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· The Willamette River Bridge located near Newberg, Ore- The first group of models is those relying on an empirically
gon, was found to have significant diagonal cracking dur- determined value of strain/stress associated with failure of the
ing an inspection conducted by the Oregon Department member for which the shear contribution of the FRP is deter-
of Transportation (ODOT) in late summer of 2001. CFRP mined; the principal equations of the analytical models in this
strips of 12 inch width were applied vertically in a U-shape group are listed in Table 2.1. The second group of models is
wrapping scheme (Williams and Higgins, 2008). those based on the determination of an effective FRP strain; the
· The Ebay Island Viaduct Bridge is a 21/4 mile long section corresponding principal equations are listed in Table 2.2. The
of westbound Washington State Route 2 that crosses over third group of models focuses on the non-uniformity of
environmentally sensitive wetlands near the outflow of the strain distribution in externally bonded FRP reinforce-
the Snohomish River into Puget Sound near Everett, ments; the corresponding principal equations are listed in
Washington. The bridge was built during the late 1960s. Table 2.3. The fourth group of models is mechanics-based
In 1996, bridge condition inspectors noted that the bot- theoretical approaches that do not rely on experimental results
toms of the existing precast concrete webs exhibited con- for regression or calibration; the principal equations of these
siderable concrete spalling accompanied with primary steel models are listed in Table 2.4.
reinforcement corrosion. In 1999, carbon fiber sheets were
bonded to the deteriorated elements for flexural strength-
2.4 Experimental Investigations
ening and to compensate for steel reinforcement loss due
Reported in the Literature
to corrosion. In addition, carbon fiber sheets were applied
with a U-wrap configuration to compensate for the shear A review was conducted of experimental investigations
capacity loss due to the cross-sectional loss of stirrups caused which included studies on (1) the behavior of concrete girders
by corrosion. The carbon fiber repairs were inspected annu- strengthened in shear with externally bonded FRP, (2) bond
ally after the completion of the repair project with no behavior of FRP-concrete interface, and (3) anchorage systems
debonding or deterioration of the carbon fiber plies being to enhance the effectiveness of FRP strengthening systems.
reported through spring 2007 (Dornsife, 2007).
2.4.1 Studies on the Behavior of Concrete
2.3 Existing Analytical Models Girders Strengthened in Shear with
Externally Bonded FRP
This section summarizes the analytical models previously
developed for determining the shear resistance of reinforced The review included 49 experimental studies, encompass-
concrete members strengthened with externally bonded FRP. ing more than 500 test specimens. The review provides infor-
Seventeen models were found in the literature. These models mation on the objectives, the methodology, the experimental
have been divided into four groups based on their approaches program, the test method, the FRP used and its orientation,
and are presented in the same units as the original papers. as well as the strengthening scheme used (configuration).
Table 2.1. Models based on experimentally determined limiting value
of FRP shear strain/stress.
Reference
Equations
Author (Year)
ts hs
2 ave d
2
VP = (for shear strips)
SP
Al-Sulaimani et al. dhw
(1994) VP = 2 ave (for shear wings)
2
dh j
VP = 2 ult (for U-jackets)
2
V f = A f E f vcu d (for FRP oriented at 0/90 degree)
Chajes et al.
(1995) V f = Af E f vcu d 2 (for FRP oriented at 45/135 degree)
* Terms are defined in notations section.

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9
Table 2.2. Models based on an effective FRP strain.
Reference
Equations
Author (Year)
0.9
V frp , d = frp E frp frp , ebw d (1 + cot ) sin
frp
Triantafillou
frp , e = 0.0119 - 0.0205 ( frp E frp ) + 0.0104 ( frp E frp ) when 0 frp E frp 1 GPa
2
(1998)
frp ,e = -0.00065 ( frp E frp ) + 0.00245 when frp E frp > 1 GPa
V f = 0.9 frp E frp fe bw d (1 + cot ) sin (Eurocode format)
Af f fe ( sin + cos ) d f
Vf = (ACI format)
sf
fe = R fu f fe = Rf fu
Based on the effective FRP stress:
R = 0.5622 ( frp E frp ) - 1.2188 ( frp E frp ) + 0.778 0.5 when frp E frp < 1.1 GPa
2
Based on bond mechanism:
0.0042 ( f c' )
2/3
Khalifa et al. w fe
(1998) R=
(E )
0.58
t
frp f fu d f
Effective width:
w fe = d f (complete wrapping)
w fe = d f - Le (U-wrap)
w fe = d f - 2 Le (side bonded)
d 2 f c' bw d
s f ,max = w f + Vs + V f
4 3
Vn = Vc + Vse + V f ,max
d f ( cot + cot f ) sin f
V f ,max = f , ave E f 2nt f w f
sf
d / 2 + 0.5 ( d f - d / 2 )
Hutchinson and f ,ave = f max
Rizkalla
df
(1999) f max = L feC
(
6.134 - 0.580ln t f E f )
L fe = e and C = constant strain rate of 110 ×10-6 mm-1
d cot se = f , ave sin f fs sy
Vse = se E s Av where
s
(continued on next page)

