 4-2: Comparison of Failure Loads Predicted by Ahmed et al.'s Model with Experimental
R e sults ......................................................................................................................
10 5
Figure 4-3: Interfacial Stresses at Plate Ends of Beam F-II-2 at Failure Load........................... 108
Figure 4-4: Interfacial Stresses at Plate Ends in Beam F-II-2 at Different Load Levels............109
Figure 4-5: Interfacial Stresses at Plate Ends of Beams F-I, F-II, and F-II-2 at 110 kN............ 109
Figure 4-6: Comparison of Failure Loads Predicted by Roberts' Model with Experimental
R e sults ......................................................................................................................
1 12
Figure 4-7: Comparison of Failure Loads Predicted by El-Mihilmy and Tedesco's Model with
E xperim ental R esults ...............................................................................................
113
Figure 4-8: Factor of Safety versus Shear Demand/Shear Strength........................................... 116
Figure 4-9: Factor of Safety versus Unplated Length to Shear Span Ratio ............................... 117
Figure 4-10: Factor of Safety versus FRP Stiffness to Balanced Stiffness Ratio....................... 118
Figure 4-11: Factor of Safety versus FRP Stiffness to Steel Stiffness Ratio.............................. 118
Figure 4-12: Factor of Safety versus Reinforcing Steel Ratio....................................................
119
Figure 4-13: Factor of Safety versus Total Stiffness to Balanced Stiffness Ratio ..................... 119
Figure 5-1 Typical Load Deflection Diagrams of FRP Strengthened and Unstrengthened RC
B e am s .......................................................................................................................
124
Figure 5-2 Strain Energy in the Strengthened Beam Before and After Debonding ................... 125
Figure 5-3: Comparison of Predicted Failure Loads with Experimental Results....................... 132
Figure 5-4: Comparison of Predicted Failure Loads with Experimental Results: Effect of
Lam in ate L en gth ......................................................................................................
132
Figure 5-5: Comparison of Est. Failure Loads with Est. Yielding Loads of Strengthened RC
B eam s .......................................................................................................................
13 3
Figure 5-6: Comparison of Est. Failure Loads with Est. Yielding Loads of Unstrengthened RC
B eam s .......................................................................................................................
13 3
Figure 5-7: Comparison of the ACI 440F Design Loads with Experimental Failure Loads......134
Figure 6-1: Flexural D esign Flow chart ......................................................................................
137
Figure 6-2: B alanced FR P R atio.................................................................................................142
Figure 6-3: Assumed Load-Deflection Response.......................................................................153
Figure 6-4: Experimental and Estimated Load-Deflection Curves of Beam F-I........................ 160
Figure 6-5: Details of Beam Used in Design Example II...........................................................
161
8
List of Tables
Table 2-1: Typical Tensile Properties of Fibers Used in FRP Systems (ACI 440F, 2000) ..... 23
Table 2-2: Typical Thermal Expansion Coefficients for FRP Composite, Concrete, and Steel ...26
Table 2-3: Tensile Properties of Laminates with Fiber Volumes of 40-60% (ACI 440F, 2000)..28
Table 2-4: Characteristics of Specimens in the Database ........................................................
52
Table 3-1: Sum m ary of Experimental Program ........................................................................
63
Table 3-2: Properties of the Carbon Fiber Fabrics and the Epoxy Resin..................................64
Table 3-3: Properties of the Cured Laminates After Standard Cure ........................................
65
Table 3-4: Sum m ary of Test Results.........................................................................................
82
Table 3-5: Ductility Indices and Ductility Ratios of Tested Beams.........................................84
Table 6-1: Comparison of Analytical and Experimental Results................................................
149
Table 6-2: Material Properties Used in Design Example II........................................................
162
9
Notation
Af
=
Afbc
-
f by
Afna
AS
AS
As
b
bf
c
d'=
d
df
E
Ef
E
Et,
E)
EIstr
EIunsr
fc=
fe
A
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
f
ff
=
=
=
ffe
=
ff
=
=
fsus
fs=
fS,
fS
f)
fy.
h
k
kf
L
Lf
L
Lo=
=
=
=
=
=
=
=
=
=
=
area of FRP reinforcement, (mm2
area of FRP reinforcement corresponding to simultaneous concrete crushing and FRP
rupture, (mm 2 )
area of FRP reinforcement corresponding to simultaneous concrete crushing and steel
yielding, (mm 2 )
maximum allowable area of FRP reinforcement, (mm 2)
area of shear reinforcement, (mm 2
area of tensile steel reinforcement, (mm2
area of compression steel reinforcement, (mm 2)
width of the beam, (mm)
width of the FRP reinforcement, (mm)
distance from extreme compression fiber to the neutral axis, (mm)
distance from extreme comp. fiber to the centroid of the comp. steel reinf., (mm)
distance from extreme comp. fiber to the centroid of the tensile steel reinf., (mm)
distance from extreme comp. fiber to the centroid of the FRP reinforcement, (mm)
modulus of elasticity of concrete, (MPa)
tensile modulus of elasticity of FRP, (MPa)
modulus of elasticity of steel,(MPa)
area under the load deflection curve at ultimate failure,(N-mm)
area under the load deflection curve at yield load,(N-mm)
bending stiffness of strengthened beam (N-mm 2
bending stiffness of unstrengthened beam (N-mm2)
compressive stress in concrete, (MPa)
tensile strength of concrete, (MPa)
compressive strength of concrete, (MPa)
stress level in the FRP reinforcement, (MPa)
effective stress in the FRP reinforcement, (MPa)
ultimate tensile strength of FRP, (MPa)
stress in the FRP reinforcement under sustained loads, (MPa)
stress in tensile steel reinforcement, (MPa)
stress in tensile steel reinforcement under service loads, (MPa)
stress in compression steel reinforcement, (MPa)
yield stress of tensile steel reinforcement, (MPa)
yield stress of shear reinforcement, (MPa)
height of a beam, (mm)
ratio of the depth of the neutral axis to the reinforcement depth
stiffness per unit width per ply of the FRP reinforcement, (N/mm) k = Ef ty
clear span of the beam, (mm)
length of FRP reinforcement, (mm)
distance between support and point load, (mm)
distance between support and end of FRP reinforcement, (mm)
10
Gf
Mbi
M
M
Msu
=
=
=
=
fracture energy, (N/mm)
moment
nominal
moment
moment
applied at time of FRP installation, (N-mm)
moment capacity, (N-mm)
demand based on service loads, (N-mm)
demand based on sustained loads, (N-mm)
Punstry
=
=
=
=
=
P,
s1
=
=
yield load, (N)
stirrup spacing, (mm)
t
=
=
=
=
nominal thickness of the FRP reinforcement, (mm)
shear resistance provided by concrete with steel flexural reinforcement, (N)
nominal shear strength, (N)
shear resistance provided by steel stirrups, (N)
shear demand based on factored loads, (N)
strain energy stored in unstrengthened beam (N-mm)
strain energy stored in strengthened beam (N-mm)
mean stress factor
mean stress factor corresponding to maximum usable compressive strain of concrete
strain level in the concrete substrate at the time of the FRP installation, (mm/mm)
M
Pdeb
Pul
V
V,
V
Vu=
Wunstr
Wstr
C
XC
Ebi
F,
CCU
Ef
Efe
Ef
E;,
=
=
=
=
=
=
=
=
=
=
Eo
=
=
=
=
y
=
C
CS1
_
moment demand based on factored loads, (N-mm)
debonding load, (N)
ultimate load, (N)
yield load of unstrengthened beam, (N)
strain level in the concrete, (mm/mm)
maximum usable compressive strain of concrete, (mm/mm)
strain level in the FRP reinforcement, (mm/mm)
effective strain level in FRP reinforcement, (mm/mm)
rupture strain of FRP reinforcement, (mm/mm)
strain level in the compressive steel reinforcement, (mm/mm)
strain level in the tensile steel reinforcement, (mm/mm)
strain corresponding to the yield point of steel reinforcement, (mm/mm)
strain corresponding to maximum concrete stress, (mm/mm)
concrete compressive force centroid factor
concrete compressive force centroid factor corresponding to maximum usable strain
of concrete
Km
=
=
Aul
=
=
=
=
=
=
yf
=
IdE
A
p,
Ps
A
strength reduction factor
bond dependent coefficient for flexure
energy ductility index
deflection ductility index
FRP reinforcement ratio
tensile steel reinforcement ratio
midspan deflection at yield load, (mm)
midspan deflection at ultimate load, (mm)
additional FRP strength reduction factor
11
1 Introduction
1.1 Repair and Strengthening of Concrete Structures
As the world's infrastructure ages, reinforced concrete structures, such as bridges and buildings,
become functionally obsolete due to a variety of reasons including environmental deterioration,
change of use, or increased structural load requirements. Maintenance and rehabilitation of these
structures is becoming a major concern in the construction industry, especially in developed
countries. American Concrete Institute estimates that repair and remediation services constitutes
about 70% of the U.S. concrete construction market, whose size is approximated to be $8
billion/year (Busel and Barno, 1996). About 230,000 of the 575,000 highway bridges in United
States were rated as structurally deficient or functionally obsolete and need -or will need renewal or rehabilitation for extending their service lives (Crasto et al, 1996). According to
California DOT, about 5000 bridges are estimated to be in need for some form of renewal or
retrofit to satisfy the current design standards and the costs associated with them are expected to
be $3 billion (Cercone and Korff, 1997). The total cost of rehabilitation nationwide, including
repair of corrosion damage and seismic upgrading has been estimated to be $212 billion
(Cercone and Korff, 1997). According to U.K Highways Agency, the total number of bridges in
U.K is around 135,000. The replacement cost for damaged bridges is estimated to be $10 billion
and nearly $ 230 million/year is spent for maintenance (Busel and Lindsay, 1997). As a result of
a major assessment program on bridges in U.K, 10,000 of the total 60,000 reinforced concrete
bridges are in the need for upgrade (Bonacci and Maalej, 2000).
The costs and challenges associated with the renewal of these structures forced government and
private organizations to search for new techniques and new materials to extend the service life of
these structures. Use of externally bonded plates is recognized as an effective technique for in
situ repair and rehabilitation of reinforced concrete structures among several other techniques
ranging from section enlargement to external pre-stressing. In this technique, external plates are
bonded with structural adhesives to the outer faces of the structural members to act as additional
reinforcement. In 1980's steel plates were used in many applications of plate bonding technique
12
but the corrosion of steel plates and the need for relatively heavy equipment for application made
fiber reinforced plastic (FRP) composites the material of choice for such applications.
1.2 Use of FRP Composites in Repair and Strengthening
With their higher strength, better corrosion resistance, reduced weight, and ease of application,
compared to steel plates, FRP composites became far more popular in construction industry in
the last decade. FRP composites are made up of high strength fibers embedded in a matrix and
show linearly elastic behavior up to failure. Although there are a variety of fibers available,
carbon and glass fibers are the most frequently used fiber types in construction industry. These
composites can be generally tailored to provide desired stiffness and strength properties.
Although their stiffness is generally less compared to steel, their ultimate strength can be much
higher than steel, depending on the amount and properties of the fibers used. Owing to their low
specific weights, they have high specific stiffness and strengths and exhibit excellent corrosion
and fatigue resistance.
Although the initial material costs are relatively high, they are generally competitive with other
repair techniques, when the costs associated with reduced labor and construction time are taken
into account. FRP composites have been used to increase the lateral strength and ductility of RC
columns by wrapping them and to increase the in plane and out of plane strength of unreinforced
and reinforced concrete walls. They are also being widely used for flexural strengthening of
slabs, and flexural and shear strengthening of reinforced concrete beams. They can be also used
for control of deflection and/or cracking in beams and slabs.
Increasing strength and ductility of RC columns by wrapping them with FRP composites is
relatively a well-established rehabilitation technique. Strengthening of reinforced concrete beams
in flexure with externally bonded FRP plates are also shown to be an efficient technique where
significant improvements in ultimate strength and serviceability properties can be obtained.
However, it has been also demonstrated in many experimental studies that, in case of RC beams
strengthened in flexure, it is not generally possible to make full capacity of the strengthening
system due to premature failure modes, i.e. delamination of the FRP plate from the concrete
substrate or debonding of the concrete cover layer at the reinforcing steel layer. Both of these
failure modes are more brittle than failure modes associated with conventionally reinforced
13
concrete beams and they significantly limit the level of strength enhancement that may be
achieved.
1.3 History of Research on Use of FRP Composites for Reinforced
Concrete Beam Retrofit
Research in this area was initiated in Europe in early eighties driven by the durability problems
encountered with the widely used method of flexural and shear strengthening by bonded steel
plates. In Germany, research at the Technical University of Braunschweig concentrated on use of
glass FRP and investigated various bonding and durability characteristics through tests on simple
tension specimens, beams and one way slabs (Rostasy, 1992). In Switzerland, studies at the
Swiss Federal Materials Testing and Research Laboratories (EMPA) concentrated on the use of
carbon FRP for strengthening of beams (Meier, 1992). The state-of-the-art work by Kaiser
(1989) explored use of CFRP plates in strengthening of beams, and identified the different
modes of failure under monotonic and cyclic loading. Promising results from Europe attracted
several researchers in the U.S. (Saadatmanesh and Ehsani, 1990; Ritchie et al., 1991;
Triantafillau et al., 1992) to work in this area. Other researchers from Canada (Mufti et al., 1991;
Neale and Labossiere, 1992; McKenna and Erki, 1994), and Saudi Arabia (Sharif et al., 1994)
soon joined the research efforts due to large scale strengthening needs of existing infrastructure
in these countries caused by durability problems associated with cold and hot climatic conditions
respectively. Beginning from early 90's, research on flexural strengthening with composites
began to flourish by joining of many researchers from all over the world (JCI, 1997).
In strengthening applications using externally bonded reinforcement, in order to provide the
required stiffness, load carrying capacity, and ductility of the retrofitted system, it is desired that
the system failure take place by rupture of the bonded composite so that the strength and
deformation capacity of the composite is fully utilized. However, initial studies in Europe on
beams reported evidence to the contrary: Although CFRP composite plates bonded to the soffits
of beams significantly increased their flexural capacity, failure was often through brittle
debonding at the concrete-CFRP interface initiating at laminate ends and shear crack locations
(Meier and Kaiser, 1991; Meier, 1995). Following studies in the U.S., Canada, and Saudi Arabia
produced similar results: They recognized the high potential of FRP composites for use in
strengthening of concrete members, but drew attention to brittle debonding failures and
14
underlined the importance of understanding such failures. It was also understood that beams
strengthened in flexure need also to be strengthened in shear (Berset, 1992; Chajes et al., 1995a;
Triantafillou, 1998; Khalifa et al, 1998; Khalifa and Nanni, 2000). This was found necessary not
only to prevent brittle failure of beams in shear, but also to decrease shear deformations in beams
to prevent debonding failures caused by differential displacements at shear crack mouths.
During the first half of 90s, research on strengthening of flexural members essentially
concentrated on generating experimental data and basic analytical and parametric studies to
explore the effectiveness of the method and to identify modes and mechanisms of failure. The
studies included use of GFRP and CFRP composites in strengthening beams of various sizes in
flexure and in shear using various bonding and anchorage configurations. Starting from midnineties, publications of design guidelines began to appear (Ziraba et al., 1994; Picard et al.,
1995; Arduini and Nanni, 1997a; Saadatmanesh and Malek, 1998; Challal et al., 1998; ElMihilmy and Tedesco, 2000b). However, these studies generally did not take debonding failures
into consideration assuming that they are prevented by appropriate means.
In addition, analytical studies have been performed to investigate the stress states at plate end
and existing crack locations, where premature debonding failures might initiate and develop
(Vichit-Vadakan, 1997; Taljsten, 1997; El-Mihilmy and Tedesco, 2001; Malek et al, 1998,
Rabinovitch and Frostig, 2000). These researchers calculated elastic stresses at the concrete-FRP
interface using continuum mechanics approach and applied various failure criteria to explain
debonding failures.
However, debonding failure criteria based on elastic stresses and continuum mechanics approach
have had limited success due to nonlinear behavior and cracking in concrete, and prompted the
use of fracture mechanics concepts to analyze the debonding process (Buyukozturk and Hearing
1997, 1998; Buyukozturk et al., 1998a, 1998b, 1999). Several other researchers also approached
the problem from fracture mechanics view and made attempts to characterize the fracture energy
of bond between concrete and FRP composites (Karbhari and Engineer, 1996; Fukuzawa et al,
1997) and to develop fracture energy based criteria for debonding failures (Taljsten, 1996;
Hearing, 2000; Lau et al, 2001; Leung, 2001).
15
1.4 Research Needs
Research in the area of structural strengthening with FRP composites is still young. Although
much has accomplished in the past fifteen years in characterization of the failure behavior and
mechanisms under monotonic loading, there is still need for research in several areas such as
effects of laminate width, thickness, and length on failure modes and loads. Previous studies
concentrating on debonding failures have generally considered beams over-designed in shear to
simplify the problem. Continued research is needed to investigate debonding failures for
specimens representing real life beam members strengthened in flexure and shear.
To prevent, or at least to postpone, the occurrence of debonding failures, external anchorage
devices may be applied to the ends of FRP plates. Anchorage may be provided in a variety of
forms including bolted anchorage systems, bonded steel sections, bonded FRP L-shaped and Ushaped sections, and clamps. It has been observed that provision of these additional anchorage
devices can increase both the ultimate strength and especially the deformation capacity of the
FRP strengthened systems. However, the level of research in this area is far from quantifying the
effects of these complex systems and more research has to be performed on this aspect.
Increased flexural capacity of RC beams strengthened only in flexure results in an increased
demand for shear capacity, which might be over the existing shear capacity of the existing beam,
and may require shear strengthening as well. This might be achieved by bonding unidirectional
or multidirectional FRP composites to the sides of the RC beams in the vertical or inclined
directions. Additional shear reinforcement may be applied in a variety of forms, including
bonding continuous sheets or strips to the sides of the beams, U-jacketing around the bottom, and
totally wrapping the beam. Providing externally bonded shear reinforcement not only improves
the shear capacity of the beam, but may also contribute to the flexural capacity of beam by
preventing debonding type failures initiated from shear cracks or at least increase the load level
at which debonding occurs by reducing the size and number of shear cracks. In addition, in case
of U-wrapped or totally wrapped configurations, external shear reinforcement will cause a more
uniform stress distribution and reduce stress concentrations at the ends of flexural FRP
reinforcement and at existing cracks locations by acting as an additional anchorage. With the
application of FRP reinforcement for shear, failure mode of the strengthened beam may shift
from debonding and shear type failures to more ductile failure modes, i.e. concrete crushing or
16
FRP rupture preceded by yielding of tensile steel reinforcement. However, the number of
research studies on RC beams strengthened both in flexure and shear is limited compared to
studies concentrating only one of them and the interaction between them was not investigated in
detail.
Due to the short history of research on use of FRP composites for structural strengthening, the
majority of studies have dealt with exploring the effectiveness of the materials and the
methodology for monotonic loading conditions, and very few studies have looked into their
performance under cyclic loading. Performance of strengthened members under cyclic loading
plays a vital role for the method to be considered for structures with variable loads, such as
bridges, and for seismic retrofitting applications. Preliminary results obtained from initial studies
in this area show that strengthening concrete beams with FRP composites improve their
performance, however, cannot prevent the cumulative damaging effects of cyclic loading, which
result in decreased residual load carrying capacity (Inoue et al., 1996; Muszynski and
Sierakowski, 1996; Shahawy and Beitelman, 1999). Significance of debonding failures is
magnified in case of cyclic loading since it was experimentally shown that debonding could
initiate and propagate at low load levels (Chuang, 1998).
Durability performance of concrete members strengthened with FRP composites is an important
factor that affects application decisions. Although FRP composites are known for their good
durability performance, it is the durability of the bond at concrete-FRP interface that raises
concerns among researchers and practitioners. Limited number of studies in this area have shown
that environmental exposure have detrimental effects on mechanical behavior of the bond in a
retrofitted system (Chajes et al., 1995b; Crasto and Kim, 1996; Toutanji and Gomez, 1997;
Mukhopadhyaya et al., 1998; Toutanji and El-Korchi, 1999), high temperature and humidity
being the most influential parameters. Transport of moisture and aggressive chemicals from the
environment can cause irreversible damages in the bond, especially at high temperatures, that
can jeopardize the integrity and safety of the strengthened member. Very little is known about
how the strengthened system is affected by various service conditions such as cyclic loading and
environmental exposure; and coupling of mechanical and environmental effects remains virtually
uninvestigated. Sufficient knowledge on these issues is essential for public safety and for
mainstream applications of FRP in structural strengthening (Scalzi et al., 1999; Buyukozturk et
al., 1999).
17
Another issue is the lack of written specifications or standards on design of such strengthening
systems that are currently available. The same situation is also valid for construction quality
control. Recently, ACI has established a committee (ACI 440-F) for selection, design and
installation of FRP systems for external strengthening, which has published a draft document in
2000 providing main design guidelines (ACI 440F, 2000). However, the above-mentioned issues
about strengthening of RC beams should be studied in detail and developed knowledge should be
incorporated into this and similar design standards for safe and reliable application of this
strengthening technique.
1.5 Research Objectives and Approach
The main objectives of this study are to experimentally and analytically study the failure
behavior and capacity of RC beams strengthened in flexure and to develop guidelines for design
of such systems. The experimental study focuses on precracked RC beams that have shear
capacities slightly over their unstrengthened flexural capacities and on the effect of external
shear strengthening on the capacity and failure mode of these beams. Whereas, the analytical
study makes an attempt to model the delamination of the FRP laminates from the RC beams
using a fracture energy based approach.
The more specific objectives are to:
" develop an understanding on the failure behavior of FRP strengthened RC beams and to
identify main parameters affecting this behavior;
" experimentally study failure behavior and capacity of FRP strengthened RC beams that
represent real world cases and the effect of external FRP shear strengthening on such
systems;
" review, evaluate, and discuss available approaches for modeling and design of such systems,
" perform an analytical study to model the delamination of FRP laminates from RC beams;
*
present a general design procedure for flexural strengthening of RC beams; and
" identify specific research areas where further improvements are required.
For these purposes, first mechanics and failure behavior FRP retrofitted concrete beams are
reviewed and summarized in detail. Parameters affecting the failure behavior are identified and
summarized together with related experimental and theoretical studies. Behavioral trends
18
observed in previous experimental studies are presented with the help of a compiled database and
areas that need further investigation are identified. An experimental study is performed on
precracked reinforced concrete beams strengthened either only in flexure or both in flexure and
shear to investigate the interaction between them and to observe the transition from brittle shear
failures to ductile flexural failures with the provision of shear strengthening in beams that have
shear capacities close to their strengthened flexural capacities. Then, theoretical models
developed for prediction of premature failure loads are reviewed, discussed, and evaluated with
the help of the results of the experimental study and other data available in the database. Design
philosophy and equations for design and analysis of RC beams are presented and design related
issues are discussed. Then, the beams in the experimental database are analyzed according to the
design guidelines of ACI Committee 440F. The observed trends are presented and areas that
need improvement are identified and recommendations are made.
1.6 Thesis Organization
Chapter 2, first, reviews properties of FRP composite materials used in construction industry.
Then mechanics and failure behavior of RC beams strengthened in flexure are summarized,
together with related experimental and theoretical work. Then, the behavioral trends observed in
previous experimental studies are presented through the use of a compiled database and the areas
of further research are identified.
Chapter 3 describes the details of the experimental program performed on precracked RC beams
strengthened either only in flexure or in both flexure and shear. Tests beams were designed to
have shear capacities close to their strengthened flexural capacities to observe the transition from
brittle shear failures to ductile flexural failures with the provision of shear strengthening. The
results are presented and discussions on failure modes, strength increases, ductility, and the shear
resistance mechanisms in strengthened RC beams are made.
Chapter 4 first reviews modeling approaches for predicting shear and debonding failure loads of
retrofitted beams. Some of these models are evaluated with the help of the data in the
experimental database. Then, philosophy of the design guidelines developed by ACI Committee
440-F is presented and safety of beams designed according to these guidelines are evaluated by
comparing the experimental results in the database with the design loads.
19
Chapter 5 develops a fracture-energy based analytical model for delamination of FRP laminates
from RC beams.
Chapter 6 presents a design procedure for design of RC beams strengthened in flexure. Design
equations are presented and design related issues are discussed.
Chapter 7 summarizes the work. Conclusions are drawn and areas for future research are
indicated.
20
2 Materials and Structural Behavior of
FRP Retrofitted Beams
This chapter reviews the FRP materials used for strengthening concrete structures and the
structural behavior of FRP retrofitted RC beams including their load-deflection behavior and
failure modes. Related experimental and theoretical studies are summarized, with a special
emphasis on debonding type failures. Interfacial stress based and fracture based approaches for
modeling interfacial stresses and associated failures are reviewed as well. Then, the behavior of
RC beams strengthened both in flexure and shear is discussed. Finally, the characteristics of
previous experimental studies on FRP strengthened beams are presented with the help of a
compiled database and research areas that need further development are discussed.
First, the components of FRP structural systems, i.e. fibers, saturating resins or bonding
adhesives, are reviewed. The properties of different fiber types and adhesives are discussed.
Then, the physical and mechanical properties of the FRP composites are reviewed. Their
stiffness and strengths are discussed together with their fatigue, creep, and environmental
resistance.
Next, the structural behavior of RC beams strengthened in flexure is reviewed and also
evaluated. First, the behavioral differences between unstrengthened and strengthened RC beams
are discussed. Then, the failure modes observed in FRP strengthened beams are reviewed
together with related theoretical and experimental work. In addition, interfacial stress based and
fracture based models developed for estimating interfacial stress concentrations and debonding
failures are reviewed. The behavior of RC beams strengthened both in flexure and shear is also
included in the review.
Finally, the results of a survey of previous experimental studies on strengthened RC beams are
presented to investigate and discuss the main parameters determining the failure modes and
ultimate strength of RC beams strengthened in flexure with FRP composites. Finally, the
research needs are identified and summarized.
21
2.1 FRP Retrofitting Systems
A variety of commercially available FRP retrofitting systems are currently being used in repair
and strengthening applications. These systems may consist of components including saturating
resins, fibers and adhesives. The fibers together with the saturating resins constitute the FRP
composite, which serves as the external reinforcement. Adhesives are used to bond pre-cured
FRP composites to concrete substrate or multiple layers of pre-cured FRP composites to each
other transferring shear between components.
There are a number of possible forms for the application of FRP systems, e.g. wet lay-up, prepreg and pre-cured systems. Wet lay-up systems involve hand or machine built-up of dry fiber
sheets or fabrics that are bound together on-site using a saturating resin. They are saturated and
cured in place. Saturating resin acts both as the matrix of the FRP composite and as the adhesive.
In pre-preg systems, the fiber sheets or fabrics are impregnated off-site with saturating resins,
and cured on-site, usually with the application of heat. In case of pre-cured FRP systems, both
the impregnation and cure processes are done off-site and the resulting FRP composite is then
bonded to concrete substrate using an appropriate adhesive.
2.1.1 Fiber Reinforced Plastic Composites
Composites are defined as the combination of two or more materials sharing an interface
between them. The main constituents of an FRP composite are the reinforcing fibers and the
polymer resin matrix that contains the fibers. The matrix holds the fibers together and transmits
the stresses between fibers. It also serves as a protective barrier between the fibers and the
environment. Although reinforcing fibers provide the composite its basic strength and stiffness,
some mechanical properties, such as in-plane and inter-lamina shear are highly matrix dependent
(Hull and Clyne, 1996; ACI 440R, 1996).
Fibers
Properties of the FRP composite are highly dependent on the orientation, length, shape,
composition and properties of the fibers. The reinforcing fibers used may be long and continuous
or short and discontinuous. They can be aligned in one or more directions or randomly
distributed in two or three dimensions. FRP composites used in the construction industry usually
incorporate continuous fibers with a unidirectional orientation. This configuration provides
22
superior strength and stiffness in the fiber axis direction. However, it results in highly anisotropic
properties and is suitable for applications where FRP composite is only subjected to tensile
stresses in the fiber direction. To obtain more isotropic properties, unidirectional fiber layers can
be stacked on each other at alternating directions varying between 0' and 900. As an alternative,
other techniques like weaving, braiding, and knitting may be used to produce multi-directionally
oriented fiber layers. These bi-directional or multidirectional fabrics are generally used in shear
strengthening applications. Another commonly used form of fiber configuration is the random
orientation of short fibers (Hull and Clyne, 1996).
Although there are a variety of reinforcing fibers that offer a wide range of mechanical
properties, glass, aramid, and carbon fibers are the most commonly used ones in FRP retrofitting
systems. The most significant property of the fibers is their elastic modulus, which should be
much larger than the elastic modulus of the matrix to allow them carry most of the stress, which
in turn requires them to be of high strength. Typical fiber properties are shown in Table 2-1.
Glass Fibers
Glass fibers are the most commonly used fibers in construction industry due to their lower price
and relatively good specific strength properties. They are of moderate strength but low modulus
compared to carbon and aramid fibers. Although they have various different types (i.e. E, A, C,
E-CR, R, S and AR), by far the most widely used ones are E-glass and S-glass. E-glass has
Table 2-1: Typical Tensile Properties of Fibers Used in FRP Systems (ACI 440F, 2000)
Fiber Type
Ultimate Strength
(MPa)
Elastic Modulus
(GPa)
Rupture Strain,
minimum, (%)
Carbon
General Purpose
220
-
235
2050
-
3790
1.2
High Strength
220
-
235
3790
-
4825
1.4
Ultra High Strength
220
-
235
4825
-
6200
1.5
High Modulus
Ultra High Modulus
Glass
E-Glass
S-Glass
345-515
515 -690
1725-3100
1375 -2400
0.5
0.2
69-72
86-90
1860-2685
3445-4135
4.5
5.4
69
3445 - 4135
2.5
3445 -4135
1.6
Aramid
General Purpose
High Performance
-
83
110- 124
23
excellent electric insulation characteristics and offers good corrosion resistance. S-glass has
higher strength and greater corrosion resistance than E-glass. It should be noted that glass fibers
and composites made from them might show degradation when exposed to moisture or high
alkaline environments and need to be protected by suitable resins or other means of surface
treatments, especially under sustained strain levels.
Carbon Fibers
Although expensive, carbon fibers are extensively used in construction industry due to their very
high strength and stiffness. They are produced from precursors of PAN, pitch, or rayon by
carbonizing them at high temperatures. They offer a wide range of strengths and stiffness
depending on fiber microstructure and treatment and are generally classified either as high
modulus or high strength, although both of these properties are relatively high. Carbon fibers are
brittle and electrically conductive, which might limit their use in certain applications.
Aramid Fibers
Aramid fibers are organic synthetic fibers offering very high tensile strengths with relatively
high elongation to failure that provides aramid fibers the capability of absorbing large amounts
of energy, i.e. toughness. They are very low weight that and have high specific strengths and
stiffness, which makes them the first choice when the specific properties are the selection
criteria. Most of them are resistant to fatigue and creep rupture. Aramid fibers are insulators of
electricity and heat and resistant to organic solvents and fuels. They are fire resistant and perform
well at high temperatures. However, some aramid fibers exhibit lower strengths in compression
and susceptible to UV degradation.
Resins
The main purpose of the matrix resin is to transfer stresses between the reinforcing fibers and the
surrounding structure, however it also protects the fibers from mechanical damage and serves as
a protective barrier between the fibers and environment, thus preventing attack from moisture,
chemicals, oxidation and etc. The properties of the matrix resin highly influence the interlaminar shear, in-plane shear and compressive properties of the composite. Fillers can be added
to polymer resins to reduce resin cost, improve mechanical properties, control shrinkage and
reduce cracking, and impart a degree of fire redundancy. Polymer matrix resins can be classified
24
as thermosetting and thermoplastic polymers, but the formers are the ones generally used in
construction industry. The most frequently used thermosetting resins in composites are
polyesters, vinyl esters and epoxies (Schwartz, 1997; ACI 440R, 1996).
Polyesters
Several types of polyester resins are available, but most common ones consist of either
orthophthalic or isophthalic acids. The original form of unsaturated polyesters, ortho polyesters,
are economical but demonstrate low mechanical properties and chemical resistance and are less
likely to be used in structural applications. Iso polyesters have improved mechanical properties
and superior thermal, moisture and chemical resistance compared to ortho polyesters, but are
more costly.
Vinyl esters
Vinyl esters are processed and cured like polyesters and widely used in similar applications.
They demonstrate better mechanical and chemical performance compared to ortho and iso
polyesters but have higher costs. They are tough, flexible and resistant to aggressive
environments including high alkali environments.
Epoxies
Although they are more expensive than polyesters and vinyl esters, epoxy polymer matrix resins
are popular in infrastructure applications. They have superior mechanical and physical properties
and show lowest shrinkage during cure. They have excellent resistance to chemicals and solvents
and have good adhesion to fillers, fibers and substrates, including concrete. However, some types
require longer curing times, and processing and application should be done with care to maintain
moisture resistance.
Physical and Mechanical Properties of FRP Composites
Fiber reinforced plastics offer physical and mechanical properties that are either comparable or
superior to many traditional construction materials. Since they can be produced with a number of
different fiber and matrix types, amount, and configurations, the physical and mechanical
properties of FRP composites vary significantly from one product to another. Performance and
properties of FRP composites are dependent on the properties of the fiber and the matrix, the
proportion of each, the interaction between them and the configuration of the fibers. Factors like
25
orientation, length, shape and composition of the fibers, physical and mechanical properties of
the resin matrix, and adhesion between fibers and matrix significantly affect the properties of the
composite. Due to their heterogeneous and anisotropic nature, FRP composites generally
demonstrate quite dissimilar properties in different directions. Furthermore, the mechanical
properties of them, like all composites, are affected by duration and type of loading, and
environmental conditions like temperature and moisture (ACI 440R, 1996; ACI 440F, 2000).
Density
FRP composites have specific gravities much lower than that of steel, in the range of 1.2 to 2.1
g/cm 3 . They are consequently easier to transport and handle, and require less falsework, which
allows faster and more economical application. Also, they do not add significant dead loads on
structure and can be used in areas of limited access.
Coefficient of thermal expansion
Thermal expansion coefficients of composites depend on several factors including types of fibers
and matrix, their volume fractions and configuration of fiber reinforcement. Table 2-2 shows
typical thermal expansion coefficients for unidirectional FRP composites with fiber volume
fractions ranging from 0.5 to 0.7, together with those of steel and concrete for comparison
purposes. The two negative values are a result of negative thermal expansion coefficients of
carbon and aramid fibers in longitudinal direction.
Strength and Stiffness
Strength and stiffness of FRP composites depend on the stiffness and strength of components,
volume fraction and orientation of fibers and method of manufacturing. They usually show
various degrees of anisotropy depending on configuration of fibers and manufacturing technique.
As expected, unidirectional FRP composites have the largest strength and stiffness values
compared to other configurations when loaded in fiber orientation.
Table 2-2: Typical Thermal Expansion Coefficients for FRP Composite, Concrete, and Steel
Direction
GFRP
Longitudinal, UL
Transverse, aXT
6 to 10
19 to 23
Coefficient of Thermal Expansion (x1O-6/C)
CFRP
AFRP
Concrete
-6 to -2
60 to 80
-i to 0
22 to 50
26
4 to 6
4 to 6
Steel
6.5
6.5
High Modulus
Carbon Plate
Carbon Plate
Glass Plate
High Modulus
Carbon Sheet
-E
Carbon Sheet
Glass Sheet
Aluminum
Steel
Concrete
0
50
100
150
200
250
Young's Modulus (GPa)
Figure 2-1: Comparison of Typical Tensile Modulus of FRP Composites with Other Construction Materials
Under tension, FRP composites behave in a linearly elastic manner up to rupture and do not
exhibit any yield point or region of plasticity. Their tensile strengths are generally much larger
than that of steel plates with same cross-sectional areas, however, their stiffness are generally
lower than steel. Figure 2-1 gives a comparison of typical tensile modulus of different forms of
FRP composites with other construction materials including concrete, steel and aluminum. In
addition to their relatively low stiffness, their failure strains are low compared to many metals,
generally less than 3%. As a consequence, the area under the stress-strain curves of them, i.e.
toughness, is relatively small. Typical tensile properties of FRP laminates with fiber volumes of
40%-60% are shown in Table 2-3. Although, CFRP composites having a wide range of
mechanical properties are available, their elastic modulus and strengths are generally much
larger than those of GFRP and AFRP composites.
