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Strengthening RC structures using FRP spike anchors in
combination with EBR systems
Enrique del Rey Castilloa, Dmytro Dizhurb, Michael Griffithc, Jason Inghamd
aLecturer, Dept. of Civil and Environmental Engineering, The University of Auckland, New
Zealand. (corresponding author) Email: edel146@aucklanduni.ac.nz
bLecturer, Dept. of Civil and Environmental Engineering, The University of Auckland, New
Zealand.
cProfessor, School of Civil, Environmental and Mining Engineering, University of Adelaide,
Australia
dProfessor Dept. of Civil and Environmental Engineering, The University of Auckland, New
Zealand.
Abstract
The use of Fiber-Reinforced Polymer (FRP) materials as Externally Bonded
Reinforcement (EBR) to strengthen and/or repair existing Reinforced Concrete
(RC) structures is widely documented, and various methods exist to increase the
bond strength and/or ensure load-path continuity between FRP composites and
the concrete substrate. The use of FRP anchors to increase the capacity of EBR
systems offers a number of critical advantages compared to other existing methods.
However, despite the significant amount of research previously undertaken on the
topic a concise summary of the experimental performance of FRP anchors has not
yet been reported. Consequently, a database consisting of five tables comprising
the results from studies focused on testing isolated FRP anchors and four additional
tables with results related to the use of FRP anchors in combination with FRP-
EBR systems to strengthen and/or repair RC structures is presented. A number of
tentative design models previously published for various failure modes are reported
and reanalyzed in a critical way, and behavioral trends were identified as an effort
to discern what models are ready to be used and what new further research is
needed in the development of design guidelines for FRP anchors.
Keywords: FRP spike anchors, Strengthening, repair, debonding, anchorage,
reinforced concrete
Preprint submitted to Composite Structures January 21, 2019
1. Introduction
Fiber-Reinforced Polymer (FRP) composites as Externally Bonded Reinforce-
ment (EBR) for the structural improvement of existing Reinforced Concrete (RC)
structures is a widely documented system, that was previously shown to be more
effective for strengthening and/or repairing RC structures compared to conven-
tional methods such as the use of metallic reinforcement or section enlargement
[1,2,3]. The main advantages of the FRP-EBR system are low mass and high
tensile capacity, plus greater durability to rain and freeze-thaw cycles [1,2] when
given the proper treatment [4,5,6] than structures strengthened with more con-
ventional materials such as concrete or steel. Among the many materials used to
fabricate FRP products only Glass Fiber-Reinforced Polymer (GFRP) and Carbon
Fiber-Reinforced Polymer (CFRP) are considered in this overview as they are most
commonly used.
FRP sheets (also referred to in the literature as plies or strips) are the core
material in the FRP-EBR system and are bonded with epoxy resins to form a matrix
that is adhered to the external surface of a structural member after appropriate
preparation to enhance the FRP-to-concrete bond strength [7,2,8]. The installation
process and the quality of workmanship have a decisive influence on the final
capacity of an intervention [9,10].
The primary deficiency of the FRP-EBR system is premature debonding of
the FRP sheets from the concrete substrate prior to development of the full tensile
strength of the FRP fibers [11,12,13]. Bizindavyi and Neale [14] undertook initial
research on this debonding mechanism, and Chen and Teng [15] subsequently
developed a model that was particularly relevant for successive studies. Chen
and Teng [15] defined the effective bond length as the length beyond which the
FRP-to-concrete bond strength is not increased and design equations based on
the model by Chen and Teng [15] were incorporated into relevant international
guidelines and standards [4,16,5,17,18,6]. The observed debonding failure
mechanism typically entails the fracture of a shallow concrete surface layer rather
than the fracture of the epoxy resin, which led to the concrete tensile strength
being incorporated into the Italian design standard CNR-DT 200 [6] to calculate
the effective bond length based on fracture energy mechanics.
The earliest attempts to increase the FRP-to-concrete bond beyond provision of
the effective bond length involved the use of additional FRP material to expand the
FRP bonding area (typically with the use of FRP U-jackets or FRP patches) [19,
20,21,22,23,24]. Mechanically fastened steel plates have also been intensively
studied as systems to increase the FRP-to-concrete bond strength [25,26,27,28,
2
29,30]. Embedment of FRP sheets into concrete to increase the FRP-to-concrete
bond strength and improve the overall ductility of the intervention has also been
investigated previously [31,32].
While the aforementioned methods have resulted in different degrees of im-
provement of FRP-to-concrete bond strength, FRP anchors [33,34,7,35,36,37,
38,39,40,8] have been highlighted as a suitable solution to improve the overall
behavior of the FRP-EBR system [41,3,42]. A commonly reported advantage of
FRP anchors is that they can be used for a wide range of RC structural elements
and applications [43,44,9,41]. Several review publications have appeared in the
last fifteen years, related to the use of FRP for construction [1] and in the civil
infrastructure [2], and to anchorage methods for FRP materials [41,3]. Kalfat
[3] only included one study on FRP anchors, while Grelle and Sneed [41] simply
summarized and categorized the anchorage methods, without discussing or com-
paring the performance of the anchorage methods. The scope of the present review
is to provide engineers and researchers with a comprehensive compilation on the
available research investigating both isolated FRP anchors and FRP anchors im-
plemented in structural members. Three sections are clearly distinct, a first section
on FRP anchors, followed by a review of the studies on isolated FRP anchors and
FRP anchors failure modes and a third section regarding the use of FRP anchors
in Case studies. The current document is not intended as a design guideline, but
rather as a compilation and critique of the existing literature, as well as a highlight
of what further research is necessary.
2. FRP anchors
FRP anchors are typically referred to as fiber anchors, fiber bolts, or FRP
dowels but for simplicity they are hereafter referred to as FRP anchors. These
anchors consist of a bundle of fibers, or a fiber sheet, with one end of the bundle
splayed out in a circular or fan shape and bonded to an FRP sheet and the other
end embedded into a pre-drilled hole using epoxy resin. FRP anchors consist of
three components, as shown in Figure 1. The dowel is inserted into the structural
member (either straight or bent at insertion angle β), the fan is the portion where
all the fibers from the FRP bundle are epoxy set to the FRP sheets, and the key
portion is the section where the fan transitions into the dowel. FRP anchors are
typically divided into two types depending on the insertion angle β, as shown in
Figure 1: straight anchors (a) and bent anchors (b and c).
FRP anchors can be impregnated, which involves allowing epoxy resin to soak
into the dowels followed by a curing period before installation [34,36], or can be
3
(a) Straight anchor – Front view
(b) Straight anchors Side view
(c) Bent anchor – Front view
(d) Bent anchor – Side view
Fig. 1. Attributes of FRP anchors
4
dry (also known as wet lay-up method), which involves allowing epoxy resin to soak
into the fibers immediately before the anchor is inserted into a pre-drilled hole with
assistance from a resin applicator gun or metal wire. Dry anchors are typically less
time-consuming to install than impregnated anchors as they require no curing time
prior to installation. Moreover, in dry anchors the distribution of epoxy resin along
the dowel is more consistent and uniform than in impregnated anchors due to better
soaking of the FRP fibers. The improvement in resin distribution when using dry
anchors is especially important in the key portion of the anchor because complete
and adequate penetration of resin can be compromised in impregnated anchors.
Early FRP anchors were hand made using rolled FRP sheets and are typically
referred to as hand-made anchors whereas later FRP anchors were manufactured
as bundles of FRP fibers.
3. FRP anchors failure modes
The main impediment to widespread implementation of FRP anchors is the
lack of design guidelines [3], although several failure modes have been identified as
contributions towards the development of these design guidelines, see Figure 2[45].
Studies regarding isolated FRP anchors have been classified below depending on
the failure modes that were under investigation. The failure modes related to
concrete-cone and concrete failure are different for straight and bent anchors, with
the results of existing research being reported in Table 1for concrete cone failure
mode of straight FRP anchors, and in Table 2for pull-out failure mode of bent
FRP anchors. The design of FRP anchors to prevent concrete failure has been
typically correlated to steel anchorage design [46,47]. Fan-to-sheet debonding
is also encountered in the existing literature, and the results are summarized in
Table 3, although only one study reported the properties of the adhesive. The
results on anchors exhibiting fiber rupture failure have been reported in Table 6for
straight anchors and in Table 7for bent anchors. For design purposes the anchor
should not limit the strength of the EBR-FRP system, and therefore all failure
modes in the FRP anchor should be avoided to favor rupture of the FRP sheet.
3.1. Concrete-cone failure modes
Ozdemir [48,49] and Ozbakkaloglu [50,10] studied the influence of the me-
chanical properties of the concrete substrate into which the dowel is introduced on
the behavior of straight hand-made impregnated anchors, using concrete prepa-
rations with compressive strengths ranging between 10 MPa and 60 MPa. A 45º
crack angle for specimens exhibiting concrete cone failure mode was observed
5
in both studies, in accordance with the findings of others (see e.g., [46,51]).
Ozdemir [48,49] observed that the hole diameter did not significantly influence
the final behavior of straight anchors and Ozbakkaloglu [50,10] identified three
failure modes, namely anchor pull-out, a combination of pull-out and concrete
cone failure, and fiber rupture in the key portion.
The Japan Society of Civil Engineers [16] and the American Concrete Institute
[52,5,53,54] recommend to round the corners of the holes to minimize stress
concentrations at the anchor bend, but no comprehensive research could be found
regarding the effect of rounding the holes on the anchor strength. Orton [55,35]
recommended the hole radius to be at least four times larger than the anchor
diameter and undertook a comparison between sandblasting the concrete surface
and having no surface treatment, with no significant difference in performance
being observed between the two conditions. Other authors have also investigated
these two parameters [56], but a more comprehensive experimental project is
needed to show the real effect that these parameters have on anchor behavior.
Straight anchors. Ozdemir [48,49] observed that larger dowels result in
stronger anchors and reported an effective embedment depth beyond which the load
capacity did not increase, which was established as 100 mm. This approach is an
oversimplification because of the narrow range of parameters under consideration,
but the study was an effective starting point for further research. Ozbakkaloglu
and Saatcioglu [50,10] determined that the reduction of average bond strength
between anchor and concrete when the anchor diameter or embedment depth is
increased is related to Poisson’s ratio and the uniformity of stress distribution
along the embedment depth. Kim and Smith [57,9] undertook a comprehensive
study of the behavior of 27 FRP anchor dowels using hand-made anchors rolled
around a metal rod and considering hole diameter and embedment depth. The
authors observed that while shallow anchors triggered the concrete cone failure
mode regardless of hole diameter, as embedment depth increased the failure mode
changed to a combination of concrete cone and debonding between dowel and
concrete and, eventually, fiber rupture.
