29-03-2012, 10:37 AM
Flexural Behavior of Fiber-Reinforced-Concrete Beams Reinforced with FRP Rebars
FlexuralBehaviorofFiber-Reinforced-ConcreteBeamsReinforcedwithFRPRebars.pdf (Size: 1.04 MB / Downloads: 132)
Synopsis: The main objective of this study was to develop a nonferrous hybrid
reinforcement system for concrete bridge decks by using continuous fiber-reinforcedpolymer
(FRP) rebars and discrete randomly distributed polypropylene fibers. This
hybrid system has the potential to eliminate problems related to corrosion of steel
reinforcement while providing requisite strength, stiffness, and desired ductility, which
are shortcomings of the FRP reinforcement system in reinforced concrete structures.
The overall study plan includes (1) development of design procedures for an FRP/FRC
hybrid reinforced bridge deck system; (2) laboratory studies of static and fatigue bond
performances and ductility characteristics of the system; (3) accelerated durability tests
of the hybrid system; and (4) static and fatigue tests on full-scale hybrid reinforced
composite bridge decks. This paper presents the results relating to the flexural
behavior of the polypropylene-fiber-reinforced-concrete beams reinforced with FRP
rebars.
Test results indicated that with the addition of fibers, the flexural behavior was
improved with an increase of ductility index by approximately 40% as compared to the
plain concrete beams. Crack widths of FRP/FRC were found to be smaller than those of
FRP/plain concrete system and the values predicted by the current ACI 440 equations.
Furthermore, the compressive failure strains of concrete in FRP/FRC beams exceed the
strain of 0.0040 mm/mm.
Keywords: concrete bridge decks; crack width; ductility; fiberreinforced
concrete; fiber-reinforced polymers; flexure; polypropylene
fiber
896 Wang and Belarbi
Huanzi Wang, Ph.D., is an assistant engineer at Biggs Cardosa Associates, Inc,
California. He received his Ph.D. degree in Civil Engineering at the University of
Missouri – Rolla. He received his BS and MS in structural engineering from the
Southeast University, China. His research interest includes the application of FRP
reinforcement to the concrete structure design. He is a member of ACI.
Abdeldjelil Belarbi, FACI, is a Distinguished Professor at the University of Missouri -
Rolla. His research interests include constitutive modeling of reinforced and prestressed
concrete as well as use of advanced materials and smart sensors in civil engineering
infrastructure. He is a member of joint ACI-ASCE committees 445, and ACI Committees
440. He is Chair of subcommittee 445-5 (Torsion) and past Chair of E801.
INTRODUCTION
Ductility is a structural design requirement in most design codes. In steel RC
structures, ductility is defined as the ratio of post yield deformation to yield deformation
which it usually comes from steel. Due to the linear-strain-stress relationship of FRP
bars, the traditional definition of ductility cannot be applied to structures reinforced with
FRP reinforcement. Several methods, such as the energy based method and the
deformation based method, have been proposed to calculate the ductility index for FRP
reinforced structures.
1-2
Due to the linear elastic behavior of FRP bars, the flexural behavior of FRP
reinforced beams exhibits no ductility as defined in the steel reinforced structures. A
great deal of effort has been made to improve and define the ductility of beams reinforced
with FRP rebars. To date, there are two approaches; one approach is to use the hybrid
FRP rebars; that is, pseudo-ductile materials are fabricated by combining two or more
different FRP reinforcing materials to simulate the elastic-plastic behavior of the steel
rebars. Belarbi, Chandrashekhara and Watkins
3
and Harris, Somboonsong, and Ko
4
tested
beams reinforced with the hybrid FRP reinforcing bars and they found that the ductility
index of those beams could be close to that of the beams reinforced with steel. This
method has shown some success in the research studies but has resulted in limited
practical applications because of the complicated and costly manufacturing process of the
hybrid rebars. The other approach is to improve the property of concrete. ACI 440
5
recommends the FRP reinforced structures be over-reinforced and designed so that the
beams fail by concrete crushing rather than by rebar rupture. Thus, the ductility of the
system is strongly dependent on the concrete properties. Alsayed and Alhozaimy
6
found
that with the addition of 1% steel fibers, the ductility index can be increased by as much
as 100%. Li and Wang
7
reported that the GFRP rebars reinforced with engineered
cementitious composite material showed much better flexural behaviors. The ductility
was also found to be significantly improved.