Although not clearly identified due testing difficulties, compressive strengths of FRP composites
are lower than their tensile strength. This is also the case for stiffness; compressive modulus of
elasticity is usually lower than the tensile modulus of elasticity. Fiber microbuckling, shear and
transverse tensile failures may be observed in FRP composites under compression. Generally,
FRP composites with higher tensile strengths also have higher compressive strengths. However,
27
Table 2-3: Tensile Properties of Laminates with Fiber Volumes of 40-60% (ACI 440F, 2000)
FRP System
Description
Young's Modulus
Property at 0'
Property at 900
(GPa)
(GPa)
Ultimate Tensile Strength
Property at 0'
Property at 90'
(MPa)
(MPa)
Rupture Strain
Property at 00
(%)
Hi gh strle ngth carlnlepoxy
0 00
0 00/900
9 +450/-45'
100-145
55-76
14-28
2-7
55-75
14-28
1025-2075
700-1025
175-275
35-70
700-1025
175-275
1.0-1.5
1.0-1.5
1.5-2.5
0 00
20-40
14-34
* 0'/900
14-21
* +450/-450
High performance aramid/epoxy
2-7
14-35
14-20
525-1400
525-1025
175-275
35-70
525-1025
175-275
1.5-3.0
2.0-3.0
2.5-3.5
48-68
28-34
2-7
28-35
700-1725
275-550
35-70
275-550
2.0-3.0
2.0-3.0
7-14
7-14
140-205
140-200
2.0-3.0
E-glass/epoxy
* 00
0 00/900
*
+450/-45
some aramid FRP composites exhibit relatively low compressive strengths. Therefore, they
should be carefully designed, particularly for compression and bending.
Creep
Creep of FRP materials is highly dependent on the level of sustained stress, configuration and
form of FRP composite and the matrix. Endurance time decreases with increased sustained stress
to short term ultimate stress ratio. The effect of sustained stresses becomes more significant
under adverse environmental conditions, especially under high temperature. Creep performance
of CFRP composites is better than both GFRP and AFRP composites, with GFRP being the
worst.
In unidirectional composites subjected to tensile stresses, the behavior of the composite is mainly
dominated by the performance of the fibers and their resistance to creep is quite well. However,
in case of compression or off-axis tensile loading, the matrix properties become more significant,
since the deformation of polymers, which have viscoelastic behavior, tend to increase with time
under sustained stresses. Therefore, unidirectional FRP composites are the most creep-resistant
form of FRP composites. 00/900 and 450/450 non-woven forms have better creep characteristics
compared to corresponding woven forms, since fibers tend to straighten out under stress in latter
ones.
28
Fatigue
Due to their anisotropic characteristics, polymeric composites experience a complex and
progressive failure mechanism under fatigue loading. The four basic failure mechanisms
associated with composites are matrix cracking, delamination, fiber breakage and interface
debonding (Hollaway, 1993). Type and degree of these mechanisms vary depending on the
material properties, stacking sequence of laminates and type of fatigue. The slopes of the S-N
curves (i.e. the measure of the relative fatigue performance) of polymeric composites are mainly
determined by the strain in the matrix, since the fatigue limit of the matrix is lower than that of
the fibers (Curtis, 1989). The matrix strain is dependent on the properties of the matrix itself, as
well as on the modulus of elasticity and the volume fraction of fibers. The slope of the S-N curve
increases as the modulus of elasticity or the proportion of the fibers in the loading direction
decreases, since this increases the likelihood of matrix damage. As a result, unidirectional
composites have much better fatigue performances compared to multidirectional composites.
Also, the fatigue performance of a composite with a given matrix can be improved only a little
by the use of stronger reinforcing fibers, since the fatigue failure is usually governed by damage
in the matrix and fiber/matrix interfaces (Owen, 1974). The fatigue performance of composites
under environmental exposure mainly depends on the sensitivity of the composite to the
properties of the matrix with respect to environmental conditions (Curtis, 1989).
The fatigue performance of CFRP composites, especially unidirectional ones, is generally
superior to other composites and is almost unaffected by moisture under room temperature. Due
to their relatively low modulus, GFRP composites experience strains that approach the cracking
strain of the matrix, which results in a reduced fatigue life. Their fatigue behavior is highly
dependent on environmental conditions, mainly due to sensitivity of individual glass fibers to
alkaline, acidic solutions, and, especially, moisture. The performance of AFRP composites under
fatigue may be excellent to poor depending on the type of loading. Their performance under
tensile/tensile fatigue is much superior than that under flexural fatigue due to the innate poor
static flexural performance of aramid fibers (Hutchinson and Quill, 1999).
Durability
Most important factors influencing the long-term durability of FRP composites are moisture,
chemicals, high temperatures and UV radiation. The extent of change in the physical and
29
mechanical properties of the FRP composite depends not only on the type and duration of the
exposure environment, but also on the properties of the composite itself. The curing method,
type of fibers, and especially physical and chemical properties of the resin matrix, determine the
reduction in mechanical properties of the composite.
Although no strict generalizations should be made about environmental resistance of FRP
composites due to dependence of it on a large number of factors, CFRP composites are generally
more durable than both GFRP and AFRP composites. Absorbed moisture may attack the surface
of glass fibers leading to a reduction in the adhesion between the fibers and the matrix, and in
turn, a reduction in the mechanical properties of the GFRP composite. Also, in case of AFRP, a
reduction in the properties of aramid fibers, and therefore in composite material properties, may
be observed due to absorbed moisture. Also, the high alkaline environment of concrete may
cause additional harm to these two types of composites.
The mechanical properties of FRP composites are highly dependent on temperature because of
the viscoelastic nature of the matrix. Differences in thermal expansion coefficients of fibers and
the matrix can cause progressive debonding and weakening of the composite under fluctuating
temperatures (Hutchinson and Hollaway, 1999). However, it should be noted that FRP
composites are not generally exposed to large temperature fluctuations in their service
environment and the effect of temperature on the composite properties is usually reversible
unless the glass transition temperature of the matrix is approached. Beyond this temperature, the
resin matrix softens and the mechanical properties of the composite are reduced due to
incapability of matrix in transferring stresses between fibers.
However, different types of chemical additives can be incorporated into the structure of the resin
matrix or various coatings may be applied to the outer surface of the composite to increase its
environmental durability, especially fire and UV resistance.
2.1.2 Adhesives
The other critical component of FRP retrofitting systems, in addition to FRP composite, is the
adhesive. Its purpose is to produce a continuous bond between the FRP composite and concrete
substrate to transfer shear stresses and develop a full composite action. For this to occur, an
adequate degree of adhesion between the involved surfaces should be established and sustained
through the service life of structure under varying environmental conditions, including high
30
alkaline or moisture environments. The mechanical and thermal properties of the adhesive, the
effects of environment and other service condition on the adhesive and on the behavior of the
joint should be carefully considered in all applications (Mays and Hutchinson, 1992).
Two-part cold curing paste epoxy adhesives are by far the most common type of adhesive used
in structural strengthening applications. Epoxy adhesives can be formulated in a variety of forms
by mixing resin, the most important component of the adhesive, with certain types of hardeners
and some other components, such as fillers, plasticizers, and etc, to obtain a broad range of
application characteristics and mechanical properties. The choice of hardener is important in
determining the curing temperature of the adhesive, however, the rate of curing, as a rule of
thumb, is doubled for every 80C rise in temperature. Generally, 6-12 hours is sufficient for most
cold curing epoxies to achieve a satisfactory degree of cure, with full cure being attained in 24
hours or so. They can also be formulated to provide enough open time for application. Epoxies
have good wetting properties for a variety of surfaces and are able to accommodate irregular or
thick bondlines. Compared to polyesters and vinyl esters, epoxies exhibit lower shrinkage, which
provides reduced residual bondline strains in cured joints. They also show reduced creep and
superior strength retention under sustained loads. And most importantly, due to their high
cohesive strength, they might dictate the joint failure to occur in the adherent, especially in case
of concrete provided that adequate surface preparation is performed.
2.2 Structural Behavior of RC Beams Strengthened in Flexure
Strengthening of beams using FRP composites involves bonding FRP plates or sheets to outer
faces of reinforced concrete beams to act as additional reinforcement and to improve their
stiffness and load carrying capacities. The general form of the load-deflection behavior of a
reinforced concrete beam strengthened in flexure by bonding an FRP plate to its tensile face has
several key differences compared to that of an unplated beam (Figure 2-2). The typical load
deflection curve of a strengthened reinforced concrete beam can be divided into three distinct
and almost linear stages (El-Mihilmy and Tedesco, 2000a). These stages will be referred to as
pre-cracking, post-cracking, and post-yielding stages in this document.
31
35
Plated
20
0
2
4
6
8
10
12
14
16
Deflection
Figure 2-2: Typical Load Deflection Behavior of Plated and Unpiated RC Beams
Pre-cracking Stage
The initial stiffness before cracking is almost identical for the two cases and the cracking load is
altered slightly by the addition of the external FRP plate, since all section including the concrete
in tension region is effective in bending and the plate has relatively little effect on the stiffness of
the beam. Similarly, the first cracking load is only slightly increased by the addition of the
composite plate, unless a very stiff plate of high-cross sectional area is used. Elastic equations,
using the uncracked transformed moment of inertia including contribution of FRP, can be used to
compute the deflection of FRP strengthened beams in this stage.
Post-cracking Stage
However, once cracking occurs, the concrete below the neutral axis becomes almost ineffective
in bending and the contribution of the FRP composite to the overall stiffness of the beam
becomes more pronounced depending on the stiffness and cross sectional area of the FRP
composite. Therefore, post-cracking stiffness of strengthened beams is significantly higher than
the tenil
that of the unstrengthened beams. Sincehtes
force inathe section is shared by the
reinforcing steel and FRP composite, the stress in reinforcing steel is lower than that in an
unstrengthened section at a given load. This might have important implications on crack widths
in concrete since the strain in the reinforcing steel is the main controlling factor on the width of
the cracks. In addition, composite plate serves as a means for transferring tensile stresses at crack
locations to intact concrete between these cracks, which results in a tension stiffening effect and
further increases in stiffness. As a result of the increased stiffness of the composite system and
32
reduced tensile stresses in reinforcing steel, the yielding stress of the steel is reached at a higher
load compared to unplated case.
Post-yielding Stage
After yielding of reinforcing steel, the overall member stiffness, which is referred to as postyielding stiffness, decreases. However, the reduction in stiffness is significantly less than that of
the unplated beam, since FRP plate continues to contribute to the bending rigidity of the section.
Although reinforcing steel has yielded, FRP composite is still capable of carrying increased
tensile stresses and the strengthened beam can sustain considerably higher loads before one of
the below explained failure modes takes place. One important point to note, which is going to be
discussed in detail later on, is that the ductility of FRP strengthened beams at failure is less than
that of unstrengthened beams due to linear elastic behavior and relatively low ultimate failure
strain of FRP composites.
The ultimate deflection of conventionally reinforced concrete beams ranges from five to 12 times
the first yield deflection. In estimating the deflections, ACI recommends use of an effective
moment of inertia, I, , originally developed by Branson based on statistical analysis of
deflections from test data. Ie is a function of uncracked moment of inertia, cracked moment of
inertia, cracking moment, and maximum moment and intended to account for stiffness variation
along the beam due to non-uniform cracking. However, in case of FRP strengthened beams,
where the ultimate deflection of the beams generally ranges two to five times the yield
deflection, using the above effective moment of inertia approach usually gives deflections less
than the observed experimental values (El-Mihilmy and Tedesco, 2000a) and an alternative
approach, which is more accurate in representing the deflection behavior of FRP strengthened
beams, is required.
Ross et al (1999) performed an elastic-plastic section analysis for predicting the response of a
rectangular, under-reinforced, FRP strengthened concrete beam. The analysis assumes trilinear
and bilinear stress-strain distributions for concrete and reinforcing, respectively and is based on
linear strain distribution in section and a multi-linear load-displacement curve divided into four
regions. All material behavior is assumed to be elastic in the first region until the tensile stress in
concrete reaches modulus of rupture. In the second region, it is assumed that the concrete below
the neutral axis is not active in bending and the concrete in compression zone behaves in a linear
33
fashion until the reinforcing steel yields. Third region represents the behavior between yielding
of steel and the point where concrete stress at compressive face of beam reaches its peak value.
Once more, a linear stress strain distribution for concrete with a peak value of
f,'
is used, and
the stiffness of the concrete section is assumed to be constant throughout the section and equal to
the slope of the stress-strain curve of concrete between the points corresponding to yielding of
steel and the peak stress in concrete.
El-Mihilmy and Tedesco separated the load deflection curve of FRP strengthened beams into
three linear stages, each representing the behavior before cracking, yielding, and ultimate
moments (El-Mihilmy and Tedesco, 2000a). An empirical approach, which is a modified form of
Branson's formula, is used to estimate the effective moment of inertia of strengthened beam
before yielding of reinforcing steel, assuming that the concrete stress-strain relationship in the
compression zone is linear up to yielding. This effective moment of inertia is estimated to be
3
Ie
= Ic,. 1+ 1-
(2-1)
M
where
MY = EJcP
f
cr
n(d - c)
(2-2)
After this point, the moment curvature relationship is assumed to be linear between the first yield
point and the failure point, compression crushing of concrete, and the curvature corresponding to
a specific moment value is calculated using linear interpolation between these points. Then,
elastic equations are used to estimate deflections in this region.
In both of the above studies, the concrete stress-strain relationship up to yielding moment is
assumed to be linear. However, this might not be the case in FRP strengthened beams, especially
in highly reinforced ones. In addition, the stress-strain behavior of concrete used in the former
one is highly idealized.
One point to note is that FRP strengthening is applied to existing beams, which have been
subjected to service loads or environmental effects. It is certain that cracks would have
developed in these beams before the application of the strengthening system and the pre-cracking
stage would not be generally observed in the load deflection behavior of these beams.
34
In addition, the effect of existing stresses and the corresponding strains in the RC beam at the
time of FRP application must be taken into account in the analysis and design of the FRP
strengthened beams. The initial strains in the surface to which FRP is bonded should be excluded
from the strain in the FRP to allow direct application of linear strain variation along the section
of the strengthened beam. The strain in the concrete substrate can be determined from the
analysis of the unstrengthened beam under all loads (without any load factors) that will be acting
on the member during the installation of FRP system. Considering that the existing RC beam will
experience a bending moment greater than its cracking moment before installation of FRP, the
initial strains may be determined from the cracked section properties of the existing beam.
2.3 Failure Modes of RC Beams Strengthened in Flexure
General failure modes of FRP retrofitted beams include concrete crushing, FRP rupture, FRP
debonding/delamination, and shear failures. These failure modes are shown in Figure 2-3.
Ideally, the ultimate load carrying capacity of a strengthened beam should be controlled by
ductile mechanisms, that is either by rupture of the FRP composite or by crushing of concrete in
compression preceded by yielding of the tensile steel. However, other premature and brittle
failure modes, such as debonding of the FRP from concrete substrate or concrete cover
delamination, and shear failures may be observed at loads lower than the theoretical flexural and
shear strength of the strengthened beams. Debonding failures may result from shear and normal
stress concentrations at the plate ends, which cause FRP plate to peel off towards the center of
the beam or may occur due to stress redistribution and vertical crack opening displacements at
Figure 2-3: Failure Modes of FRP Strengthened Beams
35
crack mouths. For safe design of retrofit applications, all failure mechanisms must be fully
understood and properly considered in analysis and design. In what follows, an overview of the
above mentioned failure modes are given mentioning relevant experimental and analytical work
available in literature.
2.3.1 Flexural Failures
Flexural failure modes include compression crushing of concrete and tensile rupture of FRP
composite. Previous studies have shown that significant increases in flexural capacity may be
obtained if premature failure modes are prevented, especially when the internal steel ratio is low
(Triantafillou and Plevris, 1992; Ross et al, 1999). However, the increase in flexural strength is
at the expense of member ductility since FRP composites exhibit linear elastic behavior up to
failure and do not have a yielding stage. To obtain an acceptable level of ductility in
strengthened member, it must be ensured, first, that tensile steel reinforcement will yield before
any other failure mode takes place. This can be achieved by defining a balanced condition,
analogous to the case of a conventional reinforced concrete beam, which corresponds to a
condition at which concrete crushing and yielding of the reinforcing steel will occur at the same
time. Using the force equilibrium in the section, the FRP area that will result in balanced
condition may be found as
Afbk
=
E
0.85f'b3d
Ef
E d
-f(CCU+ 161
E-
'U
C+ 1
-
A, f(
23
If the FRP area provided is smaller than the above balanced FRP area the tensile reinforcement
steel will yield before crushing of concrete. Otherwise, brittle compression failure will take place
before yielding of tensile steel, which is not desired in any case. Therefore, in any design
scenario, the FRP area should be limited to a certain percentage of the above calculated balanced
area for steel yielding to ensure ductile failure. For example, the total tensile force in the crosssection may be limited to a certain percentage of the compressive force associated with the
concrete, i.e. 75%, so that yielding of steel will take place before compression crushing of the
concrete (Saadatmanesh and Malek, 1998; El-Mihilmy and Tedesco, 2000b).
Then, whether concrete crushing or FRP rupture will follow steel yielding, provided that the
debonding type failures will not take place, depends on the properties of the original RC beam
36
and the FRP strengthening system. But once these parameters are known, the amount of the FRP
reinforcement used can be selected in such a way that the desired failure mode will be obtained.
Another balanced condition, similar to the one above, which corresponds to simultaneous
compression crushing of concrete and FRP rupture may be defined and the FRP area for this case
may be expressed as
K0..85 f'/,bd
Af,bc
fj
"
- As fl.
(2-4)
ECU + Ef
If the FRP area provided is smaller than the FRP area corresponding to balanced condition the
failure mode of the strengthened beam will be FRP rupture, otherwise the failure will occur by
compression crushing of concrete. In case of concrete crushing, i.e. when a large amount of FRP
composite is used, the strains in FRP reinforcement could not reach their ultimate value, which
results in a less efficient use of the FRP reinforcement. However, in case of FRP rupture, the full
capacity of the strengthening system is utilized. In addition, in this mode of failure, when FRP
ruptures, the beam capacity drops to its unstrengthened strength and continue to deform until
final failure is reached by crushing of concrete, which in a sense provides some additional
ductility.
Many researchers have analyzed the flexural behavior and strength of FRP strengthened systems
by considering the FRP composite as an external reinforcement (El-Mihilmy and Tedesco,
2000b; Saadatmanesh and Malek, 1998; Picard et al., 1995, An et al., 1991; Triantafillou and
Deskovic, 1991). Assuming full composite action and strain compatibility, force equilibrium in
the section may be used to calculate the moment capacity corresponding to concrete crushing and
FRP rupture. The nominal flexural moment capacity of a strengthened beam, corresponding to
FRP rupture (Af<Afbc), can be calculated as
6c)
c
M
$
S
"6 -Afd
2
-Af f
df -
2
(2-5)
where
'b/+'
c0.85fc'bpA,(26
37
(2-6)
The nominal capacity of flexural moment capacity of a strengthened beam, corresponding to
concrete crushing (Af>Af.b), can be calculated as
" - A sf, d
Mn-
2
0
-- AE, d, Acu
2
C
(2-7)
where c is calculated from
H
4;i
(2-8)
A =0.85fL'plb
(2-9)
B =-Af, + Af Ef eCU
(2-10)
C=-AEe,Cdf
(2-11)
C
B
2A
with the following parameters
2.3.2 Shear Failures
Shear failures may be observed in RC beams strengthened in flexure, when the shear capacity of
the original beam is not sufficient to carry the loads in the upgraded system. Shear failures are
quite brittle and should be avoided to occur by any necessary means. It has been suggested that
the shear capacity of RC beams strengthened in flexure does not change significantly from their
shear capacity in unstrengthened form (Plevris et al, 1995). It has been even stated that bonded
external reinforcement contributes to the shear load capacity of strengthened beams (Rahimi and
Hutchinson, 2001).
However, there are many instances of shear failures attributed to the presence of the flexural
strengthening plate, where the failure of the strengthened beam occurred at load levels lower
than the theoretical shear strength of the beam due to a large shear crack developed at the end of
the plate (Sharif et al, 1994; Ahmed et al, 2001). These type of failures, which are termed as
"plate end shear", are caused by stress concentrations at plate ends and become more critical as
the distance from the cutoff point of the plate to the supports increases.
38
This failure mode is studied in detail by Janzse (1997), with experimental and finite element
studies on steel plated beams. He has observed that that the plate end shear load decreases with
increasing unplated beam length. He has also developed an analytical model utilizing the
fictitious shear span length concept. It should be noted that the model does not take into account
the contribution of the internal shear reinforcement and therefore represents a lower bound for
predicting the plate end shear load.
Recently, a modified form of Janzse's formulation was presented to estimate the plate end shear
load in case of FRP retrofitted beams (Ahmed et al, 2001). They proposed to add an additional
shear stress generated as a result of replacing the steel plates used in Janzse's study with CFRP
laminates. They also included the contribution of the internal shear reinforcement into the
formulation. They compared the values predicted by the above formulation with their own
experimental results and made recommendations for design. It worths mentioning that the failure
modes obtained by Ahmed et al. is more like concrete cover separation rather than plate end
shear failure.
2.3.3 Debonding Failures
Debonding/delamination type failures cover a wide variety of failures associated with the
separation of the flexural strengthening plate from the concrete beam with or without a layer of
concrete attached to it. Ideally, the stresses developed in the plate are transferred to the beam via
the adhesive layer, cover concrete, and the interfaces between these layer. When failure occurs in
one of these layers or interfaces due to increased bond stresses or stress concentrations, the
composite action between the FRP plate and the beam is lost and eventually the plate debonds
from the beam. Since the cover concrete is generally the weakest layer among them, failure
commonly occurs by delamination of the cover concrete. Debonding of the FRP plate might
either initiate from the plate ends and propagate towards the center of the beam or start from
flexural and flexural-shear crack locations. Both of these failures are extremely brittle and take
place with little advance warning at loads much lower than the theoretical flexural capacities of
the strengthened beams.
39
Debonding From Plate Ends
Debonding initiating from the plate ends is due to the presence of high interfacial shear and
normal stress concentrations near the plate termination points, which are shown in Figure 2-4.
Termination of the plate in a nonzero positive moment region is the main cause of such stress
concentrations and associated debonding failures. When this is the case, tensile axial stresses and
corresponding strains are developed in the concrete substrate near the plate cutoff point, but no
axial stresses or strains can be developed at the free end of the plate. However, the shear stiffness
of the adhesive layer forces the laminate to develop axial strains close to the values in the
concrete substrate over a short distance from the plate ends, which requires the concurrent
development of high shear stresses in the adhesive layer and its interfaces with the FRP plate and
concrete substrate. Similarly, non zero moments and curvatures exist in the concrete beam at
plate end locations, but the free boundary conditions at the plate ends requires the plate to
maintain a zero curvature at plate ends and this forces the plate to bend away from the beam
which in turn causes the adhesive layer to be pulled vertically. Maximum vertical stress
concentration, i.e. pull, occurs at the ends of the plate and decreases inwards.
IX
I
--
~
------
--- - --- ---
L1
I
7I
Txz
UZZ
A k~
L P..
.
,
Oxx
Figure 2-4: Stresses in FRP Strengthened Beams
40
Debonding from plate ends is the most common failure mode observed in FRP strengthened
systems. The parameters affecting the debonding behavior, such as the internal steel ratio, FRP
strengthening ratio, the distance from plate ends to the supports, have been investigated through
several experimental studies.
Hearing (2000) has performed experimental tests on RC beams strengthened with CFRP plates
of varying lengths. Initial delamination cracks were introduced between the adhesive and
concrete. Beams failed through delamination in the concrete, leaving a thin layer of concrete
bonded to the delaminated FRP. It was shown that both the delamination initiation and ultimate
failure loads increased with longer laminate lengths. However, beams with longer laminate
lengths failed in a more brittle manner with sudden delamination along the entire span. The
difference between the delamination initiation and ultimate failure loads were less compared to
beams with shorter laminate lengths.
Fanning and Kelly (2001) studied the effect of the ratio of the length of the laminate within the
shear span of the beam to the shear span of the beam on the ultimate response of RC beams.
They have used four different plate lengths and observed that the effectiveness of the external
plates reduced as the plate lengths were decreased. They also observed that the beams failed by
concrete cover delamination when the strain gradient in the plate within the shear span reached
approximately the same value and suggested that this limiting strain gradient might be used for
design purposes.
The effect of the amount of internal steel reinforcement on debonding behavior of strengthened
beams was investigated by Ross et al (2000). They tested RC beams with 6 different steel
reinforcement ratios and strengthened with the same amount of CFRP plates over the full clear
span. Beams with higher reinforcing steel ratios failed through concrete crushing, whereas in
case of the ones with lower steel ratios the failure occurred by delamination between the CFRP
plates and the adhesive. Although the failure loads increased with increasing steel ratio, the
percent of strength increase compared to the corresponding control beams decreased.
Maalej and Bian (2001), performed tests on RC beams strengthened with different amounts of
external CFRP sheets. They have kept the length and the width of the FRP sheets constant while
increasing the number of plies applied. Except the beam strengthened with a single layer of
CFRP, which failed by FRP rupture, the governing failure mode was concrete cover
41
delamination. However, the failure loads and associated displacements decreased with increasing
CFRP thickness, which was attributed to the inability of the thick FRP plates to maintain strain
compatibility at large deflections, which creates high interfacial shear and normal stress
concentrations and eventually leads to premature debonding type failures. They suggested
predicting interfacial stress concentrations as functions of displacements rather than loads.
Garden et al (1998a,b) investigated the effect of plate sectional geometry on failure behavior
beams with different shear span/depth ratios, by varying the plate thickness and width while
keeping the plate area constant. They have observed that the failure loads and ductility of
strengthened beams decrease as the plate width decreases.
To summarize, plate end debonding failures are more likely to occur and failure loads associated
with this failure mode decreases with decreasing length and width of the FRP laminate or with
increasing laminate thickness. Plate end debonding is also more favored in beams having lower
steel ratios, since higher tensile stresses have to be carried by the FRP laminate at a given load
level compared to beams with higher steel ratios provided all other parameters are the same.
Debonding From Flexural/Shear Cracks
In addition to the plate ends, debonding of the FRP composite might initiate from flexural or
shear cracks and propagate towards the ends. The presence of cracks and the variation of tensile
stresses in the concrete between these cracks owing to the bond between the tension
reinforcement and the cracked concrete create axial stress gradients in the FRP plate in the
vicinity of crack locations as shown in Figure 2-4. The axial stress variations in the FRP plate
are also associated with interfacial shear stress concentrations on both sides of the cracks. In
addition, the vertical crack mouth displacements at inclined flexural-shear and shear cracks
forces FRP plate to bend locally and exert tensile stresses to the adjacent adhesive and concrete
layer (Figure 2-4). The interfacial shear and normal stress concentration in the vicinity of the
crack mouths may reach values that will initiate debonding from these locations. When this
occurs, generally, a thin layer of concrete attached to the FRP plate starts peeling off from the
concrete beam along an approximately horizontal layer. If the bending stiffness of the FRP plate
used is low, i.e. if the FRP plate may is flexible, propagation of the peeling of the FRP plate and
attached concrete may be arrested at a certain distance from the crack location. Then, the fracture
42
zone might increase in a stable manner with increased loading until it reaches a point at which
fracture takes place along the remaining length of the bonded plate and causes failure.
In addition, as the debonding process propagates along the beam, the stresses in the internal steel
reinforcement at debonded sections increase. If the internal steel has yielded in debonded
sections but it remains elastic in the bonded region, high axial stress gradients are created in the
transition region between the debonded and bonded beam sections, which in turn accelerates the
debonding process. Therefore, debonding from flexural-shear and shear cracks becomes more
pronounced after yielding of the internal steel and may become self propagating (Sebastian,
2001).
Debonding failures initiated from existing crack locations, although observed much less
frequently compared to end debonding failures, have been observed in a number of test studies.
Arduini and Nanni (1997b) reported started several debonding failures starting at one of the
flexural cracks in the constant moment region and propagating towards the end until total
delamination occurs. In all cases, the plate cutoff point was reasonably close to the supports and
only one ply of FRP sheet was used for strengthening. Upon increasing the number of plies and
increasing the distance between the plate end and supports, the failure mode shifted from
midspan debonding to end debonding.
Hearing (2000), performed tests on RC beams strengthened with CFRP plates of varying lengths.
In beams with shorter laminate lengths, delarnination was observed to propagate suddenly along
the entire length of the beam with an indistinguishable direction of propagation. Whereas in case
of specimens with longer laminate lengths delamination was observed to originate from constant
moment region and propagate towards the ends of the plate. Thus, the ultimate load was found to
increase with longer laminate lengths.
Rahimi and Hutchinson (2001), tested several RC beams with different internal steel
reinforcement and different external FRP reinforcement ratios. In all cases, the lengths of the
FRP plates used for strengthening were almost equal to the clear distance between the supports,
preventing the occurrence of plate end peeling. All debonding failures either initiated from the
constant moment zone or occurred within the shear span of the beams and resulted in plate
detachment with a layer of adhesive cement paste attached to the plate.
43
The observations from the above mentioned experimental studies suggest that debonding from
flexural and shear cracks may become the dominant mode of failure when plate end debonding
failures are prevented by using relatively thin FRP plates and extending them till the supports.
This failure mode may be critical in some applications such as strengthening of simply supported
single span bridge sections.
2.3.4 Estimation of Stress Concentrations and Modeling Debonding
Failures
Several theoretical models based on interfacial stress analysis have been developed by different
researchers to predict stress concentrations at plate ends and crack locations. In most of these
studies, failure criteria for debonding of the FRP plate have been also introduced. In addition to
these stress based models, recently fracture mechanics based approaches have been used to both
estimate stress intensities and to investigate the associated failures.
Interfacial Stress Based Models
Roberts developed approximate expressions, which consists of three stages, to calculate the shear
and normal stress distribution in the adhesive layer of reinforced concrete beams strengthened
with external plates (Roberts, 1989). In the first stage, the interfacial shear stress is calculated for
an infinitely long beam, assuming full composite action between the plate and beam. In the
following stages, the solution is modified to take into the actual boundary conditions into
account. First, an axial force that is equal to but opposite to the force calculated at plate cutoff
point in the first stage is applied at both ends of the plate, which is assumed to be a axial member
on an elastic shear foundation representing the adhesive layer. The beam is assumed to be rigid
at this and third stage. Application of the axial force results in non-zero moment and shear
stresses at the end of the plate. In the final step, equal but opposite moments and shear forces are
applied at the both ends of the plate, which is now assumed to be a beam resting on an elastic
foundation, again representing the adhesive layer. Interfacial normal stresses can be obtained
directly at the end of the third stage, while the interfacial shear stresses are obtained by
combining the stresses calculated in the first two stages. The results are compared with solutions
based on partial interaction theory, as well as experimental results (Roberts and Haji-Kazemi,
1989). It was concluded that anchorage failure would occur at a combination of shear stress
between 3 and 5 MPa and normal stress between 1 and 2 MPa. However, other studies have
44
noted that shear and normal stresses at failure may reach values higher than those predicted by
this approach and the model is conservative (Mukhopadhyaya and Swamy, 2001; El-Mihilmy
and Tedesco, 2001; Maalej and Bian, 2001). Modified forms of Roberts' solution have been also
proposed by several researchers (Ziraba et al, 1994; El-Mihilmy and Tedesco, 2001).
Vichit-Vadakan (1997) developed a simple analytical model to investigate the shear transfer
between the concrete and the FRP sheet. The shear stress at the interface is expressed as a second
order differential equation, which is mainly based on the differential longitudinal displacements
of the laminate and the soffit of the RC beam. The lateral displacements along of the bottom of
the RC beam are estimated using the moment curvature relations. Making us of these two
relations, the shear stresses at the FRP-concrete interface are calculated using an iterative
procedure. It has been shown that the magnitude of the interfacial shear stresses increase as the
distance between the laminate end and the supports increase (Buyukozturk and Hearing, 1998).
Taljsten used linear elastic theory to derive the shear and peeling stresses in the adhesive layer of
a beam with a strengthening plate bonded to its soffit and loaded with an arbitrary point load
(Taljsten, 1997). Although the bending deformations of the strengthening plate were neglected,
the axial deformations in the plate and bending deformations of the beam were considered in the
derivation. The interfacial shear stresses in the adhesive layer are related to the difference
between the longitudinal displacement at the soffit of the beam and at the upper layer of the
strengthening plate, whereas the normal stresses are related to the vertical deformation
compatibility between the beam and the strengthening plate. The results of the derived
expressions are compared with a finite element analysis. It is concluded that the biggest
geometrical influence on the level of shear and peeling stresses is the distance from the ends of
the plate to the supports and this distance should be kept as short as possible to minimize these
stresses. A performed parametric study indicates that these stresses increases with increasing
adhesive stiffness, plate thickness and plate stiffness. Decreasing adhesive layer thickness also
results in increased interfacial stresses.
Malek et al developed a similar method again based on linear elastic behavior of materials and
compatibility of deformations (Malek et al, 1998). However, the solution was not limited to an
applied point load but was more general in terms of loading. The presented method can be
applied to cases where the applied moment can be expressed by
45
M ( ) = a,$ +a24 +a 3
where
= x + L, and L, is the distance between the origin
(2-12)
and the plate cutoff point. The
results of the analytical method are verified by comparing them with finite element analysis
results. They also adopted the failure model of Kupfer and Grestle (1973) developed for concrete
under biaxial stresses and compared the results of the theoretical model with the results of an
experimental study.
Recently, Rabinovitch and Frostig (2000) presented a closed form high-order approach for the
analysis of concrete beams strengthened in flexure with externally bonded FRP strips. The
solution is based on equilibrium and deformation compatibility requirements in and between all
components of the strengthening system, i.e., concrete beam, adhesive layer, and FRP plate. The
governing equations are derived and solved with closed form analytical solutions, along with the
appropriate boundary and continuity conditions. A numerical example is given to compare the
model with the elastic foundation model developed by Malek et al and with a finite element
model. It was concluded that the shear stresses in the vicinity of the plate end are generally
similar. But there were major differences in the magnitude and character of the normal stresses
predicted by different models. The normal stress concentrations at the plate ends were much
lower in case of the elastic foundation model, which is attributed to the interaction between the
normal stresses and shear stress gradients within the adhesive layer. Due to lack of this
interaction in the elastic foundation model, it was not capable of estimating the stress distribution
in the FRP-adhesive and beam-adhesive interfaces beyond the point where the shear stress
reaches its maximum value and the shear gradient equals to zero. Both the analytical model
developed and the finite element analysis demonstrates that only the adhesive concrete interface
is subjected to high tensile stresses, whereas the adhesive-FRP interface is subjected to
compression. The parametric study is performed to examine the main parameters that affect the
level of stress concentrations. It is concluded that interfacial stresses increase with increased
plate thickness and stiffness and decreased adhesive layer thickness. It is also indicated that the
magnitude of stresses increase linearly with increasing unplated beam length.
The same approach is later extended and applied to investigate stress concentrations in FRP
strengthened beams with cracks, anchoring devices, variable FRP thickness and width, variable
adhesive layer thickness (Rabinovitch and Frostig, 2001a, 2001b, 2001c). It is concluded that
46
stresses developed at plate ends can be reduced by decreasing the thickness or increasing the
width of the plate towards its ends. In addition, it is suggested to increase the thickness of the
adhesive layer towards the ends of the plate and not to remove excess adhesive squeezed out
during the bonding of the plate to reduce the stress concentrations at these sections. It is shown
that both vertical straps and clamps are effective means for reducing the peeling stresses, mainly
due to compressive stresses induced by them.
However, Shen et al. (2001) argues that the correctness of the results of the analysis method
developed by Rabinovitch and Frostig is doubtful since the interfacial normal stresses at the
adhesive-concrete and at the FRP-adhesive interface diverge from each other as the adhesive
layer becomes thinner, although they should converge to the same value. In addition, they also
state that although the transverse normal stresses are allowed to vary across the adhesive layer
thickness, the shear stresses in the adhesive layer are still assumed to remain constant since the
longitudinal stresses are ignored in the analysis. Shen et al. presents an alternative interfacial
stress analysis model for strengthened simply supported beams subjected to a uniformly
distributed load and a uniform bending moment. The model takes longitudinal stress in the
adhesive layer into account and therefore allows for variation of shear stresses across the
adhesive layer thickness. They found that the shear stress at the concrete-adhesive is only
slightly greater than that of FRP-adhesive interface, whereas the normal stress is much higher
compared to stress at FRP adhesive interface, which again indicates that concrete adhesive
interface is the more critical interface for debonding failure. They also stated that interfacial
stresses increase as the stiffness and thickness of the plate increases or the length of it becomes
shorter. This is also found to be the case for decreasing adhesive layer thickness.
