Strength and Ductility of 

Concrete Beams Reinforced with 

Carbon FRP and Steel 

Dat Duthinh 

Monica Starnes 

U.S. DEPARTMENT OF COMMERCE 

Tech no logy Ad ministration 

Building and Fire Research Laboratory 

National Institute of Standards 

Gaithersburg, MD 20899 

and Technology 

- 

d 

0 

0 

0 

NlST CENTENNIALM 

- I 

td 

- 

National Institute of Standards 

and Technology 

Technology Administration 

U.S. Department of Commerce 

Strength and Ductility of 

Concrete Beams Reinforced with 

Carbon FRP and Steel 

Dat Duthinh 

Monica Starnes 

U.S. DEPARTMENT OF COMMERCE 

Techno logy Ad mi n ist rat ion 

Building and Fire Research Laboratory 

National Institute of Standards 

Gaithersburg, MD 20899 

and Technology 

November 2001 

U.S. DEPARTMENT OF COMMERCE 

Donald L. Evans, Secretary 

TECH NOLOGY ADMINISTRATION 

Phillip J. Bond, Under Secretary 

of Commerce for Technology 

NATIONAL INSTITUTE OF STANDARDS 

AND TECHNOLOGY 

Karen H. Brown, Acting Director 

ABSTRACT 

Seven concrete beams reinforced internally with varying amounts of steel and externally with 

carbon fiber-reinforced polymer (FRP) laminates applied after the concrete had cracked under 

service loads were tested under four-point bending. Strains measured along the beam depth 

allowed computation of the beam curvature in the constant moment region. Results show that 

FRP is very effective for flexural strengthening. As the amount of steel increases, the additional. 

strength provided by the carbon FRP laminates decreases. Compared to a beam reinforced 

heavily with steel only, beams reinforced with both steel and carbon have adequate deformation 

capacity, in spite of their brittle mode of failure. Clamping or wrapping of the ends of the 

laminate enhances the capacity of adhesively bonded FRP anchorage. Design equations for 

anchorage, allowable stress, ductility, and amount of reinforcement are discussed. 

Keywords: anchorage, beam, carbon fiber-reinforced polymers, ductility, flexure, FRP, 

reinforced concrete, repair, strengthening. 

DISCLAIMER 

Certain trade names and company products are mentioned in the text or identified in an 

illustration in order to adequately specify the experimental procedure and equipment used. In no 

case does such an identification imply recommendation or endorsement by the National Institute 

of Standards and Technology, nor does it imply that the products are necessarily the best 

available for the purpose. 

... 

111 
Contents 

1 . 

2 . 

3 . 

4 . 

5 . 

Introduction and Review ...................................................................................................... 1 

1.1. Ductility ................................................................................................................... 2 

1.2. Anchorage ................................................................................................................ 3 

Approach 4 

2.1. Beam Design ............................................................................................................ 4' 

2.2. Test Set-Up .............................................................................................................. 5 

.............................................................................................................................. 

2.3. External Strengthening ............................................................................................. 5 

................................................................................................................ 

.......................................................................................................... 

.................................................................................................................................. 

2.4. Anchorage 7 

Theoretical Prediction 7 

Results 8 

........................................................................................................................ Conclusions 13 

.......................................................................................................................................... 

...................................................................................................................................... 

.......................................................................................................................... 

Notation 14 

References 15 

Acknowledgments 16 

iv 
Strength and Ductility of Concrete Beams 

Reinforced with Carbon FRP and Steel 

1. Introduction and Review 

The use of fiber-reinforced polymer (FRP) composites for the rehabilitation of beams and slabs 

started about 15 years ago with the pioneering research performed at the Swiss Federal 

Laboratories for Materials Testing and Research, or EMPA (Meier, 1987). Most of the work 

since then has focused on timber and reinforced concrete structures, although some steel 

structures have been renovated with FRP as well. The high material cost of FRP might be a 

deterrent to its use, but upon a closer look, FRP can be quite competitive. In addition to their 

resistance to corrosion, FRP have high ratios of strength and stiffness to density. The light 

weight of FRP provides considerable cost savings in terms of labor: a worker can handle the FRP 

material, whereas a crane would be required for its steel equivalent. FRP laminates and fabric 

come in great lengths, which can be cut to size in the field, as compared with welding of steel 

plates. FRP laminates or fabric are thin, light and flexible enough to be inserted behind pipes, 

electrical cables, etc., further facilitating installation. With heat curing, epoxy can reach its 

design strength in a matter of hours, resulting in rapid bonding of FRP to the structure and 

consequently, minimum disruption to its use. 

The tensile strength of FRP can exceed 3000 MPa (compared to 400 MPa for reinforcing steel), 

and their stiffness ranges from slightly greater than that of steel for high-modulus carbon to 

about 1/3 that of steel for S-glass. FRP do not exhibit plastic yielding as steel does, however, and 

behave elastically up to an ultimate strain in the range of 1.5 % to 5 % (compared with a range of 

15 % to 20 % for reinforcing steel). This brittle behavior must be accounted for in structural 

design. 

Where FRP composites are used as external reinforcement in the rehabilitation of reinforced 

concrete (RC) beams and slabs, they increase the strength (ultimate limit state) and the stiffness 

(serviceability limit state) of the structure. Structural rehabilitation with FRP is thus motivated by 

requirements for earthquake strengthening, higher service loads, smaller’ deflections, or simply 

the need to complement deficient steel reinforcement. Care must be used to ensure that the 

concrete surface to which the strengthening is applied is sound, and the bonding between FRP 

and concrete is good. The increase in strength and stiffness is sometimes realized at the expense 

of a loss in ductility, or capacity of the structure to deflect inelastically while sustaining a load 

close to its capacity. 

A number of issues still impede the routine use of FRP as a structural strengthening material. 

Chief among them is the absence of a long record of use, causing concern about durability with 

potential users. Another concern is fire resistance, especially as rehabilitation with FRP expands 

from highway bridges to buildings. The absence of standards is also an impediment, but this is 

being remedied through the efforts of various individuals and organizations such as the 

American Concrete Institute. At the time of this writing, ACI Committee 440 has produced a 

draft “Guide for the Design and Construction of Externally Bonded FRP Systems for 

Strengthening Concrete Structures ”. The Canadian Standards Association (2000), the 

1 
(European) Federation Internationale du Beton (200 l), the (British) Concrete Society (200 l), and 

the Japan Building Disaster Prevention Association ( 1999) have published similar documents. 

