Shear-strengthening of reinforced & prestressed concrete beams using FRP: Part I — Review of previous research
International Journal of Concrete Structures and Materials
Shear-Strengthening of Reinforced & Prestressed Concrete Beams Using FRP: Part I - Review of Previous Research
Thomas H.-K. Kang
Fiber-Reinforced Polymers (FRP) are used to enhance the behavior of structural components in either shear or flexure. The research conducted in this paper was mainly focused on the shear-strengthening of reinforced and prestressed concrete beams using FRP. The main objective of the research was to identify the parameters affecting the shear capacity provided by FRP and evaluate the accuracy of analytical models. A review of prior experimental data showed that the available analytical models used to estimate the added shear capacity of FRP struggle to provide a unified design equation that can predict accurately the shear contribution of externally applied FRP. In this study, the ACI 440.2R-081 model and the model developed by Triantafillou and Antonopoulos2 were compared with the prior experimental data. Both analytical models failed to provide a satisfactory prediction of the FRP shear capacity. This study provides insights into potential reasons for the unsatisfactory prediction.
FRP; prestressed concrete; shear; strengthening; rehabilitation
Concrete structures deteriorate over time, and therefore
implementing a design approach aimed at rehabilitating critical
structural members such as beams, columns and bridge girders is
necessary. One of the problems encountered in these critical
members is their deficiency in sustaining the applied shear load over
time. Fiber-Reinforced Polymers (FRP) are composite systems of
fibers embedded in a polymeric matrix.3 Rehabilitation of
Reinforced Concrete (RC) members using FRP was introduced more
than two decades ago.4 Multiple studies, such as the ones
conducted by Khalifa and Nanni,3 Bimal and Hiroshi,5 and Pellegrino
and Modena,6,7 have shown that applying FRP to RC beams
increases the overall shear capacity of a structural member. Due to
the complex nature of shear design even in simple reinforced
concrete beams, determining the exact contribution of the Fiber
Reinforced Polymers in shear is still under investigation and the results
thus far are not really converging toward a generalized prediction
model. In order to better understand the behavior of FRP applied
externally to an RC or prestressed concrete member, a literature
review was conducted to assess the current state of the art for
shear-strengthening of members using fiber-reinforced polymers
(FRP), particularly carbon fiber-reinforced polymers (CFRP)
which is the most common material used for shear-strengthening.
The literature review was followed by an evaluation of the
existing experimental data tested by other researchers and analytical
models currently available for estimating the shear capacity
provided by the FRP.
2. Review of research on shear-strengthening using FRP
In this section, a review is presented regarding various
experimental research programs dealing with the shear contribution of
FRP, the most common material used for shear-strengthening of
concrete beams. This section also assesses the current state of the
art concerning FRP used for shear-strengthening concrete beams.
2.1 Influence of transverse reinforcement and
shear span-to-depth ratio on CFRP efficiency
Khalifa and Nanni3 tested twelve full-scale beams, of which
eight had no transverse steel reinforcement in the shear span (SO
series) and four specimens with transverse reinforcement in the
shear span (SW series). All beams were designed to fail in shear.
Two shear span-to-depth ratios (a’/d = 3 and 4) were used. The
specimens were strengthened using continuous U-wraps, wraps
bonded on the sides, and strips of U-wrapped CFRP (see Figure
1). All of these strengthening configurations were used with
various fiber orientations.
The authors studied the influence of shear span-to-depth ratio
and internal steel reinforcement on the shear capacity of externally
bonded CFRP sheets. Although specimens with transverse
reinforcement showed a lower increase in shear capacity than similar
specimens without transverse reinforcement in the shear span, the
increase in shear capacity was significantly dependent on the shear
span-to-depth ratio (a’/d). Khalifa and Nanni3 noted an 80%
Fig. 1 Various FRP configurations (Adapted from Sas et al.,
increase for an (a’/d) of 4 compared to a 40% increase for an (a’/
d) of 3, given the same amount of transverse reinforcement in the
shear span. The same observation was made for specimens
without transverse reinforcement in the shear span [an 88% increase
for an (a’/d) of 3 compared to a 138% increase for an (a’/d) of 4].