The above mentioned models provide useful and necessary information on the stresses developed
in the strengthened system. However, most of them assume linear elastic behavior in all the
constituent materials and, generally, a linear strain distribution is assumed over the cross section.
As cracking occurs in the concrete with increased stresses, the actual and the estimated stresses
will start to deviate extensively. In addition, the failure criteria of these models, which are
generally in the form of comparison of extreme stresses with the characteristic strength of the
constituent materials, will yield inaccurate results when cracking, crack propagation and local
failures occur, especially when brittle materials like concrete and certain types of epoxies are
involved. Therefore, these models are generally limited to the analysis of the members with no or
47
little damage and can only be used to evaluate the initiation of failure. Recognizing these
limitations, models based on fracture mechanics concepts have been developed.
Fracture Mechanics Based Models
Interfacial stress based methods are useful to study the stress distribution along the strengthened
beams and identify certain parameters effecting the debonding behavior. However, the effect of
flexural and shear cracks, nonlinear behavior of materials and occurrence of local failures limits
their ability to make accurate predictions about the actual stress states and failure mechanisms.
As an alternative to these models, use of fracture mechanics in the analysis and modeling of such
members has been suggested (Buyukozturk and Hearing, 1998; Buyukozturk et al, 1999).
Lau et al (2001) introduced an analytical method for determining the stress intensity factor of a
rectangular concrete beam strengthened by an externally bonded FRP plate, which has a crack at
its midspan and subjected to three point bending. They assumed linear elastic properties for
concrete and FRP and perfect bond between them. They concluded that the stress intensity
values are reduced, while the stresses in the FRP plate are increased, with increased stiffness and
thickness of the FRP plate.
Leung (2001) also developed a theoretical model for the analysis of an RC beam with a single
crack subjected to constant moment, focusing especially on the interfacial shear stresses. First a
model is developed to relate bridging stresses in the plate to crack opening and fracture
mechanics based equations are introduced to relate moment, crack length, and crack opening.
Then, these equations are solved to obtain the variation in interfacial shear stress concentrations
with moment. Performed parametric studies have shown that delamination is favored by large
member size, low adhesive thickness, low plate stiffness, and small contact area between plate
and adhesive.
Rabinovitch and Frostig (2001d), extended their closed-from high order stress analysis approach
to cover the effect of flexural and flexural shear cracks in the concrete on the structural response
in the crack vicinity and combined it with a fracture based criterion for the initiation and stable
or unstable growth of the interfacial delamination. At the stress analysis stage, they calculated
the stress and deformation fields and, then, in the fracture mechanics stage they calculated
energy release rate values based on J-Integral formulation with input from the first stage. They
48
compared the obtained energy release rate values with the fracture energies of the materials and
interfaces as a failure criterion for initiation of interfacial delamination and its growth trend at a
constant load level. Then they performed a numerical study to examine three types of
delamination at flexural cracks, flexural-shear cracks, and plate ends. The numerical study
revealed that both flexural and flexural shear crack formation are associated with extremely high
stress concentrations and a mixed mode of fracture. It is concluded that the delamination growth
is unstable in these cases since the calculated energy release rate values, which decay with
delamination growth, are higher than estimated critical ones. In case of delamination from plate
ends, stresses in the adhesive-concrete and adhesive-FRP interfaces were estimated to be higher
than the critical ones. But relatively low energy release rate values, increasing with delamination
growth, compared to the first two cases were obtained. They recommended the use of
mechanical means such as continuous or discrete jacketing to arrest delamination growth.
The mentioned studies have shown that fracture mechanics based approaches may be used to
analyze and model the delamination behavior in FRP strengthened beams. However, further
development of these models for analysis and design purposes requires a better understanding
and information on the fracture properties and behavior of the constituent materials and their
interfaces.
2.4 Behavior of RC Beams Strengthened in Flexure and Shear
In many real life cases, desired increases in the overall capacity of reinforced concrete beams
may only be achieved by simultaneous upgrade of the flexural and shear capacity of the
members, since the members are expected to be designed with reasonably closer flexural and
shear capacities. Even in cases where the primary objective of the strengthening procedure was
to increase the flexural capacity of the beam, shear strengthening may be applied to provide
some additional safety in shear, since shear failures are quite brittle and undesired, or to provide
additional resistance to premature debonding type of failures.
Although there is relatively large number of experimental and analytical studies on flexural or
shear strengthening of reinforced concrete beams, only limited number of research studies has
been performed on beams strengthened both in flexure and shear. Some of the experimental
studies involve bonding of bi-directional or multidirectional composites to the sides of the beams
or to the bottom and sides of the beams in form of U wraps so that they will contribute both to
49
the flexural and shear capacity (Norris et al, 1997; Grace et al, 1999). Some others involve,
bonding of FRP composites to the bottom of the beam for flexural strengthening and then
provision of additional layers either bonded to the sides or provided in form of U-wraps for shear
strengthening (Al-Sulaimani et al, 1994; Sharif et al, 1994).
Norris et al. (1997) tested several flexural and shear specimens strengthened with different CFRP
systems, orientations, and configurations. They concluded that the magnitude of strength
increase and the mode of failure are related to the direction of the fibers. A large increase and
stiffness were observed when fibers are placed perpendicular to the cracks, but a more brittle
failure, in form of concrete rupture near the ends of FRP, was observed in both flexural and shear
specimens. When the fibers are placed obliquely to the cracks, a smaller in increase in strength
and stiffness was observed but the failure modes were more ductile and preceded by warning
signs such as peeling of FRP.
Grace et al. (1999) examined the effect of using several FRP strengthening systems with
different patterns in strengthening reinforced concrete beams. They concluded that provision of
vertical FRP layers on top of the horizontal ones bonded to the sides of beams reduces prevents
rupture in flexural strengthening fibers, further reduces the deflections and increases the load
carrying capacity. They also mentioned that the vertical layers bonded over the entire span of the
beam reduces the diagonal cracking so that the longitudinal fibers are fully used and capacity of
the beams is significantly increased.
Al-Sulaimani et al (1994) performed tests on beams with deficient shear strengths strengthened
either in shear and/or flexure. The beams were precracked and then repaired with different GFRP
schemes, i.e. GFRP strips, wings and U jackets. All strengthened beams failed in shear, except
the ones strengthened with U jackets. In other cases, where flexural plate was provided in
addition to shear strengthening, the steel reinforcement remained elastic.
In another test program performed by the same research group (Sharif et al, 1994), precracked
beams strengthened in flexure or in both flexure and shear were tested. The beams strengthened
by GFRP plates only bonded to the bottom of them failed either by FRP rupture or by plate
debonding. When bolts were provided to the ends of the plates the failure mode of the beams
shifted to shear failure. Then, these beams were repaired in shear by side bonded plates. The
observed failure mode was concrete crushing in one case and horizontal and vertical cracking
50
around shear plate in the other. When, the GFRP plate was provided in form of I-jacket bonded
to the bottom and to the sides of the beam at end regions, the observed mode of failure was
concrete crushing.
As it is seen, there are a variety of possible failure modes that can be observed in reinforced
concrete beams strengthened both in flexure and shear. Observed failure modes are highly
dependent on the shear strengthening configuration, i.e. side plates versus U-jackets. However,
there are only a small number of studies performed in this area and more detailed studies
focusing on the interaction of flexural and shear strengthening systems and ultimate capacities
and failure modes of these systems are needed.
2.5 Experimental Database
The review of previous experimental and analytical work has shown that there are several
parameters affecting the failure mode and capacity of FRP strengthened beams, including the
distance from the plate ends to the supports, stiffness and thickness of the laminates, amount of
internal reinforcement. A database of structural experiments available in literature is compiled to
investigate the relative importance of these parameters on behavior of strengthened beams, and
to explore the general characteristics of the specimens used in previous experimental studies and
to identify, if any, research areas where more experimental data or information are required (See
Appendix I). Test data in the database is also used to evaluate several modeling approaches.
The data is extracted from journal papers published since 1991 according to the selection criteria
explained below. Only those experimental studies, in which geometrical and material properties
were adequately reported, were included in the database. The only properties assumed in the
database, if not specified, were the modulus of elasticity of the reinforcing steel, which was taken
as 200GPa, and the effective depth of the beams, which was assumed to be 0.9 times the depth of
the beam. Concrete cylinder strength was taken to be 0.8f,
in cases where only the concrete
cube strengths were reported.
The database includes 114 reinforced concrete beams strengthened in flexure using epoxy
bonded unidirectional FRP composites. All beams in the database had rectangular cross sections
and tested under four-point bending. Only beams strengthened in flexure by bonding
unidirectional FRP composites to the bottom of the beams were considered and those
51
strengthened in flexure with bi-directional FRP composites were excluded. The cases where
flexural FRP reinforcement was placed under the supports were not included in the database,
since this condition is believed to change the behavior of the system. The beams that did not
have internal steel reinforcement for flexure or shear were not also considered in the database.
The maximum clear span of the beams in the database was limited to 300 cm. to provide more
consistency in the database in terms of beam sizes. The general characteristics of the specimens
in the database are summarized in Table 2-4.
Of the 114 beams in the experimental database, 85% failed by debonding/delamination type
failures, whereas 5% failed by FRP rupture, 8% by concrete crushing, and 2% by shear. The
debonding/delamination type failures were not subdivided into categories like concrete cover
peeling or delamination initiating from shear cracks, since it was difficult to identify them from
the information given in the references and since some of them occurred in a mixed mode.
The flexural failure loads of the strengthened beams in the database, which correspond to either
concrete crushing or FRP rupture, are calculated using modified section analysis which is based
on using strain compatibility and force equilibrium (See Chapter 6 for details). The calculated
flexural failure loads are plotted with respect to the actual failure loads of test beams in Figure 25. Both of these values are normalized with the load corresponding to theoretical shear strength
of the beams calculated according to ACI 318-99. Since calculated flexural failure loads are the
maximum loads that can be theoretically achieved, they also represent the maximum shear load
that can be demanded from the beam section. Therefore, after normalization y-axis represents the
ratio of the theoretical shear demand to the calculated shear capacities of the test beams.
Whereas, the x-axis represents the ratio of the actual shear demand, i.e. the shear force applied to
the beam section at failure, to the shear capacity of the beam. It can be seen from this figure that
Table 2-4: Characteristics of Specimens in the Database
Clear span (mm)
Beam depth (mm)
Shear span / beam effective depth
Shear span / clear span
Tensile reinforcement ratio
Min
900
100
2.50
0.33
0.0032
52
Mean
1783
184
4.44
0.36
0.0100
Statistics
Max
2800
400
6.28
0.45
0.0436
Standard Deviation
645
63.9
1.32
0.04
0.0071
in most of the cases, the theoretical shear demands were less than the theoretical shear capacities
of the specimens, i.e. the beams were over-designed in shear, probably to prevent shear failures
and to isolate the desired flexural failure mode of interest. It may be also observed that most of
the beam in the database failed before reaching their shear capacities.
The ratio of the experimental failure load of the strengthened beam to that of the control beam
represents the increase in the capacity of the member due to strengthening and may be termed as
the strengthening ratio. Strengthening ratios of specimens in the database are plotted again with
respect to the ratio of the actual shear demand to the calculated shear capacity of the same beams
in. It can be seen from both Figure 2-5 and Figure 2-6 that most of the beams in the database
failed due to debonding or other failure modes before reaching their theoretical shear capacities.
It is interesting to note that in all cases, where the beams failed by FRP rupture and concrete
crushing, the strengthening ratio were between 1.0 and 2.0 and the beams that have reached
strengthening ratios over 2.0 failed by debonding of the FRP, except one case where shear failure
was observed. In addition all flexural failures took place at loads less than 0.75 of the shear
capacity of the beams. All beams that have reached 0.75 of their shear capacity at failure failed
either by debonding or shear. However the number of data points in this region is very low and
most of them are the ones that have theoretical flexural capacities higher than their shear
capacities.
Another important point to note is that there are cases where the beams failed at load levels much
lower than the theoretical shear strength of the unstrengthened beam (Nguyen et al, 2001; AlSulaimani et al, 1994). The occurrence of these shear failures implies that the provision of a
flexural FRP plate to the bottom of a RC beam may reduce the shear capacity of the beam in
certain cases. Although these shear failures took place at loads higher than the ultimate load
capacities of the corresponding control beams, they significantly reduce the capacity and
ductility of the strengthened beams.
Figure 2-7 shows the change of strengthening ratio with internal steel reinforcement ratio. As
expected the strength increase relative to the control beams are higher in beams that have lower
steel reinforcement ratios. This can be also observed from Figure 2-8, where the change of
strengthening ratio is plotted against the ratio of the axial stiffness of the steel reinforcement to
53
2.0
*
cc
I.
Debonding/Delamination
* Fiber Rupture
o Concrete Crushing
4
4
0*'
* Shear Failure
4
)
I
4
1.0 +
4
I
'4
C13
4
I
13
0
4)
* 4.
I
*
14
4
0.04iii
1.00
0.75
0.50
0.25
0.00
1.25
Exp. Failure Load / Caic. Shear Capacity
Figure 2-5: Theoretical Shear Demand/Shear Capacity versus Actual Shear Demand/Shear Capacity
A0
* Debonding
0
FRP Rupture
o Concrete Crushing
3.0-
-
----
---
o Shear Failure
0
cc
I)
4
I.+
2.0 +
--------.
I)
4
I
I*
4
,*
1.0+
n n
*
.
* 0
------------ -I
0
- -
-
-- ----- --- --- ---
i
0.00
0.25
0.75
0.50
Exp. Failure Load / Caic. Shear Capacity
1.00
Figure 2-6: Strengthening Ratio versus Actual Shear Demand/Calculated Shear Capacity
54
1.25
the balanced stiffness. The balanced axial stiffness corresponds to the total axial stiffness of the
steel reinforcement and FRP that will cause simultaneous concrete crushing and steel yielding. It
is also notable that the axial stiffness of the steel reinforcement provided, i.e. amount of steel
reinforcement, is close to balanced stiffness in cases of concrete crushing. Similarly, the change
of the strengthening ratio with the ratio of axial stiffness of FRP reinforcement to the balanced
stiffness is plotted in Figure 2-9. It can be seen that this ratio is generally small when the
governing mode is FRP rupture or concrete crushing. This is also the case when strengthening
ratio is plotted with respect to FRP to steel axial stiffness ratio (
Figure 2-10). The amount of FRP reinforcement used, and hence the ratio of its axial stiffness to
the balanced and steel axial stiffness, should be low in order it to be ruptured. Whereas in case of
concrete crushing these ratios are low since the amount of steel provided is relatively high
compared to other cases, as can be seen from Figure 2-8.
The change of strengthening ratio with the plate cutoff distance to shear span ratio is plotted in
Figure 2-11. It can be observed from the figure that there is a generally decreasing trend in
strengthening ratio as the unplated length to shear span ratio increases. For example,
strengthening ratios over 2 have been obtained only in cases where the unplated length to shear
span ratios were lower than 0.2. In addition, flexural failures, i.e. concrete crushing and FRP
rupture, have been only observed in beams that fell into the same region.
To summarize, the mode of failure of the strengthened beams are greatly affected by the relative
amounts of internal steel and FRP composite provided. When the amount, and in turn the axial
stiffness, of the internal steel is close to the balanced axial stiffness and the axial stiffness of the
FRP reinforcement provided at the same time is relatively low, the favored mode of failure is
concrete crushing. In this case, the debonding of the FRP composite is less probable since a
greater portion of the tensile stresses are carried by the steel and since concrete crushing occurs
soon after yielding of the tensile steel due to high amount of steel provided. Whereas, the rupture
of the FRP laminate is favored when the amount 4;
4VAMIA,
i.e. axial stiffness of the FRP; is
very low. Both of these flexural failure modes are more probable when the distance between the
plate ends and the supports are short.
One other important observation is that most of the beams in the experimental database were
over-designed in shear most probably to prevent shear failures and to isolate the desired flexural
55
4.0
I
I
I
*
3.0 *
*
2.
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
4
I
I
I
I
I
T
I
I
I
I
*
L
I*
*
U)
I
?I
I
I
I
I
I
-i
Th
*
*
.1
2.0
I
I
I
I
T
I
I
I
I
I
I
I
*
~
0.0 40.00
-I--
I
I
I
I
I
I
I
I
0.01
0.02
0.03
*~.
I
I
I
I
D~I
0.04
0.05
Reinforcing Steel Ratio
Figure 2-7: Change of Strengthening Ratio with Steel Reinforcement Ratio
4.0
3.00
0
C,
C
C
S
0-
2.0
+
-
-a-
t
-
C)
C
4)
-
- - - - - - - -
-
-
-
-
-
--
I
-
-
-
-
-
-
-
- -I
-
06
- ---
1~
- - -
- - - --
*
---------
Co
1.0 +
nfl
0.25
0.75
0.50
1.00
Axial Stiffness of Steel / Balanced Axial Stiffness
Figure 2-8: Strengthening Ratio versus Steel to Balanced Stiffness Ratio
56
4.0
0'
3.0
1
~
--
*
41
-
-
0)
-- -- -- -- -40
2.0
- - -
*
- - -
- - -
- - - - - -
- -
-
- - -
- - -
- - -
C
0
CA,
1.0
0-
0.0
0.0
0.1
0.2
0.3
Axial Stiffness of FRP / Balanced Axial Stiffness
Figure 2-9: Strengthening Ratio versus FRP to Balanced Stiffness Ratio
4.0
3.04.2
(5
0)
C
C
2.0 +
-
-
------- -
-
- -
0)
C
4)
**-----------
-
-
-
-
-
----
V
I-
Cl,
1.0 +
0.0
0.0
1.0
0.5
1.5
Axial Stiffness of FRP / Axial Stiffness of Steel
Figure 2-10: Strengthening Ratio versus FRP to Steel Stiffness Ratio
57
4.0
* Debonding
* FRP Rupture
ID
3.0
o Concrete
-
0
Crushing
-
o Shear Failure
--------------------I
-
(D
- -
-
CA
S.
0--
--
1.0
-
0.00
.1
4:
*
4
*
4
I.
"4
-.---
-
4-----
0.50
0.25
Unplated Length / Shear Span
0.75
Figure 2-11: Change of Strengthening Ratio with Unplated Length to Shear Span Ratio
failure mode of interest and most of them failed mainly due to debonding before reaching their
shear capacities. Therefore, there are only a little number of data exist on beams that have closer
shear and flexural capacities, which is expected to be the case for most of the real world cases. It
is possible that the shear capacity of the beam may affect the debonding behavior and flexural
capacity of the beam. Therefore, there is a need to further study and understand the behavior of
such cases.
2.6 Summary and Research Needs
Strength and stiffness of reinforced concrete beams can be improved by bonding FRP
composites to the outer faces of these members. Significant increases in the flexural capacities
may be obtained depending on the amount of existing steel reinforcement, amount of FRP
provided, and other geometrical and material properties. However, the presence of brittle
premature failure modes in addition to the ones observed in ordinary reinforced concrete beam
limit the level of strength increases that may be obtained and reduce the efficiency of the
strengthened systems.
58
Premature failures occur either by debonding from the plate ends or from flexural and/or shear
crack locations due to stress concentration at these regions. Many analytical and numerical
studies have been performed to estimate these stress concentrations based on interfacial stress
analysis and several failure criterion to model the debonding type of failures have been proposed.
In addition to these, models based on fracture mechanics have also been proposed. Although the
main parameters affecting the debonding behavior of strengthened beams have been generally
identified with these theoretical and experimental studies, much work is needed to more
accurately and reliably estimate the failure loads of these systems.
A database of structural experiments available in literature is compiled to investigate the relative
importance of these parameters on behavior of strengthened beams, and to explore the general
characteristics of the specimens used in previous experimental studies and to identify, if any,
research areas where more experimental data or information are required. This study has reveled
that the mode of failure and the ultimate capacity of the strengthened beams are greatly affected
by the relative amount of internal steel and FRP composite provided and also by unplated beam
length to shear span ratios. Concrete crushing is favored when the internal steel ratio is high and
the axial stiffness provided by the steel reinforcement is close to the balanced axial stiffness.
Whereas FRP rupture is favored when the axial stiffness of the FRP composite is very low
compared to the balanced axial stiffness. Although it is observed that debonding failures can
practically occur at any steel ratio or axial stiffness ratio, they seem to occur more frequently at
higher FRP stiffness to balanced stiffness ratios. In addition, the experimentally obtained
increases in the flexural capacities of strengthened beams seem to be decreasing with increasing
unplated length to clear span ratios.
One other important observation is that most of the beams in the experimental database were
over-designed in shear most probably to prevent shear failures and to isolate the desired flexural
failure mode of interest and most of them failed mainly due to debonding before reaching their
shear capacities. Therefore, there are only a little number of data exist on beams that have closer
shear and flexural capacities, which is expected to be the case for most of the real world cases.
The debonding behavior and in turn the flexural capacity of the beam may be affected by its
shear capacity and there is a need to further study and understand the behavior of such cases.
59
For these cases, a desired increase in capacity is generally only possible with the simultaneous
application of flexural and shear strengthening systems, since the members are expected to be
designed with reasonably closer flexural and shear capacities. Even in cases where the primary
objective of the strengthening procedure was to increase the flexural capacity of the beam, shear
strengthening may be provided to obtain some additional safety in shear, since shear failures are
quite brittle and undesired, or to provide additional resistance to premature debonding type of
failures. However, only little work has been performed on the behavior and failure modes of
beams strengthened both in flexure and shear.
Based on these observations, a test program that involves specimens that have relatively closer
flexural and shear capacities have been prepared. The beams were strengthened either in flexure
or both in flexure and shear to observe the transition from brittle to ductile failure modes with the
provision of shear strengthening. The parameters of the experimental program were selected to
be the amount of internal steel reinforcement, type of FRP reinforcement, and the shear
strengthening configuration.
60
3 Experimental Study
As identified in the previous sections, most of the test specimens used in the previous
experimental studies were over designed in shear in order to prevent shear failures and to focus
on the desired flexural failure mode of the study. However, building codes require RC beams to
have shear capacities slightly higher than their flexural capacities and this is believed to be the
case in most of the strengthening applications. In such cases, strengthening RC beams only in
flexure may result in debonding type failures much earlier than anticipated or even in shear
failures, and may require shear strengthening as well. Providing externally bonded shear
reinforcement may prevent debonding type failures initiated from shear cracks or at least
increase the load level at which debonding occurs by reducing the size and number of shear
cracks. In addition, in case of U-wrapped or totally wrapped configurations, external shear
reinforcement will cause a more uniform stress distribution and reduce stress concentrations at
the ends of flexural FRP reinforcement and at existing cracks locations by acting as an additional
anchorage. With the application of FRP reinforcement for shear, failure mode of the
strengthened beam may shift from debonding and shear type failures to more ductile failure
modes, i.e. concrete crushing or FRP rupture.
Present experimental study focused on investigation of the effect of different shear strengthening
schemes on failure mode and ultimate load capacity of FRP strengthened beams in order to
explore the transition from brittle to ductile failure modes with the use of different shear
strengthening schemes. For this purpose, a number of laboratory tests have been performed on
1.52m reinforced concrete beams strengthened either in flexure or in both flexure and shear. The
variables of the experimental study were the amount of internal steel reinforcement, the type of
FRP reinforcement, and the configuration of external shear strengthening. In what follows, first
the details of the tests are given and test results are presented. Then, observed failure modes and
capacities of the test specimens are discussed. Finally, the contribution of the test results to the
experimental database is presented.
61
3.1 Design and Details of Test Specimens
Two sets and a total number of 11 under-reinforced rectangular concrete beams, which were
designed according to the specifications of the ACI Building Code, were cast and tested. The
cross section of the beams was 203 mm x 102 mm, as shown in Figure 3-1. Each beam was
1,524 mm long and was supported over a clear span of 1,372 mm during testing. The beams in
Set I were reinforced with two #4 tensile reinforcing bars providing an area of As = 258 mm2
(Ps
= 0.010). In Sets II and III, the tensile reinforcement used were increased to two #5 bars to
provide an area of A, = 398 mm2 (Ps = 0.0 154). It should be noted that in both cases the tensile
reinforcement provided lies within the minimum (Ps,min = 200/fy = 0.0033) and maximum (ps,max
= 0. 7 5Pb = 0.030) limits of the ACI Building Code. Two #3 bars (As = 142 mm 2) were provided
as the compression reinforcement in all three sets of beams. The shear reinforcement was also
identical in all cases and consisted of 5.7 mm diameter U stirrups at a spacing of 100 mm,
providing a shear capacity slightly larger than flexural capacity in unstrengthened form.
P/2
P/2
152
I
/--
05.7
100
@P
2#3
FT
203
2#5/2#4
102
1270
76
457
-I
76
457
457
I
I
I .
wFS-HU
178
140
hilL
FS-FU
356
140
Figure 3-1: Details of Test Beams
62
Table 3-1: Summary of Experimental Program
Beam
Designation
f'
(MPa)
A,
(mm2)
Fiber
Type
External Flexural
Reinforcement
External Shear
Reinforcement
48.11
46.87
46.65
49.08
258
258
258
258
-
102mm x 0.38mm
102mm x 0.38mm
102mm x 0.38mm
178 mm x 0.38 mm
356 mm x 0.38 mm
C-Il
F-II
F-II-2
40.91
36.21
44.33
398
398
398
Hex 230C
Hex 103C
102mm x 0.38mm
102mm x 1.00mm
-
FS-HU-II
48.72
398
Hex 230C
102mm x 0.38mm
178 mm x 0.38 mm
FS-FU-II
48.71
398
Hex 230C
102mm x 0.38mm
356 mm x 0.38 mm
Set I
C-I
F-I
FS-HU-I
FS-FU-I
Hex 230C
Hex 230C
Hex 230C
-
Set II
-
-
Set III
C-Ill
49.00
398
-
FS-HU-III
51.90
398
Hex 103C
102mm x 1.00mm
178 mm x 1.00 mm
FS-FU-III
51.11
398
Hex 103C
102mm x 1.00mm
356 mm x 1.00 mm
Table 3-1 provides a summary of the experimental program and details of the specimens,
including mean concrete strength, amount of internal steel reinforcement, and the amount of
external CFRP reinforcement used for flexural and shear strengthening. Sets I consists of 3
beams, which include a control specimen, a specimen strengthened only in flexure, and two more
specimens strengthened in shear in addition to flexure. Set II includes one additional specimen
that is strengthened in flexure. Set III includes a control beam and two beams strengthened in
flexure and shear.
The specimens in all three sets, except control beams, were strengthened with a single layer of
1270 mm long x 102 mm wide CFRP sheet bonded to their tensile faces. The external shear
reinforcement was provided in form of U-wraps either over the entire shear span or half of the
shear span of the beams using 1 layer of vertical CFRP sheet, as shown in Figure 3-1. Cured Hex
230C sheets that have a design thickness of 0.381 mm were used as both the flexural and shear
reinforcement in Sets I and II, whereas Cured Hex 103C sheets that have a design thickness of
1.0 mm were used for the beams in Set III. There was an additional specimen in Set II, which
was strengthened in flexure with the use of Hex 103C sheets. All control beams were designed to
fail in flexure and failure modes of the beams strengthened in flexure and/or shear were
63
dependent on the amount of existing tensile reinforcement, the effectiveness of the shear
strengthening scheme and other test parameters.
3.2 Materials
Concrete
All beam specimens were fabricated using normal strength concrete. A ready gravel mix that
consists of standard aggregate and cement proportions, which was supplied by a local company,
was used to produce concrete with a water/cement ratio of 0.4. Two 4" x 8" cylinder specimens
per beam were also cast to determine the concrete compressive strength. One day after casting,
cylinder specimens were placed in water and kept in water for four weeks, whereas the beam
specimens were stored in a curing room in the same time interval. The average concrete
compressive strength of test beams are as indicated in Table 3-1.
Reinforcing Steel
Grade 60 steel with a minimum yield strength of 414 MPa and Young's modulus of 200 GPa, as
reported by the manufacturer, was used for flexural reinforcement in Sets I and II. However, the
flexural reinforcement used in Set III beams was Grade 80 steel with a minimum yield strength
of 552 MPa. Ribbed reinforcing bars with nominal diameters of either 12.7 mm (#4) or 15.8 mm
(#5) were used as the tensile flexural reinforcement, whereas the compression reinforcement
consisted of #3 reinforcing bars (Grade 60) having a nominal diameter of 9.5 mm. The shear
reinforcement consisted of U-shaped stirrups with a nominal diameter of 5.7 mm and yield
strength of 552 MPa.
Table 3-2: Properties of the Carbon Fiber Fabrics and the Epoxy Resin
Property
SikaWrap Hex 230C
SikaWrap Hex 103C
Sikadur Hex 300
Tensile Strength (MPa)
3,450
3,793
72.4
Tensile Modulus (MPa)
234,500
234,500
3,165
Elongation at Break (%)
1.5%
1.5%
4.8%
Flexural Strength (MPa)
-
123.4
Flexural Modulus (MPa)
3,117
64
Table 3-3: Properties of the Cured Laminates After Standard Cure
Hex 230C
Property
Hex 103C
ASTM Test
Method
Average
Value
Design
Value
Average
Value
Design
Value
Tensile Strength
894
715
849
717
D3039
Tensile Modulus
65,402
61,012
70,552
65,087
D3039
Elongation at Break (%)
1.33
1.09
1.12%
0.98
D3039
140F - Tensile Strength
814
703
847
699
D3039
140F - Tensile Modulus
67,450
59,896
69,843
63,088
D3039
140F - Elongation at Break (%)
1.16
1.00
1.13%
0.97
D3039
90 Tensile Strength
27
23
24
16
D3039
90 Tensile Modulus
5,876
5,502
4,861
3.973
D3039
90 Elongation at Break (%)
0.46
0.40
0.45
0.33
D3039
Compressive Strength
779
668
779
715
D695
Compressive Modulus
67,003
63,597
67,014
61,532
D695
Shear Strength +/-45 In Plane
63
56
52
46
D3518
Shear Modulus +/-45 In Plane
2,906
2800
2,498
2,394
D3518
FRP Sheets and Epoxy Adhesive
Two types of FRP external reinforcement were used in the experimental study. CFRP sheets
used were obtained by impregnation of unidirectional carbon fiber fabrics (SikaWrap Hex 230C
and SikaWrap Hex 103C) using an epoxy adhesive (Sikadur Hex 300). The properties of the
unidirectional carbon fiber fabrics and the epoxy adhesive, as reported by the manufacturer, are
as indicated in Table 3-2. The properties of the resulting CFRP laminates are given in Table 3-3.
3.3 Specimen Preparation
Fabrication and curing of test specimens
Concrete mixing and fabrication of the concrete specimens were performed according to the
guidelines described in ASTM standard C192/C 192M. Two 4" x 8" standard cylinder specimens
were taken per each test beam to determine the concrete compressive strength. Immediately after
casting, both cylinders and beam specimens were covered with plastic sheets to prevent
evaporation of water. One day after casting, the specimens were taken out of the molds. Cylinder
65
specimens were placed in water for curing, whereas beam specimens were moved to a curing
room and covered with wet burlaps. After a minimum curing period of 28 days, beam specimens
were moved out of the curing room and stored in the laboratory for precracking. At the same
time, compression cylinders were removed from water. After, air-drying of at least one day they
were capped and tested according to ASTM standard C 39-96 to determine their compressive
strength.
Precracking of beams
To simulate actual field conditions, all test beams were precracked prior to application of the
composite strengthening system. Test beams reinforced with #5 bars were precracked by
applying a midspan deflection of 4 mm under four point bending, whereas beams reinforced with
#4 bars were precracked by applying a midspan deflection of 3 mm. Both of these deflections
were about 75% - 80% of the midspan deflections corresponding to yielding of the tensile steel
reinforcement. Flexural cracks along the beam have developed in all cases, however shear
cracking was observed only in beams strengthened with #5 bars. The loading rate, in both cases,
was selected to be 2 mm/min. Figure 3-2 shows the load deflection curves obtained during the
precracking of beams F-I and F-II-2.
100
F-II-2
75-
0
-F-
50
50
25-
0
0.0
1.0
2.0
3.0
Midspan Deflection (mm)
Figure 3-2: Precracking Load-Deflection Curves for Beams F-I and F-II-2
66
4.0
Surface preparation
To achieve desired composite action between the reinforced concrete beams and the
strengthening system, adequate bonding between the concrete surface and CFRP sheets must be
assured. Bonding surfaces must be free of all loose particles, dust, lubricants and other
contaminants. For this purpose, concrete surfaces, where CFRP sheets to be bonded, were
mechanically ground using a hand held grinder prior to application of CFRP sheets. The cement
skin, corresponding to a depth of roughly 1-2 mm, was removed until the aggregates were
exposed and a clean sound surface was obtained. In addition, in case of beams strengthened both
in flexure and shear, the corners of the beams were rounded off in regions of U-Wraps.
Compressed air was applied in the end to remove the remaining particles and to obtain a dust
free clean surface.
Bonding of CFRP Sheets
The two-part epoxy, Sikadur Hex 300, was used both as the sealer and as the impregnating resin.
Prior to placing the carbon fiber fabric, epoxy was applied to the concrete surface with a roller
until the substrate was fully saturated. It should be noted that the applied epoxy seeps into the
cracks created as a result of the precracking procedure and results in partial repair of the cracks.
Then, the carbon fiber fabric was impregnated by applying the same epoxy from both sides of it.
The saturated fabric was placed onto the prepared concrete surfaces. The roller was used with a
slight pressure to prevent the formation of air bubbles and to level the surfaces. The composite
system was then allowed to cure at least for one week before testing.
3.4 Instrumentation and Test Procedure
A 60 kips Baldwin loading frame, which is controlled by a computer software developed by
Admet was used to perform the structural beam tests. All test beams were simply supported over
a clear span of 1357 mm and tested monotonically up to failure under four point bending (Figure
3-3). All tests were displacement controlled and the loading rate was set to be 4 mm/min in all
tests. The deflections at the midspan were measured automatically using a linear variable
differential transducer (LVDT).
67
Figure 3-3: Test Set up
Some of the beams were also instrumented with strain gauges to measure strains in the CFRP
composite and to provide additional information about the behavior of the tested beams. When
applicable, the strain gages are placed at locations 2.5cm, 20.3cm, 38.1cm away from the plate
ends, which will be respectively referred as the gages at the left or right plate ends, shear spans,
or point loads here after. An additional strain gage at the midspan location is provided in these
cases as well. The locations of these strain gages are shown in Figure 3-4.
P/2
P/2
1270
LSS
LPE
25
178
LPL
178
RPL
MS
254
254
RSS
178
RPE
178 25
Figure 3-4: Locations and Designations of Strain Gages
68
125
SI
FS-HU-I
--
10 0 ----
C-I
0-
75
o
VI
Z
0
5
10
15
Midspan Deflection (mm)
20
25
Figure 3-5: Load-Deflection Curves of Test Beams in Set I
3.5 Test Results
3.5.1 Test Results of Beams in Set I
The experimentally obtained load deflection curves of the beams in Set I are plotted in Figure 35. The control beam of Set I, Beam C-I, showed a ductile flexural behavior, as expected from an
underreinforced concrete beam. Since the beam was precracked prior to testing, no precracking
stage was observed in the load deflection behavior and the widths of the existing flexural cracks
started increasing steadily with the application of the load. The yielding of the internal steel
reinforcement started around 74.0 kN at a midspan deflection of 3.1 mm. After this point,
flexural cracks became much larger and smaller shear cracks started developing in both of the
shear spans. The eventual failure occurred at a load of 93.5 kN by concrete crushing in the
compression zone. The maximum midspan deflection recorded was 22.8 mm.
The initial stiffness of Beam F-I was almost the same with that of the control beam up to the
yield point. At a load of 86.24 kN and a deflection of 3.83 mm, the tensile steel reinforcement
started yielding. The loss in stiffness observed after yielding was not as pronounced as in the
case of control beam and the beam continued carrying higher loads. The strengthened beam
69
Figure 3-6: Failure Mode of Beam F-I
125
-r
100
RSS
--
LSS
-
-
RPE
LPL
M
75-
0
-j
- --
- -
-
NI
-- - -
- - - - --
-
L
50
-
- -- --
-
-----------------------
-----
Right Plate End
- Right Shear Span
-Right
-
25 -
-- - - - -- - -
-
Point Load
Midspan
-Left
Point Load
- - - Left Shear Span
-
0
0
0.0
0.2
0.4
0.6
Strain (%)
Figure 3-7: Measured FRP Strains Along Beam F-I
70
Left Plate End
0.8
1.0
failed at a load of 107.98 kN due to FRP rupture at a section close to a flexural crack in constant
moment region. The deflection at failure was 11.73 mm. The percent increase in ultimate
strength compared to the control beam was 16.1 %.