Recently, Naaman et al. (2001, 1999) reported on a series of tests of RC beams strengthened in 

flexure or shear with carbon FRP and loaded under static or cyclic loads, at room or low 

temperatures. The test parameters included the amounts of reinforcing steel and FRP, concrete 

cover thickness and condition (with repair mortar used to simulate damaged concrete), and 

anchorage configurations. The work includes a Substantial review of the literature, which is 

updated here. The authors found that, for a given reinforcement ratio, the ultimate load capacity 

increased but the ultimate deflection, and therefore ductility, decreased with the strengthening 

level. The three beams with various anchorage conditions (extended length, perpendicular wrap 

or normal condition, Le., with no extra effort to enhance anchorage) had the same ultimate load 

and deflection. Naaman et al. recommended limiting the increase in strength due to FRP to 20 % 

of the nominal flexural strength of the beam with the maximum steel reinforcement ratio allowed 

by the ACI 3 18 Code (American Concrete Institute, 1999). 

1.1 Ductility 

Ductility is a desirable structural property because it allows stress redistribution and provides 

warning of impending failure. Steel-reinforced concrete beams are under-reinforced by design, 

so that failure is initiated by yielding of the steel reinforcement, followed, after considerable 

deformation at no substantial loss of load carrying capacity, by concrete crushing and ultimate 

failure. This mode of failure is ductile and is guaranteed by designing the tensile reinforcement 

ratio to be substantially below (ACI 318 requires at least 25 % below) the balanced ratio, which 

is the ratio at which steel yielding and concrete crushing occur simultaneously. Thereinforcement ratio thus provides a metric for ductility, and the ductility corresponding to the 

maximum allowable steel reinforcement ratio provides a measure of the minimum acceptable 

ductility . 

The design of FRP external reinforcement for flexure is fairly rational and straightforward. It is 

based on Bernoulli’s hypothesis of strain compatibility that plane sections remain plane, which 

requires perfect bonding between FRP and concrete, and the ability of the concrete to transfer 

stresses to the FRP laminate by shear. In a beam reinforced internally with steel and externally 

with FRP, there is usually substantial reserve capacity at steel yielding. After the steel 

reinforcement yields, the beam can still carry increasing loads, albeit at a lower rate (with respect 

to deflections) than prior to steel yielding, and the FRP maintains elastic behavior until failure 

occurs suddenly. Failure is precipitated by FRP debonding, rupturing, or concrete crushing. All 

of these modes of failure are brittle, i.e., load capacity is reached with little inelastic deformation. 

The FIB (Federation Internationale du Beton) Bulletin FRP Reinforcement fur Concrete 

Structures (2001) notes that, if the design is governed by the Serviceability Limit State, the 

amount of FRP provided to the structure may be considerably higher than what is needed for the 

Ultimate Limit State. In this case, it may be difficult to fulfill ductility requirements 

(Triantafillou et al. 2001). 

2 
The Canadian Highway Bridge Design Code (CHBDC, 2000), based on the work of Jaeger et al. 

(1 997), assesses the ductility of FRP-strengthened sections with a performance factor equal to 

Mu 4~ , where M and @ are the beam moment and curvature and the subscripts u refer to the 

ultimate state, and 0.001 to the service state that corresponds to a concrete maximum 

compressive strain of 0.001. This performance factor must be greater than 4 for rectangular 

sections and greater than 6 for T-sections. 

M.oo,4.ool 

1.2 Anchorage 

Debonding or anchorage failure of the FRP occurs in the majority of tests of beams strengthened 

for flexure (64 % according to a survey by Bonacci, 1996). In only 22 % of the tests surveyed, 

rupture of the FRP was achieved, with the rest of the beams failing in shear or compression. It is 

not unusual for a carbon FRP laminate to debond at strains about half of its ultimate strain, 

oftentimes due to weakness in the concrete substrate rather than in the epoxy. In order to achieve. 

a more efficient use of this expensive material, more research on anchorage, development length 

and bond stress distribution is called for, e.g., research on the use of clamps, anchor bolts, Ushaped straps or wraps near the laminate ends, and staggered cut-off of multi-layer laminates. 

Smith and Teng (2001) reviewed existing models of debonding of the laminate end, either by 

separation of the concrete cover or interfacial debonding of the FRP laminate from the concrete. 

They found that, with only one exception, the models developed for steel-plated concrete beams 

gave better predictions than those developed especially for FRP-laminated concrete beams. On 

the other hand, Aprile et al. (2001) showed that RC beams strengthened with elasto-plastic steel 

plates or elastic-brittle carbon laminates exhibit rather different behaviors. The steel plate yields 

before the internal reinforcement does, whereas no such behavior exists for the carbon laminate. 

Also, bond stress distribution in the shear span is different for steel plates than for carbon 

laminates. 

According to Neubauer and Rostasy’s work (1997, also in Rostasy, 1998, and Jensen et al. 

1999), which has been adopted by the (British) Concrete Society in its Design Guidance For 

Strengthening Concrete Structures Using Fibre Composite Materials (2000), and the German 

Institute of Construction Technology ( 1997), the capacity of adhesively bonded anchorage is: 

N 

2 - w/b where k =LO6 21.0 is a factor that accounts for the relative width w of the 

laminate and b of the concrete member, EL is the modulus of elasticity, t the thickness of the 

1+ w/400 

F f F \=I3 

laminate, - = 0.18 - is the concrete 

cube compressive strength. The anchorage length 

J 

MPa [$aJ 

--- 

E, t MPa 

mm MPa mm f, 

surface pull-off strength, and &be the concrete 

needed to achieve this anchorage capacity is: 

(2) 

3 
The formulas above only apply for 1.5 MPa 5 f,, I 3.0 MPa. An anchorage length longer than 

Zmax does not increase the ultimate bond force above TW. Application of these formulas to the 

beams used in this study is presented in a later section. 

An alternative criterion recommended by the Concrete Society (2000) to prevent premature 

peeling failure is to limit the longitudinal shear stress between the FRP and the concrete substrate 

to 0.8 MPa, a value based on steel plate bonding. The longitudinal shear stress should be checked 

at the plate ends, where the shear force acting on the strengthened portion of the member will be 

at its greatest, and at the location in the span where the steel reinforcement first yields. Designers 

should also keep in mind that debonding of the laminate usually starts where there is significant 

shearing displacement across diagonal or transverse cracks (Swamy and Mukhopadhyaya, 1999). 

2. Approach 

The issues addressed by the study reported in this paper are: 

1. What is the flexural strength enhancement provided by FRP laminates, and is this 

enhancement predict able? 

