Detailing considerations on RC beams strengthened with CFRP bars embedded in mortar overlay

Construction and Building

MATERIALS

Construction and Building Materials 21 (2007) 1636–1646

www.elsevier.com/locate/conbuildmat

Detailing considerations on RC beams strengthened with CFRP bars embedded in mortar overlay Do-Young Moon a, Jongsung Sim a, Hongseob Oh a b

b,*

Department of Civil and Environmental Engineering, Hanyang University, 1271 Sa1-dong, Ansan 425-791, South Korea Department of Civil Engineering, Jinju National University, 150 Chilam-dong, Jinju, Kyeongnam 660-758, South Korea Received 23 June 2005; received in revised form 1 June 2006; accepted 30 June 2006 Available online 16 January 2007

Abstract Most recent studies on strengthening materials and methods for concrete structures have focused only on external bonded plates. Fiber reinforced polymer rod similar to reinforcing steel bars have rarely been considered. In this study, an experiment was performed using beams strengthened with rod-type Carbon Fiber Reinforced Polymer and high-strength mortar overlay. The beams received static and cyclic loads, and their structural behavior was compared with a non-strengthened beam. The test results show that the strengthened beams not only had improved endurance limits but also improved load-carrying capacities, stiffness values, and cracking loads as compared to a non-strengthened beam. Strengthened beams anchored with bolts throughout their entire span had more efficient structural behaviors, including composite behavior on the interface between the concrete and mortar and load-carrying capacity, than a strengthened beam anchored only on the end block.  2006 Elsevier Ltd. All rights reserved. Keywords: Anchor bolt; Composite action; Fatigue test; Fiber reinforced polymers; Flexural test

1. Introduction The use of fiber reinforced polymer (FRP) as external reinforcements for strengthening and retrofitting existing concrete structures has increased extensively due to its additional advantages over the conventional retrofitting and strengthening materials [1–3]. Accordingly, a numbers of researches have been carried out for the development of FRP performances in strengthening and retrofitting RC beams, columns and other kinds of structural members [3–5]. In parallel to the experimental studies, theoretical studies are also performed mainly to (1) determining the moment at which flexural peeling starts and the moment at which the plate separates from the reinforced concrete beam subject to shear and flexure or their interactions, (2) predicting the shear and normal stress concentrations

*

Corresponding author. Tel.: +82 55 751 3299; fax: +82 55 751 3209. E-mail address: [email protected] (H. Oh).

0950-0618/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2006.06.028

in the adhesive layer of plated reinforced concrete beams, (3) estimating the effects of existing and induced cracks and other main parameters like load locations and adhesive thickness based on fracture mechanics and finite element method, (4) simulating overall load–deflection behavior of the strengthened beam by compatibility of deformations and equilibrium of forces, and (5) suggesting the design guide lines for the externally bonded plates. [6–11] But, carbon fiber reinforced polymer (CFRP) plate, carbon fiber sheet (CFS), and glass fiber sheet (GFS) widely used for strengthening of deteriorated concrete structures have some unavoidable problems such as premature failure by various causes [1,2,5]. The adhesives that are used for either sheet or plate type FRP materials can be weakened by fire or aggressive chemicals, and partial debonding of external strengthening materials can result owing to stress concentrations [4,5]. If FRP composites such as rod and grid type FRP materials are embedded in a concrete matrix, additional strengthening benefits are expected, such as crack-bridging effects and chemical and fire resistance,

D.-Y. Moon et al. / Construction and Building Materials 21 (2007) 1636–1646

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Nomenclature a As AFRP b C Cb d fc0 ffrp fFRP fr ft fy h M Mr Mu

depth of equivalent stress block area of reinforcing steel bars area of strengthening material width of beam compliance depth of compressive zone effective depth to main reinforcement compressive strength of concrete stress of strengthening material ultimate strength of strengthening material flexural tensile strength of the concrete tensile strength of concrete yield strength of rebar height of beam external moment cracking moment ultimate moment

as well as improved load-carrying capacity [12]. The surfaces of the carbon fiber reinforced polymer (CFRP) rod used in this research were treated with artificial garnet particles to increase the bond strength. The typical strengthening scheme is depicted in Fig. 1. In this study, polymer mortar that requires only a few hours to harden was used. This is an improvement over ordinary cement mortar, which requires a minimum of several days to harden. As the mortar overlay on concrete surfaces that have deteriorated owing to strain lag or strain concentration can be separated from the concrete matrix after flexural cracking, anchor bolts are required to confine the mortar to concrete and to transfer the tensile stress in the CFRP