Khalifa and Nanni3 also noted that the maximum increase in
shear capacity was recorded for the beam that had no transverse
reinforcement and had one continuous U-wrapped CFRP ply with
fibers oriented to 90o with respect to the beam axis. The conducted
experimental program consistently shows that the externally
bonded CFRP has greater effects on specimens without transverse
reinforcement than specimens with transverse reinforcement. This
finding was later confirmed by a similar study conducted by
Pellegrino and Modena.6 They tested a total of eleven beams with and
without transverse reinforcement. All tested beams had
sidebonded CFRP sheets. Pellegrino and Modena6 concluded from
the results they obtained that the effectiveness of CFRP
reinforcement reduces when both steel and CFRP reinforcement are
present. The increase in axial rigidity of the CFRP and the ratio
between the stiffness of the transverse steel reinforcement and the
stiffness of the CFRP sheet lowered the effectiveness of the CFRP.
According to this review, it can be predicted that CFRP sheets
would be more effective in beams without (or with less) transverse
reinforcement than in similar beams with transverse
2.2 Shear failure mechanism of RC beams
strengthened with CFRP
Pellegrino and Modena6 conducted an experimental study to
observe and evaluate the failure mechanism of beams
strengthened with continuous side-bonded CFRP sheets. The parameter
considered in the study was the stiffness ratio between transverse
steel shear reinforcement and CFRP shear reinforcement (ρs,f). A
typical shear-tensile failure pattern was observed for the control
beam that had neither transverse nor CFRP shear reinforcement.
Pellegrino and Modena6 observed that all tested specimens
without transverse reinforcement presented a principal crack pattern in
a subhorizontal direction near the support and with a direction of
approximately 45o near the point of application of the load. The
number of CFRP plies applied did not alter the cracking patterns
of the beams. However, one layer of CFRP was enough to
radically modify the failure mode of the beam, as was also the case for
the beams strengthened with two or three layers. During the
experimental program, delamination was the ultimate failure mode
observed for RC beams without transverse reinforcement and
strengthened with one, two or three layers of side-bonded CFRP.
In the same experimental study, Pellegrino and Modena6 also
tested specimens with transverse steel reinforcement. Specimens
with ρs,f of 1.37 and strengthened with a single layer of CFRP
exhibited failure due to shear cracking with an inclination of about
45º. The specimens showed cracking patterns similar to those of
the beam without CFRP except for the increased ductile behavior
near failure. Specimens that had transverse steel reinforcement
with ρs,f of 0.46 or 0.68 showed cracks in the bonding zone of the
sheet followed by a peeling off of the concrete cover.
In similar experiments conducted by Khalifa and Nanni3 on
beams with U-wraps, strips of CFRP or side-bonded CFRP,
debonding was the failure mode at ultimate for all specimens that had
strips of U-wrapped CFRP plies, whereas specimens strengthened
with continuous U-wrapped CFRP failed by concrete splitting.
Note that specimens with U-wraps or side bonds did not exhibit
fracture or debonding from the concrete surface at ultimate.3
However, specimens with double layers of sheets tested by
Bimal and Hiroshi5 showed rupture along the direction parallel to
the CFRP fibers and the sheets did not debond from the concrete.
The study also shows that debonding was not generally observed
for beams strengthened with both vertically and horizontally
aligned fibers. Only one beam strengthened with vertical plies
showed debonding after concrete crushing. In specimens with a
low sheet depth, final failure occurred in concrete due to one
critical crack, whereas the beams with a higher sheet depth failed by
concrete splitting and crushing.
Sim et al.8 conducted an experiment to observe the shear failure
mechanism of RC beams strengthened with Glass Fiber
Reinforced Polymer (GFRP), Carbon Fiber Sheet (CFS) and CFRP.
They observed that the strengthening material did not affect the
shear cracking pattern of the RC beam. All beams failed following
the typical diagonal shear cracking patterns (see Figure 2), which
were observed in the specimens strengthened with vertical strips.
The strengthening materials were torn at an angle perpendicular to
the fiber orientation. They observed that specimens strengthened
with a 45o CFRP strip did not have the typical diagonal shear
cracking pattern observed in specimens strengthened with 90o or
0o fiber orientation, but rather it was found that the specimens
strengthened with CFRP strips oriented at 45o developed shear
cracks that progressed vertically to the bottom.