2. How ductile is the flexural behavior of concrete beams reinforced with steel and FRP? 

3. How effective is clamping or wrapping of the FRP laminate in enhancing anchorage? 

2.1 Beam Design 

To address these issues, a series of seven beams was tested. All beams had nominal dimensions 

of 150 mm width x 460 mm height x 2950 mm length, but the amount of flexural reinforcement, 

both steel and carbon FRP, varied. In Table 1, the beam number refers to the U.S. size of the 

flexural steel reinforcement, e.g., beam 5 contains two #5 (16 mm) bars. Beam 9, with no carbon 

FRP, was a reference beam, and beam 10, with the maximum flexural steel ratio allowed by ACI 

3 18, was not fabricated but was used in calculations. The nominal concrete strength was 40 MPa 

and the nominal yield strength of the steel reinforcement was 4 15 MPa. 

Table 1 : Beam Properties 

I 

5 I 156 

9 I 159 

10+ 1 152 

+ not fabri :ated, contains maximum permitted steel ratio 

* diagonal wrap 

4 
Shear and bearing steel reinforcements were provided in ample amount to ensure that failure 

occurred by flexure only. The shear reinforcement consisted of $43 bars (10 mm) in closed 

horizontal loops spaced at 120 mm and #3 vertical stirrups spaced at 100 mm and terminated by 

135" hooks (Figs. 1 and 2). Bearing reinforcement in the form of #3 loops were placed under the 

bearing plates (Fig. 1). 

2.2 Test Set-Up 

The beams were cast with the compression side up but were tested under four-point loading with 

the tension side up for ease of application of the FRP laminate (Fig. 1). An array of eight LVDTs 

(linear variable differential transformers), 100 mm in gage length, spaced evenly over the sides 

of the beam, parallel to its axis, and supplemented with strain gages on the concrete, steel and 

carbon FRP laminate measured the strain profile of the beam at midspan (Figs. 1 and 2). Three 

additional LVDTs measured the deflections of the beam under its supports and at midspan. 

2.3 External Strengthening 

In most cases, strengthening was performed with the application of carbon FRP laminates shortly 

after the first flexural cracks appear, at about 1/3 of the calculated ultimate moment of the 

(virgin) beam reinforced with steel only. For beams 4a and 4b, the FRP laminate was applied at 

a higher ratio of the ultimate moment of the virgin beam (MR/.V = 68 % and 52 % respectively), 

as might occur in lightly reinforced beams (Table 1). Load was maintained during the application 

of the FRP laminate and curing of the adhesive. 

External strengthening followed the procedures recommended by the manufacturer. The 

concrete surface was roughened with a scaler to expose the aggregate, then cleaned by air jet and 

acetone to rid it of loose particles and dust. The adhering face of the carbon laminate was also 

cleaned with acetone. A two-part adhesive (black and white) was mixed in 3:l proportion, until 

the color was a uniform gray, then applied with a special tool to the concrete surface to a width 

of 52 mm (104 mm for beam 4b) and a thickness of 1.5 mm. The adhesive was also applied to 

the laminate to the same thickness. The laminate was then placed on the concrete, epoxy to 

epoxy, and a rubber roller was used to properly seat the laminate by exerting enough pressure so 

the epoxy was forced out on both sides of the laminate and the adhesive line did not exceed 

3 mm in thickness. The carbon laminate was then covered with a heating tape and left' 

undisturbed to cure for 24 hours. The heating tape temperature was warm to the touch and 

estimated to be about 50" C. 

Slant-shear tests: To measure the bond strength of the adhesive, three slant-shear tests similar to 

ASTM test method C 882 were performed. In each test, a concrete cylinder 100 mm in diameter 

and 200 mm in height was sawed in half along a 30" angle to its axis. A strip of carbon FRP 

140 mm x 50 mm was bonded to both halves following the manufacturer's recommended 

procedures described above, with the rest of the matching surfaces of the concrete cylinder 

halves covered with Teflon@ tape. Compression of the test specimens subjected the adhesive to a 

shear force and a normal compressive force in the ratio of cosine 30" to sine 30". Failure 

occurred in the concrete and not at the interface of concrete with adhesive. Results showed that 

5 
one day dry cure was sufficient to develop the bond strength of the adhesive, calculated as the 

ratio of the shear force to the bonded area (Table 3). 

Bond strength (MPa) Tensile 

Concrete-concrete Carbon-concrete (measured here) strength 

2 day 14 day 1 day 2 day 7 day 7 day 

22.0 21.3 20.1 17.4 21.0 24.8 

dry cure moist cure dry cure dry cure dry cure (MPa) 

Table 2 Properties of carbon laminate 

Shear Ultimate 

strength strain 

14 day 7 day 

(MPa) (%) 

24.8 1 

*linear up to a stress of 2500 MPa and a strain of 1.60 %. 

Tensile Ultimate Thickness Modulus of 

strength strain elasticity 

960 MPa 1.33 % 0.33 mm 73.1 GPa 

Table 3 Properties of adhesive (from manufacturer, except where noted) 

StrengtWwidth Masdarea 

3 16 kN/m/layer 230 g/m’ 

Tensile strength 

30 MPa 

Ultimate strain 

1.5 Yo 

Table 5 Properties of impregnating resin (from manufacturer) 

Tensile tests: Two tensile specimens of the carbon FRP laminate 50 mm in width by 508 mm in 

total length were tested to failure. The ends of the specimens were 140 mm long and consisted 

of three layers of the laminate bonded together with the same adhesive as the one used for 

bonding to concrete. The adhesive thickness was 3 mm in specimen 1, and 1.5 mm in specimen 

2. To enhance friction, four layers of emery cloth were inserted between each face of the 

specimen and the machine grips. Failure occurred suddenly in the middle, single thickness 

region. Specimen 1 behaved linearly up to failure, whereas specimen 2 exhibited some nonlinearity toward the end of the test (Table 2). The testing machine recorded directly the tensile 

load and deformation, from which stress and strain were obtained. The modulus of elasticity was 

obtained by fitting a straight line over the linear portion of the stress-strain curve, which was 

most of the curve for specimen 1 and up to 2500 MPa for specimen 2. Since only two tensile 

tests were conducted, and the FRP laminates never failed in tension in the beam tests, the 

manufacturer’s material properties were used for analysis. 

6 
2.4 Anchorage 

The carbon laminate was 2440 112171 long and covered the middle of the tension face of the beams, 

leaving gaps of 50 mm between it and the load bearing plate at each end. For beams 4a, 6 and 

7N, clamps torqued to 400 N.m applied compressive forces estimated (from thread geometry and 

estimated fiction coefficient) to be between 15 kN and 25 kN onto the end 200 mm of the 

laminate (Fig. 3). 

For the other beams, carbon fiber fabric wraps 200 mm in width, placed on both sides of the 

beam, were used to anchor the carbon laminate. For beam 4b, six layers of wrap were placed 

diagonally at each end. For beams 5 and 8N, two layers of wrap were used, diagonally at one 

end, and transversely at the other (Fig. 4). The wrap application followed this procedure: 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

3. 