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Table 2.2. (Continued).
V f = 0.9 frp E frp fe bw d (1 + cot ) sin (Eurocode format)
Af f fe ( sin + cos ) d f
Vf = (ACI format)
sf
fe = R fu f fe = Rf fu
Khalifa and Nanni
R is the least of :
R = 0.5622 ( frp E frp ) - 1.2188 ( frp E frp ) + 0.778 0.5
2
(2000)
R=
(f ) c
' 2/3
w fe
738.93 - 4.06(t f E frp ) × 10-6
fu d f
0.006
R=
fu
fk ,e
V fd = 0.9 E f f bw d (1 + cot ) sin (Eurocode format)
f
fk ,e = f ,e max = 0.005 = 0.8 (recommended)
f V f = f f ,e , A E f f ( sin + cos ) bd (ACI format)
f ,e, A = 0.9 f ,e max, A = 0.006
0.56
f 2/3
Triantafillou and f ,e = 0.65 c ×10-3 (CFRP debonding failure mode)
Antonopoulos Ef f
(2000) 0.30
f c2 / 3
f ,e = 0.17 f ,u (shear failure combined with or followed by CFRP fracture)
Ef f
0.47
f c2 / 3
f ,e = 0.048 f ,u (shear failure combined with or followed by AFRP fracture)
Ef f
1/ 0.56
0.65 ×10-3
(E )
f f lim
=
max
f c2 / 3 = 0.018 f c2/ 3
a Af
Vf = f , tot E f eff d f
d sf
eff = 3 ×10-5 × tot
-0.6522
, tot = n f + s
Chaallal et al.
a 1 + 2a / d
(2002)
New deep beam coefficient: f , tot = + (1000 tot - 0.6 ) 1
d 12
but greater than 1 + 2 a / d
12

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Table 2.2. (Continued).
V f = 0.9 frp E frp fe bw d (1 + cot ) sin (Eurocode format)
Af f fe ( sin + cos ) d f
Vf = (ACI format)
sf
fe = R fu f fe = Rf fu
R is the least of :
R = 0.5622 ( frp E frp ) - 1.2188 ( frp E frp ) + 0.778 0.5
2
Pellegrino and
Modena
(2002) 0.006
R=
fu
{
R = R* 0.0042 ( f cm )
2/3
w fe / (E t
frp f )
0.58
fu d }
0 R* = -0.53ln s , f + 0.29 1
s , f = E s Asw E f A f
for continuous fiber sheet:
Vf = wfet f f fe sin2
for FRP strips:
Af f fe ( sin + cos ) d f
Vf =
sf
f fe = Rf fu , fe = R fu
Based on model calibration:
Hsu et al.
R = 1.4871 ( f E f / f c' )
- 0.7488
(2003)
Based on bonding mechanism:
max Le
R= 1
2 f fu t f
max = ( 5 × 10 -6 × f c'2 ) - ( 2.73 × 10 -2 × f c' ) + 925.3 ( English )
max = ( 7.64 × 10 × f -4
c
'2
) - ( 2.73 × 10 -2
×f c
'
) + 6.38 ( Metric )
* Terms are defined in notations section.
Whenever necessary, the review provides comments or com- with U-wrap and side-bonding configurations as well as on
parisons with other studies. The numerical data extracted from the use of mechanical anchorage systems to address the issue
the experimental studies were assembled in a database. of debonding. Also, few tests have been conducted on mem-
The test parameters considered in these studies are listed in bers with spans comparable to those used for bridges, and
Table 2.5. The major test parameters are (a) the geometry of fewer tests have investigated the influence of scale (i.e., model-
the beam used in the experiments, (b) beam type, (c) proper- scale versus large-scale) on the shear behavior of members
ties of concrete and steel reinforcement, (d) types of FRP, and strengthened with FRPs. Furthermore, because FRP is gener-
(e) strengthening schemes. As seen from Table 2.5, most of ally used to strengthen damaged structures, attention needs
these studies have focused on rectangular beams, although to be given to the effects of existing cracks on the behavior of
most RC bridge girders have a T-section with integrated deck the strengthened member.
slabs. The shape of the cross section is related also to the The previously developed analytical models were based
strengthening scheme. For example, rectangular beams are on the studies listed in Table 2.5, the majority of which con-
commonly strengthened by fully wrapping the member, an sidered only small-scale testing. Therefore, this research aimed
impractical solution for T-beams due to the presence of the at expanding the experimental database with results from
flange. Therefore, more focus should be placed on T-beams tests on full-scale T-beams, which are more representative