Kim and Smith compiled available data [9] regarding the behavior of anchors
exhibiting concrete related failure modes and developed a design model [51] based
on the anchorage of steel to concrete as first published by Eligehausen [46,47]
and subsequently assimilated by international design guidelines [58]. This is the
first model developed to predict anchor behavior and provides guidance for the
design of FRP anchors, see Equations 1to 3. Nevertheless, the model was not
without shortcomings, mainly because of the limited range of parameters used in
the calibration of the models and the lack of further corroboration of the model by
7
other investigators. Additionally, the concrete cone failure models did not consider
the presence of reinforcing bars or the type of coarse aggregate, which might affect
anchor strength when exhibiting this failure mode. The data used to develop the
models described in Equations 1to 3is reported in Table 1.
Ncc =9.68d1.5
eqf0
c(1)
Ncb =4.62πφdowel de⇔ ( f0
c<20M Pa)(2)
Ncb =9.07πφdowel de⇔ ( f0
c>20M Pa)(3)
Where Ncc and Ncb are the anchor concrete-cone, combined concrete-cone and
bond capacities (N) respectively, he f is the embedment depth (mm), f‘cis the
compressive strength of the concrete (MPa) and dois the hole diameter (mm). The
range of test parameters used to develop these models was 100 mm >he f >17.5
mm, 60.0 MPa >fc >10.4 MPa and 20.0 mm >do>11.8 mm.
Bent anchors. Eshwar [34] observed that the effect of embedment depth on
the capacity of bent anchors was less significant than for straight anchors and
recommended a minimum embedment depth of 50 mm and a minimum anchor
diameter of 10 mm, with this embedment depth also being supported by Orton
[55,35]. Smith and Kim [59] identified four failure modes: (1) simultaneous plate
debonding and anchor shear failure, (2) plate debonding followed by anchor shear
failure (3), plate debonding followed by anchor fan debonding mode, and (4) plate
debonding followed by anchor pull-out. While these failure modes were used for
all subsequent studies by Smith and colleagues with few modifications (see e.g.,
[60,61]), no design equations were developed for bent anchors.
The results for bent anchors exhibiting pull-out failure are presented in Ta-
ble 2. Similarly to the models previously developed for straight anchors, only the
properties considered to have an effect on the pull-out failure mode are reported,
namely the hole diameter (d0), the effective embedment depth (he f ), the concrete
compressive strength ( f0
c) and the insertion angle (β). Npo is the ultimate load
at which the anchor failed by dowel pull-out. Note that only the specimens that
exhibited the pull-out failure mode in the referenced studies have been used in
Table 2, with the anchors exhibiting other failures modes being reported in their
correspondent table.
It is important to note that all the anchors studied by Zhang et al [63] were
installed in a hole with a diameter of 14 mm but the anchors featured various cross
8
Table 1. Details of straight FRP anchors exhibiting concrete cone failure mode
Reference Specimen name he f (mm) d0(mm) f0
c(Mpa) Ncc (kN)
[9]PF-20-12-1 12 18.3 34 6.8
[9]PF-20-12-2 12 19.4 34 5.8
[9]PF-20-12-3 12 17.5 34 6.1
[9]PF-20-14-1 14 20.8 34 7.1
[9]PF-20-14-2 14 25.1 34 8.9
[9]PF-20-14-3 16 21.9 34 8.5
[9]PF-20-16-1 16 23.5 34 7.1
[9]PF-20-16-2 15 21.4 34 8.1
[9]PF-20-16-3 14 25.0 34 7.1
[9]PF-40-14-1 15 44.8 34 20.6
[9]PF-40-16-1 16 41.3 34 20.3
[9]PF-40-16-2 17 41.5 34 18.7
[10]HD12.7L25T1 24 12.7 53 8.2
[10]HD12.7L25T2 26 12.7 54 9.3
[10]HD12.7L25T3 27 12.7 56 10.2
[10]HD12.7L25T4 18 12.7 50 5.8
[10]HD15.9L25T1 26 15.9 57 10.5
[10]HD15.9L25T2 26 15.9 57 10.7
[10]HD15.9L25T3 28 15.9 60 12.1
[10]HD19.1L25T1 24 19.1 57 10.4
[10]HD19.1L25T2 22 19.1 60 9.5
[10]HD19.1L25T3 28 19.1 60 13.2
[10]ND15.9L25T1 24 15.9 27 8.4
[10]ND15.9L25T2 26 15.9 27 9.3
[10]ND15.9L25T3 24 15.9 27 9.0
9
Table 2. Details of bent FRP anchors exhibiting pull-out failure mode
Reference Specimen name he f
(mm)
d0
(mm)
f0
c
(Mpa)
β
(deg)
Npo
(kN)
[62]s1-200-2 40 14.0 28.8 90 10.0
[10]HD12.7L50 I45T1 50 12.7 54.0 45 9.1
[10]HD15.9L75 I45T1 75 15.9 54.0 45 17.0
[10]HD15.9L75 I45T2 78 15.9 54.0 45 20.9
[10]HD15.9L75 I15T1 74 15.9 53.0 15 36.5
[10]HD15.9L75 I15T2 77 15.9 54.0 15 43.0
[10]HD15.9L75 I15T3 79 15.9 54.0 15 41.3
[63]gd-200-2 40 14.0 50.3 90 3.4
[63]gd-200-3 40 14.0 50.3 90 6.1
[63]cd-134-2 40 14.0 50.3 90 9.2
[63]cd-134-3 40 14.0 50.3 90 7.7
[63]cd-200-1 40 14.0 50.3 90 9.0
[63]cd-200-2 40 14.0 50.3 90 10.3
[63]cd-200-3 40 14.0 50.3 90 4.0
[63]cd-259-1 40 14.0 50.3 90 12.1
[63]cd-259-2 40 14.0 50.3 90 12.4
[63]cd-259-3 40 14.0 50.3 90 8.6
[64]4 30 14.0 25.0 90 1.0
[65]AV/F/90/ 20/50-b 50 20.0 42.6 90 5.9
[65]AV/F/90/ 20/50-b2 50 20.0 42.6 90 7.5
[65]AV/E/90/ 20/50-1 50 20.0 42.6 90 12.3
[65]AV/E/90/ 20/50-4 50 20.0 42.6 90 16.2
[65]AV/F/90/ 20/50-1 50 20.0 42.6 90 17.0
[65]AV/F/90/ 20/50-3 50 20.0 42.6 90 10.8
[65]AV/F/90/ 20/50-4 50 20.0 42.6 90 6.6
[66]DR/W/90/ 20/50-1a 50 20.0 42.6 90 29.0
[66]DR/W/90/ 20/50-2a 50 20.0 42.6 90 38.0
[66]DR/W/90/ 20/50-3a 50 20.0 42.6 90 42.0
[66]DR/W/90/ 20/50-4a 50 20.0 42.6 90 26.0
[66]DR/P/90/ 20/50-5a 50 20.0 42.6 90 38.0
[66]DR/P/90/ 20/50-7a 50 20.0 42.6 90 38.0
[66]DR/P/90/ 20/50-8a 50 20.0 42.6 90 25.0
[66]GR/W/120/ 20/75-12a 75 20.0 42.6 120 44.0
[66]GR/W/90/ 16/100-16a ## 16.0 42.6 90 58.0
10
sectional areas, which indicated that the ratio between hole diameter and dowel
diameter does not have an influence on the behavior of the anchor. The embedment
depth controls the failure mode, with shallow depths triggering a concrete cone
failure and deeper depths triggering a combination of concrete cone and concrete
failure inside the hole. As can be observed from the work by Villanueva Laurado
et al [65,66], increasing the embedment depth significantly increases the pull-out
capacity of bent anchors. The embedment depth required to prevent concrete-cone
or dowel-related failure modes is different for straight and for bent anchors and
relationships comparable to Equations 1-3do not yet exist for bent anchors. No
clear correlation between hole diameter and anchor efficiency can be discerned
based on the existing research, as can be seen in Figure 6.
The trend in the relationship between embedment depth and anchor capacity
to resist concrete cone failure can be seen in Figure 6, and Equation4has been
proposed to calculate the ultimate pull-out load as a function of the embedment
depth, which is the only parameter to have a significant effect on anchor strength
based on the results from Table 3and Figure 6. However, it is hypothesized that an
effective embedment depth exists beyond which the anchor strength when exhibit-
ing concrete-cone or dowel-related failure modes does not increase, similarly to
the FRP-to-concrete bond behavior [15]. Additionally, it is important to note that
only two data points were obtained with a concrete compressive strength lower
than 42.6 MPa, which have been circled in red in Figure 6c. Finally, the r2value
for Equation4is only 0.5, which means that the relationship between embedment
depth and pull-out strength is weak. More data on the pull-out failure of bent
anchors is necessary to discern the exact relationship between embedment depth
and pull-out strength, to ascertain whether an effective embedment depth exists
and to verify the effect of the concrete compressive strength on pull-out strength.
Npo =0.7he f −18 (4)
Where Npo is the capacity of bent anchors to resist pull-out failure in kN and
he f is the embedment depth in mm. The range of test parameters used to develop
this model was 100 mm >he f >40 mm.