A 

Round-off concrete beam edges to a radius of 15 rnm; 

Smooth out epoxy at edges of laminate to ensure that epoxy thickness decreased fiom 3 rnm 

to 0 at a gradual slope; 

Clean concrete surface; 

Apply impregnating resin onto concrete surface with a paint brush; 

Place wrap fabric onto resin with gloved hands and smooth out; 

Work out any irregularities or air pockets with a plastic laminating roller; 

squeeze out between the rovings of the fabric; 

Apply additional resin and repeat if additional layers are required; 

Add a final layer of resin onto the exposed layer. 

let the resin 

Theoretical Prediction 

computer program was developed to calculate the moment and curvature of rectangular 

concrete beams under uniform moment, with internal steel and external carbon FRP 

reinforcements. Fig. 5 shows the assumed model used in the following steps: 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

Assume a value of compression depth c ; 

Assume a value of concrete compressive strain at extreme fiber ccM ; 

Calculate beam curvature: 1 = ; 

re 

d-c 

Compute steel strain: E,~ = - ; 

r 

h-c Determine strain in extreme tension fiber: E, = - ; 

Estimate laminate strain: E~ = E~ - E;, where the tensile strain on the concrete surface at FRP 

laminate application, Ei , is calculated from the applied load. Since the FRP laminate is 

applied with the beam under an initial load, the FRP strain is less than that based on the strain 

profile obtained from steel and concrete; 

r 

Compute concrete compressive strain as a function of distance from neutral axis: E, = - ‘cM y , . C 

Calculate force in steel: F, = A, E, E, 5 A, fy ; 

7 
9. 

10 

11 

Estimate laminate force: F‘ = 0 if E, I 0 or E, ;1 E,~; FL = A, EL E, otherwise; 

/ \2 

Determine concrete stress based on Hognestad’s parabola: 

f, Eo 

Calculate concrete force by integration of stresses: Fc = bf, 

C(4EO -&,d . 12. Locate center of concrete force (from concrete face): a = 

13. Check force equilibrium: F‘ = F, + Fr, ? 

if no, return to step 2 and assume another value of E,, ; 

14. If yes, compute moment: M = F, (d - a) + FL (h - a> ; 

15. Check for concrete crushing: E, 2 E,, ? 

4(3Eo-&,M) ’ 

if yes, beam has failed. If no, return to step 1 and assume another value of c. 

The model predicts that all the beams tested would fail by concrete crushing, including beam 4a, 

which would come close to achieving FRP rupture. The model needs hrther improvement to 

incorporate debonding or anchorage failure. In addition, the ultimate moment and curvature of 

under-reinforced steel RC beams were calculated by the current ACI 318 (1999) method. The 

following equations, based on the rectangular stress block, were used: 

(0.85f,)(0.75c)b = A,, f, 

M, = A., fy (d - 0.75~12) 

#u = E,, lc 

The concrete strength fc was estimated from linear regression of results of compressive tests 

performed within a day of the beam tests (Fig. 6). 

4. Results 

Strains obtained at midspan with LVDTs and strain gages allowed the calculation of the beam 

curvature and the tensile strain on the concrete surface when the laminate was applied (from 

linear extrapolation). This strain value is added to the strain of the laminate measured by the 

strain gage to obtain a “modified” strain. If there is no slip between laminate and concrete, the 

modified laminate strain would fall on a straight line with the other strains measured at midspan. 

In general, but not in all cases, the measurements showed a roughly linear distribution, implying 

that plane sections remained plane and there was no slip of the laminate. Straight lines were fit to 

the strain profiles, and the slopes of these lines gave the curvatures. 

The slender RC beams behaved in expected fashion under flexural loading. As loads increased, 

flexural cracks increased in number, width and depth. Shear cracks and flexural-shear cracks 

also appeared, propagating diagonally from the loads to the supports. The widest cracks, and 

oftentimes the ones that proved critical, started as flexural cracks opposite the loads, then 

propagated vertically over the entire depth of the beam due to a combination of flexure and 

vertical shear. There was considerable vertical shearing displacement at these cracks, causing the 

laminate to start debonding where it intersected the cracks (Beams 4b, 5, 7,9). 

8 
Beam 4a (clamped): Failure was initiated by debonding of the carbon FRP laminate, which 

slipped 12 m at one end. Examination of the failure surface after the load had been removed 

showed shear failure in the concrete substrate, with the adhesive and the laminate remaining 

intact. Shortly after debonding failure of the laminate, a horizontal shear failure plane also 

appeared at the level of the steel reinforcement. No sign of concrete crushing was observed. 

As shown in Fig. 7, the agreement between experimental data and theoretical prediction is close 

for moment-curvature, but not for ultimate strength. The theoretical model ignores concrete in 

tension, and consequently is less stiff than the measurements at low values of moment, before 

concrete cracks in tension. The model also does not predict debonding failure, and therefore 

allows the carbon to increase in strain up to 1.86 %, close to its rupture strain, at which point 

concrete crushes. Had the anchorage held, this beam would be balanced in terms of combined 

steel and carbon tensile reinforcements versus concrete (Le., FRP ruptures at the same time as 

concrete crushes, with steel having yielded previously). From the linear strain profile and the 

close agreement between measured and calculated moment-curvature, there appears to be strain 

compatibility of the carbon laminate with the concrete up to ultimate and sudden debonding. 

Beam 4b (wrapped): Failure was due to concrete crushing. Wide 45" shear cracks were 

observed, but there was neither anchorage failure nor debonding. As shown in Fig. 10, the 

model was less stiff than the experiment, but predicted the ultimate strength and mode of failure 

well (152 kN*m vs. 151 kN-m measured, by concrete crushing). As shown in Fig. 11, the 

measured laminate strain was less than strain compatibility would require, thus indicating some 

slip between concrete and laminate, despite the lack of supporting visual evidence. 

Beam 5 (wrapped): Wide flexure-shear cracks extended vertically above the load point at one 

end. The transverse wrap at the other end ruptured at one edge of the beam, causing the FRP 

laminate to debond abruptly (Fig. 28). There was no evidence of concrete crushing. The 

moment-curvature plot exhibited some drift in curvature while the FRP was curing (Fig. 13). The 

ultimate state was also not well predicted because of debonding of the FRP laminate. As in beam 

4b, strain compatibility between concrete and carbon was less than perfect (Figs. 14 and 15). 