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Table 2.3. Models that account for non-uniform strain distribution in FRP.
Reference
Equations
Author (Year)
f frp ,ed h frp , e ( sin + cos )
V frp = 2 t frp w frp
frp s frp
f frp , ed = D frp frp ,max
Debonding model:
2
1 - cos
zb 2 if 1
frp , z dz sin
D frp = zt
=
h frp ,e frp ,max d 2
-2
1- if > 1
E frp
frp ,max, d = 0.315 w L f c' f frp
t frp
Chen and Teng
(2003a and 2003b)
Rupture model:
zb
z dz 1+
D frp = =
zt
h frp ,e z ,max 2
f frp
0.8 f frp if max
E frp
frp ,max =
f frp
0.8 max E frp if > max
E frp
Strip spacing limitation:
h frp ,e (1 + cot )
w frp
s frp - min 2
sin
300 mm
for complete wrap:
cos
V f = cr E f t f z
sin
for composite strips:
bf cos
V f = cr E f t f z
s f sin sin
h/2
Carolin and Taljsten
(2005b) f (y)dy
= -h/2
max h
fu
cr = min bond cos 2
c max cos 2

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Table 2.3. (Continued).
h frp
V frp = 2 D f t frp w frp E frp f ,max
s frp
1 for 1.4
-2 1
Cao et al. Df = 1- × for 1.4< < 3
frp 1 - 0.2 ( - 1.4 )
2
(2005)
2.05 for 3
0.427 w 4 f c'
f ,max =
E frp t frp
* Terms are defined in notations section.
Table 2.4. Models derived from mechanics-based approaches.
Reference
Equations
Author (Year)
V f = ht p Q13 2 + Q231 +
(Q 12 2 + Q221 )
tan (c )
Malek and hv Fy
Saadatmanesh Vs = Es y Av for y <
(1998) tan (c ) s Es
hv Fy
Vs = Fy Av for y
tan (c ) s Es
Discrete formulation:
Vr = 0.25k 2 f c' ( Acf tan f + Acw tan w ) + Tv ns + TFRP
Continuous formulation:
ds
Vr = k f c' Ac (Tv + TFRP ) - Tv
s
k = 2.1( f c' )
-0.4
Tv = Av f vy
2
w frp sin
Deniaud and Cheng
TFRP = d FRPtE frp max RL + ( ns + 1) cos sin
(2001, 2004) s frp tan w
2
w frp s
TFRP = d FRPtE frp max RL sin + cos sin
s frp ds
Maximum allowable strain in FRP:
3 fc' d FRP
0.16
max = (%) ultFRP
( tE )
0.67
frp (ka sin )0.1
Remaining bonded width over initial width ratio:
0.4
d FRP
RL = 1 - 1.2 exp -
k e Leff sin
(continued on next page)