3.2. Fan-to-sheet failure mode
Kobayashi [43] hypothesized that due to the shape of the fan portion, part of
the tensile force applied to the anchor is transferred transversally to the sheet and
should be resisted by the substrate to ensure the correct transfer of forces between
anchor and sheet. An important conclusion is that the fan portions of adjacent
11
(a) Effect of embedment depth on anchor
pull-out load
(b) Effect of hole diameter on anchor pull-
out load
(c) Effect of concrete strength on anchor
pull-out load
(d) Effect of insertion angle β on anchor
pull-out load
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
050 100 150
Ultimate pull-out load Npo (kN)
Embedment depth hef (mm)
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
0.0 10.0 20.0 30.0
Ultimate pull-out load Npo (kN)
Hole diameter d0(mm)
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
0.0 20.0 40.0 60.0
Ultimate pull-out load Npo (kN)
Concrete strength f'c(mm)
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
050 100 150
Ultimate pull-out load Npo (kN)
Insertion angle (mm)
Fig. 3. Effect of dowel and substrate properties on anchor pull-out strength
12
anchors should overlap to provide a correct force transfer from the FRP sheets into
the concrete substrate, although a less efficient transverse FRP sheet can be used
instead. Niemitz [7,67] observed that anchors featuring larger splays were able to
transfer load from wider sections of sheets, increasing the force transmitted from
the sheet to the anchor and, conversely, smaller splays were able to transfer load
only from narrower sections of sheets. Splays should therefore cover the whole
width of the sheet and in accordance with the findings of other studies[35,68],
the use of a greater number of anchors that feature small splay diameters is more
efficient than the use of only a few anchors with larger splay diameter. Niemitz
[7,67] also observed that strength capacity is dependent on anchor spacing across
the width of the FRP sheet but not dependent on anchor spacing in the longitudinal
direction of the sheet, which increases the deformation capacity of the system.
Zhang [61] studied three fan configurations: (1) single-fan with fibers splayed
towards the origin of the force; (2) single inverted fan with fibers splayed away
from the origin of the force; and (3) a double fan or bow-tie. The most optimal
fan configuration was determined to be a single-fan shape oriented towards the
origin of the force, with this conclusion also supported by Hu [37]. Sun [69,70]
used hand-made dry CFRP anchors on concrete blocks but observed no significant
change in ultimate strip stress at strip fracture for anchors with a fanning angle
of 18.5ºor 32º. A fanning angle of less than 32 degrees is recommended, as no
significant effect of the CFRP strengthening system on the strength and behavior
was observed when anchors featuring such angles were used. However, the limited
number of tests performed compromise the reliability of the results. Villanueva
Llaurado et al investigated the influence of anchor fan position with respect to
the FRP sheets on the strengthening system, comparing three different positions
with an unanchored situation [71]. The three positions increased the maximum
load at which the strengthening intervention failed, with an increment of 24%
being observed when the anchor was embedded in grooves previously cut into the
concrete substrate and covered with the FRP sheet, 30% when the anchor was
bonded onto the outermost FRP sheet and 41% when the anchor was sandwiched
between two FRP sheets. The load-slip response of the three configurations was
comparable, with the three configuration showing an improvement of the slip
capacity when compared with the unanchored specimens. Unfortunately the resin
properties were not described, which hinders any comparison with other studies.
The load-slip response of the three configurations was comparable, with the three
configuration showing an improvement of the slip capacity when compared with
the unanchored specimens.
Four studies reported testing of individual anchors that exhibited the fan-to-
13
sheet debonding failure mode, but the most crucial parameter (resin properties)
was not clearly reported [43,59,69,71] such that no conclusion or comparison
can be extracted from the results on these studies. Similarly, there are a number
of studies where specimens featured more than one loaded anchor, preventing the
ability to analyze the behavior of individual anchors [7,67,72,68]. Only one
study exists where the resin properties have been reported, in which Kanitkar [73]
tested single-lap shear behavior of straight anchors. Anchors of three diameters
(9.5 mm, 13 mm and 16 mm) were used with three fan lengths (100 mm, 150 mm
and 200 mm) using the same fanning angle αof 30 degrees. However, anchor fans
are typically sandwiched between layers of FRP sheets and can feature different
fanning angles α. These aspects of FRP anchor design were not investigated and
are in need of further research. Equation 5represents the minimum value of bond
stress observed from all the tests performed, but only the tests using fan lengths of
100 mm exhibited pure fan-to-sheet debond failure.
Nsd =0.35Vsb As(5)
Where Nsd is the anchor splay debonding capacity in N, Vsb is the shear bond
strength of the epoxy resin and Asis the total area of the anchor splay bonded to
the FRP sheet.The range of test parameters used to develop these models was Vsb
= 5 MPa and 65 cm2>As>168 cm2.
All the available studies that reported isolated anchors exhibiting fan-to-sheet
debonding failure mode have been reported in Table 3, with the parameters reported
being fan area in cm2and the ultimate load at debonding Ndin kN. Despite the
early attempts by Kanitkar [73] to describe the debond failure, a thorough study
to investigate the FRP-to-FRP bonding behavior and the influence of the adhesive
properties on this behavior is necessary to develop the design equations that govern
the capacity of FRP anchors with fan-to-sheet debonding failure.
3.3. Fiber rupture failure mode
Straight anchors. The results obtained from Ozdemir, Ozbakkaloglu and Kim
were summarized by the latter [9] and a model was proposed [51]. However in their
experiments these researchers used FRP sheets rolled around a metal rod, which
did not take into consideration the physical configuration of a real FRP anchor.
Furthermore, the equation does not consider the loss of efficiency observed as the
size of FRP anchors increases [55,74,8]. The equation is therefore not applicable
for the design of FRP anchors. The results on studies reporting fiber rupture failure
mode of straight anchors are summarized in Table 6, with the attributes that have
14
Table 3. Details of FRP anchors exhibiting fan-to-sheet debonding failure mode
Reference Specimen name Fan area (cm2)Nd(kN)
[43]s15-2a000y-12 150 48.7
[43]s15-2a150n-12 150 34.9
[43]s15-2b150y-12 150 57.5
[43]s15-2b150n-12 150 38.8
[43]s15-2c150n-12 150 48.4
[43]s15-2A150h-10 150 46.7
[43]220-2b150h-15 200 58.6
[59]s1-100-2 14 3.0
[59]s2-200-2 14 4.0
[69] N5H1.4Mc 24 64.1
[69] B5L1.4Md 24 40.5
[69] B5H1Md 24 67.6
[73]S1 65 54.0
[73]S2 65 60.7
[73]S3 65 69.8
[73]S4 65 64.1
[73]S5 65 69.1
[73]S6 65 73.1
[71]R-1 130 54.3
[71]R-2 130 55.4
[71]R-3 130 48.9
[71]R-4 130 48.0
15
(a) Effect of fanning angle α on fiber
rupture capacity
(b) Effect of cross sectional area on fiber
rupture capacity
0
0.5
1
1.5
2
2.5
020 40 60 80
Normalized ultimate fibre rupture
load Nfr (kN/mm2)
Fanning angle (deg)
0
2
4
6
8
10
12
14
010 20 30 40
Normalized ultimate fibre rupture
load Nfr (kN/MPa)
Cross sectional area Adowel (mm2)
Fig. 4. Effect of anchor properties on fiber rupture strength of straight anchors
an effect on anchor capacity being the strength of the FRP material (σFRP) in MPa,
the cross sectional area of the dowel (Adow) in mm2and the fanning angle αin
degrees.
Two different cross sectional areas were used by Kobayashi [43], which is
the only study to consider the effect of fanning angle αon anchor capacity. The
anchor capacity has been normalized using those two cross sectional areas and
plotted against the fanning angle in Figure 7a, where the trend of decrease anchor
capacity for wider anchors can be clearly observed. All the other anchors reported
in Table 6featured various cross sectional areas but were tested using an insertion
angle equal to zero. The authors of these other studies used FRP materials with
different strengths, so the anchor capacity has been normalized by dividing the
ultimate load by the FRP strength to illustrate the influence of anchor cross sectional
area (or anchor size) on anchor capacity. It can be inferred from Figure 7b that the
relationship between anchor size and anchor capacity is not linear, i.e. an anchor
twice as big is not twice as strong. The available data are not sufficient to develop
a design equation to calculate the anchor capacity based on the properties of the
FRP, the cross sectional area and the fanning angle, since the available literature
is not consistent with the parameters that were investigated. Further research is
necessary to have an experimental database that considers all three parameters at
the same time.