yield moment of rebar number of fatigue cycles the section modulus of the uncracked section general reducing factor for concrete tensile strength ec compressive strain of concrete er the strain on the bottom face ecu ultimate compressive strain of concrete ey the yield strain of rebar /FRP the empirical strength reduction factor 1/r curvature D1/rts tension stiffening effect 1/r2r the curvature in the uncracked state of the unstrengthened beam at cracking moment Mr 1/r1r the curvature in the uncracked state of the strengthened beam at cracking moment Mr

My Nf W1 bp

rod to the RC member. This paper addresses the structural efficiency of strengthened concrete beams with CFRP rod and mortar overlay that is applied anchor bolts under monotonic and cyclic loading states. Two anchoring schemes were considered: one with 10 anchor bolts inserted into the concrete in a line throughout the entire span to control the flexural interface debonding failure, and the other with six anchor bolts assembled in two lines in the each end block of the beam to prevent the rip-off failure at the end block of beam. In addition, the load-carrying capacity and failure patterns of the strengthened beams were experimentally assessed, and simplified moment–curvature relationship of strengthened were verified. Also the endurance limits and fatigue responses were experimentally examined. 2. Experimental program

Fig. 1. Strengthening detail of FRP rod.

The properties of the materials used in the experimental program are summarized in Table 1, and the test variables and strengthening details for the static and fatigue tests are shown in Table 2 and Fig. 2. The specimen details and strengthening schemes are illustrated in Fig. 2. The concrete used in the specimens consisted of ordinary Portland cement, natural sand, and crushed coarse aggregate with a maximum size of 25 mm. The mixture had a 28-day cylinder strength of about 22.5 MPa. The concrete beams were cured for at least 28 days in air before overlaying. The reinforcement details and loading scheme depicted in Fig. 2. Two 13mm diameter deformed rebar were used for tensile reinforcement and two 10-mm diameter deformed rebar were used for compression reinforcement. For all of the specimens, the section of beam was 15 · 25 cm, the depth of the mortar overlay was 2.5 cm and the clear span of the beam was 270 cm. The reinforcement ratio of the flexural

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Table 1 Material properties Diameter

Concrete Mortar Rebar FRP rod

13, 10 mm 6 mm

Strength (MPa) Yield

Maximum

Bond

Flexural

–

22.5 45.0 550 2,352

– 2 – –

– 21 – –

400 –

Table 2 Test variables and strengthening scheme Specimen

Strengthening ratio

APLATE hb




Maximum strain (%)

Elastic modulus (Mpa)

– – – 1.15

0.232 · 105 0.108 · 105 2.00 · 105 1.20 · 105

Mortar overlay thickness (cm)

Anchoring scheme

Minimum and maximum stress range

Static Test

BC BS–EA BS–CA

– 0.00137(2 · /6 mm) 0.00137(2 · /6 mm)

– 2.5 2.5

– 2 line · 3bolts@5 cm at each end block 10 bolts@20 cm through entire span

– – –

Fatigue Test

BC-60 BC-70 BC-80 BS–EA-60 BS–EA-70 BS–EA-80 BS–CA-60 BS–CA-70 BS–CA-80

0.00137(2 · /6 mm)

2.5

–

0.00137(2 · /6 mm)

2.5

2 line · 3bolts@5 cm at each end block

0.00137(2 · /6 mm)

2.5

10 bolts@20 cm through entire span

0.05–0.6Pultimate 0.05–0.7Pultimate 0.05–0.8Pultimate 0.05–0.6Pultimate 0.05–0.7Pultimate 0.05–0.8Pultimate 0.05–0.6Pultimate 0.05–0.7Pultimate 0.05–0.8Pultimate

P

2-D10

BC BC BC BS–EA BS–EA BS–EA BS–CA BS–CA BS–CA

P Concrete Gauge LVDT SteelGauge

190 250

2-D13

CL

of of of of of of of of of

90 150

Overlayed mortar

CFRP rod

270 310

(a) specimen detail

65

Anchor bolt

20

20

20

20 10

110

B S -CA

5

5

35

B S -EA

(b) anchoring scheme Fig. 2. Strengthening and anchoring scheme.