Beam 6 (clamped): At midspan, on the compressive face, concrete spalled and showed severe 

distress towards the end of the test. The carbon FRP laminate then failed abruptly and showed 

evidence of interlaminar slip (about 12 mm) within the thickness of the laminate itself when 

clamps were removed. Wide vertical cracks extended over the depth of the beam above the load 

points, and a horizontal crack covered the plane of steel reinforcement (Fig. 29). When the 

failed beam was removed from the test machine by lifting it at its ends, these three major cracks 

connected and the central portion of the beam, rectangular in shape, fell off. 

As shown in Fig. 16 and prior to steel yielding, model and experiment agreed well. Beyond steel 

yielding, however, the model was less stiff than the measurements, and did not capture the 

interlaminar slip, which began at a laminate strain of 0.78 %, and caused the load to level and 

drop gradually before sudden failure at a laminate strain of 1.25 YO. Fig. 17 shows that the strain 

distribution is linear over the beam depth, and Fig. 18 shows that the predicted compression 

depth agrees better with experimental measurements before steel yielding than after. 

9 
Beam 7N (clamped): Failure was due to concrete crushing. In addition, two wide cracks 

occurred above the load points, one propagating vertically, the other diagonally and connecting 

to the crushing zone. Tapping with a coin showed some evidence of debond of the carbon 

laminate opposite the load points, but there was neither complete debond (within the epoxy or 

the concrete substrate) nor delamination (within the FRP laminate). Unfortunately, an electric 

power failure at just about the time the steel reinforcement was beginning to yield caused the 

subsequent data to be questionable, in spite of various safety measures and valiant recovery 

efforts. Prior to the incident, model and experiment agreed reasonably well (Figs. 19, 20, and 

Table 6a, b: Results 

2 1). 

Beam MV Mu M,4 ELM Em @v @U &,, @no1 

4a 44.0 93.5 2.13 10.07 0.53 113 30.6 1.75 63.8 14.6 

4b 45.0 151 3.36 9.88 0.52 111 32.7 1.86 76.4 12.1 

5 80.1 117 1.46 6.62 0.35 62.2 25.0 1.43 80.1 10.7 

6 99.2 148 1.49 7.80 0.41 46.9 26.9 1.54 115 11.7 

7N 136 179* 1.32 6.23" 0.33 33.6 20.3 1.69 105 7.69 

8N 172 204 1.19 6.10 0.32 26.7 25.3 1.45 138 8.09 

9 207 215 1.04 22.2 19.7 1.13 140 8.13 

10 252" 17.5" 1.00 --- 

z- kN-m km-' h-1 h-1 

mom mom M, 10" EL24 

--- 

Mu #,, * 

3.1 

5.3 

3.4 

3.0 

4.5 

4.6 

3.7 

MOO,400, 

Beam Failure Notes EL 

Mode ( 10") 

4a debond Ultimate (test) 10.07 

Ultimate (theory) 18.60 

4b crush Ultimate (test) 9.88 

Ultimate (theory) 13.50 

5 debond Ultimate (test) 6.62 

Ultimate (theory) 1 5.10 

6 slip Ultimate plateau 7.80 

(test) 8.49 

Ultimate (theory) 12.90 

7N crush Ultimate (test) 6.23 

Power failure 2.03 

Steel yields 2.80 

8N crush Ultimate (test) 6.10 

Ultimate (theory) 7.36 

Ei 1 

tests 

1.33 

1.31 

1.64 

0.96 

1.21 

1.66 

Beam 8N (wrapped): Failure was due to concrete crushing. The wraps held, although concrete 

diagonal shear cracks were visible underneath. The critical crack started out as flexural crack, 

opposite one of the load points, then propagated at 45O-towards midspan where it joined with the 

concrete crushing zone. The carbon FRP laminate debonded locally at its intersections with the 

~~ 

theory 

1.16 

1.17 

0.82 

0.97 

0.92 

10 

~~ ~ 

tests theory tests theory 

93.5 84.5 30.6 28.0 

119 49.2 

151 123 32.7 28.6 

152 38.4 

117 104 25.0 19.6 

139 41.1 

148 130 24.6 23.5 

148 133 26.9 25.3 

151 36.6 

217 179 20.3 29.5 
critical crack, but there was no overall debond. As shown in Fig. 22, the computer model and the 

experimental results agreed well over the entire range (predicted ultimate moment of 201 kN-m 

at a curvature of 26 km-’ vs. 204 kNm and 25 km-’ measured). The ultimate laminate strain, 

however, was calculated to be 0.703 % vs. 0.6 10 % measured, although there was no evidence of 

slip in the laminate as shown in Fig. 23. 

Beam 9 (no carbon): Failure was due to concrete crushing. In addition, two wide cracks 

occurred above the load points, one propagating vertically, the other diagonally and connecting 

to the crushing zone. As shown in Fig. 25, the agreement between model and experiment for this 

steel RC beam was reasonable (calculated ultimate moment of 207 kN-m at a curvature of 

22 km-’ vs. 2 15 Worn measured and an ultimate curvature between 19 h-’, at the peak load, and 

28 km-’ at failure). The difference in stiffness prior to steel yielding, here and in other cases 

noted above, may be due to errors in strain profile measurements, as shown, for example, in Fig. 

26. 

Results are summarized in Table 6, Figs. 30-32, and discussed below. Table 6b compares theory 

and experiments for various remarkable values of laminate strains, beam moment and curvature. 

These values include the theoretical ultimate states and the experimental ones. 

Strengthening: The application of carbon FRP laminates is very effective for flexural 

strengthening of reinforced concrete beams, provided proper anchorage of the laminate is 

ensured. In one case (beam 4b), the strengthened beam was 3.33 times stronger than the original 

beam (Fig. 30). As the amount of steel reinforcement increases, the additional strength provided 

by the carbon FRP external reinforcement decreases. The same amount of FRP reinforcement 

more than doubled the flexural strength of a lightly reinforced beam (1 1 % of balanced ratio), but 

only increased by 19 % the strength of a moderately reinforced beam (46 % of balanced ratio). 

FRP strain limit: An informal proposal circulated in ACI Committee 440 (FRP Reinforcement) 

limits the design strain level in the FRP reinforcement to KEL~ 2 0.90 EL^, where, I nb,t 

428 kN/mm 

K=l- for n E,, t 5 210 kN/mm or 

K= 105k”mm for n~,t>210k~/mm. nE,t 

n is thenumber of plies, and K is a strain limit factor for the FRP laminate. 

-- I-- - - 0.565 and KEL~ = 0.565 x 1.9 YO = 1.07 YO for the FRP laminate 186 

428 428 

1 x 155 x 1.2 

K=lused here. In the case of the beams tested here, the design strain level would thus be 57 % of the 

FRP ultimate tensile strain. Table 6a and Fig. 31 (Proposal 1) show that this strain was close to 

being achieved in beams 4a and 4b, where sufficient anchorage was provided, e.g., by clamping 

or wrapping with multiple layers of FRP fabric. For beam 4b, the six layers of end wrap probably 

would have achieved this level of strain, had the concrete not crushed first. However, beams 5 

and 6 did not come close to achieving this FRP strain, in spite of end clamps or wraps, and failed 

by FRP debond or interlaminar slip. 