Figure 3-7 shows the change of measured FRP strains along Beam F-I with increasing loading.
Initially the measured strain at the midspan section was lower than the ones measured at load
application points. However, once yielding occurred at around 86 kN, the strain in FRP at the
midspan started to increase steadily as expected. Since the steel reinforcement could not carry
any tensile stress higher than its yield stress, the increased flexural moment can only be carried
by increased stresses in the FRP reinforcement. At a slightly higher load level, the strains at the
load application points started increasing as well and catch up the strain at the midspan. The
strains were about 0.9% when failure took place by FRP rupture at a section close to the
midspan. The maximum measured FRP strain was 0.95%, about 30 percent lower than the
reported ultimate FRP strain, 1.33%. Relatively large difference between the ultimate and
measured strains can be attributed to stress concentrations at flexural crack locations.
Beam FS-HU-I, exhibited a similar load deflection behavior to that of the control beam up to the
yielding point. However, the flexural cracks observed were narrower and less densely
distributed. Yielding of the reinforcement occurred at a slightly higher load, 78.2 kN, at a
deflection of 3.3 mm. The loss in stiffness observed after yielding was not as pronounced as in
Figure 3-8: Failure Mode of Beam FS-HU-I
71
the case of control beam and the beam continued carrying higher loads. In addition to widening
of the flexural cracks after yielding, a flexural-shear crack started to develop approximately from
the midpoint of the unstrengthened shear span and extended to the point of load application with
increased loading. The strengthened beam finally failed by rupture of the flexural FRP
reinforcement at a load of 110.2 kN, which represents a 17.9% increase over the control beam.
However, the deflection at failure, 12.1 mm, was much less than the maximum deflection
observed in case of the control beam, about half of it. The location of rupture was the
intersection of the external flexural reinforcement with the external shear reinforcement, as
shown in Figure 3-8.
In case of Beam FS-FU-I, where the external shear reinforcement covers the whole shear span,
the overall behavior was quite similar to that of Beam FS-HU-I. There was no observable
increase in the preyielding stiffness compared to the control beam again, and the pattern and
distribution of the flexural cracks in the constant moment zone resembled the ones observed in
Beam FS-HU-I. The yielding of internal steel occurred at a load level 14.3% higher than the
control beam, 84.6 kN, and the midspan deflection at this point was 3.5 mm. After yielding, the
flexural cracks in constant moment region became much wider with increasing loads as usual.
No observations about the cracking in the constant shear zone could be made since the whole
shear span was covered by the external shear reinforcement. However, it is believed that the
Figure 3-9: Failure Mode of Beam FS-FU-I
72
presence of this reinforcement prevented the formation of new shear cracks or at least limited the
widths of them together with the ones that might have formed during precracking. Failure of the
beam again occurred by rupture of the flexural FRP reinforcement at the intersection of it with
the external shear reinforcement (Figure 3-9). After rupture, the flexural FRP reinforcement
debonded from the beam tearing off small concrete sections between two flexural cracks. The
ultimate load achieved, 122.6 kN, was 31.2% higher compared to the control beam, which was
also higher than that of Beam FS-HU-I. The deflection at failure was the same with the one
obtained in Beam FS-HU-I, i.e. 12.1 mm.
3.5.2 Test Results of Beams in Set I
The control beam of Set II, Beam C-II, exhibited a ductile flexural behavior, as in the case of
Beam C-I. However, due to larger amount of internal reinforcement used, the loads at yielding
and failure were higher compared to Beam C-I, as expected. Yielding of the flexural
reinforcement started around 97.0 kN at a deflection of 4.7 mm. The beam failed by compression
crushing of concrete at 120.2 kN. The ultimate deflection reached was 19.9 mm.
Beam F-II, which was strengthened only in flexure, showed an interesting behavior and failed at
----
150-
FSI-HU-II
FrII-2
FS-FU- I
125
C-1
-----
100-
F-II
z
O 75
- - - - -
0
_j
I-
0
5
-
-
- -
-
-I-
--
--
10
Midspan Deflection (mm)
--
-----
I-
15
Figure 3-10: Load-Deflection Curves of Test Beams in Set II
73
20
Figure 3-11: Failure Mode of Beam F-I
a load level much lower than expected. The pre-yielding stiffness was about 15% higher than the
control beam and both the number and widths of the flexural cracks were less compared to the
control beam. The flexural steel reinforcement started yielding at 97.1 kN, which is essentially
the same load observed in the control beam, but at a lower deflection of 4.1 mm. Just after
yielding of the steel reinforcement, a large shear crack began to develop from the end of the
external FRP reinforcement in one of the shear spans and extended up to a point close to the load
application point. The shear crack became larger and larger with increased deflection and the
beam failed by plate-end shear at 105.9 kN (Figure 3-11). Ultimate load was reached at a
midspan deflection of 5.0 mm, which is about one fourth of that observed in the control beam. It
is important to note that the ultimate load of the beam was only slightly higher than the yield
load and it was even less than the ultimate load of the control beam in spite of the external FRP
reinforcement provided.
Beam F-II-2, which was also strengthened only in flexure but this time with a thicker FRP sheet,
also failed in shear. The pre-yielding stiffness of the beam was higher than both Beam C-II and
Beam F-II since the amount of FRP reinforcement provided was larger. Yielding occurred
approximately at 120.6 kN at a midspan deflection of 4.5 mm. Soon after yielding, a shear crack
extending from the load application point to the plate end has developed similar to the one
observed in Beam F-II, as shown in Figure 3-12. Finally the beam failed due to plate end shear
at 141.6 kN. The ultimate deflection was 7.1 mm, which is much less than that of control beam.
74
Figure 3-12: Failure Mode of Beam F-II-2
150
LPELSS
- ~~~
125 -{
~
~- - -~- -- - ---~- - - ~ ::-.;
~ - ~-" -_-
RPL
- - - - -- -- - -- - - - -
RPE
...
-
100
75 -
--- -- -
- -.-.
. .
------- ------- - - --- ------
- _4 - - - -----------
--- ----
--- -------- - - -Right Plate End
0
-j
-
50 -
- -
- -------- --- -------------- -----
-Right
PoinLtLoad
-
Midspan
25 -
- ---- -- ---
-
--------------
-
-----
- ---
-Left
Point Load
L---e
- -- Left Shear Span
-- Left Plate Endl
0
0.0
0.1
0.2
0.3
Strain (%)
Figure 3-13: Measured FRP Strains Along Beam F-II-2
75
0.4
0.5
Although the calculated shear capacity of the beam was still larger than the experimentally
observed value, the relative difference was not as pronounced as in case of Beam F-II, which
failed at 105.9 kN.
FRP strains measured at different sections of the Beam F-II-2 are shown Figure 3-13. The FRP
strains at load points were almost identical throughout the loading and they were slightly larger
than the one measured at midspan. Once yielding occurred at 120 kN, the strain in FRP at
midspan section started increasing, which was again followed increases in FRP strains at loading
points. FRP strain measured at the failing shear span was almost linear up to failure. The strain
behavior observed at the ends of the FRP reinforcement was similar almost up to the yield load.
The FRP strain at the non-failing end made a sharp increase around the yield load and then
stabilized after decreasing a little bit. The FRP strain on the failing end, on the other hand, started
decreasing around yield load, but then around 125 kN the strain values started increasing rapidly
at a very high rate. The FRP strain at this end at failure was about three times larger than that on
the other end of the FRP reinforcement.
The preyielding stiffness of the Beam FS-HU-II was both higher than the control beam and
Beam F-II. Yielding of the tensile steel reinforcement occurred at 108.6 kN at a deflection of 4.0
mm. The external FRP shear reinforcement, which was provided in form of U-wraps at the ends
of the beam over half of the shear spans, prevented the development of the large shear crack that
Figure 3-14: Failure Mode of Beam FS-HU-11
76
Figure 3-15: Failure Mode of Beam FS-FU-II
caused the failure of Beam F-II. In this case, smaller flexural-shear cracks extending from the
ends of the external FRP shear reinforcement to the load application points were observed in
unstrengthened halves of the both shear spans. Since the premature plate end shear failure was
prevented the beam was able to carry much higher loads and extensive flexural cracking was
observed. Finally, at a load of 150.6 kN, a small section of the flexural FRP reinforcement,
which was about 1 cm wide, ruptured at one of the flexural cracks in the constant moment region
at a midspan deflection of 13.9 mm. After this point, the load carried by the beam started
decreasing with increased deflection and finally, at a midspan deflection of 16.4 mm, the flexural
FRP reinforcement totally ruptured, where it intersects with the external shear reinforcement.
The behavior observed in case of Beam FS-FU-II was essentially the same with Beam FS-HU-II.
Although, the preyielding stiffness was a little bit lower, the yielding of the steel reinforcement
occurred almost at the same load, 108.4 kN, but at a slightly higher midspan deflection of 4.4
mm. Since the external shear strengthening was provided over the whole shear span, the cracking
was mainly restricted to constant moment region. The beam failed by rupture of the flexural FRP
reinforcement at a flexural crack location. The ultimate load and corresponding deflection were
149.1 kN and 13.8 mm, respectively, which were almost identical with the results obtained from
Beam FS-HU-II.
77
3.5.3 Test Results of Beams in Set III
Set III consists of a control beam and two beams strengthened in flexure and shear with Hex
103C sheet. Different from previous test beams these beams were reinforced with Grade 80
tensile steel with yield strength of 552 MPa. Other parameters were all the same. The load
deflection curves of the beams in this set are plotted in Figure 3-16.
Both the yield and ultimate capacity of the control beam of Set III were larger than the control
beams of Set I and II since the internal steel reinforcement consists of Grade 80 steel. Yielding of
the flexural reinforcement started around 134.3 kN at a deflection of 5.2 mm. The beam failed by
compression crushing of concrete at 151.2 kN. Deflection at failure was 17.9 mm, which was a
little bit less than those of previous control beams.
The preyielding stiffness of Beam FS-HU-III, which was strengthened in shear over its half shear
span, was similar to that of the control beam. The tensile steel yielded at a load of 153.3 kN, and
the deflection at yielding was 5.8 mm. The beam failed at a load of 178.9 kN by shear failure in
the unstrengthened half of the shear span. The shear crack extended from the load application
point to the bottom of the beam where external shear reinforcement ends as shown in Figure 3-
200
--
FS-FU-III
FS-HU III
1 50 -
-
-
-
-- - -
- -
C-II
. 100 --
-- - - -
0
0
5
10
15
Midspan Deflection (mm)
Figure 3-16: Load-Deflection Curves of Test Beams in Set III
78
20
17. The midspan deflection at failure was 9.8 mm.
Figure 3-18 shows the measured FRP strains along the beam. As usual, the strain in FRP at the
midspan section increased in a more steep fashion after tensile steel yields. The strain in the
failing shear span was closer to the strains at the midsection, whereas strains in the other shear
span was lower compared to both. Close to the failure load, the strain in the failing shear span
increased in a more abrupt manner. The maximum strain measured was close to 0.6%, about half
of the ultimate tensile strain of FRP reinforcement.
The load deflection behavior of Beam FS-FU-II was identical with that of Beam FS-HU-III up
to its failure point. The yielding of tensile steel occurred at 152.5 kN and at a midspan deflection
of 5.6 mm. However, the beam did not fail in shear like Beam FS-HU-III since external shear
reinforcement provided over the full shear span prevented it. Concrete in the compression zone
crushed at 200.9 kN but the beam did not fail immediately and continued to deform. The ultimate
failure was due to the rupture of flexural FRP reinforcement in the constant moment region at a
midspan deflection of 18.1 mm, which was even larger than the ultimate deflection observed in
the control beam. The measured strains along beam FS-FU-IJI are plotted in Figure 3-20. The
strains at midspan and load application points were close to each other at all stages of the
loading. The maximum strains observed were close to the reported average ultimate tensile strain
of FRP, with the one measured in the midspan section being slightly higher.
3.6 Summary of Experimental Results
Table 3-4 provides a summary of the test results including loads and midspan deflections at
yielding and ultimate capactiy, together with observed modes of failure. The theoretical ultimate
flexural load capacities of the strengthened beams, Pcal, obtained by assuming full composite
action, are also provided in the table for comparison purposes (See Chapter 6 for details). Shear
capacity of the beams in the unstrengthened configuration, 2Vcaic,calculated according to ACI
418, are also given in the table.
The main effect of the external FRP shear reinforcement in form of U-wraps on beams in Set I
was to provide external anchorage to the flexural FRP reinforcement rather than providing extra
shear capacity to the beams, since the existing shear capacities of the beams were about 50%
higher than their flexural capacities in the unstrengthened configuration. The rupture of the
79
Figure 3-17: Failure mode of Beam FS-HU-III
200
LSS
RSS ..---
150
.----
-1
---------------
------------------------ ---
z
100
-
0
-j
0.#
50+
-- Midspan
---
0
0.0
0.1
0.2
0.3
0.4
Strain (%)
Figure 3-18: Measured FRP Strains Along Beam FS-HU-III
80
-- Right Shear Span
Left Shear Span
0.5
0.6
Figure 3-19: Failure Mode of Beam FS-FU-III
200
----------
--
LPL
150S
---
--
--
0
-------------
1 50
z
-------
--------- -----
--
- -- -- ------- -
RPL
100 - -
50
-
--
-
- --
- --
-----------
- --
-
- ------
----------
-- - -
--------
--
- - - - - -- - - -
--------
-
--
--
- - -
-----
Midspan
-Right
Point Load
- - - Left Point Load
0
0.0
0.2
0.4
0.6
0.8
1.0
Strain (%)
Figure 3-20: Measured FRP Strains along Beam FS-FU-III
81
1.2
flexural FRP reinforcement at the intersection of it with the external FRP shear reinforcement in
beams FS-HU-I and FS-FU-I rather than a location in the constant moment region, which was
the case for Beam F-I where no external shear reinforcement was provided, suggest that there are
stress concentrations at these locations due to the anchoraging effect. Although the difference
was not major, the lower ultimate load obtained in Beam FS-HU-I might indicate that the stress
concentrations were more pronounced in case of U-wraps provided only over half of the shear
span, which might be a result of the shear cracking in the unstrengthened halves of the shear
spans.
In case of Set II, calculated shear capacities of the unstrengthened beams were about 25% more
than their unstrengthened flexural capacities. Beam F-II, for example, failed prematurely by plate
end shear at an ultimate load much lower than its expected flexural strength. The shear failure
Table 3-4: Summary of Test Results
2
Vcac
(kN)
Failure
Mode
-
-
Flexure
16.1
103.2
154.7
FRP rupture
12.1
17.9
103.2
154.6
FRP rupture
122.6
12.1
31.2
103.5
156.1
FRP rupture
-
120.2
19.9
-
-
-
Flexure
4.1
0.1
105.9
5.0
-11.9
127.0
147.6
Plate end shear
120.6
4.5
24.3
141.6
7.1
17.8
161.8
153.1
Plate end shear
48.72
108.6
4.0
11.9
150.6
13.9
25.3
138.1
155.8
FRP rupture
48.71
108.4
4.4
11.7
149.1
13.8
24.1
138.1
155.8
FRP rupture
C-III
49.00
134.3
5.2
-
151.2
17.9
-
-
-
Flexure
FS-HU-III
51.90
153.3
5.8
14.1
178.9
9.3
18.3
192.6
157.2
Shear
FS-FU-III
51.11
152.5
5.6
13.6
200.9
18.1
32.9
192.7
157.8
Conc. Crushing
Awt
(mm)
% Inc
in Pwt
PcaIc
(kN)
93.5
22.8
-
16.6
108.6
11.7
3.3
5.9
110.2
84.6
3.5
14.6
40.91
97.0
4.7
F-II
36.21
97.1
F-II-2
44.33
FS-HU-II
FS-FU-II
fc'
(MPa)
Py
(kN)
(mm)
Ay
% Inc
in Py
P.I
(kN)
C-I
48.11
73.9
3.1
-
F-I
46.87
86.2
3.8
FS-HU-I
46.65
78.2
FS-FU-I
49.08
C-II
Beam
SetI
Set II
Set III
Py = Yield load, Ay = Yield deflection, % Inc in Py= Percent increase in yield load;
P=
Ultimate load, Awt = Ultimate deflection, % Inc in Pwt = Percent increase in ultimate load;
Pcaic = Theoretical ultimate flexural load, 2 VcaIc = Calculated shear capacity in unstrengthened state.
82
occurred at a load approximately 28% less than the calculated shear strength of the
unstrengthened beam. The failure load was even about 12 % less than the failure load of the
control beam. In other words, the addition of the external FRP flexural reinforcement did not
provide any increase to the capacity of the beam and even decreased it by causing the
development of a large shear crack due to stress concentrations at the plate ends. Beam F-II-2,
which was also strengthened only in flexure but this time with a thicker FRP sheet, failed due to
plate end shear as well. Although the failure load was slightly lower than the calculated shear
strength, it was about 30 percent more than the failure load of Beam F-II. The difference in the
behavior is believed to be partly affected by the fact that the stiffness and the yield load of Beam
F-II-2 was larger than those of F-II due to larger amount of FRP provided. In addition, the
stresses in the FRP reinforcement of Beam F-II at a given load should be lower than that of
Beam F-II-2, again due to larger amount of FRP provided. Although it is observed that provision
of FRP plate may reduce the inherent shear capacity of a reinforced concrete beam strengthened
in flexure beam, more experimental data is required to make solid conclusions about the level of
reduction in shear capacities.
The development of shear cracks developing from plate ends and causing premature shear
failures were prevented in case of Beams FS-HU-II and FS-FU-II by the external FRP shear
reinforcement and the beams were able to reach much higher flexural capacities. Both of the
beams failed by rupture of the flexural FRP reinforcements at flexural crack locations in the
constant moment region. The shift of the rupture points from the intersection of the external
flexural and shear reinforcements to the constant moment region indicates that the stress
concentrations associated with the anchoraging effect of external FRP shear reinforcement were
less pronounced in this case. This is believed to be due to larger amount of internal steel
reinforcement used in beams in Set II, which causes a larger share of the load to be carried by the
internal steel reinforcement compared to the beams in Set I and results in lower stresses in FRP
reinforcement for a given load.
In case of beams in Set II, the load levels reached were above the inherent shear capacities of the
beams in unstrengthened situation. Beam FS-HU-III failed due to shear after providing some
increase in the beam capacity. The shear failure occurred in the unstrengthened half of the shear
shear span and therefore full use of the flexural reinforcement could not be made. However, this
is corrected in case of Beam FS-FU-III, where shear reinforcement was provided over the full
83
shear span. The beam failed in a desired way by concrete crushing followed by rupture of
flexural FRP reinforcement. The provision of external shear reinforcement in form of U wraps
over the full shear span prevented both occurrence of both shear failures and debonding type
failures. The ultimate capacity of beam has increased by 33% and no loss in the ductility was
observed. The ultimate deflection reached was as large as that of the control beam. Therefore,
this beam represents an optimum design case.
The test results demonstrate that significant increases in ultimate capacities of RC beams can be
achieved by properly strengthening them with FRP composites. However, the increases in
capacities are generally at the expense of ductility as it might be easily observed from the loaddeflection curves of the beams. To quantify the ductility of the beams, the deflection and energy
ductility indices of the test beams are calculated and summarized in Table 3-5. The deflection
ductility is defined as the ratio of the midspan deflection at ultimate failure to the midspan
deflection at yielding of tension steel, whereas the energy ductility is defined as the ratio of the
Table 3-5: Ductility Indices and Ductility Ratios of Tested Beams
Beamt
(MPa)
(k)
C-I
48.11
F-I
AY
(mm)
A.t
(mm)
Deflection
Ductility
Index
Energy
Ductility
Index
Deflection
Ductility
Ratio
Energy
Ductility
Ratio
93.5
3.1
22.8
7.33
15.57
1.00
1.00
44.02
108.6
3.8
11.7
3.08
5.22
0.42
0.34
FS-HU-I
46.65
110.2
3.3
12.1
3.67
7.21
0.50
0.46
FS-FU-I
49.08
122.6
3.5
12.1
3.49
6.74
0.48
0.43
C-II
40.91
120.2
4.7
19.9
4.21
7.88
1.0
1.0
F-I
36.21
105.9
4.1
5.0
1.22
1.41
0.29
0.18
F-II-2
44.33
141.6
4.5
7.1
1.60
2.18
0.38
0.28
FS-HU-II
48.72
150.6
4.0
13.9
3.46
6.75
0.82
0.86
FS-FU-II
48.71
149.1
4.4
13.8
3.15
5.96
0.75
0.76
C-Ill
49.00
151.2
5.21
17.9
3.43
5.67
1.00
1.00
FS-HU-III
51.90
178.9
5.59
9.29
1.59
2.14
0.46
0.38
FS-FU-III
51.11
200.9
5.98
18.06
3.23
5.90
0.94
1.04
Beam
SetI
Set II
Set III
84
area under the load deflection curve at ultimate failure to the area under the load deflection curve
at yielding of tension steel, i.e.
PA
PE = Et
/ EV
=A
/AV(3-1)
(3-2)
To make a better evaluation of these ductility indices and to compare the values obtained for the
strengthened beams with those of the control beams in each series, the ductility indices of the
strengthened beams are normalized by the ductility of the control beams. The obtained deflection
and energy ratios are also presented in Table 3-5.
It can be easily seen that strengthening RC beams with FRP composites may lead to substantial
losses in the ductility, especially if the failure mode is a premature one, i.e. debonding or shear
failure. In case of Beams F-II and F-II-2, for example, which failed due to plate end shear, the
ductility of the beams are only about 20-30 % of that of the control beam. The use of U-wraps
for shear strengthening, on the other hand, could shift the failure mode from shear failure to other
flexural failure modes such as FRP rupture and concrete crushing and boost the ductility ratios
up to 75-85 % and result in increased overall load carrying capacities. Provision of external shear
reinforcement over the half or over the full shear span was almost equally effective in Sets I and
II since they both prevented the shear failures and the failure occurred by FRP rupture. However,
if the load levels increase above a certain level, which might be achieved with the provision of a
thicker flexural FRP reinforcement, shear failures might take place in the unstrengthened regions
of the shear spans, as it was the case in Beam FS-HU-III. In such cases, provision of external
shear reinforcement over the full shear span or parts of the shear span certainly makes a
difference both in terms of ultimate capacity and ductility. In case of Beam FS-FU-III, for
example, where shear reinforcement was provided over the entire shear span, the failure occurred
by concrete crushing followed by FRP rupture the ductility of the beam was as high as that of the
control beam. Both the full capacity of the concrete and the FRP reinforcement was utilized and
a favorable design situation was obtained, which suggests that reasonable capacity increases can
be obtained without reducing the ductility of the strengthened beam by properly designing the
strengthening system.
85
3.7 Discussion of Shear Resistance Mechanisms in Strengthened RC
Beams
Shear failures in reinforced concrete have been extensively studied for decades both
experimentally and theoretically. However, they are still difficult to predict accurately and failure
modes, resisting mechanisms, and the role of various parameters are still being discussed. As it is
known, shear failures occur in a sudden manner with no advance warning contrary to flexural
failures. In flexural failures, large deflections and cracking in concrete observed after yielding of
tensile steel, provided the beam is underreinforced, serves as signs of distress. In addition, RC
beam is still able to deform after yielding and signs of distress has been observed, whereas shear
failures are brittle. Therefore, reinforced concrete beams should be properly designed to ensure
that flexural failure would take place before shear failure in the ultimate state. This calls for a
conservative design for shear and the shear capacity of the member is increased beyond its
flexural capacity with the use of special shear reinforcement.
3.7.1 RC Beams With Shear Reinforcement
As mentioned above, the desirable mode of failure in flexural member is the yielding of the
tensile reinforcement in a ductile manner rather than occurrence of brittle shear failures, which
limit the capacity of the member. Therefore, an adequate safety margin between the flexural
capacity and the shear capacity should be provided with the use of vertical stirrups. By this way,
shear failures may be excluded with the contribution of reinforcing bars bridging the shear
cracks.
Prior to formation of shear cracks, the shear reinforcement is ineffective and it is practically
stress free. Therefore, it has no effect on the load that causes diagonal cracking, which is
assumed to be the same with a beam without any shear reinforcement. After development of the
diagonal cracks, the shear reinforcement starts contributing to the shear resistance of the beam
and part of the shear force is carried by the bars that transverse a crack as shown in Figure 3-21.
The total force carried by stirrups is V, = n A
,, where n is the number of stirrups traversing a
crack, A, is the cross-sectional area of the stirrup, andff,
is the tensile stress in the stirrup. Other
internal forces contributing to the shear resistance of the beam are the forces carried by the
aggregate interlock, Vi, the vertical forces carried by the uncracked section of concrete, Ve, and
the forces created across the longitudinal steel due to dowel action, Vd. (Nilson, 1997)
86
v cz
s
A fV
Af
Vi
Cx
Vd
T
ext
Figure 3-21: Shear Resistance Mechanisms in a RC Beam With Shear Reinforcement
On the other hand, it is known that the inclusion of stirrups has beneficial effects on other shear
resistance mechanisms. First of all, the presence of stirrups reduces the penetration of the
diagonal cracks into the compression, which leaves more uncracked concrete section for resisting
the compressive and shear forces at the tip of the crack. Stirrups also help development of
significant interlock forces by preventing the widening of the cracks. Finally, they increase the
shear force carried by dowel action since they provide support to the longitudinal reinforcement
by tying them into the bulk concrete. Therefore, yielding of the stirrups not only limits their own
resistance but also results in a reduction in these additional beneficial effects with increased
crack opening.
The approximate distribution of shear resisting mechanisms in a RC beam with increasing
external shear force is shown schematically in Figure 3-22. It can be seen that the shear forces
carried by the stirrups starts increasing linearly once diagonal cracking occurs. In addition, the
contribution of aggregate interlock to the overall shear capacity decreases as the shear force
increases due to gradual widening of the shear crack with increased loading. When the stirrups
yield, their contribution to shear resistance remains constant, whereas the dowel and interlock
forces decrease rapidly due to increases observed in the diagonal crack widths after yielding.
These reductions increase the stresses in the remaining uncracked concrete and failure takes
place soon after yielding of stirrups.
While the total shear carried by the stirrups at yielding can be calculated, the relative
contributions of shear transfer in uncracked concrete section, dowel action, and the aggregate
87
Vim
V
CZ
Vd
VS
Flexural
Cracking
Inclined
Cracking
Yield of
Stirrups
Failure
Figure 3-22: Shear Resistance Mechanisms in a RC Beam With Shear Reinforcement
interlock in the cracked concrete is difficult to quantify separately. Taylor (1974) states that 2040% of the shear force is carried by the compression zone shear, 30-50% by aggregate interlock,
and 15-25% by the dowel action. Therefore, it is generally assumed in a conservative manner
that the contribution of these three internal shear resistance mechanisms is equal to the cracking
shear and this total is referred to as the contribution of the concrete to the total shear resistance.
To calculate the overall shear resistance of the member, the contribution of the concrete and the
stirrups to the shear resistance are calculated separately and then simply added to each other.
3.7.2 RC Beams Strengthened in Flexure
As it is mentioned earlier, the quantification of shear transfer mechanisms and accurate
prediction of shear strength of RC beams is still difficult and remains as a concern in spite of
decades of continued research in this area. In case of RC beams strengthened in flexure the
situation becomes more complicated with the addition of the FRP plate to the system.
Although quite extensive experimental studies have been preformed on concrete cover peeling or
plate end debonding failure modes of FRP strengthened beams, there are almost only a few cases
where shear failures in the classical sense have been reported (Vichit-Vadakan, 1997; Sharif et
al, 1994). This is simply because the test beams were over reinforced in shear to prevent the
88
occurrence of this failure mode and to obtain the failure mode of interest, which is generally the
debonding failure mode.
Generally, high interfacial shear and normal tensile stress concentrations are present at the ends
of the FRP plates, which forces the development of cracks in the concrete at this section. Once
this crack has formed it may proceed along the concrete-adhesive interface or along the rebar
layer and result in debonding type failures. However, if shear strength of the beam is relatively
low, this crack may merge with the existing shear cracks in the section and form a large shear
crack from the ends of the FRP plate. The development of this crack may cause the failure of the
beam due to shear at load levels lower than the inherent shear strength of the unstrengthened
beam. On the contrary, at regions away from the ends of the FRP reinforcement, the presence of
the FRP plates may improve the shear strength of the beam by increasing the contribution of
dowel action, limiting the crack widths, or by some other mechanisms. Therefore, the shear
behavior of these two regions is believed to differ from each other and will be discussed
separately.
Shear Behavior at Plate End Region
As stated above, interfacial shear and normal stress concentrations are created at the ends of the
flexural FRP reinforcement, mainly due to compatibility requirements and boundary conditions
at the plate end section. The stress values reached at this section may reach the tensile strength of
the concrete substrate and initiate cracking at plate ends. Once these cracks are initiated, they
may merge with the shear cracks developed near the plate end region and form the so-called
plate end shear cracks as shown in Figure 3-23. Then, the failure of the strengthened beam will
take place by enlargement of this crack due to shear.
Vichit-Vadakan (1997) has studied the shear behavior of GFRP strengthened pre-cracked beams.
Although the test beams were relatively small scale and the results were somewhat scattered, she
has observed various shear failure modes different including plate end shear, flexural shear
failure, and concrete shear crushing in addition to concrete cover separation. Sharif et al. (1994)
has also observed plate end shear failure in a RC beam repaired with GFRP sheet. The beam was
again precracked before strengthening and GFRP plate was bolted for anchorage. Failure of the
strengthened beam occurred at a load level less than that calculated based on ACI code design
89
!
Figure 3-23: Plate End Shear in a RC Beam Strengthened in Flexure
strength formula. These observations suggest that precracking may have a role in the plate end
shear failures.
Plate end shear failures have been studied in detail by Jansze (1997) with experimental and finite
element studies on steel plated beams. He has also studied anchorage and plate separation
failures in steel plated beams. In these cases, where beams were reinforced in shear with stirrups
failure was observe to occur by concrete cover rip-off. Although plate end shear cracks and other
flexural-shear cracks have been also observed, they have been arrested by internal stirrups.
To investigate plate end shear failures, he tested beams with varying plate length or dimensions.
The test beams were not reinforced in shear with internal stirrups. When beams were
strengthened with plates over the entire shear span, the failure was observed to be due to a
flexural shear crack, which propagated towards the support before failure. In case of partially
plated beams, the failure was due to a shear crack developed at the end of the plate. Sometimes
additional cracks along the rebar layer at the plate end region were also observed. The failure
loads were lower compared to fully plated cases. He observed that the plate end shear resistance
decreases with increasing unplated length of the beam and the amount of external reinforcement
hardly influences the shear failure loads.
To investigate the effect of aggregate interlock he has measured the displacements at the end
regions of the steel plates with LVDTs and transformed them into normal and shear
displacements along the crack. He has observed that the root of the plate end shear crack mainly
90
shear displacement were registered whereas near the tip of the plate end shear crack mainly
normal displacements were measured. Hence, the region in which the plate end shear was
inclined to 45, the crack opened gradually and at the root of the crack the faces slide over each
other.
In case of beams tested in this study, only three of the beams were strengthened in flexure only,
namely F-I, F-II, and F_11-2. The latter two failed due to plate end shear whereas the former one
failed by rupture of FRP reinforcement. The failure load of the beams that failed in shear was
lower than the calculated shear strength of them in unstrengthened configuration. It is believed
that there were two major factors contributing to the observed lower shear strength in these
beams, one being the effect of stress concentrations at plate end locations and the other the effect
of precracking.
The beams in Set II and III were precracked by applying a midspan deflection of 4 mm, whereas
a midpan deflection of 3 mm were applied to the ones in Set I. The loads reached at the
precraking stage were about 100 kN for the former ones and about 70 kN for the latter.
Considering that the shear cracking strengths of the beams calculated by ACI's equation is about
50 kN, significant shear cracking may be expected especially in beams of Set II and Set III.
Actually, two web shear cracks were observed in these beams after the precraking stage, whereas
no visible shear cracks were observable in beams in Set I.
Upon reloading, with the flexural and inclined shear cracks already present in the system, the
stirrups will start carrying shear forces at a much earlier stage compared to an uncracked beam,
considering the mechanisms shown in Figure 3-22. In addition, the stresses in the concrete
section for a given load will be higher compared to an uncracked section due to less amount of
uncracked concrete area available to carry these stresses. Coupled with stress concentrations at
the plate end region, these increased stresses on the uncracked concrete section will make the
propagation of these existing shear cracks easier. Moreover, the contribution from aggregate
interlock mechanism is expected to be less since it greatly depends on width of the crack.
Once flexural steel reinforcement yields, the tensile forces carried by the FRP reinforcement
starts increasing and so do the stress concentrations at the plate end region. In addition, as in the
case of unstrengthened RC beams, the stresses in steel and FRP reinforcement at the plate end
91
location are proportional to the moment acting at the tip of the inclined shear crack rather than
the moment acting at the plate end section.
After yielding, the plate end shear crack initiates and merges with the existing shear cracks at
this region. They form a major shear crack, whose width increases with increased deflections
after yielding. This causes a further decrease in the resistance by aggregate interlock mechanism.
One important point to note here is that at the plate end crack location the steel reinforcement
extends on both sides of the crack and the force carried by the steel reinforcement is continuous
over the crack. However, the FRP reinforcement ends at the crack location and extends only
towards the midspan direction. Therefore, the tensile force carried by the FRP plate tries to
further open the plate end shear crack once it has formed. This causes an increased rotation about
the crack tip and hence additional widening of the inclined shear crack.
Since the steel stirrups have been loaded at a much earlier stage compared to a beam without a
shear crack and since the contribution of other shear resistance mechanisms have decreased due
mainly due to larger crack widths, the yielding of the stirrups will take place at a lower load
level. Once they yield, the crack widths will further increase and the contribution of aggregate
interlock will further decrease. Finally, the shear failure will take place. At the failure load, the
contribution to shear resistance from uncracked concrete section and from the aggregate
interlock will be less than those in case of an uncracked unstrengthened RC beam due to less
amount of uncracked concrete section and larger crack widths. Therefore, assuming the
contributions from the dowel action and the stirrups are constant, the overall shear capacity of
the beam will be reduced.
The reduction in the shear strength will depend on the relative contributions of the shear resisting
mechanisms in concrete section. However, as it mentioned before, quantification of the relative
contributions of these different mechanisms is difficult. And the actual shear strength of the
beam may be anywhere between the shear resistance provided only by the stirrups and the shear
resistance provided by the sum of the stirrups and the concrete section. Therefore, for design
purposes, it may be conservatively assumed that only the stirrups contribute to the shear capacity
of a RC beams strengthened in flexure and neglect the contributions from other mechanisms.
For example, in case of beams tested in the experimental program the shear capacity provided by
the stirrups was calculated to be 95.8 kN and the contribution of concrete calculated according to
92
ACI Code was between 50 kN and 60 kN depending on the concrete strength. Considering the
shear failure loads of Beams F-II and F-II-2, which were 105.9 kN and 141.6 kN respectively,
the suggestion that considering only stirrup contributions to the shear strength seems verifiable.
However, more test data is needed to arrive at solid conclusions and better recommendations for
design.
One might argue that this suggestion is too conservative for beam F-II-2. The difference in shear
capacities of beams F-II and F-II-2 is attributed to the difference in the yield loads of the beams
and the concrete strengths. Beam F-II has a concrete strength of 36.21 MPa, whereas beam F-II-2
has a concrete strength of 44.33 MPa. The difference in the compressive and, in turn, the tensile
strengths of the beams might affect the cracking loads of the beams and then the shear strength
of the concrete section. But the main reason causing the difference in the observed shear
strengths is thought to be the higher yield load obtained in Beam F-II-2, which was 120.6 kN.
The tensile reinforcement of Beam F-II has yielded at a lower load of 97.1 kN, due to less
amount of FRP reinforcement used. Since the plate end shear cracks were observed to develop
and merge with the existing cracks after yielding, the higher yield load obtained in case of Beam
F-II-2 is expected to result in a higher shear capacity.
On the other hand, if one compares the failure modes and failure loads of beams F-I and F-II, it
can be seen that the former fails by FRP rupture at a load of 108.6 kN, which is even slightly
higher than the failure load of the latter one, 105.9 kN, which failed by plate end shear. The
difference is thought to be a result the lower concrete strength in beam F-II and more importantly
precracking. As indicated before, the precracking loads of beam in Set I were about 70 kN,
whereas those of beams in Set II were about 100 kN. The inclined shear cracks were observable
in case of F-II at the end of precracking stage, but none were observed in case of beam F-I. As
discussed before, the presence of inclined shear cracks affects both the load that the plate end
shear cracks develop and the contribution of concrete to the overall shear capacity.