16
Table 4. Details of straight FRP anchors exhibiting fiber rupture failure mode
Reference Specimen name σFRP
(MPa)
Adow
(mm2)
Fanning angle α
(DEG)
Nf r
(kN)
[43] s12-la-1 3430 33.4 60 37.4
[43] s15-la-1 3430 33.4 42 51.2
[43] s15-2b150h-10 3430 33.4 33.7 57.1
[43] s20-la-1 3430 33.4 30 53.6
[43] s20-2b150h-10 3430 33.4 26.6 64.2
[43] s25-la1 3430 33.4 23.5 57.4
[43] s15-2a075y-12 3430 40.8 33.7 48.9
[43] s15-2a150y-12 3430 40.8 33.7 61.7
[43] s15-2b075y-12 3430 40.8 33.7 42.4
[43] s15-2c075y-12 3430 40.8 33.7 47.3
[43] s15-2c150y-12 3430 40.8 33.7 66.5
[43] s20-2b150h-12 3430 40.8 26.6 54.2
[43] s20-2c150h-12 3430 40.8 26.6 53.8
[48] w80h70f10d12 3430 13.2 0 18.7
[48] w80h70f10d14 3430 13.2 0 20.0
[48] w80h70f10d16 3430 13.2 0 16.4
[48] w80h70f16d12 3430 13.2 0 13.0
[48] w80h70f16d14 3430 13.2 0 20.1
[48] w80h70f16d16 3430 13.2 0 22.5
[48] w80h70f20d12 3430 13.2 0 12.8
[48] w80h70f20d12 3430 13.2 0 14.2
[48] w80h70f20d14 3430 13.2 0 16.4
[48] w80h70f20d16 3430 13.2 0 16.2
[48] w80h100f10d12 3430 13.2 0 25.4
[48] w80h100f10d14 3430 13.2 0 15.1
[48] w80h100f10d16 3430 13.2 0 16.4
[48] w80h100f16d12 3430 13.2 0 23.9
[48] w80h100f16d14 3430 13.2 0 15.7
[48] w80h100f16d14 3430 13.2 0 25.2
[48] w80h100f16d16 3430 13.2 0 17.7
[48] w80h100f16d16 3430 13.2 0 17.8
[48] w80h100f16d16 3430 13.2 0 24.3
[48] w80h100f20d12 3430 13.2 0 24.1
[48] w80h100f20d12 3430 13.2 0 25.2
[48] w80h100f20d12 3430 13.2 0 22.0
17
Reference Specimen name σFRP
(MPa)
Adow
(mm2)
Fanning angle α
(DEG)
Nf r
(kN)
[48] w80h100f20d14 3430 13.2 0 21.5
[48] w80h100f20d16 3430 13.2 0 19.6
[48] w80h150f10d12 3430 13.2 0 20.6
[48] w80h150f10d14 3430 13.2 0 21.1
[48] w80h150f10d16 3430 13.2 0 21.7
[48] w80h150f16d12 3430 13.2 0 12.4
[48] w80h150f16d12 3430 13.2 0 20.1
[48] w80h150f16d14 3430 13.2 0 19.3
[48] w80h150f16d16 3430 13.2 0 10.8
[48] w80h150f16d16 3430 13.2 0 12.3
[48] w80h150f16d16 3430 13.2 0 20.1
[48] w80h150f16d16 3430 13.2 0 27.4
[48] w80h150f20d12 3430 13.2 0 22.3
[48] w80h150f20d12 3430 13.2 0 20.2
[48] w80h150f20d12 3430 13.2 0 17.1
[48] w80h150f20d12 3430 13.2 0 16.2
[48] w80h150f20d12 3430 13.2 0 30.0
[48] w80h150f20d12 3430 13.2 0 24.4
[48] w80h150f20d14 3430 13.2 0 25.7
[48] w80h150f20d16 3430 13.2 0 12.3
[48] w80h150f20d16 3430 13.2 0 24.8
[48] w120h70f10d12 3430 19.8 0 17.1
[48] w120h70f16d12 3430 19.8 0 21.5
[48] w120h70f16d14 3430 19.8 0 24.6
[48] w120h70f16d14 3430 19.8 0 25.1
[48] w120h70f16d16 3430 19.8 0 20.6
[48] w120h70f20d12 3430 19.8 0 15.6
[48] w120h70f20d12 3430 19.8 0 25.1
[48] w120h70f20d14 3430 19.8 0 21.2
[48] w120h70f20d16 3430 19.8 0 14.7
[48] w120h70f20d16 3430 19.8 0 16.1
[48] w120h70f20d16 3430 19.8 0 26.0
[48] w120h100f10d12 3430 19.8 0 32.9
[48] w120h100f10d14 3430 19.8 0 29.3
[48] w120h100f10d16 3430 19.8 0 30.0
[48] w120h100f16d12 3430 19.8 0 17.5
[48] w120h100f16d12 3430 19.8 0 22.7
18
Reference Specimen name σFRP
(MPa)
Adow
(mm2)
Fanning angle α
(DEG)
Nf r
(kN)
[48] w120h100f16d14 3430 19.8 0 19.0
[48] w120h100f16d14 3430 19.8 0 29.3
[48] w120h100f16d16 3430 19.8 0 17.5
[48] w120h100f16d16 3430 19.8 0 32.5
[48] w120h100f16d16 3430 19.8 0 35.5
[48] w120h100f20d12 3430 19.8 0 24.7
[48] w120h100f20d12 3430 19.8 0 27.5
[48] w120h100f20d12 3430 19.8 0 27.1
[48] w120h100f20d14 3430 19.8 0 16.6
[48] w120h100f20d14 3430 19.8 0 17.1
[48] w120h100f20d14 3430 19.8 0 31.4
[48] w120h100f20d14 3430 19.8 0 23.5
[48] w120h100f20d16 3430 19.8 0 19.1
[48] w120h100f20d16 3430 19.8 0 20.1
[48] w120h150f10d12 3430 19.8 0 21.3
[48] w120h150f10d14 3430 19.8 0 32.3
[48] w120h150f10d16 3430 19.8 0 12.2
[48] w120h150f16d12 3430 19.8 0 20.6
[48] w120h150f16d12 3430 19.8 0 20.9
[48] w120h150f16d14 3430 19.8 0 22.9
[48] w120h150f16d16 3430 19.8 0 21.0
[48] w120h150f16d16 3430 19.8 0 22.5
[48] w120h150f20d14 3430 19.8 0 35.2
[48] w120h150f20d16 3430 19.8 0 28.9
[48] w160h70f10d16 3430 26.4 0 19.2
[48] w160h70f16d12 3430 26.4 0 28.5
[48] w160h70f16d14 3430 26.4 0 21.9
[48] w160h70f16d16 3430 26.4 0 25.1
[48] w160h70f16d16 3430 26.4 0 23.0
[48] w160h70f20d12 3430 26.4 0 21.3
[48] w160h70f20d14 3430 26.4 0 23.1
[48] w160h70f20d16 3430 26.4 0 13.7
[48] w160h70f20d16 3430 26.4 0 20.7
[48] w160h100f10d12 3430 26.4 0 21.6
[48] w160h100f10d14 3430 26.4 0 30.8
[48] w160h100f10d16 3430 26.4 0 31.3
19
Reference Specimen name σFRP
(MPa)
Adow
(mm2)
Fanning angle α
(DEG)
Nf r
(kN)
[48] w160h100f16d14 3430 26.4 0 28.5
[48] w160h100f16d16 3430 26.4 0 28.4
[48] w160h100f20d12 3430 26.4 0 32.8
[48] w160h100f20d12 3430 26.4 0 33.2
[48] w160h100f20d14 3430 26.4 0 27.2
[48] w160h100f20d14 3430 26.4 0 31.2
[48] w160h100f20d16 3430 26.4 0 16.7
[48] w160h100f20d16 3430 26.4 0 22.4
[48] w160h100f20d16 3430 26.4 0 35.6
[48] w160h150f10d12 3430 26.4 0 29.4
[48] w160h150f10d14 3430 26.4 0 22.3
[48] w160h150f10d14 3430 26.4 0 29.9
[48] w160h150f10d16 3430 26.4 0 25.3
[48] w160h150f16d12 3430 26.4 0 27.5
[48] w160h150f16d14 3430 26.4 0 19.0
[48] w160h150f16d14 3430 26.4 0 27.3
[48] w160h150f16d16 3430 26.4 0 14.8
[48] w160h150f16d16 3430 26.4 0 29.4
[48] w160h150f20d12 3430 26.4 0 22.5
[48] w160h150f20d14 3430 26.4 0 23.9
[48] w160h150f20d16 3430 26.4 0 25.5
[9] PF-40-14-3 2735 12.9 0 23.0
[9] PF-60-12-1 2735 15.2 0 32.3
[9] PF-60-14-1 2735 15.2 0 31.6
[9] PF-60-14-2 2735 15.2 0 34.4
[9] PF-60-14-3 2735 15.2 0 31.6
[9] PF-60-16-1 2735 15.2 0 26.8
[9] PF-60-16-2 2735 15.2 0 24.8
[10] HD12.7L50T8 3800 13.2 0 15.8
[10] HD19.1L50T8 3800 13.2 0 25.0
[10] HD12.7L75T7 3800 13.2 0 20.5
[10] HD12.7L75T8 3800 19.8 0 28.5
[10] HD12.7L100T3 3800 19.8 0 28.4
[10] HD12.7L100T4 3800 19.8 0 22.5
[10] HD12.7L100T5 3800 23.1 0 38.2
[10] HD15.9L100T2 3800 36.3 0 43.0
20
Bent anchors. Zhang [61] observed that the anchor strength increased when
more obtuse insertion angles βwere used and established a linear relationship
between insertion angle βand strength. Additionally, the insertion angle βof the
anchor dowel controls the deformation capacity of the FRP-EBR system, with a
larger deformation being observed when the insertion angle is greater than 90º(see
Figure 1c for a representation of angle of insertion β). Mahrenholt [64] subjected
isolated bent anchors to monotonic and cyclic loading, which were bonded to a steel
channel rather than to an FRP sheet, compromising the reliability of the results.
Additionally, small anchors were used with a limited range of cross-section area
and the influence of the fanning angle αon anchor capacity was not considered.
Nevertheless, the results revealed that embedment depth, annular gap size, and
fiber-to-resin ratio do not affect the shear strength of the anchor. In addition, the
results showed that reversed load cycles induced failure due to low-cycle fatigue
despite good energy dissipation capability.
The results on bent FRP anchors exhibiting fiber rupture failure are reported
in Table 7, where the trend of efficiency drop as the anchor size increases can
be observed. The efficiency of the anchors featuring the fan facing opposite the
origin of the force (α=-30) was a third of that of the anchors featuring the fan facing
towards the origin of the force (α=30), but the anchor slip of the former was over
three times larger than the slip of the latter. Both the efficiency and the anchor slip
of anchors featuring bow-tie fans were smaller than the efficiency and the anchor
slip of anchors that featured other types of fan configurations. A more obtuse
angle βresults in stronger anchors but smaller anchor slip, which results in a more
brittle behavior after the FRP-to-concrete debonding occurs. The anchors tested
by Sun [69] performed significantly better than the anchors previously reported
[59,37,63,61]. The most likely cause for the poor performance of anchors from
previous studies is that inadequate soaking of the dowel and key portion occurred
as a consequence of the construction process. The dry fibers can be seen in [59]
Figure 10b and [61] Figure 9, and the problem was identified by Zhang [8]. A
complete and thorough impregnation of all the fibers in the anchor is critical to
achieve a correct and optimum behavior. The anchors tested by Mahrenholt [64]
were isolated, with the FRP anchor fan not bonded to an FRP sheet, which explains
the reduced efficiency when compared to the results from Sun [69]. Mahrenholtz
proposed a model that reflects the extremely low (6%) efficiency observed on
the tests, with the calculation of the lower bound characteristic capacity of bent
anchors exhibiting the fiber rupture failure mode being reported in Equation 6.
Vf r =0.06Adowel fF RP (6)
21
where Vf r is the anchor fiber rupture capacity in N, Adowel is the cross sectional
area of the FRP material used to manufacture the anchor in mm2, and fF RP is the
ultimate tensile strength of the sheet used to manufacture the anchor in MPa. The
range of test parameters used to develop this model was 201 mm2>Adowel >79
mm2and fF RP=4800 MPa.