This paper presents research result on the flexural behavior of concrete beams
reinforced with FRP rebars and concrete containing polypropylene fibers. The different
behaviors of plain concrete beams and FRC beams are also discussed.
FRPRCS-7 897
EXPERIMENTAL PROGRAM
A total of 12 beams making 6 testing groups were investigated. Each testing group
was composed of two similar beams, one subjected to monotonic loading and the other
subjected to repeated loading/unloading. The experimental variables included FRP rebar
size (#4 vs. #8), rebar type (GFRP vs. CFRP), and plain concrete vs. FRC.
Materials
FRP Rods--three types of commonly used FRP rods were adopted in this study:
namely the #8 (25mm) glass fiber reinforced polymer (GFRP), #4 (13 mm) GFRP, and
#4 (13mm) carbon fiber reinforced polymer (CFRP), as shown in Fig. 1. The surface of
the GFRP rods is tightly wrapped with a helical fiber strand to create indentations along
the rebar, and sand particles are added to the surface to enhance its bonding strength. For
the #4 GFRP, the pitch of the fiber strand is about 25.4 mm and helically rounded about
60 degrees to the longitudinal direction. For the #8 GFRP, the pitch of the fiber strand is
22 mm and helically rounded about 75 degrees to the longitudinal direction. The surface
of the CFRP is very smooth, as shown in Fig. 1. The resin used for these bars is epoxy
modified vinyl-ester for both GFRP rebar and CFRP rebar. Based on the information
provided by the manufacturer, the ultimate tensile strengths for #4 GFRP, #8 GFRP and
#4 CFRP are 690 MPa, 552 MPa, and 2,069 MPa, respectively. The elastic moduli are 41
GPa, 41 GPa, and 124 GPa, respectively.
Polypropylene Fibers--currently, many fiber types are commercially available
including steel, glass, synthetic, and natural fibers. To fulfill the total steel-free concept,
polypropylene fiber was used in this study. The fibers were fibrillated and commercially
available in 57 mm length.
Concrete--the concrete mix used in this study was based on an existing MoDOT mix
design. For practical application, the volume fraction (Vf ) of 0.5% of polypropylene
fibers was used to make the FRC and take the benefits of the fibers, while ensuring good
workability of concrete. It should be noted that the purpose of this study was to
qualitatively investigate the benefits gained from the fibers to the FRP reinforcing system
The different volume fraction’s effect was not a variable to be investigated in this study.
The compression strength of concrete on the day of testing was 30 MPa and 48 MPa for
FRC and plain concrete, respectively.
Test Specimens
The beams were 178 mm wide, 229 mm high, and 2032 mm long. To avoid shear
failure, traditional #3 steel U-shape stirrups with a spacing of 89 mm were used as shear
reinforcement at both ends of the beams. To minimize the confining effect of the shear
reinforcement on the flexural behaviors, no stirrups were used in the testing regions (pure
bending regions). A concrete clear cover of 38 mm was used for all beams. All beams
were designed to fail by concrete crushing, as recommended by the current ACI 440. This
was accomplished by using a reinforcement ratio greater than the balanced reinforcement
ratio ρb.
898 Wang and Belarbi
The notation for the specimen’s identification is as follows: the first character, “P” or
“F”, indicates plain concrete or FRC; the second character, “4” or “8”, indicate the rebar
size in English designation used as reinforcement; the last character, “C” or “G”,
indicates the rebar type, CFRP or GFRP. Details of the specimens are shown in Table 1.
Test Setup and Procedures
Beams were subjected to a four-point flexural testing, as shown in Fig. 2. Beams
were instrumented with three LVDTs in the testing region (pure bending region) to
monitor the mid-span deflection and determine the curvature. FRP rebars were
instrumented with strain gauges to measure rebar deformation. Two LVDTs were
mounted at the top surface of the beam to record the compressive concrete strain. In the
testing region, Demac gages were bonded to the beam surface, 38 mm above the bottom
(the same level as the longitudinal rebars) to measure the crack widths. A microscope
was also used to measure the crack width at the rebar location. Another two LVDTs were
mounted at the ends of the beam to record the relative slips between the longitudinal
rebar and the concrete (the longitudinal rebars were protruded about 10 mm from the
ends). Load was applied in increments by a hydraulic jack and measured with a load cell.
Three increments were taken up to the initiation of cracking and ten increments up to
failure. At the end of each load increment, the load was held constant, crack patterns were
photographed, and near mid-span crack widths were recorded.