11 
Anchorage: The level of strain achieved here in the FRP at midspan corresponds to a load 

greater than the anchorage capacity that can be achieved by bond only. Using Eq. (1) and (2) and 

fabe = 1.25fc = 52.5 MPa, one obtainsJ = 2.52 MPa, lmm= 190 mm, Tmm = 22.1 kN = 0.153 FL~ 

for w = 50 mm, and T- = 37.7 kN = 0.131 FL~ for w = 100 mm (beam 4b). The design values of 

Tma are conservative and are lower than 95 % of Neubauer and Rostasy’s measurements (1997). 

The best fit to their data is obtained if the coefficient of 0.5 in Eq. (1) is changed to 0.64 in the 

expression for Tma (Rostasy, 1998), giving Tma = 28.3 kN = 0.197 FL~ for w = 50 mm, and 

Tma = 48.3 kN = 0.168 FL~ for w = 100 111111. Fig. 31 shows the anchorage capacity in terms of 

strains. 

For comparison, values between 32 % and 53 % of FRP ultimate strain were achieved at 

midspan for w = 50 mm, and 52 % of ultimate strain was achieved for w = 100 mm (Table 6a). 

Mechanical clamping and adhesion anchored the laminate in beam 4a to a strain of 1.01 % (53 % 

of rupture), whereas a diagonal wrap with six layers anchored the carbon laminate in beam 4b to 

a strain of 0.988 %, (52 % of rupture), without slip. Since beam 4b failed by concrete crushing, 

it is not known how much more effective this wrap would have been. A transverse wrap with two 

layers (beam 5), however, failed at a laminate strain of 0.662 % (35 % of rupture). 

It should be noted that Neubauer and Rostasy measured anchorage capacity by double shear, 

push-out tests, whereas the force required to anchor the ends of the FRP larninate in a four-point 

bending test is lower than the maximum tension at midspan, depending on how much of the 

laminate has debonded in the shear span. Since the present experiments show significant 

debonding in the shear span, usually initiating at the flexural-shear cracks below the load points, 

the data indicate that clamping or wrapping combined with adhesion can double or triple the 

anchorage capacity that can be expected from bond only. This agrees with the results of Jensen et 

al. (1999), who showed that the addition of transverse strips enhances the anchorage capacity 

from 30 kN to 45 kN. They also showed that clamping produced by three or more steel plates 

and bolts that do not puncture the carbon strips enhances the ultimate anchorage capacity from 

30 kN to 90 kN. 

Ductility: The curvature at ultimate load of beams reinforced with steel and carbon FRP varies 

between 1.43 and 1.86 times that of a beam with a steel reinforcement ratio of 75 YO of the 

balanced ratio (maximum allowed by ACI, Fig. 30). Thus, beams reinforced with steel and 

carbon FRP have adequate deformation capacity in spite of their brittle failure modes (concrete 

crushing, laminate debonding or delamination). 

The Canadian Highway Bridge Design Code (CHBDC 2000) ductility criterion is reasonable 

(Fig. 30). All the beams (4b, 7N and 8N) that failed by concrete crushing fulfilled the criterion, 

whereas the beams that failed by debond or delamination did not (beams 4a, 5 and 6). Beam 9, 

which is a normal RC beam with no external FRP strengthening, falls slightly short of the 

criterion. Fig. 25 shows, however, that beam 9 resists moments only slightly less than the peak 

moment at curvatures much greater than that which corresponds to the peak moment. A more 

relaxed interpretation of the moment-curvature data, obtained by taking ultimate at concrete 

crushing, would make beam 9 satisfy the criterion. 

12 
Results (Table 6a) show that Naaman et al.’s recommendation (1999) to allow an increase in 

moment due to strengthening up to 20 % of the moment of beam 10, which has the maximum 

reinforcement ratio allowed by ACI, is reasonable (Fig. 32). Only in beam 4b, which has very 

low steel and very high carbon reinforcement ratios, does strengthening produce an increase in 

moment greater than 0.20 x 252 kN-m = 50.4 M-m. Beam 4a is at the limit of the recommended 

allowable moment increase, and all the other strengthened beams would satisfy the criterion. 

Some of the beams tested, however, did not fail by concrete crushing, and their flexural capacity 

with proper FRP anchorage is not known from this study. 

5. 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

Conclusions 

The application of carbon FRP laminates is very effective for flexural strengthening of 

reinforced concrete beams, provided proper anchorage of the laminate is ensured. As the 

amount of steel reinforcement increases, the additional strength provided by the carbon FRP 

external reinforcement decreases. 

Mechanical clamping or wrapping with FRP fabric combined with adhesion is effective in 

anchoring the FRP laminate and increases the anchorage capacity above that expected for 

adhesive bond only. 

If proper anchorage is provided, such as by wrapping or clamping, the effective strain limit 

(or stress level) currently proposed informally-for FRP reinforcement by ACI 440 is close to 

being achievable for this particular type of carbon FRP. For lightly (steel) reinforced beams, 

this design stress level in the FRP can add substantially and economically to the beam 

strength. 

The curvature at ultimate load of beams reinforced with steel and carbon FRP varies between 

1.43 and 1.86 times that of a beam with a steel reinforcement ratio of 75 % of the balanced 

ratio (maximum allowed by ACI). Thus, beams reinforced with steel and carbon FRP have 

adequate deformation capacity in spite of their brittle failure modes (concrete crushing, 

laminate debonding or delamination). 

The Canadian Highway Bridge Design Code (CHBDC 2000) ductility criterion is reasonable. 

All the beams (4b, 7N and 8N) that failed by concrete crushing fulfilled the criterion, 

whereas the beams that failed by debond or delamination did not (beams 4a, 5 and 6). 

Naaman et al.’s recommendation (1999) to allow an increase in moment due to strengthening 

up to 20 % of the moment of beam 10, which has the maximum reinforcement ratio allowed 

by ACI, is reasonable. 

A proper design procedure for FRP external strengthening should take into account 

enhancement of FRP anchorage by mechanical clamping, wrapping with FRP fabric, or other 

means. With that knowledge, and the existing anchorage data (Neubauer and Rostasy 1997), 

rational and efficient designs are possible. 