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Table 2.4. (Continued).
Side bonding:
1 sin w f
VRd , f = min {0.9 d , hw } f fed 2t f
Rd sin p f
design effective stress for side bonding:
2
z rid ,eq leq
f fed = f fdd 1 - 0.6
min{0.9d , hw } z rid ,eq
sf
zrid ,eq = min {0.9d , hw } - le - sin
f fdd / E f
U-wrap or complete wrapping:
1 wf
VRd , f = 0.9d f fed 2t f ( cot + cot )
Rd pf
design effective stress for U-wrapping:
1 le sin
f fed = f fdd 1 -
3 min{0.9d , hw }
Monti and Liotta design effective stress for complete wrapping:
(2005)
1 l e sin 1 l e sin
f fed = f fdd 1 - + ( R f fd - f fdd ) 1 -
6 min {0.9 d , hw } 2 min {0.9 d , hw }
Ef tf where: f ctm = 0.27 Rck 2 / 3
le =
2 fctm
0.80 2E f Fk
f fdd =
f ,d tf
2 - wf p f
where: Fk = 0.03kb f ck f ctm kb = 1
1 + w f 400
w f min ( 0.9d , hw ) sin ( + ) sin
lb l
f fdd ( lb ) = f fdd
2- b (for lb < le)
le le
r r
R = 0.2 + 1.6 c where 0 c 0.5
bw bw
a 2 + d 2 - (1 - 2 ) a (a + d ) - a 2 2
= if <
cu 2d 2 ( a2 + d 2 )
(a 2
+ d2 ) -a 1
= (1 - ) if
Sim et al.
(2005)
cu 2 (a 2
+d 2
) 2
1 1
= if >
cu 2 2
V and Af Ap f py
= = v sy + ( sin + cos )
bh b e cu b t cu
* Terms are defined in notations section.

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Table 2.5. Summary of experimental studies.
Properties and Parameters
Concrete Type of
Number of Tests
Geometry Type of Beam and Steel FRP Strengthening Scheme
Rectangular Section
Two-Side Bonding
Concrete Strength
Beam Spanning
Beam Spanning
Beam Spanning
Complete Wrap
Regular Beams
Angle to Long.
Angle to Long.
Reinforcement
Reinforcement
7 ft

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Table 2.5. (Continued).
Properties and Parameters
Concrete Type of
Number of Tests
Geometry Type of Beam and Steel FRP Strengthening Scheme
Rectangular Section
Two-Side Bonding
Concrete Strength
Beam Spanning
Beam Spanning
Beam Spanning
Complete Wrap
Regular Beams
Angle to Long.
Angle to Long.
Reinforcement
Reinforcement
7 ft

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of FRP sheet-concrete interfaces have been widely studied. and the local bond stress-slip relationship. Bond behavior is
Various test methods have been developed to evaluate the influenced by the mechanical and physical properties of the
average interfacial bond strength. These methods include concrete, FRP composite, and adhesive; the influencing fac-
single-lap-type, double-lap-type, bending-type, and inserted- tors are listed in Table 2.6.
type tests, as shown in Figure 2.1. Among the interface param- In evaluating FRP-concrete interface bond behavior, the
eters evaluated are average shear bond strength, effective bond bond stress-slip (-s) relationship is the most important
length, maximum shear bond stress, interfacial fracture energy, factor. For FRP sheets bonded to concrete, this relationship
Load
Load Load
Concrete
Rebar
FRP
Notch FRP
Concrete
Bond Length
(a) Single-lap shear bond test (b) Double-lap shear bond test
Load
Steel
Plate
Load Load
FRP
Concrete
Notch
FRP
Bond Length
(c) Bending-type shear bond test (d) Inserted-type shear bond test
Figure 2.1. Test methods to evaluate the bond strength.