Each testing parameter was investigated using two identical specimens, as shown in
Table 1. One beam was loaded monotonically to failure. The other beam was subjected to
repeated loading/unloading cycles at 40% and 80% of its capacity to evaluate the residual
deflection, residual crack width, as well as the energy absorption capacity.
TEST RESULTS AND DISCUSSIONS
This section will provide a summary of the overall flexural behaviors of the
FRP/FRC hybrid system in terms of crack distribution, load-deflection response, relative
slip between the rebar and concrete, cyclic loading effect on flexural behavior, and strain
distribution in concrete and reinforcement. Comparison between FRP/Plain concrete
system and FRP/FRC system is also discussed.
Crack Spacing
Table 2 shows the average crack spacing at 40% and 80% of the flexural capacity.
With the increase of load, crack spacing slightly decreased. Interestingly, by comparing
the crack spacing between the plain concrete beams and the FRC beams, the crack
spacing was virtually the same at 80% of ultimate load for both plain concrete and FRC
beams, while the crack spacing of the FRC beams was about 20% smaller than that of
plain concrete beams at service load (40% of ultimate load).
Studies suggest that the flexural cracking can be closely approximated by the
behavior of a concrete prism surrounding the main reinforcement and having the same
centroid. Cracks initiate when the tensile stress in the concrete exceeds the tensile
strength of concrete, ft’. When this occurs, the force in the prism is transferred to the
FRPRCS-7 899
rebar. Away from the crack, the concrete stress is gradually built up through the bond
stress between the rebar and the concrete. When the stresses in the concrete are large
enough and exceed the tensile strength of concrete ft’, a new crack forms. The above
mechanism is demonstrated in Fig. 3(a).
With the addition of fibers, the mechanism of crack formation is slightly changed, as
shown in Fig. 3(b). Some tensile loads can be transferred across the cracks by the
bridging of fibers. Thereby, the stress in the concrete comes from not only the bond stress
but the bridging of fibers as well. With the contribution from the fibers, less bond stress is
needed to reach the same cracking stress. Consequently, the spacing of crack is smaller in
the FRC beams than in the plain concrete beams (S2 < S1 as shown in Fig. 3).
At the high level of load, due to loss of bond between the fibers and concrete, fibers
are pulled out and the contribution from the bridging of fibers is diminished.
Crack Width
During the tests, crack widths were measured by the Demac gages. Fig. 4 through 6
show the relationships between the crack width and the applied moment. In the following
section, several currently available models to predict the crack width are discussed and
compared with test results.
Based on the well-known Gergely-Lutz
8
equation, the current ACI 440 recommends
a similar equation to calculate the crack width of the FRP reinforced member as follows:
3
2200
k f d A
E
w
b f c
f
= β (1)
where w is the crack width at tensile face of the beam,
A is the effective tension area per bar,
dc is the thickness of concrete cover measured from extreme tension fiber to the
center of the closest layer of longitudinal bars,
ff is the stress in the FRP reinforcement,
β is the coefficient to converse crack width corresponding to the level of
reinforcement to the tensile face of beam, and
kb is the coefficient that accounts for the degree of bond between the FRP bar and
the surrounding concrete. ACI 440 does not give a mathematical relationship
between kb and the bond strength. It suggests a value of 1.2 for deformed FRP
bars if kb is not experimentally known.
Toutanji and Saafi
8
reported that the crack width is a function of the reinforcement
ratio. They proposed the following equation to predict the crack width:
3
200
f d A
E
w
f c
f f
β
ρ
= (2)
where ρf is the reinforcing ratio.
Based on the equivalent beam concept, Salib and Abdel-Sayed
10
proposed the
following equation:
900 Wang and Belarbi
3
3 2 3
w 0.076 10 {( E / E )( u / u ) } f d A
f c
/
s f b,s b, f
= × × × β
−
(3)
By substituting Es=29000 ksi, Equation 3 becomes
2 3 3
2200
f d A
u
u
E
w
f c
( / )
b, f
b,s
f
× β
= × (4)
where ub,f and ub,f are the bond strengths of steel rebar and FRP rebar, respectively.
In Equation 4, the values of ub,f and ub,f need to be evaluated and decided upon. For
traditional steel rebar, according to ACI 318-02,
11
'
c
y b
d
f
f d
l
25
= (neglecting the adjusting
coefficients) and based on the definition of the development length,
2
,
( )/ 4
b d b s y s y b
π d l u = f A = f π d (5)
one gets:
'
b,s c
u = 6.25 f .