2.3 Behavior of RC beams shear-strengthened
with various FRP types, sheet configurations
Retrofit of concrete members with CFRP sheets is an efficient
and cost-effective method. However, since the technique has been
introduced, engineers have designed various sheet configurations
for FRP, all of which have altered the behavior of the RC beam
depending on how the FRP was applied. Bimal and Hiroshi5
tested eight beams that had different carbon fiber reinforced
polymer (CFRP) sheet configurations and depths. All tested beams
were designed to fail in shear. The beams used in the experimental
program did not have any internal shear reinforcement in the shear
span. Bimal and Hiroshi5 concluded that the rupture strength of a
carbon fiber sheet with vertical fibers is greater than the rupture
strength of a carbon fiber sheet with horizontal fibers. The
experimental program also shows that the shear capacity of a beam tends
not to increase proportionally with additional sheet layers, since
the ultimate failure is governed by concrete cracking or splitting
and by a loss of aggregate interlock. Following the experimental
program, Bimal and Hiroshi5 found that increasing the sheet depth
by 50% resulted in a 108% increase in shear capacity for
specimens that had two CFRP sheets bonded on the sides. A 76%
increase was also noted when the U-wrapped sheet depth was
increased by 2 in. (a 50% increase from the original depth).
Specimens strengthened with additional layers of sheet showed only a
3% increase in ultimate shear strength compared to similar
specimens without additional layers of CFRP. The study showed that
the extra layer of CFRP did not increase resistance but only
allowed additional anchorage to the first layer.
Along the same lines, Khalifa and Nanni3 reported that the
increase in shear capacity was not proportional to the increase in
CFRP amount. During the experimental study conducted by
Khalifa and Nanni,3 specimens strengthened with 3 in. wide strips
spaced at 5 in. exhibited the same failure mechanism and did not
yield a significant increase in shear capacity compared to
specimens strengthened with 2 in. wide strips spaced at 5 in. Note that
even a 50% increase in the CFRP strip width did not generate a
noticeable increase in the shear capacity of the beams.
Sim et al.8 observed the behavior of RC beams
shear-strengthened with GFRP, CFS and CFRP and came to the conclusion that
interestingly the different strengthening material did not exhibit a
relationship to the strengthening effect. Sim et al.8 also noticed that
when beams were strengthened with a 45o fiber orientation, the
strengthening effect was increased by more than 10% in each
specimen compared to specimens with 90o fiber orientation.
2.4 Behavior of prestressed concrete beams
shear-strengthened with CFRP
Prestressed concrete (PC) is a widely used technique in
construction, especially for bridge girders. For such structural
members, repair is often needed when the bridge is sustaining cyclicly
overloaded traffic. Researchers have started to shift their focus
from repairing RC members to repairing PC members using
external CFRP; however, there is a lack of research on
shear-strengthening of the PC members with CFRP.
Reed and Peterman9 conducted both flexural and shear tests on
three full scale bridge girders that were replaced by the Kansas
Department of Transportation. The three damaged girders were
saw-cut in half longitudinally so that six single tee specimens were
tested. Since an immediate bond-slip can be caused by an
extended web shear crack into the transfer length,10 Reed and
Peterman9 used two distinct setups for the shear test. They tested
two girders with no overhang (NOH) and three girders with
overhang (OH). This test setup provided an understanding of the
influence of CFRP on the propagation of web shear cracks into the
transfer length of the prestressing steel.9 The shear capacity results
for the tested specimens showed that the NOH specimens failed
by a bond-slip that was induced by shear crack propagating into
the transfer zone of the prestressing reinforcement. On the other
hand, the OH specimens showed a higher shear capacity than the
NOH specimens. The increase was likely due to the longitudinal
CFRP wrap holding the web shear cracks closed and increasing
the shear contribution due to aggregate interlock.
Another study conducted by Murphy et al.11 showed that the
failure mode of PC girders strengthened in shear with externally
bonded FRP was affected by the stiffness of top and bottom
flanges and debonding of the FRP.
3. Assessment of previous experimental data and analytical models for CFRP shear contribution
In this section, an interpretation of the available test data and a
discussion of the current analytical approaches is presented. An
interpretation of the available test data helps identify the
parameters that have a certain impact on the shear contribution of CFRP.