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Table 2.6. Factors influencing the bond behavior at
FRP-concrete interface.
Elements Influencing Factor
Modulus of elasticity, thickness, surface
Concrete condition, strength, drying shrinkage, water
content
Modulus of elasticity, strength, thickness,
Continuous Fiber Sheet
stiffness, length/width of sheet, weave
FRP
Bonding Resin
application Modulus of elasticity, strength, glass
Primer
transition temperature, spread
Putty
Loading condition Bending, shearing, punching, cyclic
Ambient temperature, moisture, sun light
Environmental actions
radiation, etc.
is determined by the strain distributions in the FRP, and exceeds the effective bond length, no further increase in fail-
the local bond stresses measured in the FRP sheets. Several ure load can be achieved. However, a longer bond length may
empirical -s relationships have been proposed including a delay complete debonding and thus improve the ductility.
elasto-plastic model (Sato et al., 1997 and De Lorenzis et al., Several studies have been performed to determine effective
2001); a bilinear model based on interfacial fracture energy bond length. Figure 2.4 shows the effective bond lengths cal-
(Yoshizawa et al., 2000); a model based on the Popovic's culated by analytical models and equations stipulated in
expression (Nakaba et al., 2001); and a shear softening model many current code and design guidelines versus the rigidity
(Sato et al., 2000). of FRP reinforcement (Ef f). As shown in the figure, most
The experimental studies have shown that the bond shear studies have reported that effective bond length increases as
stress at the FRP-to-concrete interface increases rapidly with the stiffness of FRP sheets increases. However, two studies
increases in the interfacial slip until it reaches the peak stress (Maeda et al., 1997 and ACI 440.2R-08) show a different
(bond strength) as illustrated in Figure 2.2. After this point, trend, probably because these models were derived using a
interfacial softening (or micro-cracking) starts, together with very limited experimental database.
a decrease in the interfacial shear stress and an increase in the The analytical models for effective bond length and bond
interfacial slip. strength were derived based on small-scale tests; the bond
There is no agreement among researchers on the shape behavior of full-size beams may be different than that pre-
of the model, however, use of fracture mechanics implicitly scribed by these models. Thus, full-scale tests would provide
leads to a very simple generic expression that considers only data to calibrate/improve these models.
the FRP stiffness and interfacial fracture energy (defined as
the area beneath the bond stress-slip curve) for the determi-
2.4.3 Anchorage Systems to Enhance
nation of bond capacity. Debonding occurs first within the
the Effectiveness of FRP
effective bond length (defined as a length over which the
Strengthening Systems
majority of the bond stress is maintained, see Figure 2.3) as
a result of debonding of a very thin layer of concrete rather When a proper anchorage system is not provided, failure
than debonding at the FRP/concrete interfaces. When the of FRP-strengthened reinforced concrete members is com-
bonded length of FRP along the FRP-concrete interface monly manifested by debonding of the FRP. Therefore, vari-
Bond Stress Bond Stress Bond Stress
Slip Slip Slip
(a) Cutoff type (b) Bilinear type (c) Tensile softening type
Figure 2.2. Various bond stress-slip models.

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Le technique requires no surface preparation work but con-
siderable labor for cutting the grooves.
99.99 % of Max Load Another system used to prevent debonding of FRP is anchor
99.9 % of Max Load spikes (Eshwar et al., 2003; Eshwar et al., 2008; Orton, 2007;
Local bond stresses
96.0 % of Max Load Niemitz, 2008). Each anchor spike consists of a precured fiber
80 % of Max Load portion and a dry fiber portion (see Figure 2.6). The anchor
50 % of Max Load spikes may be constructed in situ. First, fibers are bundled
20 % of Max Load together, and half of the fiber length is covered with plastic or
duct tape. The uncovered bundled fibers are then impreg-
nated and thoroughly saturated with resin. Finally, the satu-
rated fibers are passed through a circular hole in a steel plate,
or die, to obtain the desired diameter of the anchor spikes.
The dry fibers are used for bonding purposes and trimmed to
Free Loaded end
the appropriate length according to specific requirements.
Figure 2.3. Concept of effective bond length based Following surface preparation of the concrete, holes of the
on stress distribution (Ueda and Dai, 2005). desired diameter and depth are drilled and partially filled
with saturant. The laminate is then applied, and while it is
wet, the precured portion of each spike anchor is inserted into
ous types of anchorage systems, including the near surface the holes. The dry fibers are spread around the layer in a
mounted system (NSM), fiber reinforced polymer anchor circular fashion, and a layer of saturant is then applied (see
spikes, additional horizontal strips, and various mechanical Figure 2.6).
anchorage systems have been studied to evaluate their effect An additional horizontal FRP strip applied on top of the ver-
on FRP failure by debonding. tical FRP strips has also been used as an anchorage system
Many experimental studies have demonstrated the effec- (Hutchinson and Rizkalla, 1999; Schnerch, 2001). This tech-
tiveness of the NSM system (Khalifa and Nanni, 2000; De nique is very easy to install and requires no more labor than
Lorenzis, 2002; Micelli et al., 2002). In this system, a bent other anchorage systems. However, different levels of effective-
portion of the end (or a region near the end) of the FRP ness have been reported. Schnerch (2001) reported that the hor-
reinforcement is embedded into the concrete, as shown in izontal strip neither delays nor prevents debonding, and it does
Figure 2.5. For fiber sheets, the bend is created during wet not increase the contribution of the FRP to the shear strength
lay-up, and in the case of laminates, it is pre-formed. This of the beam at failure. Test results reported by Hutchinson
12
Maeda et al. (1997)
Neubauer and Rostasy (1997)
Niedermeier (1996)
10 JCI (2003) - Sato Model
JCI (2003) - Iso Model
Chen and Teng (2001)
Effective Bond Length, Le (in.)
8 Niu and Wu (2000)
Kanakubo et al (2003) -1
Kanakubo et al (2003) -2
Ueda and Dai (2004)
6
Ueda and Dai (2005)
Foster and Khomwan (2005)
Miller and Nanni (1999)
4 Ben Ouezdou et al. (2008)
ACI 440 (2008)
CSA S806 (2002)
2 fib-TG9.3 (2001) Appendix 1
fib-TG9.3 (2001) Appendix 2
Eurocode 8-3 (2004)
Concrete Society (2004)
0
100 150 200 250 300 350 400 450
Stiffness of FRP reinforcement, Ef tf (kip/in)
Figure 2.4. Effective bond length versus FRP rigidity.