Villanueva Llaurado developed an extensive database, compiled in two publi-
cations [65,66] but all the anchors featured the same size and a fanning angle α
equal to zero was used, with the anchor end outside of the concrete being bundled
instead of fanned out. This testing set-up compromises the reliability of the model
when fiber rupture failure mode is investigated, as anchors typically feature a fan
rather than a bundled end. Additionally, the insertion angle βdoes not have any
influence on the load capacity, contradicting the results from previous studies. A
possible reason for this discrepancy might be the incorrect saturation of the fibers
that can be observed in some of the pictures reported in the studies, which could
also explain the difference in efficiency observed between the three studies by the
same authors. Despite the drawbacks, Villanueva Llaurado completed an extensive
database and developed a load capacity model for bent anchors exhibiting fiber
rupture failure mode based on the reduction of strength in FRP stirrups reported by
the FRP design standard developed by the Japan Society of Civil Engineers [16].
The equation to calculate the average tensile capacity of bent anchors exhibiting
the fiber rupture failure mode is reported in Equation 7.
Vf r =0.002Adowel fF RP(he f +50rb
β
π)(7)
where Adowel is the cross sectional area of the FRP material used to manufacture
the anchor in mm2,fF RP is the ultimate tensile strength of the sheet used to
manufacture the anchor in MPa, he f is the effective embedment depth in mm, rbis
the bend ratio at the key portion in degrees, and βis the insertion angle in degrees
as defined in Figure 1. The range of test parameters used to develop this model
was 201 mm2>Adowel >314 mm2,fFR P=1900 MPa, 125 mm >he f >50 mm,
2.5 mm >rb>0.3 mm, and 135 >β>90.
The failure load (Nf r ) of FRP anchors that exhibited fiber rupture failure mode
is reported in kN in Table 7, together with the parameters that have an effect
on anchor fiber rupture capacity, namely the tensile strength of the FRP material
(σFRP) in MPa, cross sectional area of the dowel (Adowel) in mm2, the fanning
angle αin degrees and the insertion angle βin degreed.
The results from bent anchors reported in Table 6 have been normalized sim-
ilarly to the results reported in Figure 7for straight anchors, and are presented
22
Table 5. Details of bent FRP anchors exhibiting fiber rupture failure mode
Reference Specimen
name
σFRP
(MPa)
Adowel
(mm2)
α
(deg)
β
(deg)
Nf r
(kN)
[59]1s1-100-1 2735 11.7 30 90 5.0
[59]1s2-100-2 2735 11.7 30 90 5.0
[59]1s2-100-3 2735 11.7 30 90 10.0
[59]1s1-200-3 2735 23.4 30 90 15.0
[59]1s1-200-5 2735 23.4 30 90 8.0
[59]1s2-200-1 2735 23.4 30 90 12.0
[59]1s2-200-3 2735 23.4 30 90 17.0
[10] HD15.9L75 I30T1 3800 33.0 0 30 30.9
[10] HD15.9L75 I30T2 3800 33.0 0 30 34.0
[37] LBF1 3163 41.9 BT30 90 4.7
[37] LBF2 3163 41.9 BT30 90 3.7
[37] SBF1 3163 21.0 BT45 90 1.6
[37] SBF2 3163 21.0 BT45 90 2.7
[63] gd-200-1 1595 34.0 30 90 9.5
[63] gi-200-1 1595 34.0 30 90 11.1
[63] gi-200-2 1595 34.0 30 90 8.1
[63] gi-200-3 1595 34.0 30 90 10.8
[63] ci-134-1 3090 17.6 30 90 11.4
[63] ci-134-2 3090 17.6 30 90 6.9
[63] ci-134-3 3090 17.6 30 90 11.3
[63] ci-200-1 3090 26.2 30 90 13.2
[63] ci-200-2 3090 26.2 30 90 13.7
[63] ci-200-3 3090 26.2 30 90 14.9
[63] ci-259-1 3090 33.9 30 90 15.1
[63] ci-259-2 3090 33.9 30 90 17.0
[61] sf-200-1 3022 26.2 30 90 15.1
[61] sf-200-2 3022 26.2 30 90 15.7
[61] sf-200r-1 3022 26.2 -30 90 5.8
[61] sf-200r-2 3022 26.2 -30 90 5.4
[61] sf-200r-3 3022 26.2 -30 90 4.7
[61] bf-200-1 3022 26.2 BT30 90 5.9
[61] bf-200-2 3022 26.2 BT30 90 3.5
[61] bf-300-1 3022 39.3 BT30 90 16.4
[61] bf-300-2 3022 39.3 BT30 90 8.3
[61] bf-400-1 3022 52.4 BT30 90 14.0
23
Reference Specimen
name
σFRP
(MPa)
Adowel
(mm2)
α
(deg)
β
(deg)
Nf r
(kN)
[61] bf-400-2 3022 52.4 BT30 90 4.8
[61] bf-400-3 3022 52.4 BT30 90 11.3
[61] da-45-1 3022 26.2 30 45 9.8
[61] da-45-2 3022 26.2 30 45 6.4
[61] da-67.5-1 3022 26.2 30 67.5 8.6
[61] da-67.5-2 3022 26.2 30 67.5 9.6
[61] da-101.3-2 3022 26.2 30 101.3 11.5
[61] da-123.8-1 3022 26.2 30 123.8 5.3
[61] da-123.8-2 3022 26.2 30 123.8 7.8
[69]2B5H1.4Sb 1034 90.3 32 90 61.8
[69]2B5H1.4Lb 1034 90.3 18.5 90 61.8
[69]2B5L1.4Mc 1034 90.3 22.5 90 69.8
[69]2U5H1.4Ma 1034 90.3 22.5 90 54.3
[69]2U5H1.4Mb 1034 90.3 22.5 90 58.7
[69]2B5H1Ma 1034 64.5 22.5 90 59.6
[69]2B5H1Mb 1034 64.5 22.5 90 62.7
[69]2B5H1Mc 1034 64.5 22.5 90 64.1
[69]2B5L1Ma 1034 64.5 22.5 90 63.2
[69]2B5L1Mb 1034 64.5 22.5 90 46.3
[69]2B5L1Mc 1034 64.5 22.5 90 55.6
[69]2B5L1Md 1034 64.5 22.5 90 60.1
[69]2B5L1Me 1034 64.5 22.5 90 62.7
[69]2U5M1Lh 1034 64.5 18.5 90 45.4
[64] 1 2121 8.3 BT30 90 1.8
[64] 2 2121 11.6 BT30 90 1.9
[64] 6 2121 11.6 BT30 90 5.4
[64] 10 2121 16.5 BT30 90 7.0
[64] 11 2121 16.5 BT30 90 6.2
[64] 12 2121 16.5 BT30 90 6.4
[64] 13 2121 16.5 BT30 90 6.6
[64] 14 2121 16.5 BT30 90 7.3
[64] 15 2121 16.5 BT30 90 5.7
[64] 16 2121 16.5 BT30 90 7.0
[64] 17 2121 16.5 BT30 90 7.4
[64] 18 2121 16.5 BT30 90 7.4
[64] 19 2121 16.5 BT30 90 6.6
24
Reference Specimen
name
σFRP
(MPa)
Adowel
(mm2)
α
(deg)
β
(deg)
Nf r
(kN)
[64] 20 2121 16.5 BT30 90 7.2
[64] 3 2121 23.1 BT30 90 4.1
[64] 5 2121 23.1 BT30 90 9.7
[64] 7 2121 23.1 BT30 90 12.4
[64] 8 2121 23.1 BT30 90 5.4
[64] 9 2121 23.1 BT30 90 6.7
[64] 21 2121 23.1 BT30 90 9.0
[64] 22 2121 29.7 BT30 90 10.5
[65] NA/F/90/16/ 100-1 4800 27.3 0 90 8.4
[65] NA/F/90/16/ 100-2 4800 27.3 0 90 8.4
[65] NA/F/90/16/ 100-3 4800 27.3 0 90 16.2
[65] NA/F/90/16/ 100-4 4800 27.3 0 90 15.8
[65] NA/F/90/20/ 100-1 4800 27.3 0 90 12.8
[65] NA/F/90/20/ 100-2 4800 27.3 0 90 14.3
[65] NA/F/90/20/ 100-3 4800 27.3 0 90 18.2
[65] NA/F/90/20/ 100-4 4800 27.3 0 90 17.2
[65] R/F/90/16/ 100-1 4800 27.3 0 90 17.7
[65] R/F/90/16/ 100-2 4800 27.3 0 90 14.3
[65] R/F/90/16/ 100-3 4800 27.3 0 90 16.2
[65] R/F/90/16/ 100-4 4800 27.3 0 90 23.1
[65] R/F/120/20/ 75-1 4800 27.3 0 120 12.3
[65] R/F/120/20/ 75-1 4800 27.3 0 120 11.8
[65] R/F/120/20/ 75-3 4800 27.3 0 120 14.3
[65] R/F/120/20/ 75-4 4800 27.3 0 120 17.7
[65] R/F/120/20/ 100-1 4800 27.3 0 120 24.1
[65] R/F/120/20/ 100-2 4800 27.3 0 120 11.8
[65] R/F/120/20/ 100-3 4800 27.3 0 120 15.8
[65] R/F/120/20/ 100-4 4800 27.3 0 120 15.8
[65] AV/F/90/20/ 75-1 4800 27.3 0 90 12.8
[65] AV/F/90/20/ 75-2 4800 27.3 0 90 14.8
[65] AV/F/90/20/ 75-3 4800 27.3 0 90 18.2
[65] AV/F/90/20/ 75-4 4800 27.3 0 90 13.3
[65] AV/E/90/20/ 75-1 4800 27.3 0 90 17.2
25
Reference Specimen
name
σFRP
(MPa)
Adowel
(mm2)
α
(deg)
β
(deg)
Nf r
(kN)
[65] AV/E/90/20/ 75-2 4800 27.3 0 90 14.3
[65] AV/E/90/20/ 75-3 4800 27.3 0 90 11.8
[65] AV/E/90/20/ 75-4 4800 27.3 0 90 17.2
[65] AV/E/90/20/ 50-2 4800 27.3 0 90 15.8
[65] AV/F/90/20/ 50-2 4800 27.3 0 90 15.3
[65] AV/F/90/20/ 100-1 4800 27.3 0 90 16.2
[65] AV/F/90/20/ 100-2 4800 27.3 0 90 16.7
[65] AV/F/90/20/ 100-3 4800 27.3 0 90 16.2
[65] AV/F/90/20/ 100-4 4800 27.3 0 90 16.2
[65] AV/E/90/20/ 100-1 4800 27.3 0 90 17.2
[65] AV/E/90/20/ 100-2 4800 27.3 0 90 18.7
[65] AV/E/90/20/ 100-3 4800 27.3 0 90 14.3
[65] AV/E/90/20/ 100-4 4800 27.3 0 90 14.3
[65] AV/E/90/20/ 125-1 4800 27.3 0 90 16.2
[65] AV/E/90/20/ 125-2 4800 27.3 0 90 19.2
[65] AV/E/90/20/ 125-3 4800 27.3 0 90 22.2
[65] AV/E/90/20/ 125-4 4800 27.3 0 90 18.7
[65] AV/F/90/20/ 125-1 4800 27.3 0 90 22.2
[65] AV/F/90/20/ 125-2 4800 27.3 0 90 14.3
[65] AV/F/90/20/ 125-3 4800 27.3 0 90 15.8
[65] AV/F/90/20/ 125-4 4800 27.3 0 90 19.7
[65] R/F/90/20/ 100-1 4800 27.3 0 90 16.7
[65] R/F/90/20/ 100-2 4800 27.3 0 90 20.7
[65] R/F/90/20/ 100-3 4800 27.3 0 90 17.7
[65] R/F/90/20/ 100-4 4800 27.3 0 90 21.7
[65] R/F/120/20/ 75-1 4800 27.3 0 120 12.3
[65] R/F/120/20/ 75-1 4800 27.3 0 120 11.8
[65] R/F/120/20/ 75-3 4800 27.3 0 120 14.3
[65] R/F/120/20/ 75-4 4800 27.3 0 120 17.7
[65] R/F/120/20/ 100-1 4800 27.3 0 120 24.1
[65] R/F/120/20/ 100-2 4800 27.3 0 120 11.8
[65] R/F/120/20/ 100-3 4800 27.3 0 120 15.8
[65] R/F/120/20/ 100-4 4800 27.3 0 120 15.8