Shear Behavior away from the Plate End Region
The shear behavior of FRP strengthened beams away from the ends of the FRP external
reinforcement may be expected to be different from the shear behavior observed at the plate end
regions. The presence of the FRP plates in these regions may improve the shear strength of the
93
beam by increasing the contribution of dowel action, limiting the crack widths, or by some other
mechanisms.
On contrary to the ends of FRP plates, the effect of interfacial stress concentrations diminishes
and the shear stress distribution along the plate becomes uniform as we get away from the ends.
Therefore, the possibility of development of flexural shear cracks and formation of a large shear
crack by merging with the inclined shear cracks has been decreased. Also, with the FRP
reinforcement attached to the bottom of the beam, it will postpone the development of cracks by
helping the concrete to carry tensile forces or at least limit the size and width of flexural and
flexural shear cracks after cracking. This will increase the contribution of the aggregate interlock
mechanism to the shear capacity of the beam. In addition, the concrete below the steel
reinforcement will also contribute to the shear capacity of the beam in some extent on contrary to
unplated beams where only the concrete area above the steel reinforcement is considered in shear
capacity calculations.
In addition, the FRP reinforcement can contribute more directly to the shear capacity of the
member by increasing the shear stiffness of the beam or by contributing to the dowel action, as
shown in Figure 3-24. The FRP plate, now, extends on both sides of the crack and contributes to
the dowel action together with steel reinforcement. In addition, with the FRP plate extending
over both sides of the crack, the tensile forces in FRP plate will resist to widening of the shear
crack on contrary to the plate end section where the FRP plate was trying to further open the
1------
-------------
-----------------
j
....
4- C
~ cz
A~fA
V
T
d
f
Vb'-
Vext
Figure 3-24: Shear Resistance Mechanisms in a RC Beam Strengthened in Flexure away from Plate Ends
94
developed plate end shear crack since it was only present on one side of the crack. By this way,
the contribution of the concrete section to the overall shear capacity will be increased.
The increases in the shear strength of FRP plated beams can be observed when the development
of plate end shear cracks is prevented, for example by providing anchorages or external shear
strengthening at the end region of the FRP plate. This might be the case for strengthened beams
where the FRP plates are extended till the supports as well.
In the experimental program of this study, for example, the provision of external shear
strengthening over the plate end region of Beam FS-HU-II prevented the development of the
plate end shear crack, which caused the failure of Beam F-II before reaching its calculated shear
capacity. In this case, the failure mode of the beam shifted from plate end shear to FRP rupture
due to relatively low amount of FRP reinforcement used.
However, in case of beam FS-HU-II, the area of flexural FRP reinforcement was larger and the
beam was able to carry higher loads. The failure of the beam took place by shear failure in the
unstrengthened portion of the shear span. The failure load, 178.9 kN, was about 14% above the
calculated shear strength of the beam. When the external shear reinforcement was provided over
the full shear span, the shear failures were totally prevented and the failure took place by flexural
failure modes.
Considering that the contribution of the flexural FRP plates to the shear capacity of the member
will not be extensive, their effect on shear strength can be neglected for practical design
purposes. However, it is suggested, whenever possible, to extend the FRP plates till the supports
or provide end anchorage or shear strengthening at the end region to prevent early shear failures,
which will also help to prevent or postpone the occurrence of debonding type failures.
3.8 Contribution of Results to The Experimental Database
To see the contribution of the experiments performed to the experimental database, the figures
given in Chapter 2 are presented again with the inclusion of data from the current study.
Although the beams in the experimental database only consists of reinforced concrete beams
strengthened in flexure, test beams that are also strengthened in shear were not excluded while
incorporating current experimental data to better visualize and discuss the contribution of shear
strengthening. However, they are identified with arrows in the first two figures.
95
The calculated versus experimental failure loads of the strengthened beams normalized with the
shear capacities are plotted in Figure 3-25. It can be seen from this figure that the experimental
results provide data in the desired region where the calculated flexural strengths are close to the
shear capacities of the beams. In addition, strengthening ratios of specimens versus ratio of shear
demand to shear strength of strengthened beams are plotted in Figure 3-26. It can be seen that
the test beams resulted in strengthening ratios of approximately 1.3, except beam F-II that failed
early in shear. The resulting shear demand to shear capacity ratios of the specimens were
between 0.75 to 1.25, depending on the amount of reinforcement used and more importantly
depending on whether or not the external shear strengthening is provided.
The reinforcing steel ratios of the beams were 0.100 or 0.154. As it can be seen from Figure 327, the steel ratios were higher compared to most of the other beams in the database and this is
one of the main reasons for the relatively low strengthening ratios obtained in this study
compared to others. The steel to balanced axial stiffness ratios of the beams versus the
strengthening ratios are plotted in Figure 3-28. Similar to the reinforcing steel ratios, the steel to
balanced axial stiffness ratios of the beams were also generally higher than the others beams in
the database. The ratio was between 0.60 and 0.83 for the test beams. Since the FRP to balanced
axial stiffness ratios of the beams, which are also given in Figure 3-29, were between 0.014 and
0.042, the total tensile reinforcement to balanced axial stiffness ratios were lower than 1.0, which
assures yielding of steel before concrete crushing takes place. The beams with lower FRP to
balanced stiffness ratios failed, i.e. 0.014, failed through FRP rupture, whereas the ones with
higher ratios, 0.042, failed either by shear or concrete crushing depending on shear
strengthening.
3.9 Concluding Remarks
The use of FRP composites as externally bonded reinforcement offers an effective means for
strengthening of reinforced concrete beams. Test results in the experimental program have
demonstrated that improvements in both serviceability and ultimate capacity of reinforced
concrete beams can be achieved by bonding FRP composites to the surfaces of these beams.
However, the desired strength increases can only be obtained by properly designing the system
to avoid premature failure modes or at least to postpone the occurrence of these failure modes to
a certain stage so that a more efficient use of the FRP composite can be achieved.
96
2.0 .I
.
+ Debonding/Delamin ation
I.
o FRP Rupture
o Concrete Crushing
0
cc
C)
(a
* Shear Failure
*
c FRP Rupture (Curre nt Study)
o
o
C13
*
0
*1
Concrete Crushing ( Current Study)
Shear Failure (Curre nt Study)
*
I
o
1.0 +
C)
I
*
I
4)
0
0.
0
- -- -- - --
0.0 1
0.00
.*
*
.
*.
.1
-
0.25
i
i
I
0.50
0.75
1.00
1.25
Exp. Failure Load / Caic. Shear Capacity
Figure 3-25: Theoretical Flexural Capacity/Shear Capacity versus Shear Demand/Shear Capacity
4.0
I.
I
. Debonding
0
0
3.0
+-
-
- ------
*I
:#*
0)
.M
2.0+
--------
* Shear Failure
* FRP Rupture (Current Study)
S
0
a)
*
S.
-
o FRP Rupture
o Concrete Crushing
o Concrete
S
Crushing (Current Study)
0 Shear Failure
(Current Study)
-S
++
0 S.
S
I)
0
*
1.0
00 1
0.00
- -
**
0.25
-
*
-
-
I~.
-
-
j
*S
0.50
0.75
--
--------
1.00
Exp. Failure Load / Caic. Shear Capacity
Figure 3-26: Strengthening Ratio versus Shear Demand/Shear Capacity
97
--
1.25
4.0
I
I
I
I
I
I
I
*
3.0
+
0
-
I
I
I
I
I
I
I
I
I
I
I
**------------------------------------------------------------------------------------*
*
.E
I
I
I
I
I
*
*
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
~
*
I
*
2.0 +
1
*
*
CA
j~3 ~;
*
bAA
*
I
1.0+±
I
00
)I
I
0.0
0.00
I
I
I
I
0.01
0.02
I
I
0.03
0.04
0.05
Reinforcing Steel Ratio
Figure 3-27: Change of Strengthening Ratio with Steel Reinforcement Ratio
4.0
3
3.0
-
-
+
- --
- - - -- -
- - - - - ----- - -----
- --
----
-
-- -
0)
cc
2.0
-
-
-- --------------- - - -- - - -- --- --
--
----
0)
-
1.0
0.0
0.25
0.50
-
-
---
--
0.75
1.00
Axial Stiffness of Steel / Balanced Axial Stiffness
Figure 3-28: Strengthening Ratio versus Steel to Balanced Stiffness Ratio
98
4.0
I
I
I
I
I
I
I
I
I
0
--
-
--
-
-
-
-
I
I
I
DI
I
I
I
-
-
-
- - - - -
-
I
I
I
I.
I
-I
--
I
-
--
-
-
-
-
I
I
1
I --
1
-
-
-
-
-
-
-
-
-
-
-
-
-
0)
- - - -- -
0.0
0.00
0.05
-
0.10
-
-
-
-
-
0.15
---
-
0.20
0.25
Axial Stiffness of FRP / Balanced Axial Stiffness
Figure 3-29: Strengthening Ratio versus FRP to Balanced Stiffness Ratio
The test results of beams in Set I demonstrate that there are stress concentrations at the
intersection regions of the external flexural and shear reinforcement due to anchorage effects. As
it was the case in the experiments, the stresses in these regions might reach critical values and
result in the rupture of the FRP composites. Therefore, the design of such systems must take into
account these effects by considering the flexural and shear strengthening systems as a whole.
In case of beams in Set II, the interaction between the two strengthening systems were not that
critical since the amount of internal steel used was more compared to the beams in Set I and the
rupture location shifted to the constant moment region, when it is the mode of failure. Failure of
beams F-I and F-II-2 through plate end shear at load levels lower than the unstrengthened shear
capacities of these beams indicate that flexural strengthening might have negative effects on the
shear capacity of the beam. In case of Beam F-I, the failure load was even less than that of the
control beam. Therefore, it is strongly suggested to provide additional means for increasing shear
strength while strengthening reinforced concrete beams with shear strengths close to the
strengthened flexural capacity. The provision of external shear reinforcement prevented the
occurrence of these shear failures and the beams failed by FRP rupture in a more ductile manner
compared to shear failures. Shear strengthening provided over the full shear span and over the
99
half shear span were found to be equally effective for these cases since failure occurred due to
FRP rupture before the occurrence of any premature failures.
However, the failure of beam FS-HU-III due to shear in the unstrengthened region of the shear
span showed that the region that external shear reinforcement is provided might make a
difference when strengthened flexural capacity of the beam goes beyond the unstrengthened
shear capacity of the beam. In Beam FS-FU-III, the occurrence of such a shear failure was
prevented by providing shear reinforcement over the entire shear span and the beam failed by
concrete crushing followed by FRP rupture, making full use of concrete and FRP reinforcement.
In addition to increases in strength, no decrease in ultimate deflection was observed, resulting in
a ductility level as high as that of the control beam. These observations suggest that reasonable
capacity increases can be obtained without reducing the ductility of the strengthened beam by
properly designing the strengthening system, i.e. providing U wraps along the shear span.
The lower shear strengths obtained in these cases are attributed to well known stress
concentrations at plate end locations and to the effects of precracking. It is argued that the cracks
initiated at plate end locations due to high stress concentrations merges with existing shear
cracks in the section and forms a large shear crack. Increased size and width of shear cracks
causes reductions in concrete sections contribution to shear capacity by reducing the aggregate
interlock and the amount of uncracked concrete section. In addition, tensile force developed in
FRP plate tries to further open the developed shear crack since it only extends on one side of the
crack.
Therefore, it is believed that the shear strength at this region of the beam is expected to be
between the shear capacity provided only by the contribution of the stirrups and shear capacity
calculated by including the contributions from both the stirrups and the concrete section. Based
on these observations, considering the brittle nature of shear failures it is conservatively
suggested to neglect the contribution of concrete section to shear capacity of beams strengthened
only in flexure and only take the contributions from stirrups into account.
On the other hand, at regions away from plate ends, the FRP plates are believed to improve the
shear strength of strengthened beams. First of all, the negative effects of stress concentrations at
plate ends are not present here and the shear stress distribution is more uniform. FRP
reinforcement attached to the bottom of the beam will help the concrete section to carry tensile
100
stresses and postpone the development of cracks. After cracking occurs, it will limit the size and
width of flexural and flexural shear cracks after cracking and by extending on both sides of the
crack, the tensile forces in FRP plate will resist to widening of the shear cracks, which will in
turn increase the shear resistance mechanisms in concrete. In addition, the concrete below the
steel reinforcement will also contribute to the shear capacity of the beam in some extent.
Moreover, the FRP reinforcement will itself contribute to the dowel action by extending on both
sides of the crack together with the steel reinforcement.
However, for practical design purposes the enhancement in shear capacity of the member due to
FRP plates may be neglected, since the contribution of the flexural FRP plates to shear capacity
will not be extensive. But it is suggested to extend the FRP plates till the supports or provide end
anchorage or shear strengthening at the end region to prevent early shear failures whenever
possible. This will also help either to totally prevent debonding type failures or to increase the
load levels they occur.
101
4 Review and Evaluation of Debonding
Models and Design Guidelines
Plate end debonding failures are the most common mode of failure observed in RC beams
strengthened in flexure using FRP composites. Plate end debonding occurs either by concrete
cover separation or by delamination of the FRP laminate with a thin layer of concrete attached to
it. There have been many attempts to estimate the capacity of strengthened beams associated
with these types of failures. Some of these models were based on shear capacities of the beams,
whereas some others were based on interfacial stresses along the FRP-adhesive-concrete
interface. In what follows, some of the proposed plate end debonding failure models are
reviewed and evaluated by comparing the failures loads estimated by them with experimental
data in the experimental database.
First, two models developed for predicting plate end shear failure loads (Jansze, 1997; Ahmed et
al, 2001) are presented and discussed. The plate end shear failure loads predicted by these
models are compared with the experimental failure loads of beams in the database, which have
failed by plate end debonding. Then, the general characteristics of interfacial stress based models
used for estimation of stress concentrations at plate ends are discussed. The approximate model
developed by Roberts (1989) is used to investigate interfacial stresses at the end regions of the
beams tested in the experimental part of the present study. The failure loads predicted by this
model and by the model of El-Mihilmy and Tedesco (2001), which is a modification of the
former, are again compared with actual debonding failure loads of the beams in the database.
Finally, the general outline and important details of the design guidelines developed by ACI
Committee 440F for flexural strengthening of RC beams are presented. Through implementation
of the proposed guidelines and analysis of the beams in the experimental database, the calculated
design loads are compared with corresponding experimental failure loads to investigate the
safety introduced into such systems by the suggested design procedures.
102
4.1 Plate End Shear Models
Plate end shear failures observed in RC beams strengthened in flexure using steel plates were
studied in detail by Jansze (1997) through experimental and finite element studies. An analytical
model utilizing the fictitious shear span length concept was also developed as part of the study.
Based on the model developed by Kim and White (1991) for predicting the load and location at
which a shear crack initiates in a reinforced concrete beam, Jansze developed equations for
predicting the load corresponding to the initiation of shear cracking at the plate end. The critical
shear force at the plate end section of the RC beam that will cause shear failure is given as
VPES
(4-1)
PESbd
where
TPES =0.18 3P
d(
+d 200
(1
P
aP,mod =44
s1Op
f,
(4-2)
2
dLo
(4-3)
p
In the above equations LO is the distance from the plate end to the support and
modified shear span. If
ap, 2 d
ap,1 md
is the
obtained from Eqn. (4-3) is larger than the actual shear span ap,
then the modified shear span should be taken as equal to the actual one. Comparing the results of
the above model with various experimental results, Jansze found that the models showed a lower
bound value of 0.84 in case of steel plated beams and 0.83 in FRP strengthened beams and
suggested that load predicted by the above model should be multiplied by 0.83 for design
purposes. It should be noted that the above model does not take into account the contribution of
the internal shear reinforcement and therefore represents a lower bound for predicting the plate
end shear load.
Although the model is developed for steel plated beams with no internal shear reinforcement, it
has been used to estimate the load at which plate end shear cracks develop since the stirrups can
be assumed to be ineffective before shear cracking. The failure loads of the beams F-I, F-II, and
F-II-2 predicted by this model are 94.4 kN, 104.3 kN, and 111.53 kN, respectively. The
estimated loads were obviously conservative compared to the observed failure loads since the
model does not take the contribution of stirrups into account. Figure 4-1 gives a comparison of
103
0
-J
a)
X
S1 .2
0.0
5 --
.. .. ..
.. . .. . .
.. . .. . .
... .9.1
0
00
CU)
0.
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Est. Delamination Load / Calc. Flexural Failure Load
1
Figure 4-1: Comparison of Failure Loads Predicted by Jansze's Model with Experimental Results
failure loads predicted by Janzse' model with experimental failure loads of beams in the
database. Only those beams in which the failure mode were concrete cover separation are
included. The predicted loads are generally conservative, but there are a number of cases where
the experimental failure load is lower than the predicted values.
Recently, a modified form of Jansze's formulation was presented to estimate the plate end shear
failure loads in case of FRP retrofitted beams (Ahmed et al, 2001). They proposed to add an
additional shear stress generated as a result of replacing the steel plates used in Jansze's study
with CFRP laminates. They also included the contribution of the internal shear reinforcement
into the formulation. In contrary to Jansze, Ahmed et al proposed to use a fictitious shear span
equal to the average of the calculated shear span, ap,mod, and the true shear span, ap, while
calculating rPES. With these modifications, the plate end shear failure load becomes,
VFES =(zPES ±AVMOD)bd
where
104
(4-4)
ArTMOD
=,rPESbd
(
SSP
S
s
Itrcrjbaj
Itrcr,pbj
r -4.121
+6188.5
411(4-5)
bd
Sp and Sf in the above equation are the static moment of area of the FRP plate about the neutral
axis of a cracked section transformed to concrete and that of an equivalent steel plate. The width
of the equivalent steel plate is taken to be equal to that of the FRP plate but the thickness of it is
modified to produce the same tensile force with FRP laminate, assuming the yield strength of the
steel plate is 550 MPa. Itrcr,p and Itrc,,f are the moments of inertia of transformed cracked FRP and
equivalent steel plated sections, respectively. The second term in the above equation accounts for
the original shear strength T different from that of reference beams, where T is calculated
according to the ACI code
=0.15776f+
(
f
17.266p
) +d0.9
ap
___
(4-6)
sb
The plate end shear loads predicted by this model are generally higher than those predicted by
Janzse's model. The ratio of the predicted failure loads to experimental failure loads of test
1.5,
-0
Cz
1.2::D
1
r
0
a,
E
.
X
_0
c" 0.75
0
E
0.5 F
a)
C,)
w
0.25
F
0'
0.3
II
0.4
0.5
I
I
0.6
0.7
I
0.8
0.9
1
Est. Delamination Load / Calc. Flexural Failure Load
Figure 4-2: Comparison of Failure Loads Predicted by Ahmed et al.'s Model with Experimental Results
105
beams in the experimental database that failed by concrete cover separation are shown in Figure
4-2. The predicted failure loads are higher compared to the loads estimated by Jansze's model
and in some cases this ratio is as high as 1.5 resulting in unconservative predictions. However,
the failure load predictions of Ahmed et al's model are highly dependent on the relative shear
capacities of the considered beams with respect to the shear capacities of the reference beams
tested in their study. For example, the failure loads of the beams F-I, F-II, and F-II-2 predicted
by this model are 68.9 kN, 72.6 kN, and 83.9 kN, respectively, which are lower than those
predicted by Janzse's model.
4.2 Interfacial Stress Based Models
As mentioned in Chapter 2, various theoretical models have been developed to investigate the
interfacial stress concentrations at plate ends. All of these models assume linear elastic material
properties. Most of these models use the key assumption that the shear and normal stresses in the
adhesive layer are constant across the thickness of it. With this assumption, relatively simple
closed form solutions can be obtained. In addition to these approximate models, higher order
models, which consider variation of stress in the adhesive layer and satisfy the zero shear stress
condition at the plate ends, have developed as well (Rabinovitch and Frostig, 2000; Shen et al.,
2001).
Although the formulation of these models may differ from each other based on the assumptions
used, the interfacial stresses predicted by these models are generally reasonably close to each
other. This is especially true for the interfacial shear stresses, whereas the magnitude of the
normal stresses calculated by higher order approaches are somewhat different from those
predicted by approximate models. However, when one considers the assumption of linear elastic
properties, these minor differences in the calculated stresses are believed to be less important and
use of one of the approximate methods is expected to be adequate for analysis purposes.
The simplest of the approximate methods is the one developed by Roberts (1989). This solution
is general in terms of loading conditions on contrary to some other approximate models
developed. The simplicity of the solution and the generality of the loading make this model
attractive for analysis and design purposes.
106
The solution proposed by Roberts consists of three stages. In the first stage, the interfacial shear
stress is calculated for an infinitely long beam, assuming full composite action between the plate
and beam. In the following stages, the solution is modified to take into the actual boundary
conditions into account. First, an axial force that is equal to but opposite to the force calculated at
plate cutoff point in the first stage is applied at both ends of the plate, which is assumed to be a
axial member on an elastic shear foundation representing the adhesive layer. The beam is
assumed to be rigid at this and third stage. The application of the axial force results in non-zero
moment and shear stresses at the end of the plate. In the final step, equal but opposite moments
and shear forces are applied at the both ends of the plate, which is now assumed to be a beam
resting on an elastic foundation, again representing the adhesive layer. The interfacial normal
stresses can be obtained directly at the end of the third stage, while the interfacial shear stresses
are obtained by combining the stresses calculated in the first two stages.
The maximum shear and normal stresses at the plate cut-off points,
rmax
and
a
, were
approximated with the following expressions
1/2~
k
Tmax
[VO
+
b t
EMO
bJ
(d - c)
E'bftf
Iba
-1/4
-
4f
zrmax = Tmax
(4-7)
I
(4-8)
where V and MO are the shear force and bending moment at the plate cut-off point. I and If
are the cracked transformed moment of inertia of strengthened beam cross section in terms of
FRP plate and moment of inertia of FRP plate, respectively. The shear stiffness and normal
stiffness of the adhesive layer are given by
ks = Ga
b
k
=
Ea t
(4-9)
(4-10)
However, it has been indicated, based on comparison with experimentally measured shear
stresses in steel plated beams, that this solution may underestimate the magnitude of the stresses
107
4
3.5-
3-
CL
2.5 (I,
CD
C
0
2 1.5
0.5
0
0.
5
10
20
15
25
30
35
4
Distance from Plate End (mm)
Figure 4-3: Interfacial Stresses at Plate Ends of Beam F-II-2 at Failure Load
by as much as 30%. Therefore, it was recommended to replace the bending moment MO with M*,
the moment at a distance (h+tf)/2 away from the plate end for design purposes.
The formulation of Roberts has been implemented to investigate the interfacial stresses at the
ends of the beams tested in the experimental program. Figure 4-3 shows the distribution of
predicted interfacial shear and normal stresses in the adhesive layer of Beam F-II-2 at its failure
load. An adhesive layer thickness of I mm is assumed and used in the calculations. As it can be
clearly seen, the zero shear stress condition at the end of the plate is not satisfied. However,
results of higher order theoretical models and finite element studies have indicated that the shear
reduces to zero at the free end over a very short distance, on the order of the adhesive layer
thickness, with negligible reduction in the maximum calculated value. The interfacial shear
stresses decrease steadily with increasing distance from the plate end and then stabilize.
The interfacial normal stresses are confined to a short distance at the end of the FRP plate.
Normal stresses diminish rapidly with increasing distance from plate end and reach zero in a few
millimeters. After this point, the normal stresses change sign and become negative, i.e.
compression. However, the predicted peak compression stresses are much smaller than the peak
tensile stresses obtained at plate end and they diminish quite rapidly as well.
108
4
CL
Shear Stress
2
3 -
U)
U,
E
Normal Stress
z
-i
0
25
0
100
75
50
150
125
Load (kN)
Figure 4-4: Interfacial Stresses at Plate Ends in Beam F-II-2 at Different Load Levels
3-
2.5
2
F-I-2
(A
(A
*a
1.5
Ch
F-1
zE
a
%%F-11
0
5
10
15
20
25
3
0.5
Distance from Plate End (mm)
Figure 4-5: Interfacial Stresses at Plate Ends of Beams F-I, F-TI, and F-II-2 at 110 kN
109
The peak shear and normal stresses at the ends of the FRP plate of beam F-II-2 as a function of
the applied load are given presented in Figure 4-4. Both shear and normal stresses increase
linearly with increasing applied load since the interfacial shear stress is formulated as linear
functions of the shear and moment at the plate end section (See equation (4-7), which increase
linearly with increasing loads under for four point loading configuration. This is also the case for
the peak normal stress at plate end since it is expressed as a linear function of the maximum
shear stress at plate end. The interfacial shear stresses also increase linearly with increasing
distance between the plate cut-off point and supports. This is again due to the fact that the shear
and moments at the plate end section increases linearly as this section shifts away from the
support.
The predicted interfacial stress distribution at plate end region of beams in the experimental that
are strengthened only in flexure at a load of 110 kN are shown in Figure 4-5 for comparison
purposes. The largest interfacial stresses are obtained in case of beam F-II-2, which is
strengthened with a 1mm thick FRP sheet, whereas the other two beams were strengthened with
a 0.4 mm thick FRP sheet. Both the interfacial shear stresses and, especially, normal stresses
increase with increasing FRP thickness. Also, a comparison of the stresses obtained for beams FI and F-II indicates that the interfacial stresses are higher in case of beam F-I, which has a lower
steel reinforcement ratio compared to beam F-II. Due to less amount of steel reinforcement used
in beam F-I, for a given load level, the stresses carried by the FRP reinforcement is larger
compared to beam F-II. Although this fact is not explicitly stated in the formulation of interfacial
stresses, it is indirectly included in terms c and I, which represent the depth of the neutral axis of
cracked section and the moment of inertia of transformed cracked section. Being all other
parameters the same, both the neural axis depth and the moment of inertia of the beam is lower
in case of a beam with lower steel reinforcement ratio. Since the effect of I on interfacial stresses
is more pronounced, the resulting shear stresses and in turn the normal stresses are higher in case
of beam F-I.
Although the formulation of Roberts model is believed to be valid and reasonably accurate,
considering the assumptions it and similar models have been based on, care should be taken in
the use of it. First of all, Roberts interfacial stress analysis model, and others as well, are based
on the crucial assumption that all the constituent materials have linear elastic properties.
Although the model considers the cracking in concrete in the calculation of the neutral axis and
110
then in the calculation of the transformed cracked moment of inertia, the validity or accuracy of
the results obtained with the use of the same values after yielding of the reinforcing steel is
doubtful. Once the reinforcing steel yields, its contribution to the moment of inertia diminishes.
Although the location of the neutral axis changes with tensile steel yielding, the reduction in
moment of inertia is much more pronounced. Since the moment of inertia is directly used in the
denominator of equation (4-7), the interfacial shear and normal stresses after yielding are
believed to be larger after yielding of the steel provided that the same formulation is still valid.
This might have important implications for analysis purposes. For example, if one compares the
interfacial stresses in beams with different steel ratios, with all other parameters being the same
such as beams F-I and F-II, the predicted interfacial stresses for a given load level would be
found higher for the beam with lower steel ratio since its transformed moment of inertia is lower
compared to the other one. But once yielding occurs, the moment of inertias become comparable
in both cases since the contribution of the tensile steel should be neglected.
In addition, if one considers two beams with identical properties, except the thickness of FRP
used for strengthening such as beams F-II and F-II-2, similar arguments may be made. Before
yielding the predicted stresses in case of the beam with higher FRP ratio will be larger than the
one with lower FRP ratio due to higher FRP thickness. However, after yielding the difference in
the predicted stresses between the two cases will become less pronounced since the relative
reduction in the moment of inertia for beam with lower FRP ratio will be more. Because the
contribution of tensile steel to the moment of inertia is relatively larger in case of beams that
have less amount of FRP reinforcement.
As mentioned before, as long as the methods for calculating the moment of inertia of the
strengthened beam are the same, the differences in the interfacial stress values predicted by
different interfacial stress analysis methods are minor. However, the use of different moment of
inertias may result in large deviations in estimated stresses.
Once the interfacial stresses are calculated by one of these methods, it should be possible to
establish a practical failure criterion for bond failure and failure of the adhesive or the concrete
substrate due to concentrations of shear and normal stresses. For example, Roberts indicated that
the failure is likely to occur at shear stresses between 3 to 5 MPa combined with normal stresses
III
1
-0
0
-J
....... .... .....
0) 0 .7 5 -.
.. . .
LL
c
0.5
.
...
6..
.
00
E
0.25-
01
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Est. Delamination Load / Calc. Flexural Failure Load
Figure 4-6: Comparison of Failure Loads Predicted by Roberts' Model with Experimental Results
oetween 1 to 2 MPa. However, it is also mentioned that these limits are also expected to depend
on the strength of the epoxy and the adjacent concrete.
To evaluate the accuracy of the proposed failure criterion, the failure loads of the beams in the
experimental database that failed by concrete cover separation predicted by this model are
calculated. The failure is assumed to take place when the shear stress at the plate end reaches 5
MPa and M* the moment at a distance (h+t)/2 away from the plate end, is used in calculation of
the stresses. As it can be seen from Figure 4-6, the predicted failure loads are much lower than
the experimentally observed values resulting in highly conservative estimations. The use of Mo
instead of M* results in less conservative values but the data becomes scattered and predicted
loads in some cases becomes unconservative.
Other failure criteria for calculating the failure loads have been also proposed for example Malek
et al. (1998) adopted a failure model for concrete under biaxial stresses. The principal stresses at
the plate end section are calculated and compared with the adopted failure criterion. The failure
loads predicted by this approach are scattered. Although it sometimes results in unconservative
values probably due to the use of uncracked moment of inertia in calculating the stress
112
concentrations, for beams with the plates terminated at very close to the supports the model
predicts debonding loads, which are relatively high.
El-Mihilmy and Tedesco (2001) modified Roberts model for predicting stress concentrations at
plate ends by assuming an adhesive thickness of 1.5 mm and a Poisson ratio of 0.3 for the
adhesive layer. Based on statistical analysis of previous test data they implemented empirical
constants for calculation of maximum shear and normal stresses at plate ends and suggested to
replace the moment M* used by Roberts with
M* =M OV2
(4-11)
In which
L L
-< 0.1
=1.35 -12.5-. L -,'L
(4-12)
2
In addition, they have adopted and used the failure criterion for concrete under a biaxial state of
stress proposed by Tasuji et al. (1978). They compared the predictions with a relatively small
1 .5
1
1
1
1
I
I
1.25 0
1
IL
6.
X
0
-j
0.75-
C
E
0.5-
C
(U
.~.~~~.~. .
Qn
w
-..
.
-.
..
0.25k
0.3
0.4
0.9
0.8
0.7
0.6
0.5
Est. Delamination Load / Calc. Flexural Failure Load
1
Figure 4-7: Comparison of Failure Loads Predicted by El-Mihilmy and Tedesco's Model with Experimental
Results
113
number of beams in their database and obtained pretty good correlation between predicted and
observed failure loads. Figure 4-7 shows the failure loads predicted by this model and the test
results of beams in the database of this study, which failed by concrete cover separation.
Although good correlation is obtained for some of the test beams, the loads predicted are
generally over conservative for most of the cases. This is especially true for beams strengthened
with pre-preg FRP plates.
One other important point to note about interfacial stress based failure models for plate end
debonding is that most of them are over sensitive to the thickness of the adhesive layer, except
the model of El-Mihilmy and Tedesco that assumes a thickness of 1.5 mm for the adhesive layer.
However, it is difficult to control the thickness of the adhesive layer in application of the FRP
strengthening system, especially on site, and any model that is oversensitive to adhesive layer
thickness should not be used for design purposes. In addition, it has been found that the thickness
of the adhesive layer has a minor effect on debonding loads obtained in experimental studies
(Quantrill et al, 1996a,b; Swamy, 1987).
4.3 Evaluation of ACI 440F Guidelines for Flexural Strengthening
Recently, American Concrete Institute has established Committee 440F to develop guidelines for
design of externally bonded FRP systems for strengthening concrete structures. The committee
has developed design recommendations based on limit states design principles, which sets
different levels of safety against the occurrence of both serviceability and ultimate limit states by
incorporating several capacity reduction factors in different forms throughout the design process
of flexural strengthening.
4.3.1 ACI 440F Draft Guidelines for Flexural Strengthening
The document introduces the guidelines to determine the nominal flexural capacity of an FRP
strengthened member based on strain compatibility, internal force equilibrium, and the
controlling mode of failure. In addition to the capacity reduction factor associated with FRP
material properties, the use of an additional reduction factor of 0.85 is suggested for the
contribution of the FRP reinforcement to the flexural strength, to account for the lower reliability
of the FRP reinforcement compared to the internal steel.
114
To prevent the occurrence of the premature failure modes, the committee suggests to limit the
strain in the FRP reinforcement to a certain percentage of its ultimate strain by introducing a
factor,
KM,
that takes values between 0.2 and 0.9 depending on the stiffness and thickness of the
laminate and given as
nE
K
for nEtf tf : 214,000
(nEftoin N/mm)
428,000
1107,000
for
nE Stf' > 214,000
nEf tf
The K,, term is, however, only based on a general recognized trend and on the experience of
engineers practicing in the design of bonded FRP systems, as stated in the draft. It does not
include the effects of various other parameters such as the internal steel ratio, the distance from
the plate curtailment point to the supports, or the shear strength of the original beam, on the
debonding/delamination behavior. A better understanding of the failure modes and continued
investigation of relative effects of the above stated factors on debonding behavior are expected to
yield more accurate methods for predicting delamination.
In addition, to avoid failures at the termination of the laminate, it is suggested to extend the FRP
reinforcement a distance d past the point along the span corresponding to the cracking moment,
Mcr, under factored loads in case of simply
supported beams. Anchorage
of the FRP
reinforcement is also recommended if the factored shear force at the termination point is greater
than 2/3 of the concrete shear strength (Vu > 0.67Vc). However, no details about the type or
properties of the anchorages that should be used are provided.
To account for reduced ductility of FRP strengthened flexural members, ACI committee
incorporates the philosophy of ACI 318 Appendix B, where a section with low ductility must
compensate with a higher reserve of strength. The higher reserve of strength is achieved by
applying a strength reduction factor of 0.70 to brittle sections as opposed to 0.90 for ductile
sections, i.e. the strain in the steel at the point of concrete crushing or failure of the FRP
(including delamination or debonding) is at least 0.005. Finally, when the strength and ductility
requirements are met, the serviceability conditions of the strengthened member are analyzed
using an elastic analysis and the stresses in the steel and FRP reinforcement are checked with the
allowable limits.
115
4.3.2 Evaluation of Safety
To assess the safety of RC beams strengthened in flexure, the beams in the experimental
database, including the specimens from the present study, were analyzed based on the guidelines
provided in ACI 440F Draft. Perfect bond between the FRP and RC beam was assumed and
strain and force compatibility were used to determine the moment capacity corresponding to
concrete crushing or FRP rupture (including delamination and debonding). Since concrete might
not have reached its ultimate compressive strain in case of FRP rupture, a modified form of
Hognestad's stress strain curve for concrete have been used in the analysis (See Chapter 6).
The environmental capacity reduction factors and the strength reduction factor applied at the end
of the analysis to account for decreased ductility of strengthened flexural members were not
included in the analysis. Only the capacity reduction factor, 0.85, applied to the contribution of
the FRP reinforcement to the nominal capacity and the factor,
Kn,
introduced to limit strains in
the FRP reinforcement to prevent premature failure modes were implemented. One important
point to note is that, in most of the experimental specimens no anchorage was provided at the
ends of the FRP reinforcement, as opposed to ACI 440F's requirement when factored shear force
at the termination point is greater than 2/3 of the concrete shear strength. However, since all of
the tests were performed on simply supported beams under four-point bending, it is difficult to
1.75
1 5
+ Debonding Failure
V
*FRP Rupture
0+
-j
o
Concrete Crushing
i
Shear Failure
IL
1.001. --- - - 0
.1
r
e
- - -
-
s
r
I-----------
e
4)1
C
.0
0.2
Exp. Fair
Lod/C4.
0.00.7
Iha
.00
1.2
Caaity
_
0.25
0.00
0.25
0.50
0.75
1.00
Exp. Failure Load ICaic. Shear Capacity
Figure 4-8: Factor of Safety versus Shear Demand/Shear Strength
116
1.25
find a case where the section shear force in the shear spans were less than the 2/3 of the concrete
shear strength.