For FRP rebar used in this study, based on the previous bond study (Belarbi and
Wang
12
),
'
b, f c
u = 9.25 f . Based on this approximate values of ub ub,f and ub,f , Equation 4
become
3
1700
f d A
E
w
f c
f
= β (6)
All the above equations were developed based on the Gergely-Lutz model. However,
different researchers proposed different models to account for the bond strength effect
and/or reinforcement ratio effect on the crack width.
As shown in Figs. 4 through 6, the Salib et al. model gives reasonable predictions of
the crack width for both plain concrete beams and FRC beams. For the Toutanji et al.
model, the prediction values show poor correlation with the experimental results. When
for low reinforcing ratios, (for the CFRP beams, ρ=0.67%), the model overestimates the
crack width. Vice versa, for high reinforcing ratios (#4 GFRP beams, ρ=2.2%, and #8
GFRP beams, ρ=3.3%), the model underestimates the crack width. Therefore, it may be
concluded that it is the bond characteristics rather than the reinforcing ratio that affect the
crack width.
The predictions based on current ACI 440 equations were also compared with the
test results. The accuracy of the equation largely depends on the value of kb. Even when
selecting kb =1.0, one can see that the predictions are still conservative.
Fiber Effect on Crack Width-
With the addition of fibers, the crack widths were slightly decreased at the same load
level, especially at the service load, as shown in Fig. 4 through 6.
As shown in Table 3, the crack widths were smaller in the case of FRC beams as
compared to plain concrete beams at the service load. As discussed earlier, the crack
spacing was decreased at the service load due to the contribution from the fibers. Since
FRPRCS-7 901
the crack width is proportionally related to the crack spacing, the crack width is expected
to be smaller in the FRC beams at service loads.
Load-Deflection Response
Figs. 7 through 9 show the typical experimental moment-deflection curves for plain
concrete beams and FRC beams reinforced with different types of FRP rebars. With the
increasing of moment, cracks occurred in the testing region when the moment exceeded
the cracking moment Mcr. Consequently, the flexural stiffness of the beams was
significantly reduced and the curves were greatly softened. As expected, due to the
linear-elastic behavior of the FRP rebars, the FRP reinforced beams showed no yielding.
The curves went up almost linearly until the crushing of concrete.
Fiber Effect on Moment-Deflection Curves
In order to compare the flexural behaviors between plain concrete beams and FRC
beams, all the load-deflection curves of the plain concrete beams were normalized, based
on the following rules: 1) moment was divided by a coefficient CM, defined as
ACI FRC
ACI plain
M
M
M
C
−
−
= , where MACI-plain and MACI-FRC are theoretical ultimate capacities
computed based on ACI 440 for beams with concrete strengths equal to the plain concrete
beams and the FRC beams, respectively; 2) deflection was divided by a coefficient CD,
defined as
ACI FRC
ACI plain
D
C
−
−
Δ
Δ
= , where Δ
ACI-plain and Δ
ACI-FRC are theoretical deflection based
on ACI 440 for beam with concrete strengths equal to the plain concrete beams and FRC
beams at the service load (40% of the ultimate load), respectively.
As shown in Table 4 and Figs. 7 through 9, with the addition of fibers, the ultimate
moments and deflections were increased. The plain concrete beams failed in a more
brittle and explosive manner. Once it reached the capacity, the concrete was crushed and
the load dropped suddenly and violently. FRC beams failed in a more ductile way as the
load dropped more gently and smoothly.
Theoretical Correlation
Deflection at mid-span for a simply supported beam of total length L and subjected
to a four-point flexural test is given as
c e e
mid
GI
Ph a
( L a )
E I
Pa
10
3 4
24
2
2 2
Δ = − + (7)
The first term on the right is from the flexural component, and the second term is
from the shear component. In this study, testing beams had a span-depth ratio of 2.67.
Based on calculation, it was found that the shear component was about 3% of the flexural
component. It was, therefore, neglected for simplicity. Thus, Equation 7 becomes
( L a )
E I
Pa
c e
mid
2 2
3 4
24
Δ = − (8)
Current ACI 440 recommends the following expressions to calculate the effective
moment of inertia Ie:
e g
I = I when
a cr
M ≤ M ;