[65] R/F/135/20/ 75-1 4800 27.3 0 135 16.2
[65] R/F/135/20/ 75-2 4800 27.3 0 135 18.2
[65] R/F/135/20/ 75-3 4800 27.3 0 135 20.7
26
Reference Specimen
name
σFRP
(MPa)
Adowel
(mm2)
α
(deg)
β
(deg)
Nf r
(kN)
[65] R/F/135/20/ 75-4 4800 27.3 0 135 18.2
[65] R/F/135/20/ 100-1 4800 27.3 0 135 21.7
[65] R/F/135/20/ 100-2 4800 27.3 0 135 19.2
[65] R/F/135/20/ 100-3 4800 27.3 0 135 16.2
[65] R/F/135/20/ 100-4 4800 27.3 0 135 21.2
[66] DR/W/90/20/ 75-2b 4800 27.3 0 90 36.0
[66] DR/W/90/20/ 100-4c 4800 27.3 0 90 41.0
[66] DR/W/90/20/ 125-3d 4800 27.3 0 90 55.0
[66] DR/P/90/20/ 75-7b 4800 27.3 0 90 29.0
[66] DR/P/90/20/ 75-8b 4800 27.3 0 90 43.0
[66] DR/P/90/20/ 100-7c 4800 27.3 0 90 35.0
[66] DR/P/90/20/ 100-8c 4800 27.3 0 90 36.0
[66] DR/P/90/20/ 125-6d 4800 27.3 0 90 35.0
[66] GR/W/90/16/ 100-14a 4800 27.3 0 90 36.0
[66] GR/W/90/20/ 100-13b 4800 27.3 0 90 42.0
[66] NS/W/90/16/ 100-13c 4800 27.3 0 90 21.0
[66] NS/W/90/16/ 100-14c 4800 27.3 0 90 21.0
[66] NS/W/90/20/ 100-13d 4800 27.3 0 90 32.0
[66] NS/W/90/20/ 100-14d 4800 27.3 0 90 35.0
[66] NS/W/90/20/ 100-16d 4800 27.3 0 90 43.0
[66] GR/W/120/20 /100-10b 4800 27.3 0 120 30.0
[66] GR/W/120/20/ 100-11b 4800 27.3 0 120 39.0
[66] GR/W/120/20/ 100-12b 4800 27.3 0 120 30.0
[66] GR/W/135/20/ 100-11d 4800 27.3 0 135 40.0
[71] O-3 4800 27.3 30 90 54.5
1These results were not accurately reported on the original paper,
they have been estimated from graphs
2Ultimate force calculated by static equilibrium, not recorded
27
in Figure 8. The same effects as in straight anchors can be observed in Fig-
ure 8, with the load capacity increasing non-linearly as the anchor increases in size
and the load capacity decreasing as the fanning angle increases. The anchors were
stronger when the insertion angle was more obtuse, which makes the anchor behav-
ior more similar to the behavior observed on straight anchors, as can be observed
in Figure 8c. Despite the relatively extensive database collected on bent anchors
exhibiting the fiber rupture failure mode, a comprehensive and methodical study
with adequately installed anchors is necessary to investigate the effect of anchor
size and fanning angle αamong other parameters on the strength and deformation
capacity of the anchors. Finally, preliminary results indicate that FRP anchors
are sensitive to fatigue loading but further research is necessary to investigate this
aspect.
4. Case studies
4.1. Shear strengthening and/or repair of a beam
The optimum solution for strengthening RC beams in shear is to fully wrap the
beam with FRP sheets. In some cases this solution is difficult or even impossible
to achieve, usually due to the presence of a physical obstruction such as an RC
slab on top of the beam. As a substitute for fully wrapping the beam, FRP anchors
can be installed on the sides of the beam. Figure 6illustrates three hypothetical
strengthening schemes, a first solution on the left where the fully wrapped member
detail has been drawn assuming that in the foreground there is no slab present
on top of the beam, followed by examples showing the use of bent and straight
anchors.
Jinno [75] installed four different configurations of CFRP sheets and CFRP
bundled straight anchors on RC beams having an RC slab on top of the beam,
and observed that the most efficient configuration was beams featuring anchors
penetrating the slab and making closed loops around the beam. The FRP anchors
did not fail in any of the tests, which prevents any further conclusion regarding the
behavior or efficiency of the anchors.
Quinn and Kim [76,77,56] determined that FRP sheets had be anchored to
the structure when a beam could not be fully wrapped but that it was not crucial
to bond the FRP sheets to the concrete surface if the anchors were correctly
installed, enabling the system to achieve the optimal capacity. Several design
recommendations were developed but a comprehensive design methodology is still
required. The authors observed that the shear strength of the RC-FRP composite
does not linearly improve as the amount of FRP material increases.
28
(a) Effect of cross sectional area on fiber
rupture load
(a) Effect of fanning angle α on fiber
rupture load
(c) Effect of insertion angle β on fiber rupture load
0
100
200
300
400
500
600
700
800
900
025 50 75 100
Normalized ultimate fibre rupture
load Nfr (N/deg)
Cross sectional area Adowel (mm2)
0
0.5
1
1.5
010 20 30 40 50
Normalized ultimate fibre rupture
load Nfr (kN/mm2)
Fanning angle (deg)
0
0.5
1
1.5
010 20 30 40 50
Normalized ultimate fibre rupture
load Nfr (kN/mm2)
Fanning angle (deg)
Fig. 5. Effect of anchor properties on fiber rupture strength of bent anchors
29
Fig. 6. Different FRP-EBR configurations for shear strengthening of an RC beam with slab
Koutas [39] observed that different types of fibers had no significant influence
on the capacity of the beam and that bent anchors performed twice less efficiently
than nearly straight anchors. It was also found that increasing the amount of FRP
material in the anchors by 67% led to only an 11% increase in the shear strength of
the beam, with the reason for this non-proportional pattern being that the anchors
installed above the shear crack in the beam were only lightly stressed. Baggio [38]
used bundled dry GFRP bent anchors in five RC beams, three of which were pre-
cracked and repaired before installing the anchors. The GFRP anchors prevented
debonding of the GFRP sheets, resulting in the beam failure mode shifting to
GFRP rupture and thus optimizing the use of material. The anchored beams
reached strength levels similar to those of the fully wrapped beams.
The results on RC beams strengthened in shear with FRP anchors in which the
FRP anchors failed are reported in Table 6, with the geometrical and reinforcing
properties of the specimens and the FRP anchor details being summarized in
Figure 7. The difference between having more/fewer and larger/smaller anchors,
the insertion angle and especially the influence of the shear crack location and
width on the anchor and beam behavior are all critical features that require further
research.
4.2. Flexural strengthening and/or repair of a beam
FRP sheets are typically installed on the soffit of a beam to take full advantage
of the lever arm between the compressed top surface of the concrete beam and the
tension of the FRP sheets mounted on the bottom surface of the beam, thereby
increasing the beam flexural capacity. The use of FRP anchors is typically limited
30
[56]
Six CFRP
anchors
Adow=71 mm2
σFRP=1063 MPa
α=30 β=90
711
127
610
356
Top:
As=3225 mm2
fy=476 MPa
Bottom:
As=6450 mm2
fy=558 MPa
f’c=27 MPa
Stirrups:
2 legs @ 250mm cc
As=71 mm2
fy=476 MPa
CFRP anchors
CFRP sheets
[39]
Each carbon
anchor
Adow= 25.5 mm2
σFRP=1062 MPa
α=30
Dimensions in mm
1750
600
500
300
80
220
20
140
Stirrups:
2 legs @ 100mm cc
As=50.3 mm2
fy=548 MPa
f’c=22.6 MPa
(cubic specimens)
Top:
As=402 mm2
fy=543 MPa
Bottom:
As=1018 mm2
fy=546 MPa
Fig. 7. Details of the studies on shear strengthening of RC beams
31
Table 6. Results of beams strengthened in shear
Reference Specimen FRP variation Np
(kN)
δp
(mm)
Np/Nc
(%)
δp/δc
(%)
[56] 3-C No FRP 467 NR - NR
[56] 3-S No anchors 485 NR 4 NR
[56] 3-S21 double size anchor 681 NR 45 NR
[56] 3-NBP1 no FRP-to-concrete bond 525 NR 12 NR
[56] 3-IA1 β=110 645 NR 38 NR
[56] 2.1-C No FRP 574 NR - NR
[56] 2.1-S2 756 NR 32 NR
[39] CON No FRP 74 4.253 NR NR
[39] U2C No anchors 103 4.753 39 12
[39]U2C-
AN3Ch 3 anchor per side β=90 111 6.33 50 48
[39]U2C-
AN3Cin 3 anchor per side β=155 150 7.03 103 65
[39]U2C-
AN5Cin 5 anchor per side β=155 158 6.53 114 53
1Span/depth ratio = 3
2Span/depth ratio = 2.1
3Exact values not reported, estimated from graph
4NR = Not Reported
32
Fig. 8. Flexural strengthening of an RC beam
to bent anchors introduced into the beam to enhance FRP-to-concrete bonding
strength, but are not always required throughout the whole beam length, see
Figure 8.