The nominal load capacities of the beams in the database, calculated according to the above
procedure, normalized by the experimental failure loads are shown in Figure 4-8. It can be seen
from this figure that there are many cases where the safety of the strengthened systems were less
than one. In case of all beams that failed through concrete crushing or FRP rupture, the
implementation of the design procedure resulted in satisfactory safeties. All test beams in the
experimental database that have predicted flexural capacities lower than their experimental
capacities failed through either debonding or shear. For example in cases of Beams F-II and F-II2, which failed by plate end shear, the experimental failure loads were 25% and 10% lower than
the value predicted by the above procedure, respectively.
The ratios of the failure loads calculated according to ACI 440F design guidelines and the
experimental failure load are plotted in Figure 4-9 with respect to the corresponding unplated
length to shear span ratios. Although the number of data points was relatively low, the specimens
that have unplated length to shear span ratios over 0.2 generally failed at load levels lower than
that estimated by the ACI 440 F design guidelines and although the data is scattered there seems
1.75
-
* Debonding
* Fiber Rupture
0
o Concrete Crushing
*
I
~1.00
- -
I
o Shear
Failure
-44 -------------
0I
Cu
*
0
0.25
0.00
0.25
0.50
Unplated Length / Shear Span
Figure 4-9: Factor of Safety versus Unplated Length to Shear Span Ratio
117
0.75
1.75
+ Debonding
VU
0
0I
o Fiber Rupture
o Concrete
L)
Crushing
* Shear Failure
I.-
~
I
$
-
1.00 4
$
I
-* -
-
--
*
0
$1
-|
0
$1
0.25 1
0.00
0.05
0.10
i
i
0.15
0.20
0.25
Axial Stiffness of FRP / Balanced Axial Stiffness
Figure 4-10: Factor of Safety versus FRP Stiffness to Balanced Stiffness Ratio
1.75
+ Debonding
o Fiber Rupture
"0
0
o Concrete Crushing
-j
(D
o Shear Failure
U-
6.
X
U
~0
-
1.00
- - ---------------
*0*
0.25
0.0
0.5
1.0
Axial Stiffness of FRP / Axial Stiffness of Steel
1.5
Figure 4-11: Factor of Safety versus FRP Stiffness to Steel Stiffness Ratio
118
1.75
+ Debonding
0
+
e
I
Fiber Rupture
o
Concrete Crushing
Shear Failure
Io
LL
I.
w
1.00
- -----
---- --
-
--- -----
-- -- ---- - - -- ---0
I
0
4)
0 25
0.00
0.01
0.02
0.03
0.04
0.05
Reinforcing Steel Ratio
Figure 4-12: Factor of Safety versus Reinforcing Steel Ratio
1.75
* Debonding
0
o
Fiber Rupture
o
Concrete Cru ~hing
4
I
I
o Shear Failure
4
LL
** $
C.
w
*
-
M
0
4
I
*
-. 7
$
0)
$
*
4
4
4
I
I
4
-*~4---I
$1
4----
I
4
I
0
1
40
4
4
*
*
0.25
4
*
*
A
- -
*
4
4
*
I
*
1.00 +
~
*.
4.
0
I
I
I
-
0.25
0.50
0.75
1.00
Total Axial Stiffness / Balanced Axial Stiffness
Figure 4-13: Factor of Safety versus Total Stiffness to Balanced Stiffness Ratio
119
to be a decreasing trend with increasing unplated length to shear span ratios. The lower
experimental failure loads in this region may attributed to the increase in interfacial normal and
shear stresses as the distance between the plate cutoff point and support increases, which is not
considered in ACI 440F.
The change of the ratio calculated design loads to experimental failure loads with the reinforcing
steel ratio is plotted in Figure 4-12. The predicted failure loads are observed to be generally
lower than the experimental failure loads for low steel reinforcement ratios. The predicted failure
loads are over the experimental ones when the steel reinforcement ratio goes beyond 0.02,
mainly since concrete crushing becomes the governing failure mode. The change in the factor of
safeties with respect to the total stiffness ratio to the balanced stiffness ratio is presented in
Figure 4-13. However, no specific trend is observable.
The effects of FRP stiffness to total stiffness ratio and the FRP stiffness to steel stiffness ratio on
the factor of safeties are presented in Figure 4-10 and Figure 4-11, respectively. ACI 440 F
design procedure was more successful in estimating the failure loads of beams when these ratios
were lower. This trend is again mainly attributed to the governing modes of failure, which are
generally observed to be FRP rupture or concrete crushing when these to stiffness ratios are low.
AS mentioned earlier the design procedure of ACI 440 F is successful in estimating the failure
loads of beams that fail in concrete crushing or FRP rupture. However, it cannot consistently
predict the failure load when debonding or shear type of failures takes place.
4.4 Concluding Remarks
Two models for predicting plate end failure loads, namely Jansze's and Ahmed et al's models,
have been presented and discussed. The predictions of Jansze model have been found to be
conservative since this model does not take the internal stirrups into account. The model
developed by Ahmed et al., which is an extension of Jansze's model to include the contribution
of stirrups, has found to generally give higher failure loads compared to the first one. But its
estimations might result in unconservative predictions.
In addition to plate end shear models, the general characteristics of interfacial stress base models
used for estimation of stress concentrations at plate ends have been discussed. They assume
linear elastic material behavior and the interfacial stresses predicted by these models are
120
generally reasonably close to each other. However, this is only true if the moments of inertias
used in the formulation are close to each other since the predicted stresses are quite sensitive to
the value of the moment of inertia. For example, models that use uncracked transformed moment
of inertia predict lower stress concentrations at plate ends compared to others that use cracked
transformed moment of inertia.
Once the stresses at the plate end section are calculated by these methods, a failure criterion is
usually implemented to estimate the failure loads. At earlier studies, failure criteria that depend
on the maximum value of the shear stress at plate end have been used. But, then, considering that
the failures generally take place in the concrete substrate, failure criteria depending on biaxial
stress state at the plate end section has been adopted and the principal stresses at this location are
compared with the values obtained from the adopted failure criteria. The comparison of the
results predicted by some of these models have shown that the failure loads predicted by
Roberts' and El-Mihilmy and Tedesco's models generally result in over conservative predictions,
whereas the loads predicted by Malek et al.'s model is scattered and sometimes results in
unconservative predictions. The difference mainly results from the use of uncracked moment of
inertia by Malek et al. on contrary to the use of cracked moment of inertia in the other two cases.
In addition, the models of Roberts and El-Mihilmy and Tedesco replace the moment at the plate
end section with the moment at a certain distance away from the plate end, which obviously
increases the calculated stresses at the plate cutoff point.
In addition, interfacial stress based models are over sensitive of the thickness of the adhesive
layer. However, the control of its thickness during bonding of FRP composites is difficult to
control, especially on site. Moreover, it has been experimentally observed that the effect of the
adhesive layer thickness on the failure load is minor. Therefore, any model that is over sensitive
to this parameter should not be used for design purposes.
The difficulties in accurately estimating the stress distribution in the constituents of the FRP
strengthening system due to material non-linearity and effect of cracking on stresses and failure
behavior calls for development of other methods for estimating the debonding failure loads of
FRP strengthened systems. Moreover, most of the present methods are mainly concerned with
the calculation of crack initiation load but not with the propagation of it once it is initiated. The
121
brittle nature of debonding failures suggests that fracture mechanics based approaches can be
useful in modeling these failures.
The implementation of the proposed design guidelines developed by ACI Committee 440F for
flexural strengthening and comparison of the resulting design loads with the failure loads of the
beam in the experimental database have shown that use of ACI 440F design guidelines in its
current form might result in unsafe designs, especially in cases where the governing modes of
failure are debonding or shear type failures. Although the proposed guidelines were able to
predict the failure capacities of beams when the mode of failure is concrete crushing or FRP
rupture, the factor of safeties obtained in case of premature failures might be unsatisfactory.
There is a need for development of more accurate and reliable models for predicting the
debonding and shear failure loads and incorporation of these models to the current ACI 440 F
design guidelines to obtain more efficient and reliable designs. Parameters that affect the failure
behavior of strengthened beams, such as the amount of steel reinforcement and distance from the
plate curtailment point to the support, should be included in these models. Until that stage, either
more conservative approaches should be used for design of FRP strengthened beams or external
anchorages or shear strengthening systems should be provided to prevent brittle failure modes, as
suggested by ACI 440F.
122
5 Fracture Energy Based Plate End
Delamination Model
The previous chapter has demonstrated the need for development of more accurate and reliable
models for predicting the delamination failure loads of FRP strengthened beams and
incorporation of these models into design guidelines to obtain more efficient and reliable
designs. The brittle nature of debonding failures suggests that fracture mechanics based
approaches can be useful in modeling these failures.
In what follows, a relatively simple fracture based model to estimate the plate end delamination
loads of FRP strengthened RC beams is proposed. The model is based on the assumption that the
fracture energy dissipated during the delamination of the FRP plate from the RC beam is equal to
the difference in the strain energies of the strengthened RC beam before and after the debonding
process. First, the details and the formulation of the proposed delamination model are given.
Next, the amount of fracture energy dissipated during the delaminaton process is evaluated
through review of previous experimental and theoretical research work on FRP-concrete bonds
and interfaces. Delamination of FRP from RC beam mainly involves mode II fracture
propagation since the thickness and hence the bending stiffness of the FRP plate is very low
compared to the RC beam. Considering that the delamination of the FRP plate occurred with a
thin layer of concrete attached to it, the fracture energy dissipated during this process is assumed
to be equal to the mode II fracture energy of the concrete substrate, which is approximately
estimated to be 20 times the mode I fracture energy of concrete estimated by the formula given
by CEB-FIB Code. Finally, delamination loads predicted by the proposed model are compared
with the experimental failure loads of beams in the experimental database that failed by plate end
delamination.
123
5.1 Fracture Energy Based Model for Plate-End Delamination
Figure 5-1 shows the typical load deflection diagram of an FRP strengthened RC beam together
with that of the same beam in the unstrengthened state. The initial stiffness of the strengthened
beam before yielding of the tensile steel is higher than that of the same beam in the
unstrengthened state due to contribution of the FRP composite to the beam stiffness. Therefore,
the yielding load of the strengthened beam is higher but the deflections at yielding are generally
very close to each other. After yielding of the tensile steel, the stiffness of the unstrengthened
beam drops abruptly but the strengthened beam is still able to carry increased loads after yielding
since FRP reinforcement can carry increased tensile stresses. Once debonding of the flexural
FRP reinforcement occurs, the load that can be carried by the strengthened beam drops to the
level that can be carried by the beam in its unstrengthened state.
Assuming that the debonding of the FRP plate takes place in a brittle manner at a certain critical
load level, the energy dissipated during this process can be assumed to be equal to the difference
in the recoverable strain energies of the beam before and after debonding. The strain energies
stored in the strengthened beam before and after fracture are conceptually shown in Figure 5-2.
The difference between the areas of the upper and lower triangle gives the energy dissipated
during the delamination of the FRP plate from the RC beam.
It is important to emphasize that this model is only valid if the debonding process takes place in a
Deflection
Figure 5-1 Typical Load Deflection Diagrams of FRP Strengthened and Unstrengthened RC Beams
124
L
Energy Dissipated
During Debonding
Strain Energy
After Debonding
Deflection
Figure 5-2 Strain Energy in the Strengthened Beam Before and After Debonding
brittle manner, so that the difference between the strain energies of the strengthened beam before
and after debonding can be taken equal to the fracture energy dissipated during the delamination
of the FRP laminate. This is believed to be the case in strengthened beams that fail through
delamination of the FRP plate from the RC beam with a thin layer of concrete attached to it,
where failure occurs in a sudden manner when the critical load level is reached. Although
delamination at plate ends and flexural and shear crack mouths may initiate at load levels below
the ultimate failure load, these local delaminations are limited in size and the amount of fracture
energy dissipated at these locations may be neglected compared to the fracture energy dissipated
during the overall delamination of the plate at failure.
In beams that fail through concrete cover separation, however, the above argument is not valid
since the failure does not occur in a sudden manner. In this case, failure occurs long after
concrete cover separation initiates and after it propagates a certain amount along the rebar level.
The fracture energy dissipated during the propagation of the concrete cover separation before the
ultimate failure cannot be neglected. In addition, the stress distribution along the beam and the
stiffness of the beam changes as the debonding crack propagates along the rebar layer. Therefore,
the introduced model can only be used to estimate failure loads associated with the delamination
of the FRP plate from plate ends with or without a thin layer of concrete attached to it, but not to
estimate failure loads related to concrete cover separation.
125
5.1.1 Delamination Criteria and Model
The strain energy W stored in a member can be found by integration of the strain energy density
over the volume. Neglecting volume forces, the strain energy stored in a flexural member can be
expressed by considering only the normal and shear components as
W =- 1J-U
+--r2dv d
With the insertion of stress terms O
=
(5-1)
xG"
2 ,E
My and rY
I
Vk
A
= -,
the strain energy equation is related
to the applied loading
W
Vk2
I ( My)2 +
I
=-
2V
G
A
dV
(5-2)
Assuming that the effect of the shear components is negligible, the strain energy stored in a
flexural member can be written as
W =
2
Finally recognizing that I =
j
I2
E
2
dAdx
(5-3)
y2 dA, the equation can be further simplified to
M2
W=
dx
(5-4)
L
For the four point bending test set up, the beams can be discretized into several sections with
similar moments of inertias and applied loadings. The strain energy stored in the strengthened
beam can be found by evaluating the above integral over the length of the beam separately in
these discrete sections
W,
k M2
LPM2
L/2 M
=2
dx + 2
dx + 2
2sEI
2EI,,
sEI,
20
126
dx
(5-5)
where EIunstr and EIstr are the bending stiffness of the beam in unstrengthened and strengthened
states, respectively.
Similarly, the evaluation of the same integral over the same beam in the delaminated state, which
is taken to be the same as the beams original state before strengthening since the beam returns to
its unstrengthened condition and capacity after delamination provided that there is no major
damage in the beam, gives
z2 JM
Wlntr
L 2L/2
2
22E1M
L
0 2EIunstr
(5-6)
dx
dx+2
=2
2EIunstr
Expressing the moments in terms of applied loads for the four point bending configuration,
above strain energy expressions become
deb
WL
= ,-4
EIst L 0 +
Wuntr =
Pdeb
EI,,,
1
___,2,
El
4
where
K2E,
3
3
2L
3
EIun,,,
3
+
~
E~
+--
L L
2
__
d=
- A
2
4
Pu2nstr
=
B
4
(5-7 )
(5-8)
and Putnstr,y, are the debonding load of the strengthened beam and yielding load of the
unstrengthened beam, respectively. The strain energy released during debonding is assumed to
be equal to the difference of the two calculated strain energies.
The resistance of the strengthened beam to the debonding can be evaluated by considering the
fracture energy required to delaminate the FRP composite from the RC beam. The systems
resistance to debonding can be found by integrating the crack resistance over the whole length of
the FRP plate.
Lf
Drs =
Lf
JGfbfdx = Gfbj
0
dx =Gfbf Lf
0
where Gt is the fracture energy of the failing material.
127
(5-9)
Equating the fracture resistance of the beam to the energy released during the debonding process,
the debonding load can be found as
Ps
=
IA r(GbL+
2
""ntr'
B-
(5-10)
5.1.2 Evaluation of Fracture Energy Dissipated
One critical aspect in the application of the above model is the appropriate evaluation and
representation of the fracture energy dissipated during delamination process. As mentioned
before, Gf in the above formula is the fracture energy of the failing material or the interface.
delamination at the FRP-adhesive-concrete interface may take place within one or more of the
constituent materials or interfaces depending on the elastic and fracture properties of these
materials and interfaces (Buyukozturk et al, 2002). The existing flexural and shear cracks will
also affect the propagation path of the delamination as well.
However, in most of the previous experimental studies, the failure is observed to be by
delamination of the FRP plate with a thin layer of concrete attached to it. Therefore, provided
that proper adhesives are used and no construction errors have been made during installation
process, it may be assumed that the fracture will take place in the concrete layer. Therefore, the
use of the fracture energy of the concrete seems to be more appropriate in most cases.
Debonding of the FRP laminates from the RC beam generally involves a mixed mode fracture
depending on the location and configuration of the cracks (Rabinovitch and Frostig, 2001;
Buyukozturk and Hearing, 1998). For example, flexural cracks located in regions of the beams
with large moments, tend to open with increased loading and introduce high interfacial shear
stresses. Fracture crack propagation along the FRP-concrete interface or within the concrete
substrate involves mode II fracture (Buyukozturk and Hearing, 1998; Leung, 2001; Wu, 1997).
In addition, debonding of the FRP from the plate ends mainly involves mode II fracture
propagation as well (Yuan and Wu, 2000), since the thickness and hence the bending stiffness of
the FRP plate is very low compared to the RC beam. Based on these observations, it may be
assumed that the propagation of the FRP delamination is generally in the shearing mode (mode
II) and the fracture energy associated with this mode of failure, may be used in the above
formulation.
128
The fracture energy of FRP-concrete bonds or joints has been studied by several researchers (DeLorenzis et al, 2001; Karbhari and Engineer. 1996; Taljsten, 1996; Kimpara et al, 1999;
Neubauer and Rostasy, 1999). A number of different failure modes including delamination
within the concrete substrate, adhesive, FRP composite or their interfaces, have been observed in
tests performed by these researchers. The failure modes and the associated fracture energies
obtained in these studies are found to be dependent on the properties of the strengthening system,
concrete strength, surface preparation and other factors.
Taljsten (1996) developed a fracture mechanics model for FRP plates bonded to concrete and
loaded in shear. To verify the developed model, experiments have been performed on single lap
FRP-concrete specimens. In all cases, failure was observed to take place in the concrete
substrate. Since the fracture energy is needed in the developed model, tests to estimate mode I
and mode II fracture energies of the concrete have been also performed. However, since it is
difficult to measure the pure mode II fracture energy of the concrete only approximation tests to
estimate the mode II fracture energy were performed. Comparison of experimental results with
the theoretical one have shown that the use of mode I fracture energy in the formulation
underestimates the bond capacity, whereas the use of mode II fracture energy generally
overestimates it. However, the tests results were much closer to the theoretical values when
mode II fracture energy was used, they were even higher in some cases.
Neubauer and Rostasy (1999) conducted a series of double lap shear tests on CFRP-concrete
bonded joints. They concluded that, for both concrete fracture failures and FRP delamination
failures the fracture energy could be calculated using
G, =
kbcf,
(5-11)
where f, is the tensile strength of the concrete. kb is a factor that considers the influence of the
plate width relative to the width of the concrete member, which usually does not exceed 1.3,
whereas cy is a factor introduced to take all secondary effects into account. The mean value of it
was found to be 0.202 based on 70 bond tests.
De-Lorenzis et al (2001) performed tests on flexural specimens to investigate the effect of
bonded length, concrete strength, ply width, and number of plies on the bond properties. They
also theoretically analyzed the local bond slip relationships and evaluated the fracture energy. An
129
average value of 1430 N/m was obtained for the fracture energy. The fracture energy reported is
the fracture energy related to delamination along the concrete-adhesive interface, since this was
the observed mode of failure in all tests. They indicated that to this value should be compared
with the fracture energy related to the shearing of the concrete layer underneath the FRP
laminate, which is mentioned to be dependent on concrete tensile strength and surface
preparation, to determine the bond failure mode and calculate the corresponding failure loads
since the lower of the two Gf values would control. In an attempt to correlate the fracture energy
corresponding to crack propagation in concrete to the concrete tensile strength, they calculated
Gf values from experimental data available in literature, but could not obtain any consistent
relationship.
As mentioned previously, almost all of the plate delaminations observed in experimental studies
were in the concrete substrate. Therefore, mode II fracture energy of the concrete can be used as
a first attempt to model the fracture energy dissipated during this process. However, it is difficult
to measure and accurately quantify the pure mode II fracture energy of concrete. Swartz et al
(1988) have concluded from their tests that mode II fracture energy is 8 to 10 times larger than
mode I fracture energy, whereas Bazant and Pfeiffer (1986) indicated that mode II fracture
energy is 25 to 30 times larger than mode I fracture energy. The large difference between mode I
and mode II fracture energies is mainly due to influence of aggregate interlock and friction.
Recently, Reinhardt et al (1997; 2000) has proposed new testing approaches for measurement of
pure mode II fracture energy of concrete. They concluded that the mode II fracture energy of
concrete is about 20 to 25 times of its mode I fracture energy.
For practical purposes, mode I fracture energy of the concrete may be estimated using the
formula suggested by CEB-FIB Code (1993). Based on extensive test data, a simple formula that
relates fracture energy GF (N/m) to the mean compressive strength of the concrete f,' (MPa) is
proposed
GF= aF(fc)
(5-12)
The empirical coefficient aF depends on the maximum aggregate size. For example, for a
maximum aggregate size of 16 mm, it is given as 6. Once the mode I fracture energy of concrete
130
is estimated with this method, mode II fracture energy of it can be approximately taken equal to
20-25 times of this value.
It should be mentioned that the fracture energies obtained in the above mentioned FRP-concrete
investigation studies are also an order of magnitude higher than the mode I fracture energy of the
concrete used in these studies. Therefore, the use of mode II fracture energy of concrete in the
proposed delamination model should give reasonable results. However, the fracture properties of
concrete-adhesive and adhesive FRP interfaces should be studied in detail together with the
fracture properties of concrete, adhesive, and FRP.
5.1.3 Comparison with Experimental Results
To check the reliability of the proposed model, the loads predicted by the above procedure are
compared with the failure loads of beams found in literature that failed by delamination of the
FRP laminate from the plate ends with a thin layer of concrete attached to it. The number of this
kind of failure in literature is somewhat limited compared to concrete cover separation failures
and comparison data mainly consists of experiments performed at MIT (Hearing; 2000). A
fracture energy that is equal to 20 times the mode I fracture energy of concrete calculated by the
CEB-FIB method is used in the analysis.
The ratios of the estimated delamination failure loads to the experimental failure loads are shown
in Figure 5-3 and Figure 5-4. As it can be seen from these figures, most of the estimated failure
loads are between 75% and 100% of the experimental failure loads and the model predicts the
failure loads fairly. The results seem consistent and less scattered compared to plate end shear
and interfacial stress based models evaluated in the previous sections. The average of the
estimated delamination loads to experimental failure loads was 0.83 with a standard deviation of
0.11. In addition, it can be observed from Figure 5-4 that the model has satisfactorily estimated
the failure loads over a wide range of FRP length to beam length ratios.
The ratios of estimated failure loads to the estimated yield loads of the RC beams in their
strengthened and unstrengthened states are shown in Figure 5-5 and Figure 5-6, respectively. As
it can be seen, delamination loads corresponding to strength increases between 25% and 125% of
the capacity in the unstregthened state were obtained. All of the estimated delamination loads
were above the yield strength of the strengthened beam. In addition, the ratio of the estimated
delamination loads to the yield loads of the strengthened and unstrengthened beams tend to
131
1.5
F
1.25
0
-j
1
LL
C.
CU
0.75-
0
0
CU
E 0.5
-
CU
0.25
II
01
0. 3
0.4
I
I
I
I
0.5
0.6
0.7
0.8
0.9
Est. Delamination Load / Calc. Flexural Failure Load
1
Figure 5-3: Comparison of Predicted Failure Loads with Experimental Results
1.5
1 .25 CU
0
-J
1
LU
8
...........
--
7.
~0 0.75C
0
-J
C
0
C
0.5
-
E
0.25 k
0
0. 4
I
0.5
I
I
I
0.6
0.7
0.8
Length of FRP Laminate / Length of Beam
I
0.9
1
Figure 5-4: Comparison of Predicted Failure Loads with Experimental Results: Effect of Laminate Length
132
2
E
cz
u 1.75
-
5~ 1.5
-
--
.
-..
-...-
0
0
1.25
1
6
co
0
0.75
-j
E0.5 F
CZ
0 0.25
U'
0.3
0.4
0.8
0.9
0.5
0.6
0.7
Est. Delamination Load / Calc. Flexural Failure Load
Figure 5-5: Comparison of Est. Failure Loads with Est. Yielding Loads of Strengthened RC Beams
2. 5
E
( 2.2
.. -
-.
5-
(D
-
-o1.7
6
-oS1.
1.2
c
0.
0. 5 -0
c
-j
55 --
00
0
*=0.
.fj
.. . . . . . ..
0.
. . .
LU
0.3
0.4
0.8
0.9
0.6
0.7
0.5
Est. Delamination Load / Calc. Flexural Failure Load
1
Figure 5-6: Comparison of Est. Failure Loads with Est. Yielding Loads of Unstrengthened RC Beams
133
1.75
1
-
1.5-
0
-J 1.25-Cz~
~0
0.75 4
2
..
. .
.. ..
.1
05
0
0 .2 5 -.
0
0.4
....
0.5
.. . . . . . . . . . . ..
0.6
0.7
0.8
Length of FRP Laminate / Length of Beam
... ... .
0.91
Figure 5-7: Comparison of the ACI 440F Design Loads with Experimental Failure Loads
increase as the length of the FRP plate increases, as expected. The model is able to capture this
aspect as well.
To see how design according to ACI 440-F design guidelines results in these cases, the nominal
design loads of the same beams are also calculated according to the proposed ACI 440-F design
guidelines. As mentioned before, ACI 440-F design guidelines introduce a limit on the effective
strain in the FRP laminate to prevent the occurrence of the premature failure modes, which is
dependent on the stiffness and the thickness of the laminate. The ratios of the calculated design
loads to the experimental failure loads are shown in Figure 5-7. It can be easily seen that the
design loads obtained with the use of ACI 440F design guidelines are unconservative for low
FRP laminate length to beam span ratios. The obtained results are more scattered compared to
the ones obtained with the proposed delamination model (See Figure 5-4). Although the design
loads become more conservative with increasing laminate lengths, it is observed that the
suggested design guidelines fails to account for different laminate length. As mentioned in
Chapter 4, the length of the FRP laminate should be included in ACI 440-F design guidelines as
one of the design parameters.
134
Although no delamination failure was observed in the tests performed in this study, delamination
loads predicted by the model is compared with the failure loads of the beams strengthened only
in flexure and tested as part of this study. The model predicted failure loads of 151.6 kN, 171.7
kN, and 187.4 kN for beams F-I, F-II and F-II-2, respectively. In all cases, the predicted
delamination loads were higher than the experimentally observed failure loads. Since no
delamination failures were observed until the ultimate failure of the test beams, which took place
either by FRP rupture or plate end shear at lower load levels than the predicted values, the
predictions of the model was satisfactory in this case as well.
The proposed model does not require tedious calculations as some of the other proposed models
and more importantly it produces consistent results. The ratio of the predicted versus
experimental failure loads are not scattered as in the case of other models. Until more reliable
and accurate methods are developed and made available, it can be used for design purposes.
5.2 Concluding Remarks
A relatively simple fracture based model to estimate debonding loads is proposed. The model
assumes that the fracture energy required for debonding of the FRP plate from the RC beam is
equal to the difference in the strain energies of the strengthened RC beam before and after the
debonding process. Further assuming that the failure takes place in the concrete substrate and
using the mode II fracture energy of the concrete which is assumed to be 20 times the mode I
fracture energy of concrete estimated by the formula given by CEB-FIB Code, the energy
dissipated during delamination process is calculated. Equating this to the difference in strain
energies, the failure load of the beam is estimated.
Comparison of the model predictions with test results of beams in the experimental database that
failed by plate end delamination has revealed that the model was successful in estimating the
delamination loads over a wide range of FRP plate to beam length ratios. The results seem
consistent and less scattered compared to plate end shear and interfacial stress based models and
evaluated in the previous sections. The model offers a relatively easy and reliable tool for
estimation
of delamination failure loads but further investigations on more accurate
representation of the fracture energy dissipated during debonding process are required.
135
6 Design for Flexural Strengthening
In what follows, a general design procedure for flexural strengthening of RC beams is presented.
Five major phases of the procedure, together with the several sub-steps, are explained and related
design equations are given. These phases and main steps of the design procedure are illustrated
in Figure 6-1. Throughout the design procedure, it is assumed that related material properties
and structural dimensions are known. It is also assumed that other structural members and the
structure as a whole are capable of carrying the upgraded loads.
First, the retrofit materials are selected depending on loading and environmental exposure
conditions considering other factors as well. Then, the flexural design of the retrofit system is
made through modified section analysis without considering the debonding type failures. In this
phase, first balanced FRP reinforcement ratios ensuring ductile failures are calculated and the
amount of FRP reinforcement required to carry the increased loads are estimated. Then,
considering these values together with existing beam and practically
available FRP
reinforcement dimensions, the thickness and width of the FRP reinforcement to be used are
selected and the flexural capacity of the system is determined. In the third phase, the shear
capacity of the upgraded system is evaluated and the need for a shear strengthening is
investigated. The fourth design phase is the one that debonding type failures are investigated. In
this phase, first, the failure loads associated with delamination type failures are calculated for the
selected FRP dimensions with the use of the fracture energy based model developed in this
study. If the calculated debonding failure loads do not reach the desired design load capacity, the
dimensions of the FRP reinforcement are changed, i.e. the length or width of it is increased, to
obtain higher debonding failure loads. Finally, in the last phase, the serviceability performance of
the strengthened beam is evaluated. The stresses in the steel under service loads and the stresses
in the FRP reinforcement under sustained and fatigue load are calculated and compared with the
allowable design stresses. In addition, the load deflection behavior of the strengthened beam may
be investigated as well.
136
Phase I: Selection of
Retrofit
Determine beam dimensions
Determine existing material properties
Select retrofit material properties
Materials
Phase II: Flexural Design
with Section
Analysis
Calculate balanced FRP area for steel
yielding
Estimate amount of FRP required
Choose FRP area to be used
Change retrofit
ratio
Calculate balanced FRP area for FRP
rupture
Determine failure mode and corresponding
moment capacity
no
Phase III: Evaluation of
Shear
Capacity
Is existing
shear capacity
sufficient?
yes
Phase IV: Design for
Delamination
Failures
no
Can shear
strengthening
be applied?
lamrinnate
Investigate shear
+-yes
Choose dimensions of the FRP
'7
retrofit
Increase length or
width of FRP
Calculate delamination capacity
yes
Is delamination
Can FRP
no
changed?
sufficient?
no
yes
Phase V: Serviceability
Check
Calculate stresses in tensile steel and FRP
laminate under service loads
|Can
external
ys anchorage be
ys
applied?
Are these
stresses
allowable?
noV
yes
Finalize Design
Figure 6-1: Flexural Design Flowchart
137
n
n
6.1 Phases of the Design Procedure
6.1.1 Phase I: Selection of Retrofit Materials
The first phase of the design procedure is the selection of the strengthening system components,
in other words FRP composite and the epoxy adhesive. The selection should be done based on a
variety of factors including environmental exposure conditions, loading type, level of desired
capacity upgrade, serviceability considerations, material and construction costs, and others.
Although characteristic properties of strengthening systems might change from product to
product, some general observations can be made about the above stated factors. CFRP
composites, for example, are generally known to be more resistant to environmental exposure
conditions compared to GFRP and AFRP composites. They are also resistant to creep-rupture
under sustained loading and fatigue failure under cyclic loading. On the other hand, AFRP and
GFRP composites demonstrate better impact resistance than CFRP composites.
However, the mechanical properties of the FRP composite, i.e. tensile strength and modulus of
elasticity, are generally the most important parameters in the selection process. These depend
highly on the type of fiber used and on the form of the composite, i.e. wet-lay up system or prepreg systems. CFRP composites generally provide much higher tensile strength and stiffness
properties, especially the latter one. The mechanical properties of the pre-preg systems are also
better compared to wet-lay up systems, mainly due to higher volume fraction of fibers.
Although the structural adhesives used with FRP materials are generally provided as a system,
the choice of the adhesive is of great importance to provide composite action over the anticipated
design life of the strengthening system. Typically, the epoxy adhesive is much stronger than
concrete, favoring bond failure in the concrete substrate rather than the bond interface. Fracture
properties of the adhesive should be also considered in the design process, especially in
evaluation of brittle debonding failures.
6.1.2 Phase ll: Flexural Design with Section Analysis
The second phase of the design procedure involves flexural design of the system with modified
section analysis, which is based on strain compatibility, using existing beam dimensions and
properties together with the selected FRP properties. The key design criterion for flexural
strengthening design of RC beams is that the tensile steel reinforcement should yield before any
138
other flexural failure takes place to provide sufficient ductility to the system. This must be
assured by limiting the amount of FRP provided to a certain value corresponding to simultaneous
concrete crushing and steel yielding. Once this is satisfied, the amount of FRP area required to
obtain the desired flexural capacity can be estimated considering FRP composite as an additional
reinforcement. After selection of the FRP dimensions to be used, the failure mode of the system,
i.e. FRP rupture or concrete crushing, may be determined comparing the area of FRP provided
with the balanced FRP area corresponding to simultaneous concrete crushing and FRP rupture.
Then, the flexural capacity of the system may be calculated based on the governing failure mode.
When the strength requirements of the strengthened system are met, the serviceability
performance of the system should be investigated.
The following assumptions are made throughout the flexural analysis and design of RC members
strengthened with externally applied FRP reinforcement:
* There is perfect bond between FRP reinforcement and concrete (No slip).
*
Plane sections remain plane after loading (Bernoulli's principle).
* The FRP reinforcement has a linear elastic stress-strain relationship to failure.
" The reinforcing steel shows a linear elastic-perfectly plastic behavior.
" The maximum usable compressive strain in concrete is 0.003.
" The concrete has no tensile strength.
One important point to note, before presenting the design equations, is that when the failure
mode of the FRP strengthened beam is not concrete crushing of concrete, whether or not
followed by steel yielding, concrete in compression region may not reach its ultimate strain. In
this case, although use of Whitney stress block concept for concrete may give reasonably
accurate results, a more accurate model for concrete strains and stresses at the ultimate limit state
may be considered. Throughout the following, a modified form of Hognestad's concrete model
will be used together with the associated mean stress and concrete compressive force centroid
factors, a and 7, respectively. The former converts the actual stress-strain relationship into a
rectangular stress-strain equivalent, whereas the latter is used to determine the centroid of the
compression zone. Concrete model of Hognestad consists of a parabolic region followed by a
linearly decreasing region, whose equations can be given as
139
For cc ! 60
and for co
(6-1)
6cc :eu ,
where co = 2f,"/ Ec.
C
fc = fc 1-0.15
1
(6-2)
CCU -C
fe" used in the above equations is given as a fraction of ultimate
compressive strength of concrete, e.g. fc"~ 0.92f' for 30Mpa < fe' <45MPa. The mean stress
and concrete compressive force centroid factors, a and y, corresponding to this idealized
concrete model can be expressed as,
For cc
gCO,
a = (cc
--
3
(_C_02
(6-3)
4 -(c
/co)
12 - 4(cc /cO )
and for co
cc
CCU ,
a=1-
-2X2+
y =1-
where X=
-6XE2e6
X
3ec
-
-4
(6-4)
(6-5)
2_
2cc
+6XO
0 C
C2
+662 -4Xc7
+12X8 0 82+12e 2 -6Xc 3
(6-6)
0.15
However, throughout the rest of the document,
fc"
is assumed to be equal to
f', whereas
co is
assumed to be 0.002, to simplify the design equations. The maximum usable compressive strain
of concrete,
e,, is taken equal to 0.003, as mentioned earlier. These assumptions greatly
simplify the calculation of the mean stress and concrete compressive force centroid factors.
When cc = CCU , i.e. when concrete reaches its ultimate compressive strain, these factors are
expressed as acu and y,
respectively.
140
Existing Substrate Strain
The effect of the initial stresses and the corresponding strains in the RC beam at the time of FRP
application must be taken into account in the design of the strengthened beam. The strains in the
surface to which FRP is bonded should be considered as initial strains and should be excluded
from the strain in the FRP to allow direct application of linear strain variation along the section
of the strengthened beam.
The initial strains in the concrete substrate can be determined from the analysis of the
unstrengthened beam considering all loads (without any load factors) that will be acting on the
member during the installation of FRP system. Considering that the existing RC beam will
experience a bending moment greater than its cracking moment before installation of FRP, the
initial strains may be determined from the cracked section properties of the existing beam. Initial
tensile strain at the bottom face of the concrete,
bi',
due to a moment,
Mbi
,acting on the beam at
the time of FRP application can be obtained from
ebi =
MEi(h-
CO
(6-7)
C Cr,tr
where h = depth of the beam,
chi
= depth of the neutral axis, EC = modulus of elasticity of
concrete and Icrtr = moment of inertia of transformed cracked section. The given equation can be
further simplified assuming the stresses created by the applied moment are within the elastic
ranges of the member, which is generally the case under normal service conditions and loads.