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20
The four methods used to anchor the FRP sheets as shown
in Figure 2.7 are (a) nail type, (b) semi-closed type, (c) sub-
variation of semi-closed type, and (d) closed type.
Sato et al. (1997) concluded that the shear strength of
beams can be improved by transverse wrapping of FRP sheets
if adequate anchoring is provided by steel plates and bolts and
recommended the use of long anchor bolts that penetrate the
full web. This anchorage system, however, creates stress con-
centrations where the anchors are placed, and the bolts lead
to discontinuity of the FRP system.
Matthys (2000) conducted a project to strengthen four
continuous reinforced concrete beams in shear and flexure,
by supporting them with masonry columns. Bond/anchorage
tests indicated a 44% increase in anchorage capacity with
the use of steel bolted connections. Mechanical anchorage
resulted in a less brittle failure mode due to the transition to an
external tensioning system after debonding and to increased
displacements resulting from CFRP slip.
Schuman (2004) conducted a comprehensive study on
Figure 2.5. Construction of a NSM Anchorage System.
anchorage systems for shear strengthening of reinforced
concrete (RC) beams. A mechanical anchorage system was
and Rizkalla (1999) indicated that using the horizontal strip applied to increase the shear contribution of CFRP systems
increased the shear contribution of FRP by 16 percent. by embedding anchor rods into the cross section with various
Mechanical anchorage systems have been used widely to bearing plates, (e.g., GFRP plate). The anchorage systems are
prevent premature FRP debonding. Steel angles, steel or FRP possible, the four methods described by Schuman (2004) can
composite plates, and anchor bolts are examples of most be summarized as (1) complete wrapping through the flange
commonly used mechanical anchorage systems. (called complete wrap), (2) FRP laminate extended into the
Sato et al. (1997) conducted a series of tests using various flange, (3) bonded steel anchors with bearing plates (called
anchoring methods to develop a shear strengthening tech- two-side bonding), and (4) GFRP plate anchors.
nique for beams and a method of estimating their effective- The two particularly important conclusions from Schuman's
ness. The test results showed that sufficient strength can be (2004) research are (1) the FRP composite alone provides the
achieved only if the CFRP sheets are mechanically anchored. T-beam with little additional ultimate load and displacement
capacity and creates a more brittle failure mode and (2) the use
of properly embedded and sized anchors allows the vertical ties
to remain intact during failure. These anchors then force a
more ductile compression zone and ensure a shear/flexural
failure mode.
Schuman (2004) also concluded that short anchors (Fig-
ure 2.8) lead to an increase in load carrying and displacement
capacity and cause the CFRP reinforcement to be activated
before the steel reinforcement yields but deeper anchors (Fig-
ure 2.8) allow the CFRP reinforcement to be activated earlier,
thus delaying yielding in the steel stirrups.
For all mechanical anchorage systems configurations, the
embedment length, diameter of the anchor, and the bearing
strength of the plate are primary considerations. Regarding
embedment length, longer anchors are more effective, but
they increase the amount of labor required and present the
risk of damaging the concrete and steel reinforcement. The
diameter of the anchor must be chosen based on the failure
modes of the connection (e.g., bearing of the plate, spalling of
Figure 2.6. Anchor spikes. concrete, and yielding or rupture of the anchor).