13 
Notation 

distance fiom compression extreme fiber to center of compression 

cross sectional area of carbon FRP laminate 

area of steel flexural reinforcement 

beam width 

compression depth 

beam depth 

laminate modulus of elasticity 

steel modulus of elasticity 

concrete force 

laminate force 

steel force 

concrete cylinder compressive strength 

concrete cube compressive strength 

ultimate laminate strength 

concrete surface pull-off strength 

yield strength of steel flexural reinforcement 

beam height 

anchorage length needed to develop Tma 

moment 

moment at application of FRP laminate 

measured ultimate moment of tested beam 

calculated ultimate moment of virgin beam 

beam moment at a concrete maximum compressive strain of 0.001 

number of plies 

radius of curvature 

laminate thickness 

capacity of adhesively bonded anchorage 

laminate width 

location measured from the neutral axis (0 I y I c) 

strain at which concrete attains its compressive strength (= 0.0025) 

tensile strain on concrete surface at application of FRP laminate 

concrete compressive strain 

compressive strain on concrete extreme fiber 

concrete ultimate strain (= 0.003) 

tensile strain on concrete extreme fiber 

laminate strain 

maximum laminate strain (at beam failure) 

laminate rupture strain 

steel strain 

FRP strain limit factor 

balance ratio of steel flexural reinforcement 

ratio of steel flexural reinforcement 

concrete compressive stress 

beam curvature 

14 
aU 

4~ 

@vb 

@.ool 

ultimate curvature of tested beam 

calculated ultimate curvature of virgin steel RC beam 

calculated ultimate curvature of RC beam with 75 % of balanced steel ratio 

beam curvature at a concrete maximum compressive strain of 0.001 

References 

American Concrete Institute ( 1999), “Building Code Requirements for Structural Concrete,” ACI 

3 18-99. 

Aprile, A., Limkatanyu, S. and Spacone, E. (2001), “Analysis of RC Beams with FRP Plates”, 

ASCE Structures Congress, Washington D.C. 

Bonacci, J.F. (1996), “Strength, Failure Mode and Deformability of Concrete Beams 

Strengthened Externally with Advanced Composites,” Proceedings of the 2nd International 

Symposium on Advanced Composite Materials in Bridges and Structures, Montreal, Canada, pp. 

4 19-426. 

Canadian Standards Association (2000), Canadian Highway Bridge Design Code, Section 16, 

“Fibre-Reinforced Structures”, Rexdale, Ontario. 

Concrete Society (2000), “Design Guidance for Strengthening Concrete Structures Using FRP 

Composite Materials”, Technical Report No. 55, Crowthome, Berkshire, UK. 

German Institute of Construction Technology ( 1997), “Strengthening of Reinforced Concrete 

and Prestressed Concrete with Sika Carbodur Bonded Carbon Fiber Plates”, Authorization No. 

2-36.12-29, Berlin. 

Jaeger, L.G., Mufti, A.A. and Tadros, G. (1997), “The Concept of the Overall Performance 

Factor in Rectangular Section Reinforced Concrete Members”, Proc. 3rd Int. Symp. on NonMetallic (FRP) Reinforcement for Concrete Structures, Sapporo, Japan, Vol. 2, pp, 55 1-559. 

Japan Building Disaster Prevention Association (JBDPA, 1 999), “Seismic Retrofitting Design 

and Construction Guidelines for Existing RC Buildings with FRP Materials”. 

Jensen, A.P., Petersen, C.G., Poulsen, E., Ottosen, C. and Thorsen, T. (1999), “On the 

Anchorage to Concrete of Sika CarboDur CFRP Strips”, Int. Congress: Creating with Concrete, 

Dundee, Scotland. 

Meier, U. (1 987), “Bridge Repair with High Performance Composite Materials”, Material und 

Technik, Vol. 15, pp. 125-128. 

Naaman, A.E., Park, S.Y., Lopez, M.M., and Till, R.D. (2001), “Parameters Influencing the 

Flexural Response of RC Beams Strengthened Using CFRP Sheets”, FRPRCS-5, University of 

Cambridge, UK, pp. 117-125. 

15 
Naaman, A.E., Park, S.Y., Lopez, M.M., Stankiewicz, and Pinkerton, L. (1999), “Repair and 

Strenthening fo RC Beams Using CFRP Laminates”, University of Michigan Reports No. 

UMCEE 99-04,97- 12,98-2 1,98-3 8,98-39, Ann Arbor, MI. 

Neubauer, U. and Rostasy, F.S. (1 997), “Design Aspects of Concrete Structures Strengthened 

with Externally Bonded CFRP Plates”, Concrete and Composites, Proc. 7‘h Int. Conf. on 

Structural Faults and Repair, Vol. 2, pp. 109-1 18, ECS Pub. Edinburgh, Scotland. 

Rostasy, F.S. (1 998), “Assessment of S&P CRP Structural Strengthening System”, Expert 

Opinion No. 98/0322, Scherer & Partners Construction System, Brunnen, Switzerland. 

Smith, S.T. and Teng, J.G. (2001), “Strength Models for Plate End Debonding in FRP - 

Strengthened RC Beams”, FRPRCS-5, University of Cambridge, UK, pp. 4 19-428. 

Swamy, R.N. and Mukhopadhyaya ( 1 999), “Debonding of Carbon-Fibre-Reinforced Polymer 

Plate fkom Concrete Beams’, Proc. Instn. Civil Engineers, Structures and Buildings, Vol. 134, 

Nov., pp. 301-317. 

Triantafillou, T., Matthys, S., and Taerwe, L. (2001), “ Design of Concrete Members 

Strengthened with Externally Bonded FRP Reinforcement”, FRPRCS-5, University of 

Cambridge, UK, pp. 157-1 66. 

Acknowledgments 

The authors thank Frank Davis for overall technical assistance with the tests, and Fahim Sadek, 

Joannie Chin and especially Nicholas Carino for their critical review of a first draft of this paper. 

The authors are also grateful to the SIKA Corporation for supplying Carbodur laminates, Sikadur 

30 adhesive, Sikawrap Hex 230C and Sikadur 330 impregnating resin. The material properties 

used in this work reflect manufacturer’s published data at the time. 