3.1 Experimental data on key parameters
influencing CFRP shear-strengthening
Since the introduction of CFRP shear-strengthening techniques
two or three decades ago, researchers have been compiling
experimental data in order to better predict the shear contribution of
CFRP. Traintafillou and Antonopoulos,16 Bousselham and
Chaallal12 and Sas et al.13 have compiled a comprehensive list of
experimental data from over 30 different studies conducted on RC
beams, and the list was reorganized by Ibrahim Ary.14 The list has
more than 150 beams strengthened with CFRP, Aramid FRP and
GFRP. This section particularly investigates the parameters
relevant only to beams strengthened with CFRP, and reexamines the
compiled data in a different context. Note that this database
comprehends a significant update from the one Bousselham and
Chaallal12 assembled. The investigated parameters include the
compressive strength of concrete, the internal transverse steel
shear reinforcement, the longitudinal steel reinforcement, the shear
span-to-depth ratio and the relationship between the applied CFRP
configuration and the mode of failure. The data used for
interpretation include T-shaped beams and rectangular beams. The
increase in shear due to CFRP contribution is defined as follows:
Fig. 3 Interaction between the compressive strength of
concrete and increase in shear due to CFRP.
where Vf is the difference in shear capacity between the control
specimen and the strengthened specimen and Vt is the total shear
capacity of the beam. That increase was used as a basis for
measuring the influence of the aforementioned parameters.
Figure 3 shows the interaction between the compressive strength
of concrete and the increase in shear due to CFRP. To quantify the
effect of the compressive strength against the CFRP, the ratio of
(Ef ρf / f’c2/3) was used, where Ef is the modulus of elasticity of the
CFRP, ρf is the CFRP ratio and f’c is the compressive strength of
the concrete. The general trend resulting from this graph is that the
increase in shear due to CFRP appears to become more important
as the ratio of (Ef ρf / f’c2/3) increases. This means that specimens
constructed with a higher compressive strength exhibit a lower
increase in shear capacity due to CFRP application. This trend is
consistent up to a value of about (Ef ρf / f’c2/3 = 8).
The interaction between transverse shear reinforcement and
CFRP was quantified using the ratio of (Esρw / Ef ρf), where Es is
the elastic modulus of steel reinforcement, ρw is the steel shear
reinforcement ratio, Ef is the elastic modulus of the CFRP and ρf is
the CFRP shear reinforcement ratio (see Figure 4). The general
trend here is that the contribution in shear capacity of the CFRP
decreases as the ratio of (Esρw / Ef ρf) increases. This means that
the more internal steel reinforcement there is in a specimen, the
less effective the increase in shear due to CFRP is. The
interpretation of this graph was also confirmed by Khalifa and Nanni,3 who
also found that the increase in shear was far more significant in
specimens without transverse reinforcement than in specimens
with transverse reinforcement.
The shear span-to-depth ratio (a’/d) appears to be an influential
parameter, where a’ is the shear span and d is the effective depth.
Figure 5 shows that as the (a’/d) ratio increases, the effective shear
contribution of the CFRP also increases. Also, the relation
between the type of failure of the specimens and the (a’/d) ratio is
notable. It is found from Figure 5 that most of the tested
specimens with an (a’/d) less than or equal to 2.5 failed by CFRP
fracture while specimens with an (a’/d) greater than or equal to 2.5
failed by FRP debonding. This information indicates that beams
with a relatively short shear span tend to experience fracture of the
CFRP during loading, whereas for beams with relatively longer
shear span, the CFRP sheet is likely to debond from the concrete
during loading. Additionally, Khalifa and Nanni3 also found that
in some cases the increase in shear doubled for specimens having
an (a’/d) of 4, compared with specimens with an (a’/d) of 3,
regardless of internal shear reinforcement. This raises questions
about the effectiveness of CFRP in deep beams since they have a
lower (a’/d) (for a constant shear span distance of a’). Triantafillou15
linked the scale effect to the importance of the bond surface area.
The deeper the beam is, the more important the CFRP
contribution is to the shear resistance; therefore, the amount of CFRP may
need to be substantially increased for the deep beams. More
research would be needed for shear-strengthening of deep beams
The longitudinal reinforcement, even though used mainly for
flexural reinforcement, has a certain influence on the shear
performance of CFRP. Figure 6 shows that the largest increase in shear
due to CFRP was recorded in specimens with a small amount of
longitudinal reinforcement. In specimens with longitudinal
reinforcement, the increase in shear due to CFRP appears to be
decreasing as the ratio of (Esρs / Ef ρf) increases up to a value of
approximately 3. This means that the contribution of CFRP is
reduced in specimens with a relatively large amount of
Figure 7 shows the strengthening configuration and the failure
mode that resulted from 73 tested specimens. Note that 100% of
the fully wrapped specimens failed in fracture regardless of the
shear span-to-depth ratio. Since the specimens were fully
Fig. 6 Interaction between longitudinal mild steel amount and
increase in shear due to CFRP.