Ebi
=
MEi(h-kd)
C cr,tr
(6-8)
where k = ratio of the depth of the elastic neutral axis to the effective depth, d . It should be
noted that the effect of the thickness of FRP has been neglected in the above equations, since it is
generally much smaller compared to the height of the beam. With the initial strain, ebi. in hand,
the effective strain,
,e,, and the corresponding effective stress, fe, in the FRP can be calculated
from
141
ft =
6
-
(6-9)
b ! 6fu
ff, = Ef -e,
f
(6-10)
where ef = strain level in FRP , 6fu = rupture strain of FRP, ffu = ultimate tensile strength of
FRP, and Ef= tensile modulus of elasticity of FRP.
Balanced FRP ratio for steel yielding
As mentioned above the key criterion for flexural design is that the yielding of the tensile
reinforcing steel must be assured before any other failure takes place. Since the tensile failure
strains of FRP composites are much larger than the yield strain of steel, FRP rupture before
yielding does not have to be taken into account in this respect. However, concrete crushing may
take place before yielding of tensile steel. A balanced FRP ratio that corresponds to simultaneous
yielding of tensile steel and crushing of the concrete in a strengthened reinforced concrete beam
may be defined, as shown in Figure 6-2. Under the given assumptions, the balanced FRP ratio
can be obtained from force equilibrium in the section and from the geometry of the strain
distribution using similar triangles.
The neutral axis location at balanced condition,
cb,
can be computed from the geometry of the
strain distribution as:
b
-CS
=u
caf,
CU
Csb = Asbfs'
A
cb
-W -------------
Z
---------
cb =
afbCb
d'
h
- - -- As
-----------------6S =EY
Afb
L-~~---------
6fb < efu
Figure 6-2: Balanced FRP Ratio
142
T = Asfy
W T =Af
(6-11)
CCU +=
Using the calculated value of
cb ,
the compressive force in the concrete,
Cc,,
and the stresses in
compressive steel, f' , and FRP composite, fj,, at balanced condition can be expressed,
respectively, as
CC, = af'bc
f,'f
=
(6-12)
d
Eec
f.
(6-13)
Cb
d
fjb = Ef
-Cb
8Cu
-
ebi )
f
U
(6-14)
With these in hand, the force equilibrium in the section yields
Alb ff,
+
Af, - A'ff' = af'bC,
(6-15)
where A,th = balanced FRP area, A S = tensile steel area, and A'S = compressive steel area. Solving
the above equation for A.,
Afi =
(af'bc,
-
A, fl, +Af'
(6-16)
fjb
Finally, balanced FRP ratio is found by dividing the above equation by bd ,
P
Ab
bd
1
flbbd
(a'b
- A, f +Af,)
(6-17)
Equation (6-17) can be further expressed in terms of p, = balanced reinforcing steel ratio for the
corresponding singly reinforced section, p' = compressive steel ratio, and p = tensile steel ratio
143
Pjb -
(P f, + P','b - PfY)
(6-18)
fjb
where P = abCb
fc, ,p-
f, e +6
A'
, and p' =S.
bd
bd
If the FRP ratio, p, , is smaller than the balanced FRP ratio, pb,, the tensile reinforcement steel
will yield before crushing of concrete. Otherwise, brittle compression failure will take place
before yielding of tensile steel. To obtain an acceptable level of ductility, the total compressive
force in the concrete can be limited to 75% of the compressive force in the concrete at balanced
condition.
Cc <0. 7 5Cb
(6-19)
The compressive force associated with concrete for a strengthened beam can be found from
equilibrium of forces as
C = raf'bc = Af fl,+ A, f,
-
A' f'
(6-20)
Using Equations (6-20), (6-15), and (6-19), the maximum allowed tensile force in the FRP can
be written as
0. 7 5 afc'bc, + A'f,'- As f
(A fje
From this equation the maximum FRP area, A1,max
'
(6-21)
and the corresponding maximum FRP ratio,
Pf,max, can be obtained as
Afmax =
j1 I0.75afc'bcb +Afs'- As f,
Pf,,a =
I10.75Pb +
ffe
144
Pfs'- A f
(6-22)
(6-23)
In the above equations, effective stress in FRP, fe, and compressive stress in the compressive
steel,
f', can only be found
after calculating the depth of the neutral axis, c, as explained in the
following sections.
Estimation of Required FRP Area
The nominal moment capacity of a R/C beam can be found by summing the moments of the
forces acting on the cross section about any point on the cross section. However, the tensile force
carried by the FRP is unknown at the initial design stage of a strengthened beam. This difficulty
can be overcome by summing the moments about the centroid of the force in the FRP. The
resulting expression for nominal moment capacity, Mn, of a singly reinforced section is given by
- M" - =af'bc(df- c)- A,f,(d, -d )
(6-24)
where MU = ultimate design moment. The above equation can be rearranged in a quadratic form
and c can be calculated as
C-
B
-4;fC
(6-25)
2A
in which
C
A = afc'b
(6-26)
B =-afcbdf
(6-27)
=Mn+ Afjd
-d)
(6-28)
Knowing the depth of the neutral axis, the stress in the FRP can be found from the geometry of
the strain distribution
fj, = Ef (CC
-
145
6bi
(6-29)
Case-SC:
Compression crushing of concrete (fj,
f, )
If the effective stress in FRP. computed from above equations by taking a = acu, is less than the
tensile strength of FRP, the beam will fail by compression crushing of concrete after yielding of
tensile steel. Using the equilibrium of forces acting on the section, the required FRP crosssectional area, Af , can be calculated from
Al
=
af'bc - AfI, <Afmax
(6-30)
fie
Case-SR:
Rupture of FRP (ff,> f1U)
If the computed effective stress in FRP exceeds the tensile strength of FRP, the beam will fail by
rupture of the FRP after yielding of tensile steel. In this case, the concrete does not reach its
ultimate strain in compression. And the strain in the extreme concrete fiber, eC, which is
required to determine the corresponding parameters, a and y, can be found from linear strain
distribution corresponding to FRP rupture
cc
= (-
+
c
bi)
(6-31)
However, as it can be clearly seen from the above equations, the equilibrium equation (6-1)
requires a trial and error procedure to solve for c. As a first guess, the neutral axis depth
corresponding to simultaneous compression crushing of the concrete and FRP rupture, cc,,
which is defined as follows, can be used.
C
C
(6-32)
+
+8
Ecu
,i
+
bi
The actual value of the neutral axis depth should be smaller than the one calculated with the
above equation. Once the depth of the neutral axis is found, the required FRP cross-sectional
area, A.
, can
be calculated from
146
Af -
jaf'bc - AS f,
(6-33)
A,
fJ4
Calculation of Moment Capacity for Selected FRP Area
Once the required area of FRP for carrying the ultimate moment is approximately calculated
using the above procedure, the actual area of the FRP to be used can be selected. This decision
depends on the dimensions of the commercially available FRP products as well as the
dimensions of the strengthened beam. Once this decision is made, further analysis can be done to
refine the design and to investigate the serviceability issues including deflection, creep, fatigue.
In what follows, the ultimate moment carrying capacity of rectangular beams for given
strengthening parameters, i.e. FRP thickness and area, are analyzed. As mentioned earlier, the
yielding of the tensile steel reinforcement will be assured by setting an upper limit on the FRP
ratio, Equation (6-23), and the tension steel will be assumed to be yielding throughout the
following analysis. In addition, the failure of the strengthened beam will be assumed to take
place either by compression crushing of concrete or by rupture of FRP composite, preceded by
yielding of tensile steel in both cases, assuming no premature failures will take place before
flexural failures.
As stated earlier, the condition corresponding to simultaneous compression crushing of concrete
and FRP rupture is referred to as "balanced condition for FRP rupture". Using the linear strain
diagram, FRP area corresponding to the balanced condition for FRP rupture is calculated as
Afbc
=
(aCffcbcfc - Asf)
(6-34)
ffu
where c,
is given by Equation (6-32). If the FRP area, Af , is smaller than the FRP area
corresponding to balanced condition,
Abc ,
the failure mode of the strengthened beam will be
FRP rupture, otherwise the failure will occur by compression crushing of concrete.
If failure occurs by compression crushing of concrete, the nominal moment capacity of the beam
can be determined from
n=
= As ff(d -c)+A,
147
f
-
cC
(6-35)
where ff, is given by equation (6-29), and c is calculated using equation (6-25) with the
following parameters
A= acu f'b
B =-Af
+ A 1 Ef(
f e +
(6-36)
8i
)
C =-AEfcudf
(6-37)
(6-38)
If failure mode of the strengthened beam is FRP rupture, i.e. fe = f1 , the nominal moment
equation becomes
M =
A, fY (d -7X) + A,. ffu(d,' - yc )
(6-39)
where c can be calculated using the following formula obtained from equilibrium of forces
A, f, + Af ff,
af'b(6-40)
However, since the mean stress factor , a, is dependent on e , and in turn on c, a trial and error
procedure is required. First, an initial value for ec is assumed, corresponding a is calculated
and inserted in above equation. The obtained value of c is used to back calculate ec using
equation (6-31). Then the calculations are repeated using the back-calculated value of ec until
the inserted and back-calculated values of ec converge to each other. Once c or cc are
determined, the nominal moment capacity of the strengthened beam can be easily calculated
from equation (6-39).
Verification of Flexural Analysis
To verify the results of the section analysis procedure, the ultimate load capacities predicted by
the above-explained procedure are compared with the available test data in literature. The
ultimate load represents the sum of the two equal concentrated loads applied to beams, which are
tested under four-point bending over a simple span, at failure. The results are presented in Table
6-1. The results clearly indicate that the section analysis is quite accurate in predicting the
148
Table 6-1: Comparison of Analytical and Experimental Results
Reference
Beam
Designation
%
Failure
Mode
(kN)
(kN)
difference
Pcalc
Pexp
Ahmed (2001)
DF1
FR
101.5
118.0
-14.0
Arduini (1997b)
B2
FR
174.4
170.0
2.6
Chajes (1995)
El, E2, E3
FR
16.1
15.3
5.2
GI, G2, G3
FR
17.7
15.5
14.2
F-I
FR
103.7
108.6
-4.5
FS-HU-I
FR
104.1
110.2
-5.5
FS-FU-I
FR
103.8
122.6
-15.3
FS-HU-II
FR
140.7
150.6
-6.6
FS-FU-II
FR
140.7
149.1
-5.6
FS-FU-III
CC
198.7
200.9
-1.1
4B, 4C, 5D
CC
121.3
107.8
12.5
5B, 5C, 5D
CC
133.7
146.4
-8.7
6B, 6C, 6D
CC
149.5
158.4
-5.6
A
CC
306.7
320.0
-4.2
B
CC
264.0
255.0
3.5
2
FR
14.4
13.2
9.1
3
FR
17.0
17.3
-1.7
Karaca (2002)
Ross (1999)
Saadatmanesh (1991)
Triantafillou (1992)
ultimate load capacity of reinforced concrete beams strengthened with FRP, provided that the
failure mode is either concrete crushing or FRP rupture.
6.1.3 Phase III: Evaluation of Shear Capacity
In Chapter 4, it was mentioned that inclined cracking and interfacial stress concentrations at the
ends of FRP plates result in reductions in the inherent shear capacity of RC beams strengthened
only in flexure and the actual shear strength of the beam may be anywhere between the shear
resistance provided only by the stirrups and the shear resistance provided by the sum of the
stirrups and the concrete section. Therefore, the shear capacity of the member may be expressed
as
1
V=k 6
bd +
A
f~
sV
where 0 < k < 1.0.
149
(6-41)
For design purposes, it was conservatively suggested in Chapter 4 to assume that only the
stirrups contribute to the shear capacity of a RC beams strengthened in flexure and neglect the
contributions from other mechanisms. This recommendation was based on a limited number of
experiments and needs further verification. Therefore, it is suggested to take the factor k = 0.5,
i.e. include half of the concrete's shear capacity to the overall shear capacity, until further results
are available. However, it is still suggested to use external anchorages or shear strengthening at
end region of the FRP plates when the shear demand exceeds the shear capacity provided by the
stirrups.
The shear capacity of the strengthened system must be checked to see whether or not the shear
capacity provided by the stirrups is sufficient to carry the upgraded load capacity. If the shear
strength provided by the stirrups is not sufficient then, as a first option, provision of end
anchorages or shear strengthening at the end region of the flexural FRP plate can be considered.
When either of these is provided, the premature shear failures due to presence of flexural FRP
plate can be prevented. Although the provision of end anchorages or shear strengthening at the
ends of the flexural FRP plate are observed to increase the shear capacity of the beam compared
to its unstrengthened configuration, the contribution of them in shear capacity should be
neglected until their contribution is verified or quantified reliably by further research.
If the required shear capacity is more than the inherent shear capacity of the member in
unstrengthened configuration, then, the shear capacity of the beam must be upgraded by
provision of external FRP shear reinforcement over the full shear span of the beam. Many
researchers
have developed methodologies for design and analysis of external shear
strengthening systems (Khalifa and Nanni, 2000; Triantafillou and Antonopoulos, 2001) and the
readers are referred to these documents since the details of shear strengthening are beyond the
scope of this work.
6.1.4 Phase IV: Design for Delamination Failures
The next step in design is, given the dimensions and properties of the FRP laminate, to estimate
the moment that corresponds to the delamination failure of the member and compare it with the
desired moment capacity and the flexural capacity of the beam using the analysis developed in
Chapter 5.
The delamination load of a strengthened RC beam under four point bending was given as
150
=
Pun
VA
(G-b Lf + "
(6-42)
)
4
where
A=
-
r
1
Li +
EIun,,
and
B =
4
1
EIst
2 Lp
LO
3
3
E
+
Lp L
2
(6-43)
(6-44)
EIust
3
2 )
The fracture energy Gf in Equation (6-42) was assumed to be 20 times the mode I fracture energy
of the concrete, which might approximately be estimated from the formula suggested by CEBFIB Code (1993) using the mean compressive strength of the concretefc' (MPa)
GF=
F(fc ) 0
7
(6-45)
where aF = 6 for a maximum aggregate size of 16 mm.
If the delamination load calculated is lower than the desired capacity of the beam, then as a first
option the length of the FRP laminate should be increased to increase the fracture surface area
and the resistance to delamination. If this is not possible or sufficient, the width of the FRP plate
may be increased as a second option. However, this will require an iteration of the whole design
process, since the cross-section of the FRP plate is being modified. If this modification was not
also sufficient to reach the desired capacity, then a different type of FRP laminate may be
considered for strengthening application. Another option in all of these mentioned cases is to
provide anchorages to increase the delamination resistance of the laminate.
6.1.5 Phase V: Serviceability Check
After the ultimate capacity requirements of the strengthened beam have been satisfied, the
serviceability requirements of the strengthened beam can be checked. First of all, it must be
verified that the stresses in the tensile under service loads are less than the yield stress of it to
avoid plastic deformations. Then, the stresses in the FRP reinforcement should be checked to see
if the stress under sustained loads is lower than the allowed creep-rupture stress limits. This
151
check must also be performed for fatigue loading, if the member is subjected to fatigue loads. In
addition, the load deflection behavior of the strengthened beam can be analyzed if desired.
ACI 440 F suggests that the stress in the tensile steel reinforcement under service loads should be
less than 0.8 times the yield strength of the steel. The stress in the tensile steel under service
moment, Ms, can be calculated using transformed section approach. Assuming that the materials
are in the linear range under service loads, the stress in the tensile steel can be expressed as,
IM, +biAf E (h-kdI 3)(d -kd)E
AsE,(d -kd I 3)(d -kd )+ A E(h-kd 3)(h-kd)
(6-46)
=s,
Similarly, the stresses in the FRP reinforcement due to a moment, ms,, created by sustained
loads can be calculated from
ffSMb+i
A, Ej(h -kd
/ 3)h--kd)Ef
AsE(d -kd I3)(d - kd)+ Af Ef(h -kd I 3)(h -kd)
biE
The calculated stresses can then be compared with the allowable stresses limits.
Load Deflection Behavior of Strengthened Beams
The ultimate deflection of ordinary RC beams ranges from five to twelve times the first yield
deflection. In estimating the deflections, ACI recommends use of an effective moment of inertia,
Ie, which is a function of uncracked moment of inertia, cracked moment of inertia, cracking
moment, and maximum moment. With this approach it is intended to account for stiffness
variation along the beam due to non-uniform cracking. However, in case of FRP strengthened
beams, where the ultimate deflection of the beams generally ranges two to five times the yield
deflection, using the above effective moment of inertia approach usually gives deflections less
than the observed experimental values [El-Mihilmy and Tedesco, 2000a] and an alternative
approach is required.
The load-displacement curve of a singly reinforced beam strengthened with FRP composite may
be divided into four regions, where load-displacement relationship in each region is assumed to
be linear, as shown in Figure 6-3. Load deformation behavior in each of these regions are
explained and analyzed in detail in the following sections.
152
AL
Concrete at
ultimate compressive strain
C
Concrete at
peak compressive stress
Region 4: Post-Peak Stress Region
Steel yielding
Region 3: Post-Yielding Region
Region 2: Post-Cracking Region
Concrete cracking
Region 1: Elastic Region
Deflection
Figure 6-3: Assumed Load-Deflection Response
For a simply supported beam loaded under four-point bending, the load corresponding to a given
moment value can be expressed as
P2M
(6-48)
a
where a is the distance between the support and the concentrated load. In addition, the slope of
the load deflection curve for four-point bending may be determined from
Kip- =
48EI2
(3L 2 - 4a)a
(6-49)
where EIi is the bending rigidity of the strengthened beam and L is the clear span of the beam.
Then, assuming that bending rigidity is constant between two given loads, Pi and P1_,, the
incremental deflection between the given loads may be calculated using the following equation,
iP
-P
K
24EI.
(3L - 4 a2)
V
-
(6-50)
And, the deflection of the beam, t5, at load Pi may be expressed as
9i = i-5,--Ai
where 8,5_ is the deflection of beam at load P_
153
(6-51)
In the analysis, the reinforcing steel is assumed to be perfectly elastic-plastic and the FRP
composite is assumed to have a linear stress-strain behavior up to failure as before. For the
concrete, Hognestad's idealized stress-strain curve for concrete in compression is used. Also, the
concrete is assumed to be able to carry tensile stresses up to its modulus of rupture, f,. But once
cracking occurs, the contribution of the concrete below the neutral axis to bending is neglected.
The slope of Hognestad's stress-strain curve at any strain,
For e
CO ,
£
E()
=E
6,
is equal to
1C
(6-52)
where Ec =4730Vf'. For strain values larger than co, the slope of the stress-strain curve is
negative and this portion is neglected in stiffness calculations.
The contribution of the concrete in compressive region to the flexural rigidity of the beam, EI,,
at any given concrete strain in the extreme compression fiber, CC , may be expressed as follows
bc'
=
EIC = JE()y2dA = KEC
(6-53)
0
The parameter K is used to convert the stiffness of the concrete above the neutral axis into an
equivalent linear one and equal to
For ec < 6O,
and for co
K
6>
cc
=1
3c
4co
K =
4 c
(6-54)
(6-55)
(655
Region 1: Elastic Region
In this region, all material behavior is assumed to be linearly elastic and the depth of the neutral
axis can be easily calculated by using elastic analysis as
E(bh2 I 2)+ E, Ad + EfAfd(
ECbh+ E, A+EA
(6-56)
Then, the flexural rigidity of the beam may be calculated using the uncracked transformed
section properties, which includes the contribution of concrete, steel and FRP
154
EI = Ec
bc'
3
+ E'
b(h -c)'
3
+ EsA,(d - c)2 + Ef Af (d1 - c) 2
(6-57)
The concrete below the neutral axis will crack when the tensile stress on bottom of the beam
reaches the modulus of rupture, f,. The cracking moment can then be calculated as
MI=(EII/Ec)fr
(6-58)
(h - c)
Having determined the flexural rigidity of the strengthened beam in elastic region and the
cracking moment, the cracking load and the corresponding deflection can be determined by using
equations (6-48) through (6-5 1), taking the initial displacement '58_1 equal to 0.
Region 2: Post-cracking region
This region represents the behavior of the beam between the cracking and the yielding moment.
As stated earlier, the concrete below the neutral axis is assumed to be totally cracked and its
contribution to bending is neglected in calculations. The bending rigidity of the strengthened
beam in this region is taken to be constant and equal to the value just before yielding of
reinforcing steel.
The strains in extreme concrete compression fiber may be expressed in terms of the yield strain
of the reinforcing steel as
C=
C
d-c
(6-59)
From equilibrium of forces in section, the depth of the neutral axis can be obtained by using the
following parameters in Equation (6-25)
A = af'b
(6-60)
B =-As.f + Af EfCc
(6-61)
C=-Af Ef ccd 1
(6-62)
However, since the mean stress factor , a , is dependent on e , and in turn on c, a trial and error
procedure is required. First, an initial value for ec is assumed, corresponding a is calculated
155
and inserted in the above equation. The obtained value of c is used to back calculate e using
Equation (6-59). Then the calculations are repeated using the back-calculated value of ec until
the inserted and back-calculated values of ec converge to each other.
Having determined the depth of the neutral axis, the yield moment can be calculated as
M2
=A
f,(d
- yc)+ AfEfe
d -c
c (df -C)
(6-63)
In addition, the bending rigidity of the strengthened beam may be determined from
EI 2 = KEc
bc 3
3
+ EsAs(d -c)
2
+ Ef A1 (d -c)
2
(6-64)
The yielding load and corresponding deflection can be calculated by inserting the yielding
moment, M2' and the bending rigidity of strengthened beam, EI 2 , in equations (6-48) through
(6-51), together with the cracking moment, M, and the corresponding deflection 51.
Region 3: Post-yielding region
This region represents the beam behavior between the yielding of the tensile steel and the point
that the peak stress of the concrete in compression is reached, i.e. strain in extreme concrete
compression fiber reaches co. Since the tensile steel has yielded and a perfectly elastic-plastic
behavior is assumed for it, the contribution of the tensile steel to the flexural rigidity of the beam
is neglected in this region.
Again using the equilibrium of forces in section, the depth of the neutral axis for this condition
can be obtained by using the following parameters in Equation (6-25)
A = afc'b
(6-65)
B =-Af, + A,Efe 0
(6-66)
C =-AfE ,e0 d
(6-67)
where a is the mean stress factor corresponding to co.
Once the depth of the neutral axis is determined, the moment carried by the section, when the
strain in extreme concrete fiber reaches co, can be calculated using
156
M
3
= Af,(d
- yc) + Af Efeo
c
(d1 - X)
(6-68)
Since the reinforcing steel is assumed to be perfectly elastic-plastic, the bending rigidity in postyielding region may be obtained by deleting the second term in equation (6-64)
E 3 = KEC
3
+ Eb A (df -c)2
(6-69)
The load and deflection corresponding to the point at which strain in extreme compression fiber
becomes
eo can be calculated by inserting the moment M 3 and the bending rigidity of
strengthened beam in this region, E13 , in equations (6-48) through (6-51), together with the
yielding moment, M 2 , and the corresponding deflection
52.
Region 4: Post peak stress region
The last region represents the beam behavior after the extreme compression fiber in concrete has
reached its peak stress, i.e. strain in extreme concrete fiber in compression reaches CO. Although
FRP composite may rupture or debond before compression crushing of concrete, it will be
assumed that the concrete strain will reach its ultimate value, e,, at the end of the region
regardless of the failure mode, solely, for the purpose of determining the slope of the loaddeflection curve. The actual failure mode may be determined by using the analysis described
earlier in the text.
The analysis of the beam behavior in this region is almost the same with the one in post-yielding
region, except that e
and the corresponding factors should be used in equations (6-65) through
(6-69) instead of co. For the purpose of completeness, the equations are given below. Using CCU
instead of co, the parameters that should be used in (6-25) to determine the depth of the neutral
axis become
A = af'b
(6-70)
B =-A, f + Af EfCCU
(6-71)
C = -Af Ef CCU d
(6-72)
157
Finally, the moment carried by the section and the bending rigidity of the strengthened beam,
when the strain in extreme concrete fiber reaches e, , can be calculated using
M4 =
Asf, (d - yc)+ A, Eecu
El =iE~
bc 3
4
EI4 = iE -+ EJ Af(df -c)
It should be noted all the factors, a, y, and
K
(d-
yc)
2
(6-73)
(6-74)
, used in the above equations are the ones
corresponding to sEC . The load and deflection corresponding to the point at which strain in
extreme compression fiber reaches e, can be calculated by inserting the moment M 4 and the
bending rigidity, El4 , in equations (6-48) through (6-5 1), together with the moment M3 and the
corresponding deflection 3s .
6.2 Worked Examples
In this section, the use of the design procedure presented in the previous sections is illustrated
with the help of two design examples.
6.2.1 Worked Example 1:
The design example considered here involves the design of the specimen F-I used in the
experimental part of this thesis. The details of the test specimen and the material properties can
be found in Section 3.1 and will not be repeated here. The design problem is to upgrade the
capacity of the beam to 22.5 kN-m. Phase I of the design process is not considered here since
FRP to be used is already specified.
Phase 1I: Flexural Design
Balanced FRP Area for Steel Yielding
The maximum area of FRP that may be used was calculated using Equation (6-16).
Af by =1247mm 2
Following the guidelines, the FRP area that can be used should not exceed 0. 7 5A, = 935.3mm2
158
Estimation of Required FRP Area
The required FRP area to carry the upgraded design moment 22.5kN-m is estimated either from
Equation (6-30) or Equation (6-33), whichever is appropriate, to be
A1
req =
31.5mm 2
Calculation of Moment Capacity for Selected FRP Area
With the estimated amount of FRP area required in hand, the actual dimensions of the FRP
reinforcement to be used may be selected depending on the dimensions of the commercially
available FRP products as well as the dimensions of the strengthened beam. In this case, an FRP
reinforcement that is 102mm wide and 0.38mm thick providing an area of 38.8mm 2, which are
the same with the FRP dimensions used in the experimental program. Then, the balanced FRP
area for FRP rupture is calculated from Equation (6-34) for given FRP dimensions
A,
- 101.0mm
2
Since the selected FRP area, Af , is smaller than the FRP area corresponding to balanced
condition,
Afb
,
the failure mode of the strengthened beam will be FRP rupture. The moment
capacity corresponding to this flexural failure mode is calculated with the use of Equation (6-39)
M, = 23.7kNm
Phase Ill: Evaluation of Shear Capacity
The shear capacity provided by the stirrups calculated using Equation (6-41) with k=O is 95.7kN,
which corresponds to a moment of
Mn = 20.7kNm
With the inclusion of half of the concrete's contribution to the shear capacity, i.e. taking k=0.5,
the moment corresponding to the shear capacity of the member becomes
M, = 27.8kNm
159
Based on these results, the shear capacity of the member is assumed to be adequate to carry the
upgraded moment. However, since the shear corresponding to the design moment is larger than
the shear capacity provided by the stirrups use of end anchorages or shear strengthening at the
end region of the plate is suggested.
Phase IV: Design for Delamination
Using the equations presented in Section 6.1.4, the moment corresponding to the delamination
load of the member is calculated to be
Mn = 31.9kNm
which is higher than the required moment capacity. Therefore, the beam is considered to be safe
in terms of delamination.
Phase V: Serviceability Check
Only the load deflection behavior of the strengthened beam is considered for this case. The load
deflection response of the beam is estimated making use of the procedure detailed in Section
6.1.5. Figure 6-4 shows the estimated load deflection response of the beam together with its
125 1
Experimental
100 1
Theoretical
"...
....
75-
0
-1
50-
25-
0
0
8
4
12
Midspan Deflection (mm)
Figure 6-4: Experimental and Estimated Load-Deflection Curves of Beam F-I
160
16
experimental load deflection curve. The precracking region was not considered in the analysis,
since the beam was precracked before strengthening. The estimated yield load was lower than
the experimentally observed one and this created a deviation of the estimated response from the
experimental one in the post-yielding region. However, the proposed method was able to capture
the general load deflection behavior and the estimated slopes of the load deflection curves in the
pre-yielding and post-yielding regions match quite well with the experimental observations.
6.2.2 Worked Example 11:
The second example involves the design of a RC beam specimen previously tested by Hearing
(2000). The dimensions of the beam are as shown in Figure 6-5 and the material properties are
as given in Table 6-2. The design objective is to upgrade the nominal moment capacity of the
beam to 18kN-m. The mechanical properties and the width and thickness of the FRP laminate,
50mm x 1mm, are going to be taken equal to the values given in the indicated reference to be able
to compare the design results with experiments. In addition, Phase I and Phase V of the design
process will not be considered here.
Phase 11: Flexural Design
Balanced FRP Area for Steel Yielding
The maximum area of FRP that may be used was calculated using Equation (6-16).
Afbk = 1040mm 2
Following the guidelines, the FRP area that can be used should not exceed 0. 7 5A,,
P/2
600
P/2
=
780mm 2
200
#3 @ 150
2#3
220
2#3
F
50
Lf
1800
Figure 6-5: Details of Beam Used in Design Example II
161
Table 6-2: Material Properties Used in Design Example II
Property
Concrete
Steel
FRP
Tensile Strength (MPa)
2.8
413
2400
Compressive Strength (MPa)
34.5
-
-
Elastic Modulus (GPa)
25.4
210
155
Estimation of Required FRP Area
The required FRP area to carry the upgraded design moment 18kN-m is estimated to be
A
req =
21.4mm 2
Calculation of Moment Capacity for Selected FRP Area
With the estimated amount of FRP area required in hand, the actual dimensions of the FRP
reinforcement to be used may be selected depending on the dimensions of the commercially
available FRP products as well as the dimensions of the strengthened beam. However, as
mentioned above, the dimensions of the FRP laminate will be taken to be the same as the ones
used in the experimental program, i.e. 50mm x 1.0mm providing an area of 50.0mm2 . The
balanced FRP area for FRP rupture is calculated from Equation (6-34) for given dimensions as
AbC =
53.7mm 2
Since the selected FRP area, Af , is smaller than the FRP area corresponding to balanced
condition, Afbc, the failure mode of the strengthened beam will be FRP rupture. The moment
capacity corresponding to this flexural failure mode is calculated with the use of Equation (6-39)
Mn =34.7kNm
which is much larger than the desired moment capacity. However, as it will be seen later in the
design process that the delamination load rather than the flexural failure load controls the design
in this case.
162
Phase Ill: Evaluation of Shear Capacity
The shear capacity provided by the stirrups is calculated to be 141.7kN, which corresponds to a
moment of
Mn = 42.5kNm
which is larger than the desired flexural moment capacity of the upgraded beam.
Phase IV: Design for Delamination
Since the length of the FRP laminate is not specified yet, as a first attempt, the length of the FRP
laminate is taken to be equal to 900mm. The moment corresponding to the delamination load of
the member for selected laminate length is calculated to be
Mn =16.4kNm
which is lower than the required moment capacity. Therefore, in the second trial, the length of
the FRP laminate is increased to 1200mm, keeping the width of it constant. The moment
corresponding to the delamination load for the increased laminate length is found to be
Mn =18.5kNm
The calculated moment is slightly over the required moment capacity and, thus, a laminate length
of 1200mm is found to be sufficient for design.
The moment capacity of the same beam is also calculated using the guidelines provided by ACI
440-F. The factor Km, for given laminate dimensions and properties is 0.64, that is the effective
strain in FRP laminate should be limited to 64% of its ultimate strain to prevent premature failure
modes. The nominal moment capacity of the beam in this case is found to be 23.6kNm,
irrespective of the laminate length used since the length of the FRP laminate is not considered in
the design process of ACI-440F. Comparison of the experimental failure moment, 20.9kNm, with
the design moment calculated according to ACI 440-F reveals that use of ACI 440-F guidelines
may result in unconservative designs, especially in cases where the delamination resistance of
the FRP laminate controls the design.
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6.3 Concluding Remarks
A design procedure for flexural strengthening of RC beams that consists of five major phases is
presented and related design equations are given. First, retrofit materials are selected depending
on loading and environmental exposure conditions considering other factors as well. Then, the
flexural design of the retrofit system is performed without considering the debonding type
failures. In this phase, first balanced FRP reinforcement ratios ensuring ductile failures are
calculated and the amount of FRP reinforcement required to carry the increased loads are
estimated. Then, considering these values together with existing beam and practically available
FRP dimensions, the thickness and the width of the FRP laminate to be used are selected and the
flexural capacity of the system for selected dimensions is calculated. In the third phase, the shear
capacity of the upgraded system is evaluated and the need for a shear strengthening is
investigated. In the fourth design phase the load corresponding to delamination of the FRP plate
is calculated. If the delamination loads do not reach the desired design load capacity, the
dimensions of the FRP reinforcement are changed, i.e. the length or width of it is increased, to
obtain higher debonding failure loads. Finally, in the last phase, the serviceability performance of
the strengthened beam is evaluated. The stresses in the steel under service loads and the stresses
in the FRP reinforcement under sustained and fatigue load are calculated and compared with the
allowable design stresses. In addition, the load deflection behavior of the strengthened beam may
be investigated as well.
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7 Summary, Conclusions, and Future
Work
As the world's infrastructure ages, reinforced concrete structures, such as bridges and buildings,
become functionally obsolete due to a variety of reasons including environmental deterioration,
change of use, or increased structural load requirements. Maintenance and rehabilitation of these
structures is becoming a major concern in the construction industry, especially in developed
countries. The costs and challenges associated with the renewal of these structures forced
government and private organizations to search for new techniques and new materials to extend
the service life of these structures. Use of externally bonded plates is recognized as an effective
technique for in situ repair and rehabilitation of reinforced concrete structures among several
other techniques ranging from section enlargement to external pre-stressing. In this technique,
external plates are bonded with structural adhesives to the outer faces of the structural members
to act as additional reinforcement. In 1980's steel plates were used in many applications of plate
bonding technique but the corrosion of steel plates and the need for relatively heavy equipment
for application made fiber reinforced plastic (FRP) composites the material of choice for such
applications.
With their higher strength, better corrosion resistance, reduced weight, and ease of application,
compared to steel plates, FRP composites became far more popular in construction industry in
the last decade. FRP composites are made up of high strength fibers embedded in a matrix and
show linearly elastic behavior up to failure. Although their stiffness is generally less compared to
steel, their ultimate strength can be much higher than steel, depending on the amount and
properties of the fibers used.
Strengthening of reinforced concrete beams in flexure with externally bonded FRP plates are
also shown to be an efficient technique where significant improvements in ultimate strength and
serviceability properties can be obtained. However, it has been also demonstrated in many
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experimental studies that, in case of RC beams strengthened in flexure, it is not generally
possible to make full capacity of the strengthening system due to premature failure modes, i.e.
delamination of the FRP plate from the concrete substrate or debonding of the concrete cover
layer at the reinforcing steel layer. Both of these failure modes are more brittle than failure
modes associated with conventionally reinforced concrete beams and they significantly limit the
level of strength enhancement that may be achieved.
7.1 Research Needs
Although much has been accomplished in the characterization of the failure behavior and
mechanisms of RC beams strengthened in flexure, there is still need for research in several areas
including but not limited to characterization and modeling of premature failures, interaction of
external flexure and shear strengthening systems, the effect of cyclic loading and environmental
exposure on failure mode, capacity, and serviceability of such systems.
Most of the previous studies concentrating on debonding failures have generally considered
beams over-designed in shear to isolate and study this failure mode. However, the relative shear
strength of the beam might affect the debonding behavior of the beam. Continued research is
needed to investigate the premature failures in specimens representing real life beam members
that have shear capacities closer to their strengthened flexural capacities.
In addition, increased flexural capacity of RC beams strengthened only in flexure results in an
increased demand for shear capacity and additional shear strengthening might be required in
such cases as well. Providing externally bonded shear reinforcement will not only improve the
shear capacity of the beam, but may also contribute to the flexural capacity of beam by
preventing debonding type failures initiating from shear cracks or from plate ends, or at least
increase the load level at which debonding occurs by reducing the size and number of cracks and
providing anchorage at plate ends in some configurations. With the application of FRP
reinforcement for shear, failure mode of the strengthened beam may shift from debonding and
shear type failures to more ductile failure modes, i.e. concrete crushing or FRP rupture.
However, the number of research studies on RC beams strengthened both in flexure and shear is
limited compared to studies concentrating only one of them and the interaction between them
was not investigated in detail.