16 
2950mm 

I 6x 1Oomm 

205 mm +I I IIIII Laminate y 

/ Strain gage 111111 

I 'I 

815 mm 1120 mm 815 mm 

Fig. 1 Beam reinforcement and test set-up 

40 mm 

Variable area 

#3 bars 

10 mm 

10 mm 

x 50 mm 

I 

Fig. 2 Beam cross-section showing stirrups at shear span 

and LVDTs at midspan 
Channel 

Steel plate - 

Rubber pad ’ 

END VIEW 

355 

J Ste :el bearing k. !k - Laminate Pad 

J25mmO 

threaded rod 

50 

J 

SIDE VIEW 

Fig. 3 Clamping of ends of laminate 

200 mm 200 mm 

Laminate r 

355 mm 

Fig. 4 End wraps using carbon fiber fabric 
h 

V 

n 

45.0 

44.0 

43.0 

42.0 

u) 41.0 

E 40.0 

0 39.0 

E 

5 

2 

v 

b) 

c, 

Q) 

> 

u) 

Q) 

.- 

0 

A A 

d 

V 

Fig. 5 Beam stresses and strains 

- 

- 

- 

- 

a 

' -Best fit line ~ 

fc = 0.0264t + 39.53 

0 

0 20 40 60 80 100 120 140 

Time (days) 

Fig. 6 Compressive strength of concrete 
140 

120 

.c1 

60 

40 E 

20 

0 

- Experimental data 

--e - Theoretical values 

0 10 20 30 40 50 60 

Curvature (km-') 

Fig. 7 Curvature vs. moment (beam 4a) 

o Moment = 81 kN m 

1 x Moment = 93 kN m 

-2000 3000 8000 13000 

Strain (p) 

Fig. 8 Strain profiles (beam 4a) 

140 I ' - Experimental data 1 

1 

€ 100 

-g 80 1 - o - Theoretical values 

dFW applied 

Fig. 9 Compression depth vs. moment (beam 4a) 
160 1 1 

140 

120 

g 100 Y 

E 80 

60 

E 40 

20 

0 

n 

E 

Y 

E 

E 

0 

Ca 

0 

0 

J 

.- 

.w 

I - Experimental data 

--8 - Theoretical values 

0 10 20 30 40 50 

Curvature (km-') 

Fig. 10 Curvature vs. moment (beam 4b) 

-5000 0 5000 IO000 15000 

Strain (w) 

Fig. 1 1 Strain profiles (beam 4b) 

100 - 

120 

W 1 

Fig. 12 Compression depth vs. moment (beam 4b) 
160 

140 

g 120 

g 100 W 

E 80 

60 

40 

20 

0 

I& Laminate applied 

1 st Flexural cracks - o - Theoretical values 

G I 

0 10 20 30 40 50 

Curvature (km-’) 

Fig. 13 Curvature vs. moment (beam 5) 

+ Moment = 24 kN mo Moment = 41 kN m 

Moment = 61 kN m 

A Moment = 81 kN m 

o Moment = 102 kN m 

x Moment = 117 kN m 

-3000 -1000 1000 3000 5000 7000 9000 11000 

Strain (w) 

Fig. 14 Strain profiles (beam 5) 

160 

140 

- 120 E 

100 

80 

60 

I 40 

Y 

20 

0 

FRP applied 

50 100 150 

c (mm) 

Fig. 15 Compression depth vs. moment (beam 5) 
160 I I 

140 

120 E 

2 80 

60 

40 

2 100 Y 

n 

E 

v 

E 

S 

0 

a 

0 

0 

J 

.- 

c, 

- 0 - Theoretical values 

0 10 20 30 40 

Curvature (km-’) 

Fig. 16 Curvature vs. moment (beam 6) 

/ 

m Moment = 41 kN m 

A Moment = 61 kN m 

+ Moment = 81 kN m 

Moment = 102 kN m 

A Moment = 122 kN m 

0 Moment = 142 kN m 

x Moment = 148 kN m 

-3000 2000 7000 12000 

Strain (HE) 

Fig;. 17 Strain profiles (beam 6) 

160 i I 

140 

g- 120 

f 100 v 

E 80 

60 

I 40 

20 

0 

Fig. 18 Compression depth vs. moment (beam 6) 
25G 

200 

E 5 150 

100 

50 

0 

n 

c, 

E 

I 

200 - 

E 5 150 - 

n 

c, 

c 

n 

E 

E 

Y 

S 

0 

a 

0 

0 

J 

.- 

c, 

- Laminate applied 

1 st Flexural cracks I -+Theoretical values ! 

0 5 10 15 20 25 30 35 

Curvature (km-') 

Fig. 19 Curvature vs. moment (beam 7N) 

4N 1 -1 77 h " / 

1 0 Moment = 163 kN m I x Moment = 175 kN m 

-4000 -2000 0 2000 4000 6000 8000 10000 

Strain (p) 

Fig. 20 Strain profiles (beam 7N) 

\ 

Experimental 1 

data 

Theoretical J 

/FRP 

applied values 

0 !' I 

50 100 150 200 

c (mm) 

Fig. 21 Compression depth vs. moment (beam 7N) 
200 

LI 

E 

f 150 

100 

Y 

Y 

P 

50 

0 

Laminate applied 

1st Flexural cracks , I 

0 5 10 15 20 25 30 

Curvature (km-') 

Fig. 22 Curvature vs. moment (beam 8N) 

/ 

+ Moment = 49 kN m 

o Moment = 93 kN m 

Moment = 122 kN m 

A Moment = 163 kN m 

o Moment = 183 kN m 

x Moment = 203 kN m 

-4000 -2000 0 2000 4000 6000 8000 10000 

Strain (p~) 

Fig. 23 Strain profiles (beam 8N) 

200 - 

150 - 

100 

E 

4 

c 

Experimental 

Theoretical applied 

values 

0 !' I 

50 100 150 200 

c (mm) 

Fig. 24 Compression depth vs. moment (beam 8N) 
E loo - E 

50 - 

d / - Experimental data l-----7 1 - 0 - Theoretical values 

0 I 

0 5 10 15 20 25 30 

Curvature (km-') 

Fig. 25 Curvature vs. moment (beam 9) 

0 Moment = 81 kN m 

A Moment = 122 kN m 

0 Moment = 163 kN m 

-2000 -1000 0 1000 2000 3000 4000 

Strain (p~) 

Fig. 26 Strain profiles (beam 9) 

250 

200 

E $, 150 w 

S 

E loo 

B 

50 

0 

- Q - Theoretical y 

values 10 

Fig. 27 Compression depth vs. moment (beam 9) 
Fig. 28 Failure of transverse wrap and debonding of laminate (Beam 5) 

Fig. 29 Flexural and shear cracks. Compression failure (Beam 6) 
4a 4b 5 6 7N 8N 9 10 

Fig. 30 Moment and curvature ratios 
0.01 2 

0.01 

0.008 

0.006 

0.004 

0.002 

0 

4a 

0 FRP strain 

OProposal 1 

H anchorage 

4b 5 6 7N 8N 9 10 

Beam Number 

Fig.3 1 Measured FRP strain, calculated anchorage 

capacity and a proposed FRP limit strain 
300 

250 

200 

i 

Ly_ - 150 C 

E 

g 100 

50 

0 

4a 4b 5 6 7N 8N 

Beam Number 

9 

-. . Fig.32 Moment increase and a proposed strengthening lirmt