Eshwar [78] used GFRP bent anchors to investigate the influence of concrete
surface unevenness as a result of curved soffit on FRP-to-concrete bond strength.
Premature debonding is more likely to occur when curved soffits are present in
a beam, although the use of GFRP anchors was found to eliminate premature
peeling. The main conclusion from both studies is that anchors prevent premature
FRP-to-concrete debonding while also delaying the manifestation and widening
of cracks.
Kim [79,80] and Orton [55,35] demonstrated that FRP anchors can help to
ensure the continuity of the load path across a beam-column joint assemblage
where the beam-bottom longitudinal reinforcing bars were not continued through
the joint. The FRP anchors increased the toughness and integrity of the RC
frame and enabled the subassembly to resist progressive collapse due to loss of
capacity of the supporting column under extreme loading such as blast, impact, or
earthquake. Additionally, Orton found that installing anchors on a 1:4 ratio slope
achieved the same results as installing the anchors on a flat surface. Kim [62] next
tested dynamically the under-reinforced beam-column joint assemblages strength-
ened following the same configuration. These joints also performed satisfactorily
when subjected to dynamic loads. Strengthening beams with discontinuous bot-
tom longitudinal reinforcing bars is comparable to strengthening columns with
33
Fig. 9. Flexural strengthening of an RC slab
discontinuous longitudinal reinforcing bars.
4.3. Strengthening of slabs
The objective of strengthening RC slabs is to increase the load capacity of the
slab by bonding FRP sheets to the soffit, in conjunction with FRP bent anchors
introduced into the slab to enhance the FRP-to-concrete bonding strength or straight
anchors inserted into the perimeter wall or beam to transfer the load from the FRP
sheet into the structure as shown in Figure 9. FRP anchors are not always required
throughout the whole slab length. Slabs featuring an opening where FRP materials
were used to strengthen the perimeter of the opening have been the subject of
previous studies.
The results found in the literature regarding RC slabs strengthened with FRP
anchors that presented anchor failure have been summarized in Table 7, with the
details of the specimens being reported in Figure 10. The most important FRP
anchor parameters are described in Table 7, followed by the peak load in kN
(Np), the mid-span deflection at peak load in mm (δp), the strengthening ratio in
percentage in terms of peak load (Np/Nc) and in terms of mid-span deflection at
peak load (δp/δs) (note that the mid-span deflection at peak load was not given for
the control specimen, using the value from the slab with only FRP sheets instead).
Teng and Lam [11,12] determined that the sheet debonding failure mode can
be prevented if correct anchorage of the FRP sheets to the structure is provided,
although only one slab with FRP anchors was tested. In the slab featuring FRP
anchors, the peak load of the slab was improved by up to 3.5 times and the mid-
span deflection at peak load by 9 times [11] and 24 times [12], while increasing
the efficiency of the material used. This procedure enables designers to predict
the flexural strength of an FRP retrofitted RC slab using the plane-section design
34
method. These conclusions were also supported by Piyong [81].
Kim [36] strengthened RC perforated slabs with FRP sheets and bent FRP
anchors and observed that installing anchors in two rows oriented parallel to
the reinforcing bars at a distance of 300 mm in the transverse direction resulted
in a 16% improved post-debonding strength compared to the unanchored slabs.
However, it was noted that installing the anchors at a closer spacing was expected
to provide a higher load capacity and higher post-debonding strength, although
specimens with these features were not tested. Details of the slabs tested by Kim
are not reported herein, due to the specific shape of the slab, the reader is referred
to the original publication [36]. Hu [37] observed that slabs featuring more and
smaller anchors performed better than when using fewer and larger anchors, which
concurs with the results of previous studies, see for example the strengthening ratio
of slab S3 (152%) when compared with the ratio of slab S4 (116%) as reported
in Table 7. It was concluded that anchors should be placed in the shear span area
as opposed to being installed in the constant moment area (mid-span) where the
anchors exhibited poor efficiency. This effect can be observed when the relatively
low peak load improvement of 116% and 100% observed in specimens S4 and
S6 respectively, which featured anchors in the whole span, is compared with the
significantly higher peak load improvement of 155% and 153% observed in slabs
S5 and S7 respectively. The influence of anchor location on anchor behavior was
observed to be related to the mechanisms leading to the initiation of debonding and
the location at which these mechanisms commence, as subsequently identified by
[6]. Anchors installed with close spacing were found to reduce the propagation of
debonding caused by concrete cracking and increase beam deflection at mid-span
while anchors with close spacing were found to increase mid-span deflection but
not increase strength. Smith [82,83] also reported the results of this research.
Zhang [8] and Smith [74] observed that slabs with bow-tie anchors installed
were more resistant to FRP-to-concrete debonding because the bonding area was
larger than that of the other slabs. The influence of dowel insertion angle βon the
slab behavior was investigated and in accordance with previous conclusions by the
same authors [61], slabs featuring anchors having obtuse insertion angles exhibited
higher strength capacity than slabs with anchors featuring acute insertion angles.
As an example, slab S2.5 with anchors inserted 90 degrees into the slab exhibited
a 28% increment in peak load and a 93% increment in mid-span deflection at
peak when compared to slab S2.4 that feature anchors with an insertion angle β
of 67.5 degrees. The influence of the location of anchors was also thoroughly
investigated, and this parameter was found to have a significant influence on the
strength and especially on the deflection capacity of the slabs. Anchors located
35
Figure 1 Specimen details for studies on flexural strengthening of slabs 1
Table 1 Results for flexural strengthening of slabs 2
f’c=39.9-56.8 MPa
(cubic specimens)
1000
1000
400
2200
100
150
2400
150
100
150
120
30
As=157 mm2
fy=566 MPa
Fig. 10. Specimen details for studies on flexural strengthening of slabs
in the shear span area were more effective than anchors located in the constant
moment region, which were mostly ineffective. An example of this behavior is
the comparison between slabs S2.9 and slab S2.10. While the peak load was
comparable between the two slabs, the mid-span deflection at peak load of the
slab with anchors installed at the end (S2.10) was 73% higher than that of the slab
with the anchors installed in the middle (S2.9). Slabs with anchors installed close
to each other such as slabs S8, S2.7 and S2.9 reached higher mid-span deflection
and peak load, but for slabs with anchors installed further apart such as slab S2.8
only a significant improvement in mid-span deflection was observed. Despite the
thoroughness of these studies the results are compromised because of the limited
number of tests performed for each specimen configuration and further research
is necessary to investigate the influence of insertion angle βon the strength of
anchors installed in real structures. Additionally, all the slabs had the same size
and reinforcing details and further research is necessary to confirm the conclusions
from these studies on specimens having different characteristics.
4.4. Seismic strengthening of columns
Two different seismic FRP-EBR strengthening schemes for RC columns have
been identified in the literature, with one scheme intended to improve shear be-
havior and/or the confinement of the column and the other designed to increase
flexural strength at the column-base joint (see Figure 11). The use of FRP anchors
in the first scenario is necessary only when a physical obstruction exists (typically
a wall, which creates a gap in the FRP confinement as shown in Figure 11), and
increases the drift capacity of the columns when compared to the as-built columns.
The second scenario requires the use of FRP anchors to transfer forces from the
36
Table 7. Results for flexural strengthening of slabs
Reference Specimen FRP variation Np
(kN)
δp
(mm)
Np/Nc
(%)
δp/δc
(%)
[83]S1 No FRP 20.3 - 0 -
[83]S2 Only FRP sheets 41.7 25.5 105 0
[83]S3 11 BT30 β90 total area 332 mm2regu-
larly spaced 51.2 41.6 152 63
[83]S4 6 BT30 βtotal area 166 mm2 regularly
spaced 43.9 37.3 116 46
[83]S5 8 BT30 β90 total area 332 mm2 regu-
larly spaced unanchored middle 51.8 42.0 155 65
[83]S6 2 BT30 β90 total area 166 mm2 on each
end 40.6 31.8 100 25
[83]S7 8 BT45 β90 total area 332 mm2 regu-
larly spaced with unanchored middle 51.5 53.7 153 110
[83]S8 4 BT45 β90 total area 332 mm2 + 2
BT30 41.9 mm2 on each slab end 54.3 48.8 167 91
[74]S2.1 No FRP 22.7 - 0 -
[74]S2.2 Only FRP sheets 36.5 27.8 61.0 0
[74]S2.3 8 BT30 β90 total area 410 mm2 unan-
chored middle 47.3 43.7 108 60
[74]S2.4 8α30 β67.5 total area 210 mm2 unan-
chored middle 40.8 35.9 80 32
[74]S2.5 8α30 β90 total area 210 mm2 unan-
chored middle 49.4 51.3 118 125
[74]S2.6 8α30 β135 total area 210 mm2 unan-
chored middle 51.8 57.7 129 112
[74]S2.7 32 α30 β90 total area 210 mm2 unan-
chored middle 52.7 58.2 132 114
[74]S2.8 4α30 + 4 α14 β90 total area 210 mm2
at ends 38.5 50.0 70 120
[74]S2.9 8α30 + 4 α14 β90 total area 214 mm2
at ends 49.6 86.2 119 216
[74]S2.10 8α30 + 4 α14 β90 at ends + 2 α30 β90
in middle total area 214 mm2 49.1 66.2 117 143
37
Fig. 11. Seismic strengthening of RC columns
vertical FRP sheets on the columns to the RC base and reduces the drift up to the
moment when the anchors fail, which corresponds with the peak load. After an-
chor failure the ductility of the column was similar to that of the as-built specimens
because the column continued to behave as per the as-built specimen. The results
found in the literature regarding RC columns strengthened with FRP anchors that
presented anchor failure have been summarized in Table 8, with the details of the
specimens being reported in Figure 12.