166
Another issue is the lack of written specifications or standards on design of such strengthening
systems that are currently available. Although some attempts have been made for developing
guidelines for design of FRP systems for external strengthening, the above-mentioned issues
about strengthening of RC beams should be studied in detail and developed knowledge should be
incorporated into design standards for safe and reliable application of this strengthening
technique.
7.2 Objectives
The main objective of this study was to experimentally and analytically study the failure
behavior and capacity of precracked RC beams strengthened in flexure as a basis for design. The
experimental study focused on precracked RC beams that have shear capacities slightly over
their unstrengthened flexural capacities and on the effect of external shear strengthening on the
capacity and failure mode of these beams. Whereas, the analytical part was involved with
modeling the delamination of the FRP laminates from the RC beams using a fracture energy
based approach and development of related design equations.
7.3 Summary
7.3.1 Materials and Structural Behavior of FRP Beams
FRP materials used for strengthening concrete structures and the structural behavior of FRP
retrofitted RC beams including their load-deflection behavior and failure modes are reviewed.
Related experimental and theoretical studies are summarized, with a special emphasis on
debonding type failures since they are the most common but the least desired failures. It has been
shown in these studies that the amount of internal steel reinforcement, the thickness and stiffness
of the FRP and the adhesive layers, and the unplated beam length affect both the interfacial stress
concentrations and the debonding failure loads. Among these parameters, the adhesive layer
thickness and the unplated beam length are generally considered to be the most influential ones.
Investigation of the characteristics of previous experimental studies on FRP strengthened beams
with the help of a compiled database has revealed out that most of the test beams in these studies
were over-designed in shear, to prevent shear failures and to isolate the desired flexural failure
mode of interest and only a little number of data exist on beams that have closer shear and
flexural capacities, which is expected to be the case for most of the real world cases. Since the
167
shear capacity of a beam is thought to be influential on the debonding behavior and flexural
capacity of the beam, there is a need to further study and understand the behavior of such cases.
For these cases, a desired increase in capacity is generally only possible with the simultaneous
application of flexural and shear strengthening systems, since the members are expected to be
designed with reasonably closer flexural and shear capacities. Even in cases where the primary
objective of the strengthening procedure was to increase the flexural capacity of the beam, shear
strengthening may be provided to obtain some additional safety in shear, since shear failures are
quite brittle and undesired, or to provide additional resistance to premature debonding type of
failures. However, little work has been performed on the behavior and failure modes of beams
strengthened both in flexure and shear.
7.3.2 Experimental Study and Discussion of Observed Failure Modes
A test program that involves specimens that have relatively closer flexural and shear capacities
have been prepared. The beams were strengthened either in flexure or both in flexure and shear
to observe the transition from brittle to ductile failure modes with the provision of shear
strengthening. The parameters of the experimental program were the amount of internal steel
reinforcement, type of FRP reinforcement, and the shear strengthening configuration.
It has been observed in the experimental study that beams strengthened only in flexure may fail
in shear at load levels lower than the inherent shear of the beam in unstrengthened state. This
decrease in shear capacity is attributed to effect of existing inclined cracks in the shear span
formed during pre-cracking and the presence of stress concentrations at plate ends. The load at
failure is also thought to be dependent on the yielding load of the strengthened beam. Therefore,
for design purposes, it is conservatively suggested to only consider the shear strength provided
by the stirrups and neglect contributions from the concrete section.
These premature shear failures were not observed when external shear strengthening is provided
over the end region or over the shear span of the strengthened beams. In these cases, shear
capacity of the member was observed to be above its unstrengthened configuration and the
failure modes shifted from shear failures to flexural failure modes, except one case. When the
plate end shear failures are prevented by necessary means, the flexural FRP plate may contribute
to the shear capacity of the member through dowel action or by resisting the widening of the
168
shear cracks. However, these contributions should be neglected in design until more reliable
results are obtained by further research.
When the shear strengthening is provided only over a portion of the shear span, shear failures
may be observed in the unstrengthened region of the beam, if the applied loads increase beyond
the shear capacity of the member. The use of external FRP shear strengthening over the full
shear span of the beam prevents these failures as well, provided that no failure in the external
shear strengthening system takes place.
Provision of external shear strengthening in form of U-wraps not only prevents shear failures,
but also prevents the occurrence of debonding failures by providing anchorage to the flexural
FRP plate, decreasing stress concentrations at plate ends, and reducing the width of the cracks. In
addition to increases in the load levels reached, significant increases in the ductility of the
strengthened beams may be obtained by provision of them as well. When properly designed, the
ductility of the strengthened beams may be as high as or even more than those of the
corresponding unstrengthened beams.
7.3.3 Review and Evaluation of Debonding Models and Design Guidelines
Existing modeling approaches for plate end shear failures are presented and discussed. The plate
end shear failure model of Janzse is implemented and the failure loads predicted by this model is
compared with the failure loads of beam in the database that failed by concrete cover separation.
It was seen that the predicted failure loads were quite conservative since this model was mainly
developed fro beams with no internal shear reinforcement. The improved form of this model,
developed by Ahmed et al., made an attempt to include the contribution of the stirrups to the
failure load, but the failure loads of this model in some cases may be unconservative and the data
seems to be scattered.
In addition to plate end shear failure models, failure models based on interface stresses are also
discussed. The interfacial stresses predicted by most of these models are quite close to each other
provided that the same moments of inertia are used in the formulation. They mainly differ in the
criteria they use for failure of the concrete at the plate end section or the adhesive layer.
However, these models are based on linear elastic material properties and quite sensitive to the
thickness of the adhesive layer. The failure loads predicted by implementation of Roberts'
formulation are found to be over conservative, sometimes as low as 10% of the failure load, and
169
the loads estimated by El-Mihilmy and Tedesco's model are found to be scattered, changing
from 20% to 110% of the experimental failure loads.
The comparison of the design loads predicted by implementation of the current design guidelines
provided by ACI Committee 440F with the failure loads of the beams in the experimental
database have revealed that design according to these guidelines might result in unsafe designs,
especially in cases where the governing modes of failure are debonding or shear type failures.
Although, the proposed procedure was able to predict the failure capacities of beams when the
mode of failure is concrete crushing or FRP rupture, the factor of safeties obtained in case of
premature failures might be unsatisfactory.
There is a need for development of more accurate and reliable models for predicting the
debonding and shear failure loads and incorporation of these models to the current ACI 440 F
design guidelines to obtain more efficient and reliable designs. Parameters that affect the failure
behavior of strengthened beams, such as the amount of steel reinforcement, distance from the
plate curtailment point to the support and inherent shear strength of the unstrengthened beam,
should be included in these models. Until that stage, either more conservative approach should
be used for design of FRP strengthened beams or external anchorages or shear strengthening
systems should be provided to prevent brittle failure modes, as suggested by ACI 440 F.
7.3.4 Fracture Energy Based Plate End Delamination Model
An easy to implement fracture energy based model to estimate plate end delamination failure
loads is developed. The model is based on the assumption that the fracture energy dissipated
during the delamination of the FRP plate from the RC beam is equal to the difference in the
strain energies of the strengthened RC beam before and after the debonding process. Considering
the fact that almost all of these type of failures take place in the concrete substrate and using the
mode II fracture energy of the concrete, which is assumed to be 20 times the mode I fracture
energy of concrete estimated by the formula given by CEB-FIB Code, the energy dissipated
during delamination process is calculated. Equating this to the difference in strain energies, the
failure load of the beam is estimated.
Comparison of the model predictions with test results of beams in the experimental database that
failed by plate end delamination has revealed that the model was successful in estimating the
delamination loads over a wide range of FRP plate to beam length ratios. The results seem
170
consistent and less scattered compared to plate end shear and interfacial stress based models
reviewed. The model offers a relatively easy and reliable tool for estimation of delamination
failure loads, but further investigations on more accurate representation of the fracture energy
dissipated during debonding process are required.
7.3.5 Design For Flexural Strengthening
A general design procedure for flexural strengthening of RC beams that consists of five major
phases is presented and related design equations are given. The first phase of the design
procedure is the selection of the retrofit materials depending on loading and environmental
exposure conditions considering other factors as well. Then, the flexural design of the retrofit
system is made through modified section analysis without considering the debonding type
failures. In this phase, first balanced FRP reinforcement ratios ensuring ductile failures are
calculated and the amount of FRP reinforcement required to carry the increased loads are
estimated. Then, considering these values together with existing beam and practically available
FRP reinforcement dimensions, the thickness and width of the FRP reinforcement to be used are
selected and the flexural capacity of the system is determined. In the third phase, the shear
capacity of the upgraded system is evaluated and the need for a shear strengthening is
investigated. Based on experimental results, it has been conservatively proposed to assume that
only the stirrups contribute to the shear capacity of an RC beam strengthened only in flexure.
However, when external anchorages or shear strengthening is provided at the end region of the
FRP plate, the shear capacity of the strengthened beam can be taken equal to that of an
unstrengthened one. The fourth design phase is the one that debonding type failures are
investigated. In this phase, first, the failure loads associated with debonding type failures are
calculated for the selected FRP dimensions and properties. If the calculated debonding failure
loads do not reach the desired design load capacity, the dimensions of the FRP reinforcement are
changed to obtain higher debonding failure loads. Finally, in the last phase, the serviceability
performance of the strengthened beam is evaluated. The stresses in the steel under service loads
and the stresses in the FRP reinforcement under sustained and fatigue load are calculated and
compared with the allowable design stresses.
171
7.4 Conclusions
Use of externally bonded FRP composites is recognized as an effective method for repair and
rehabilitation of RC beams. Although much research has been performed on this subject in the
last decade, there is still need for better understanding and modeling of premature debonding
type failures associated with RC beams strengthened in flexure and development of design
guidelines for safe and reliable application of this method.
Experiments performed in this study have shown that beams strengthened only in flexure may
fail in shear at load levels lower than their theoretical shear capacities in unstrengthened
configuration. These premature shear failures may be prevented by provision of shear
strengthening over the end region or over the shear span of the strengthened beams. However, in
case of partially strengthened beams, shear failures may occur in the unstrengthened shear spans
of these beams. In addition, provision of external shear strengthening in form of U-wraps not
only prevents shear failures, but also the occurrence of debonding failures by providing
anchorage to the flexural FRP plate. It has been experimentally shown that, when properly
designed, the ductility of the strengthened beams may be as high as or even more than those of
the corresponding unstrengthened beams.
A fracture energy based model to estimate plate end delamination failure loads is developed. The
model is based on the assumption that the fracture energy dissipated during the delamination of
the FRP plate from the RC beam is equal to the difference in the strain energies of the
strengthened RC beam before and after the debonding process. Comparison of the model
predictions with failure loads of beams in a compiled experimental database that failed by plate
end delamination has revealed that the model is successful in estimating the delamination loads
over a wide range of FRP plate to beam length ratios. The results are observed to be consistent
and less scattered compared to other debonding models and design guidelines reviewed in the
study. The model offers a relatively easy and reliable tool for estimation of delamination failure
loads and it is incorporated into a general design procedure developed for flexural strengthening
of RC beams.
172
7.5 Future Work
The experimental part of this study has concentrated on the failure modes of FRP strengthened
RC beams that have shear capacities slightly higher than their unstrengthened flexural capacities,
which represent most of the real world cases. The beams were either strengthened only in flexure
or both in flexure and shear. In the former case, shear failures at plate end regions have been
observed at load levels lower than the theoretical shear capacities of these beams indicating that
the shear capacity of such beams may be adversely affected by the presence of flexural
strengthening systems. However, the number of beams tested in this study was limited and
additional work is required to further study this failure mode. Effect of parameters such as FRP
laminate length and width should be also investigated in these studies.
Although no debonding failures have been observed in this study, it is believed that the failure
behavior and capacity of strengthened beams in such cases are affected by the shear strength of
the beams. The effect of stirrup spacing or external shear strengthening systems on failure mode
and capacity of beams strengthened in flexure should be investigated. For example, current study
only included external shear strengthening in form of U wraps and it should be extended to other
shear strengthening configurations such as FRP sheets bonded to the sides of the beams.
Moreover, the majority of the previous research studies have dealt with monotonic loading
conditions, and few researchers have looked into their performance under cyclic loading.
Performance of strengthened members under cyclic loading plays a vital role for structures
subjected to variable loads and for seismic retrofitting applications. Cyclic loading might
significantly affect the delamination behavior of the beams and might have detrimental effects on
the overall behavior of the strengthened beam. This aspect of the problem should be investigated
before safe retrofit of concrete structures that might be subjected to cyclic or earthquake loads.
Another topic that needs further research is the long-term behavior of FRP strengthened systems
under various environmental conditions. Although FRP composites are known for their good
durability performance, the integrity of the concrete-FRP interface is a major concern and the
bond behavior might be adversely affected by environmental effects such as freeze thaw cycles,
high temperatures, or slat water exposure. In addition, coupling of mechanical and environmental
effects might even aggravate the degradation process. Sufficient knowledge on these issues is
essential to increase the safety and reliability of FRP strengthened concrete members.
173
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180
Appendix I: Experimental Database
Ref.'
Beam
A '
FM2
L
Lp
b
mm
mm
mm
mm MPa GPa MPa MPa GPa mm mm 2 mm mm 2 MPa mm mm 2 MPa GPa mm mm mm mm MPa GPa
kN
kN
AF2
1500
500
125
225 41.0 30.0
-
568
185
200
101
25
56.5
553
71
56.5
6.5
7.2
3.0 1100 75 0.33 3500 240
83.0
55.0
CCS
AF21
1500
500
125
225 41.0 30.0
-
568
185
200
101
25
56.5
553
71
56.5
6.5
7.2
3.0 1200 75 0.33 3500 240
85.7
55.0
CCS
AF3
1500
500
125
225 41.0 30.0
-
568
185
200
101
25
56.5
553
71
56.5
6.5
7.2
3.0 1300 75 0.33 3500 240
96.5 55.0
CCS
AF4
1500
500
125
225 41.0 30.0
-
568
185
200
101
25
56.5
553
71
56.5
6.5
7.2
3.0 1400 75 0.33 3500 240
111.0 55.0
CCS
DF
1500
500
125
225
42.0 30.0
-
568
185
200
151
25
56.5
553
100
56.5
6.5
7.2
3.0 1400 75 0.17 3500 240
118.0 75.0
FR
DF2
1500
500
125
225
42.0 30.0
-
568
185
200
151
25
56.5
553
100
56.5
6.5
7.2
3.0 1400 75 0.33 3500 240
120.0 75.0
CCS
DF4
1500
500
125
225
40.5 30.0
-
568
185
200
151
25
56.5
553
100 56.5
6.5
7.2
3.0 1400 75 0.67 3500 240
125.0 75.0
CCS
AG94
CP
1200
400
150
150
37.7
-
450
200
120
339
25
56.5
450
200 56.5
AM97
SM2
1100
420
320
160
36.0 27.0 2.7
550
200
110
226
50
226
550
100 56.5
37
SM3
1100
420
320
160
36.0 27.0 2.7
550
200
110
226
50
226
550
100 56.5
37
SM4
1100
420
320
160
36.0 27.0 2.7
550
200
110
226
50
226
550
100 56.5
37
SM5
1100
420
320
160
36.0 27.0 2.7
550
200
110
226
50
226
550
100
56.5
SM6
1100
420
320
160 36.0 27.0 2.7
550
200
110
226
50
226
550
100
ST2
1100
420
320
160 36.0 27.0 2.7
550
200
110
226
50
226
550
ST3
1100
420
320
160
36.0 27.0 2.7
550
200
110
226
50
226
ST4
1100
420
320
160 36.0 27.0 2.7
550
200
110
226
50
MM2
2100
950
160
320 36.0 27.0 2.7
550
200 270
402
MM3
2100
950
160
320 36.0 27.0 2.7
550
200 270
MM4
2100
950
160
320
36.0 27.0 2.7
550
200
MT2
2100
950
160
320
36.0 27.0 2.7
550
MT3
2100
950
160
320
36.0 27.0 2.7
A3
2000
700
200
200
A4
2000
700
200
200
AOO1
AM97
h
f,'
Ec
ft
fy
E,
d
A,
d'
fy,
s
As,
a
ta
Lf
bf
tf
ff.
1050 100 3.00 200
Ef
69.0
S
2
1000 300 1.0 3510 235 135.0 100.0
DB
2
1000 300
1.0 3510 235
115.0 100.0
DB
2
1000 300
1.0 3510 235
155.0 100.0
DB
37
2
1000 140
1.0 3510 235
145.0 100.0
DB
56.5
37
2
900 300 2.0 3510 235
142.0 100.0
CCS
100
56.5
49
2
1000 300
1.0 3480 235
125.0 100.0
DB
550
100
56.5
49
2
1000 300
1.0 3480 235
155.0 100.0
DB
226
550
100 56.5
49
2
1000 300
1.0 2940 380 155.0 100.0
DB
50
402
550
100 56.5
37
2
1900 150
1.0 3510 235 152.0 125.0
DB
402
50
402
550
100 56.5
37
2
1900 150
1.0 3510 235 135.0 125.0
DB
270
402
50
402
550
100 56.5
37
2
1700 150
3.0 3510 235 160.0 125.0
CCS
200
270
402
50
402
550
100 56.5
49
2
1900 150
1.0 3480 235 160.0 125.0
DB
550
200
270
402
50
402
550
100 56.5
49
2
1900 150
1.0 3480 235 150.0 125.0
DB
33.0 25.0 2.6
540
200
163
308
37
308
540
150
56.5
26
11
1700 150
1.3 2906 167
110.0 72.0
ccS
33.0 25.0 2.6
540
200
163
308
37
308
540
150
56.5
26
11
1700 150
1.3 2906 167
110.0 72.0
ccS
-
181
16
Pit Pc.t
64.4
Ref.1
FPO1
GH98
GH98
HBOO
Beam
L
Lp
b
h
f,'
Ec
ft
fy
E,
d
A,
d'
As'
mm
mm
mm
mm
MPa GPa MPa MPa
GPa
mm
mm2
mm
mm
A5
2000
700
200
200
33.0 25.0 2.6
540
200
163
308
37
B2
2500
1100
300
400
30.0 26.0
1.9
340
200
350
399
B3
2500
1100
300
400
30.0 26.0
1.9
340
200
350
F5
2800
1100
155
240
80.0 39.2
5
532
204
F6
2800
1100
155
240
80.0 39.2
5
532
204
F7
2800
1100
155
240
80.0 39.2
5
532
F8
2800
1100
155
240
80.0
39.2
5
532
F9
2800
1100
155
240
80.0 39.2
5
FlO
2800
1100
155
240
80.0 39.2
lAu
900
300
100
100
1Bu
900
300
100
I1B2u
900
300
ICu
900
2Au
s
2
As,
fta
2
Ea
ta
bf
mm
mm
mm MPa GPa
kN
kN
2.6 2906 167
90.0
72.0
CCS
tf
ff.
Ef
P.It Pc
M2
MPa
mm
mm
308
540
150
56.5
26
11
1700 150
50
266
340
100
101
-
-
2300 300 0.17 3000 400
170.0 95.0
FR
399
50
266
340
100
101
-
-
2300 300 0.51 3000 400
230.0 95.0
DB
203
339
37
226
306
125
56.5
-
-
-
2030 120
1.2 2400 155
100.0 68.1
CCS
203
339
37
226
306
125
56.5
-
-
-
2030 120
1.2 2400 155
103.0 68.1
CCS
204
203
339
37
226
306
125
56.5
-
-
-
1876 120
1.2 2400 155
97.5
68.1
CCS
204
203
339
37
226
306
125
56.5
-
-
-
1876 120
1.2 2400 155
64.0
68.1
CCS
532
204
203
339
37
226
306
125
56.5
-
-
-
1700 120
1.2 2400
155
62.0
68.1
CCS
5
532
204
203
339
37
226
306
125
56.5
-
-
-
1700 120
1.2 2400
155
82.0
68.1
CCS
49.1 33.5
4.2
350
215
84
84.8
16
56.5
350
51
28.2 30.8 11.6
2
860
90
0.5
1273 111
39.6
17.0
CCS
100
49.1 33.5
4.2
350
215
84
84.8
16
56.5
350
51
28.2 30.8 11.6
2
860
65
0.7
1273 111
36.5
17.0
CCS
100
100
49.1
33.5
4.2
350
215
84
84.8
16
56.5
350
51
28.2 30.8 11.6
2
860
65
0.7 1273 111
36.3
17.0
CCS
300
100
100
49.1
33.5
4.2
350
215
84
84.8
16
56.5
350
51
28.2 30.8 11.6
2
860
45
1.0 1273 111
31.9
17.0
CCS
900
340
100
100
49.1
33.5
4.2
350
215
84
84.8
16
56.5
350
51
28.2 30.8 11.6
2
860
90
0.5
1273 111
38.5
14.9
DB
2Bu
900
340
100
100
49.1
33.5
4.2
350
215
84
84.8
16
56.5
350
51
28.2 30.8 11.6
2
860
65
0.7 1273 111
34.0
14.9
CCS
2Cu
900
340
100
100
49.1
33.5
4.2
350
215
84
84.8
16
56.5
350
51
28.2 30.8
11.6
2
860
45
1.0 1273 111
35.6
14.9
CCS
3Au
900
400
100
100
49.1
33.5
4.2
350
215
84
84.8
16
56.5
350
51
28.2 30.8
11.6
2
860
90
0.5 1273
111
39.0
12.5
DB
3Bu
900
400
100
100
49.1 33.5
4.2
350
215
84
84.8
16
56.5
350
51
28.2
30.8
11.6
2
860
65
0.7
1273 111
34.5
12.5
DB
3Cu
900
400
100
100
49.1 33.5
4.2
350
215
84
84.8
16
56.5
350
51
28.2 30.8
11.6
2
860
45
1.0 1273 111
30.7
12.5
DB
lUl.Om
900
300
100
100
44.0
-
-
350
215
84
84.8
16
56.5
350
51
28.2 28.4
8.6
2
860
67
0.8 1414 111
36.5
17.0
CCS
2U1.Om
900
300
100
100
44.0
-
-
350
215
84
84.8
16
56.5
350
51
28.2
8.6
2
860
67
0.8
1414 111
32.0
17.0
CCS
3U1.Om
900
340
100
100
44.0
-
-
350
215
84
84.8
16
56.5
350
51
28.2 28.4 8.6
2
860
67
0.8
1414 111
34.0
14.9
DB
4U1.Om
900
400
100
100
44.0
-
-
350
215
84
84.8
16
56.5
350
51
28.2
28.4 8.6
2
860
67
0.8 1414 111
34.5
12.5
DB
5Ul.Om
900
400
100
100
44.0
-
-
350
215
84
84.8
16
56.5
350
51
28.2 28.4 8.6
2
860
67
0.8 1414 111
34.6
12.5
DB
Al
1800
600
200
260
20.5
25.4 2.8
418
210
220
142
40
142
418
120
142
24.8 2.7
900
50
1.0 2400 155
65.3
60.1
D
A2
1800
600
200
260
20.5
25.4 2.8
418
210
220
142
40
142
418
120
142
24.8
2.7
1200
50
1.0 2400 155
81.4
60.1
D
A3
1800
600
200
260
20.5
25.4 2.8
418
210
220
142
40
142
418
120
142
24.8
2.7
1500
50
1.0 2400 155
83.0
60.1
D
182
MPa GPa mm
Lf
28.4
Ref.
MIO
NDOI
RHOl
Beam
L
Lp
b
h
mm
mm
mm
mm
A4
1800
600
200
260
20.5
25.4 2.8
BI
1800
600
200
260
20.5
25.4 2.8
B2
1800
600
200
260
20.5 25.4
B3
1800
600
200
260
B4
1800
600
200
Cl
1800
600
C2
1800
C3
C4
2
fe'
E,
ft
fy
E,
d
GPa
mm
mm 2 mm mm 2 MPa mm
418
210
220
142
40
142
418
120
418
210
220
142
40
142
418
2.8
418
210
220
142
40
142
20.5 25.4
2.8
418
210
220
142
40
260
20.5 25.4
2.8
418
210
220
142
200
260
20.5 25.4 2.8
418
210
220
600
200
260
20.5 25.4 2.8
418
210
1800
600
200
260
20.5
25.4 2.8
418
1800
600
200
260
20.5
25.4 2.8
1350
500
115
150
30.3
26.0
3
1350
500
115
150
30.3
26.0
4
1350
500
115
150
30.3 26.0
5
1350
500
115
150
A950
1330
440
120
Al100
1330
440
Al150
1330
B1
Pa GPa MPa MPa
As
d'
As'
fyv
s
As
fta
2
Ea
ta
Lf
bf
tf
ffu
Ef
Pult Peco,
FM2
MPa GPa mm mm
mm mm MPa GPa
kN
kN
142
24.8
2.7
-
1800
50
1.0 2400 155
98.1
60.1
D
150
142
24.8
2.7
-
900
50
1.0 2400 155
66.9
60.1
D
418
150
142
24.8
2.7
-
1200
50
1.0 2400 155
69.7
60.1
D
142
418
150
142
24.8
2.7
-
1500
50
1.0 2400 155
91.8
60.1
D
40
142
418
150
142
24.8
2.7
-
1800 50
1.0 2400 155
87.2
60.1
D
142
40
142
418
200
142
24.8
2.7
-
900
50
1.0 2400 155
74.1
60.1
D
220
142
40
142
418
200
142
24.8
2.7
-
1200 50
1.0 2400 155
85.3
60.1
D
210
220
142
40
142
418
200
142
24.8
2.7
-
1500 50
1.0 2400 155
94.8
60.1
D
418
210
220
142
40
142
418
200
142
24.8
2.7
-
1800
1.0 2400 155
90.5
60.1
D
-
534
184
120
236
30
157
365
60
56.5
-
1.47
-
1200 115 0.11 3400 230
72.0
59.0
FR
-
534
184
120
236
30
157
365
60
56.5
-
-
1200 115 0.22 3400 230
86.0
59.0
CCS
-
534
184
120
236
30
157
365
60
56.5
-
-
1200 115 0.33 3400 230
82.0
59.0
CCS
30.3 26.0
-
534
184
120
236
30
157
365
60
56.5
-
-
1200 115 0.44 3400 230
79.0
59.0
CCS
150
32.1
-
-
384
200
120
157
30
56.5
400
50
56.5
-
12.8
1.5
950
80
1.2 3140 181
56.2
42.3
CCS
120
150
32.1
-
-
384
200
120
157
30
56.5
400
50
56.5
-
12.8
1.5 1100
80
1.2 3140 181
57.3
42.3
CCS
440
120
150
32.1
-
-
384
200
120
157
30
56.5
400
50
56.5
-
12.8
1.5 1150
80
1.2 3140 181
58.9
42.3
CCS
1330
440
120
150
44.6
-
-
400
200
120
56.5
30
56.5
400
50
56.5
-
12.8
1.5 1100 80
1.2 3140 181
49.2
14.6
S
B2
1330
440
120
150
44.6
-
-
466
200
120
628
30
56.5
400
50
56.5
-
12.8
1.5
1100 80
1.2 3140 181
130.1 103.0
CCS
C5
1330
440
120
150
25.1
-
-
384
200
140
157
30
56.5
400
50
56.5
-
12.8
1.5 1100 80
1.2 3140 181
71.0
48.3
CCS
CIO
1330
440
120
150
25.1
-
-
384
200
135
157
30
56.5
400
50
56.5
-
12.8
1.5 1100
80
1.2 3140 181
68.0
46.3
CCS
C20
1330
440
120
150
25.1
-
-
384
200
125
157
30
56.5
400
50
56.5
-
12.8
1.5 1100
80
1.2 3140 181
63.0
42.3
CCS
A4
2100
750
200
150
44.0 25.0 3.0
575
210
120
157
30
101
575
150
56.5
25
7.0
2.0 1930 150
0.8 1532 127
61.9
26.3
DB
A5
2100
750
200
150
44.0 25.0
3.0
575
210
120
157
30
101
575
150
56.5
25
7.0
2.0 1930
150
0.8 1532 127
63.2
26.3
DB
A6
2100
750
200
150
44.0 25.0 3.0
575
210
120
157
30
101
575
150
56.5
25
7.0
2.0 1930 150
1.2 1532 127
59.4
26.3
DB
A7
2100
750
200
150
44.0 25.0 3.0
575
210
120
157
30
101
575
150
56.5
25
7.0
2.0
1930 150
1.2 1532 127
70.6
26.3
DB
A8
2100
750
200
150
44.0 25.0 3.0
575
210
120
157
30
101
575
150
56.5
25
7.0
2.0
1930 150
0.8 1532 127
65.2
26.3
DB
A9
2100
750
200
150
44.0 25.0 3.0
575
210
120
157
30
101
575
150
56.5
25
7.0
2.0
1930 150
0.8 1532 127
63.9
26.3
DB
183
mm
50
Ref.'
RC99
Beam
L
Lp
b
h
mm
mm
mm
mm
B3
2100
750
200
B4
2100
750
B5
2100
B6
f'
E,
fyv
s
As,
MPa
mm
mm
101
575
75
56.5
25
30
101
575
75
56.5
157
30
101
575
75
120
157
30
101
575
210
120
157
30
101
575
210
120
157
30
44.0 25.0 3.0
575
210
120
402
ft
fy
Es
d
As
MPa GPa MPa MPa
GPa
mm
mm
150
44.0 25.0 3.0
575
210
120
200
150
44.0 25.0
3.0
575
210
750
200
150
44.0 25.0
3.0
575
2100
750
200
150
44.0 25.0 3.0
B7
2100
750
200
150
B8
2100
750
200
bf
mm
mm
mm MPa GPa
kN
kN
7.0
2.0 1930 150
0.4 1532 127
55.2
57.6
DB
25
7.0
2.0 1930 150
0.4 1532 127
52.5
57.6
DB
56.5
25
7.0
2.0 1930 150
1.2 1532 127
69.7
57.6
DB
75
56.5
25
7.0
2.0 1930 150
1.2 1532 127
69.6
57.6
DB
575
75
56.5
25
7.0
2.0 1930 150
1.8
1074
36
59.1
57.6
DB
101
575
75
56.5
25
7.0
2.0 1930 150
1.8 1074
36
61.6
57.6
DB
30
101
575
75
56.5
25
7.0
2.0 1930 150
0.4 1532 127
74.9
57.4
DB
2.0 1930 150
0.4 1532 127
77.2
57.4
DB
AS'
mm
mm
157
30
120
157
210
120
575
210
44.0 25.0 3.0
575
150
44.0 25.0 3.0
200
150
2
FM 2
Lf
d'
2
fta
2
Ea
ta
MPa GPa mm
tf
ff,
Ef
Puit Pont
C3
2100
750
C4
2100
750
200
150
44.0 25.0 3.0
575
210
120
402
30
101
575
75
56.5
25
7.0
C5
2100
750
200
150
44.0 25.0 3.0
575
210
120
402
30
101
575
75
56.5
25
7.0
2.0 1930 150
1.2 1532 127
103.1 57.4
DB
C6
2100
750
200
150
44.0 25.0 3.0
575
210
120
402
30
101
575
75
56.5
25
7.0
2.0 1930
150
1.2 1532 127
101.4 57.4
DB
C7
2100
750
200
150
44.0 25.0 3.0
575
210
120
402
30
101
575
75
56.5
25
7.0
2.0 1930 150
1.8 1074
36
87.1
57.4
DB
C8
2100
750
200
150
44.0 25.0
575
210
120
402
30
101
575
75
56.5
25
7.0
2.0 1930 150
1.8 1074
36
86.7
57.4
DB
lB
2742
914
200
200
54.8
414
200
152
142
48
142
414
102
142
2740 203 0.45 2206 138
80.1
26.7
D
IC
2742
914
200
200
54.8
414
200
152
142
48
142
414
102
142
2740 203 0.45 2206 138
71.2
26.7
D
2B
2742
914
200
200
54.8
414
200
152
259
48
142
414
102
142
2740 203 0.45 2206 138
97.9
46.7
D
2C
2742
914
200
200
54.8
414
200
152
259
48
142
414
102
142
2740 203 0.45 2206 138
71.2
46.7
D
2D
2742
914
200
200
54.8
414
200
152
259
48
142
414
102
142
2740 203 0.45 2206 138
80.1
46.7
D
3B
2742
914
200
200
54.8
414
200
152
400
48
142
414
102
142
2740 203 0.45 2206 138
109.0 62.3
D
3C
2742
914
200
200
54.8
414
200
152
400
48
142
414
102
142
2740 203 0.45 2206 138
108.1
62.3
D
3D
2742
914
200
200
54.8
414
200
152
400
48
142
414
102
142
2740 203 0.45 2206 138
108.6 62.3
D
4B
2742
914
200
200
54.8
414
200
152
568
48
142
414
102
142
2740 203 0.45 2206 138
107.6
71.2
CC
4C
2742
914
200
200
54.8
414
200
152
568
48
142
414
102
142
2740 203 0.45 2206 138
104.6 71.2
CC
4D
2742
914
200
200
54.8
414
200
152
568
48
142
414
102
142
2740 203 0.45 2206 138
111.3 71.2
CC
5B
2742
914
200
200
54.8
414
200
152
774
48
142
414
102
142
2740 203 0.45 2206 138
146.9
115.7
CC
5C
2742
914
200
200
54.8
414
200
152
774
48
142
414
102
142
2740 203 0.45 2206 138
146.9 115.7
CC
5D
2742
914
200
200
54.8
414
200
152
774
48
142
414
102
142
2740 203 0.45 2206 138
145.5 115.7
CC
6B
2742
914
200
200
54.8
414
200
152
1020
48
142
414
102
142
2740 203 0.45 2206
138 1 169.1 133.5
CC
3.0
184
Ref.'
Beam
6C
SA94
TT92
L
Lp
b
h
f,'
E,
ft
fy
Es
mm
mm
mm
mm
MPa GPa MPa MPa GPa
2742
914
200
200
54.8
-
-
414
200
d
As
d'
2
As'
mm
152
1020 48
s
AsV
fta
E,
ta
Lf
bf
tf
ffu
Ef
Pult Pcont
kN
mm2 MPa GPa mm mm mm mm MPa GPa
142
414
102
142
-
-
-
2740 203 0.45 2206 138
153.1 133.5
CC
102
142
-
-
-
2740 203 0.45 2206 138
153.1 133.5
CC
6D
2742
914
200
200
54.8
-
-
414
200
152
1020 48
142
414
P1
1180
393
150
150
37.7
-
-
450
200
114
157
36
56.5
450
60
56.5
-
-
1.0 1030 100
P2
1180
393
150
150
37.7
-
-
450
200
114
157
36
56.5
450
60
56.5
-
-
1.0 1030 100 2.0
2
1220
458
76
127
44.7 31.6
-
517
200
ll1 33.2
0
0
517
40
33.2
-
-
-
1070 42.6 0.2 1450 186
3
1220
458
76
127 44.7 31.6
-
517
200
111
33.2
0
0
517
40
33.2
-
-
-
4
1220
458
76
127 44.7 31.6
-
517
200
111
33.2
0
0
517
40
33.2
-
-
5
1220
458
76
127 44.7 31.6
-
517
200
111
33.2
0
0
517
40
33.2
-
6
1220
458
76
127
44.7 31.6
-
517
200
111
33.2
0
0
517
40
33.2
7
1220
458
76
127 44.7 31.6
-
517
200
111
33.2
0
0
517
40
8
1220
458
76
127 44.7 31.6
-
517
200
111
33.2
0
0
517
40
kN
FM2
MPa mm
mm mm
mm
fyV
2
170 15.5 67.0
53.0
FR
15.5 68.0
53.0
CCS
13.2
8.6
FR
1070 60.5 0.2 1450 186
17.3
8.6
FR
-
1070 63.2 0.65 1450 186
29.6
8.6
DB
-
-
1070 63.2 0.65 1450 186
30.5
8.6
DB
-
-
-
1070 63.3
0.9 1450 186
27.9
8.6
DB
33.2
-
-
-
1070 63.3 0.9 1450 186
25.6
8.6
DB
33.2
-
-
-
1070 63.9 1.9 1450 186
37.3
8.6
DB
1.0
170
Ahmed et al (2001); Al-Sulaimani (1994); Arduini (1997b), Arduini et al(1997); Fanning and Kelly (2001); Garden et al (1998a); Garden et al
(1998b); Hearing (2000), Maalej (2001); Nguyen et al(2001), Rahimi and Hutchinson (2001); Ross et al (1999); Sharif et al (1994);
Triantafillou and Antonopoulos (2002).
2. Failure Modes: CC = Concrete Crushing; FR = FRP Rupture; S = Shear Failure; CCS = Concrete Cover Separation, D = Delamination along FRP Concrete
Interface; DB = Concrete Cover Separation / Delamination / Mixed Modes;
1. References:
185
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