wrapped, debonding of the CFRP was hardly observed. In the
Uwrapped specimens (CFRP applied on three sides in a U shape),
debonding was observed for 61% of the tested beams while a little
over 1/3 of the total U-wrapped specimens showed fracture of the
CFRP at failure. The side-attached specimens failed massively
(95%) with the CFRP debonding from the concrete at failure, and
only 5% of side-attached beams failed with the CFRP being
fractured. Figure 7 also shows that debonding of the CFRP is a serious
issue especially in side-attached specimens. The debonding
appears not to be an issue for the fully wrapped specimens. A
clear conclusion could not be drawn for the U-wrapped specimens
probably because of the varied shear span-to-depth ratio which
plays an important role in the failure mode of the tested
3.2 Assessment of existing analytical models
estimating FRP shear contribution
This subsection summarizes two analytical models: 1) the
model in the ACI 440.2R-081 recommendations and 2) the model
developed by Triantafillou and Antonopoulos.2 Both models have
been developed to evaluate the shear contribution of externally
bonded Fiber Reinforced Polymers (FRP). Assessment of the
existing prediction models was based on a database of
experimental results assembled by Triantafillou and Antonopoulos,2
Bousselham and Chaallal12 and Sas et al.,13 which was reorganized by
Ibrahim Ary.14 Note that for general model assessment, data for all
different kinds of FRP materials were included, not exclusively
3.2.1 Triantafillou and Antonopoulos model prediction
Triantafillou and Antonopoulos2 defined the total shear
contribution of the FRP as:
Vf = ------- ρf Ef ε febwd(1 + cotβ) sinβ
where γ frp is the partial safety factor for FRP (1.15 for carbon), bw
is the web width of the member, ρf is the FRP area fraction, εfe is
the effective strain in the FRP, Ef is the stiffness of FRP, β is the
angle of fiber direction to the longitudinal axis of the member and
Vf is the added shear capacity of the FRP.
This analytical model introduced the effective strain (εfe) of the
FRP into the prediction of the added shear capacity of FRP.
Additionally, it also considers the type of FRP, the strengthening
configuration and the effect of the concrete compressive strength on
the effective FRP strain. The effective FRP strain for beams fully
wrapped with FRP is defined as:
ε fe = 0.17⎜⎛⎝ f--E--′c-f-2-ρ--⁄-f-⎟⎞⎠3- 0.3ε fu (
and the effective FRP strain for beams side-attached or
Uwrapped with FRP is defined as:
ε fe = min 0.65⎝⎜⎛ f--E--′c-f-2-ρ--⁄-f-⎠⎟⎞3- 0.65 × 10–3, 0.17⎜⎝⎛ f--E--′c-f-2-ρ--⁄-f-⎟⎠⎞3- 0.3ε fu (
Figure 8 shows a comparison of the values derived from the
model developed by Triantafillou and Antonopoulos2 and the
experimental values obtained, also comparing the different FRP
configurations (i.e., side-attached, U-wrapped and fully wrapped).