Matsuzaki [84] demonstrated for the first time that columns with spandrel
walls strengthened in shear with FRP sheets plus anchors installed and subjected
to cyclic pseudo-static loading performed better than specimens without FRP or
with only FRP sheets. The improvements observed ranged from 14% to 35% in
terms of peak load and between 83% and 120% in terms of drift at peak load.
Additionally, a shifting in failure mode was observed to occur from brittle shear
failure to ductile flexural failure, with rupture of the CFRP sheets occurring only
after the main reinforcing bars yielded.
Kim [79,62,85,86] reached the same conclusion as Matsuzaki, that FRP
anchors can be used as a substitute for full wrapping to shift the failure mode from
brittle splice failure to ductile yielding of the reinforcing bars. Specimens having
more and smaller anchors achieved higher deformation levels than specimens with
fewer and larger anchors, as can be observed from specimen 5-CR20-C, which
achieved a drift improvement of 118% in the direction with large anchors and
227% in the direction with smaller anchors. However, the full height of the column
has to be strengthened, as strengthening only the shear regions of the column (top
38
and bottom) would shift the shear failure towards the middle of the column but not
prevent shear failure. A subsequent and more thorough study on the performance
of lap splices in RC columns [86] involved the monotonic horizontal loading (with
no vertical loading) of three square RC columns and one rectangular RC column
that were laterally displaced until a decrease in load was observed. The columns
were next repaired using epoxy resin injected into the cracks and CFRP sheets
anchored into the columns, and two RC columns were strengthened without first
being cracked. The columns were then loaded cyclically up to the limit of the
actuator with columns from both interventions achieving similar peak load and
drift ratios, which implies that a moderately damaged column can be repaired to a
similar degree as a non-damaged column. The number of anchors used to fasten
the sheets had no significant effect on the strength of the columns, but the drift
capacity increased when more anchors were installed (see also [79,62]).
Vrettos [87] demonstrated that the application of CFRP sheets as longitudinal
reinforcement anchored to the column base with CFRP anchors is a satisfactory
method to improve the flexural behavior of RC columns. The column with three
anchors per side (3_1.5) was observed to have worse behavior than specimens with
two anchors per side, but it was noted that this conclusion was counterintuitive and
that a possible explanation for the premature failure was an incorrectly installed
anchor. It was also claimed that anchor efficiency increased linearly with anchor
size, but that statement is wrong. When comparing the two specimens with two
anchors reported in Table 8, the anchors installed in specimen 2_1.5 featured
a dowel area 50% larger than the anchors installed in specimen 2_1, but the
former was only 16-17% stronger than the latter. The shear strengthening scheme
investigate by Matsuzaki [84] and Kim [86] increased the drift observed in the
columns, while the flexural strengthening investigated by Vrettos [87] reduced the
drift, stiffening the column.
4.5. Strenghening of walls
Qazi [88] tested three RC shear walls in-plane and observed a significant
improvement in terms of strength, deformation capacity, and energy dissipation
capacity in the two FRP-strengthened walls compared to the non-strengthened
wall. The presence of CFRP anchors in one of the walls did not significantly
changed the behavior of the wall having only FRP sheets installed. It was noted
that a plausible reason for this observation could be the location of the anchors,
which were positioned near the edge of the walls and may have had limited the
effect of the anchors on wall behavior.
39
[86]
Loading
direction
2743
457
457
457
483
406
406
406
406
406
610
610
2032
914
Longitudinal:
As=3927 mm2/
side
fy=434 MPa
Stirrups:
2 legs As=157 mm2
@ 406 mm cc
fy=483MPa
Longitudinal:
As=4909 mm2/
side
fy=434 MPa
Longitudinal:
As=9818 mm2/
side
fy=434 MPa
Stirrups:
3 legs As=236 mm2
@ 406 mm cc
fy=483MPa
Stirrups:
2 legs As=471 mm2
@ 406 mm cc
fy=483MPa
f’c=30.0-38.6 MPa
152
102
102
178
r=51 mm
CFRP anchors
CFRP jacket
[87]
Dimensions in mm
250
250
20
Longitudinal:
As=616 mm2
fy=545 MPa
Height=1600 mm
Stirrups:
2 legs As=100 mm2
@ 200 mm cc
fy=351MPa
f’c=17.1 MPa
(cubic specimens)
Fig. 12. Details of the studies on seismic strengthening of RC columns
40
Table 8. Results for seismic strengthening of columns
Reference Name FRP variation Np
(kN)
ϕp
(%)
Np/Nc
(%)
ϕa/ϕc
(%)
[84] 1A No anchors 231 0.6 - -
[84] 2A 3 α24 274 1.2 19 100
[84] 3A 3 α24 263 1.1 14 83
[84] 5B No anchors 226 1.1 - -
[84] 6B 3 α12.5 303 2.2 34 100
[84] 7C No anchors 219 0.5 - -
[84] 8C 3 α30 299 1.1 35 120
[84] 9C 3 α30 277 1.1 26 120
[86]1-A-S8-M
Control 116 1.1 - -
No anchors 150 1.9 29 73
155 2.3 34 109
[86]2-A-S8-M
Control 112 1.1 - -
4 anchors Ad ow =180mm2167 4.5 49 309
166 4.8 48 336
[86]3-B-S10-M
Control 125 1.0 - -
8 anchors Ad ow =180mm2197 5.5 70 400
8 anchors Ad ow =90mm2195 8.6 68 682
[86]4-C-R20-M
Control 238 1.1 - -
16 anchors Ad ow =90mm2500 2.1 110 91
8 anchors Ad ow =180mm2547 2.3 130 109
[86]5-C-R20-C
Control 238 1.1 - -
8 anchors Ad ow =180mm2321 2.4 35 118
16 anchors Ad ow =90mm2323 3.6 36 227
[86]6-C-R20-C
Control 238 1.1 - -
20 anchors Ad ow =130mm2328 2.4 38 118
16 anchors Ad ow =90mm2323 3.6 36 227
[87] C No anchors 38 3.8 - -
[87] 2_1.5 2 anchors Adow =55.5mm251 2.4 35 -37
[87] 3_1.5 3 anchors Adow =37.0mm247 2.8 26 -26
[87] 2_1.0 2 anchors Adow =37.0mm244 2.5 17 -35
1Straight anchors, Adow el=13.9 mm2σF RP =4005MPa. Cyclic loaded with an axial load of 424 kN
2σFR P =986MPa. M = Monotonically loaded until failure without axial load applied and
then repaired or strengthened. C= Cyclic loaded without axial load applied.
3σFR P =986MPa. Cyclic loaded without axial load applied.
41
5. Conclusion
The results extracted from the studies analyzed are summarized here. Conclu-
sions that have been consistently reported or adequately demonstrated in isolated
anchor studies are compiled, and the outcomes of the case-study research are
outlined. Finally, several topics meriting further research are summarized.
The most significant conclusions from the prior work analyzed are:
•Numerous studies have highlighted the importance of quality of workman-
ship on FRP-to-concrete bond strength [9,10,8].
•When designing FRP anchors it is necessary to carefully consider the differ-
ent failure modes present in the anchor-concrete substrate system.
•Kim and Smith [51] developed a design model to calculate the strength of
straight FRP anchors exhibiting pull-out and concrete cone failure, but a
design model for all the other failure modes is yet to be developed.
•A non-linear relationship between anchor size and ultimate strength has been
reported in several studies, [48,49,77,89]
•As the insertion angle βincreases the anchor strength reduces, and Zhang
[61] reported the liner relationship between insertion angle and strength.
•The insertion angle βof the anchor dowel controls the deformation capacity
of an anchor, with the anchors exhibiting a larger deformation capacity when
obtuse insertion angles were used.
•The fan portion of an anchor should cover the whole width of the FRP sheet
[7,67,68], have a single-fan shape, and be oriented towards the origin of
the force applied in the FRP sheet [37,61]. Adjacent anchor fan portions
should overlap to ensure a correct force transfer mechanism from the FRP
sheet into the structure.
•The configuration of more and smaller anchors is preferable to fewer and
larger anchors, e.g. [55,74,8].
•The anchor location is a crucial parameter, regardless of whether the retrofitted
element is a beam [78,90,39] or a slab [36,82,37,83].
Topics meriting further research:
42
•More research is needed to develop analytical and numerical models to
design FRP anchors, validate existing models by improving their accuracy,
and extend the range of parameters considered and the scope of applicability.
•Further research is required to investigate the effect of the type of adhesive
on bond behavior of FRP anchors and the influence of cyclic loading, creep,
and fatigue on the strength of the anchors.
•Standardized construction methods are required to produce more uniform
installations and reduce potential uncertainty in the installation process.
•More research is necessary for all types of case studies in order to increase
the range of parameters under investigation, including structural member
geometries, material properties, and loading protocols, among others. Seis-
mic strengthening of RC columns and walls with FRP is a topic requiring
particular attention.
43
Appendix A. Notation
The following symbols are used in this paper:
Adowel = dry cross section area of the anchor dowel in mm2;
As= area of steel reinforcement in mm2;
Na= peak load of the specimen featuring FRP anchors in kN;
Nc= peak load of the control specimen in kN;
Ncb = anchor capacity force for concrete cone combination failure mode in kN;
Ncc = anchor capacity force for concrete cone failure mode in kN;
Nd= anchor capacity force for fan-to-sheet debonding failure mode in kN;
Nf r = anchor capacity force for fiber rupture failure mode in kN;
Ns= peak load of the specimen featuring FRP sheets in kN;
d0= hole diameter in mm;
he f = dowel embedment depth in mm;
f0
c= measured concrete compressive strength in MPa;
f0
y= measured steel yield stress in MPa;
fFRP = FRP tensile strength in MPa;
rb= bend ratio at the key portion in degrees;
α= fanning angle in degrees;
β= insertion angle in degrees;
δa= deflection at peak load for the specimens featuring FRP anchors in mm;
δc= deflection at peak load for the control specimen in mm;
δs= deflection at peak load for the specimens featuring FRP sheets in mm;
φdowel = cured dowel diameter in mm;
ϕa= drift at peak load for the specimen featuring FRP anchors in %;
ϕc= drift at peak load for the control specimen in %; and
σFRP = laminate tensile strength of the FRP material.
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