The first observation is that this model underestimates the shear
contribution of FRP in fully wrapped specimens. For specimens
strengthened with side-attached or U-wrapped FRP, Figure 8
shows that for most of the U-wrapped specimens, the model’s
prediction is close to the experimental values and in most cases
overestimates the contribution of FRP to the overall shear capacity of
the beam. For side-attached specimens, the model’s prediction is
not as good as for U-wrapped specimens. Since this model does
not consider the bond mechanism between the FRP and concrete,
an accurate prediction may not be possible.16
The accuracy of the model developed by Triantafillou and
Antonopoulos2 in predicting the capacity of strengthened
rectangular beams and T-beams is shown in Figure 9. The shear
contribution of FRP in T-beams is overestimated by this prediction
where Vf is the added shear capacity of the FRP, df is the effective
depth of FRP, sf is the spacing of FRP strips, ffe is the effective
tensile stress of FRP and Af is the area of FRP. In contrast to the
method developed by Triantafillou and Antonopoulos,2 this
analytical approach takes into account the bond mechanism that exists
between the concrete and the applied external FRP. The
contribution of the FRP to the overall shear is based on the fiber
orientation and an assumed crack pattern.3 This method also uses the
effective strain approach but with the exception of limiting the
maximum strain that can be achieved by the FRP to 0.4%. This
number is mainly based on several test results and experience
from industry professionals. The ACI 4401 analytical approach
introduced the bond-reduction coefficient (κv), which is a function
of the concrete strength, the strengthening configuration and the
stiffness of the FRP. The bond reduction coefficient (κv) is defined
in ACI 440 as:
where le is the active bond length defined as the length over which
the majority of the bond stress is maintained, k1 is a modification
factor that is a function of the concrete strength, k2 is a
modification factor that is a function of the strengthening configuration and
ε fu is the ultimate strain of the FRP. The effective strain derived
from this method is defined as:
κv = -------------e-- ≤ 0.75
εfe = κvεfu ≤ 0.004
model. The actual contribution of FRP is underestimated by this
model only in few cases for T-beams. On the other hand, the
model does a relatively decent job estimating the shear
contribution of FRP in rectangular beams even though it still overestimates
a good chunk of the rectangular beams. Overall, the Triantafillou
and Antonopoulos model prediction is a good starting point for
estimating the shear capacity of FRP in fully wrapped or
Uwrapped rectangular beams.
3.2.2 ACI 440.2R-08 model prediction
The ACI 440.2R -08 analytical approach defines the shear
contribution of FRP as:
Vf = -A---f---f-f-e--(---s--i--n----β----+-----c---o---s---β---)---d--f
Figure 10 shows a comparison between the ACI 4401 model
prediction and the experimental values. The FRP shear
contribution was compared for various strengthening configurations and
Figure 10 clearly shows that the ACI model underestimates the
FRP shear capacity of fully wrapped specimens. In the case of
Uwrapped or side-attached specimens, the model presents scattered
data around the experimental values, with most of the
sideattached specimens being overestimated. This method, in
comparison with Triantafillou and Antonopoulos’ analytical approach,
shows more scattered data around the line.
The ACI 4401 prediction appears to underestimate the FRP
shear contribution in rectangular beams according to Figure 10.
Most of the predictions derived from this model for rectangular
beams are on the safe side of the line separating experimental
values and theoretical values. This can be linked to the fact that the
bond reduction factor along with consideration of the active bond
length reduces the estimated value. In comparison with
Triantafillou and Antonopoulos model, the ACI 4401 model prediction has
a similar accuracy in estimating the FRP shear contribution in
rectangular beams (see Figures 8 and 10). For T-beams, the model
overestimates the contribution of FRP to the overall shear capacity
of the specimen. This model appears to be more suitable for
conservative design of fully wrapped rectangular specimens (see
Figures 9 and 11).
The use of Fiber Reinforced Polymers (FRP) for
shear-strengthening of reinforced and prestressed concrete members is a widely
used technique in the industry. In this study, using the compiled
extensive prior data, the parameters affecting the shear capacity of
externally bonded CFRP were identified and the accuracy of
analytical models was evaluated. Based on this research, the
following conclusions were drawn.
The increase in shear due to CFRP is higher for a lower
concrete compressive strength and/or for a lower amount of
The shear capacity of the CFRP decreases (i.e., CFRP is less
effective) as the internal steel reinforcement is increased.
Conversely, the capacity increases as the shear span-to-depth ratio is
increased. Furthermore, the larger the shear span-to-depth ratio is,
the more likely debonding will occur.
The comparison with previous experimental data indicates that
the accuracy of the model developed by Triantafillou and
Antonopoulos2 in predicting the capacity of strengthened rectangular
beams is relatively good, while the prediction for T-beams and
some rectangular beams is not safe.
A similar trend is the case for the ACI 4401 model, though
showing more scatter than the Triantafillou and Antonopoulos
Both models can be conservatively used for the fully wrapped
FRP, though this application is not common. However, both
models are not safe to be applied to the side-attached FRP.
The work presented in this paper was supported by U.S.
DOTRITA grant under No. DTRT06-G-0016/OTCREOS10.1-21. The
authors would like to thank the second author’s undergraduate
students, Deanna Quickle and Caroline Weston, for their active
participation in the FRP research program at the University of
Oklahoma. The views expressed are those of the authors, and do
not necessarily represent those of the sponsor.
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