reinforcing steel bars was q = 0.139 (As/bd), and the amount of strengthening FRP rod was 2 · /6 mm. To prevent brittle shear failure, the specimens were built with 10mm-diameter stirrups that were equally spaced every 100 mm. To improve the composite action between strengthening material and repaired mortar, each end block of beam was reinforced with two different schemes by anchor bolts as depicted in Table 2 and Fig. 2 that summarized the

strengthening details of the test beams. Each end block of beam BS–EA was reinforced by six anchor bolts, arranged in two lines of three bolts as depicted in Fig. 2. The 10 anchor bolts used with beam BS–CA were inserted into the mortar along the centerline of the soffit area of a beam section through the entire span. In the fatigue tests, the stress levels of the reference and strengthened specimens were set to 60%, 70%, and 80% of the ultimate loads obtained from the static test results summarized in Table 3.

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Table 3 Static test results Specimen

Static test Yield load (Pyield) (kN)

Failure pattern

BC

BS–EA

BS–CA

-Initial flexural crack propagated at 15 kN -Compressive failure of top concrete after rebar’s yielding -Maximum crack width and crack spacing are 1.2 cm and 10.9 cm, respectively -Flexural failure -Interface debonding at mid-span after rebar’s yielding -Spalling of overlayed mortar -Maximum crack width and crack spacing are 0.1 cm and 7.8 cm, respectively -Flexural failure -Maximum crack width and crack spacing are 0.1 cm and 8.4 cm, respectively

Failure load (Pultimate) (kN)

Test

Theory

Test

Theory

40

39

48

39

43

44

68

78

44

44

75

78

Repair materials overlayed in bottom surface of concrete beam were used premix typed cementious polymer mortar. Overlaying materials were applied in layers of 2.5 cm thick vertical spans in concrete. Strengthening and overlaying on concrete surface by polymer mortar were applied as following procedures as depicted in Fig. 3. (1) Bottom surface of concrete was prepared for by chipping and sand blasting. (2) Anchor bolts were inserted in the concrete layer and two reinforcing FRP rods for strengthening whose diameter was 6 mm were embedded in overlayed layer prior to overlaying. An anchor bolts that was

arranged in either only end block of the FRP rod used for panel BS–EA, or same spacing through whole soffit area of beam as depicted in Fig. 2 were used for panel BS–CA. (3) The surface was damp (saturated surface dry) with no glistening water. (4) Liquid adhesive was applied as a prime coat by a brush to improve the composite action. (5) The repairing mortar was mixed by own methods suggested by manufacturer. (6) The mortar was placed while the prime coat is wet. The mortar must be scrubbed into the substrate, filling all pores and voids. And the overlayed beams were then cured for at least seven days in air

Fig. 3. Strengthening procedure of strengthened RC beam using FRP rod.

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D.-Y. Moon et al. / Construction and Building Materials 21 (2007) 1636–1646

before strengthening so that the strength of overlaying materials should be reach enough to strengthening work. The shear-span to depth ratio (a/d) was set to 3.5. An actuator with a 1000-kN capacity was used for the static and fatigue tests. Cyclic loads were applied at a rate of 2 Hz by an actuator for fatigue test. An automated data acquisition system acquired the test data such as strain and deflections. Displacement transducers were used to record the beam deflections at the midpoint and 1/4 point of the span to obtain the beam deflection profiles. Electrical resistance strain gages were bonded to the tensile rebars and FRP rods, as depicted in Fig. 3, to measure the strain profiles. 3. Test results and discussions 3.1. Static test 3.1.1. Failure patterns Static test results are summarized in Table 3 and the crack patterns of each specimen are depicted in Fig. 4. The yield strength of the rebar was estimated from the load–strain relationship of the tensile rebar. The unstrengthened BC specimen exhibited a typical flexural failure, as shown in Fig. 4(a). After the development of the initial crack at 15 kN, the tensile reinforcement yielded at 40.6 kN, and finally failed at 48 kN. As the load increased, major flexural

cracks propagated to the compression side and the crack width expanded until the beam failed completely. The maximum crack width at failure was 12 mm. The beams strengthened with FRP rod developed numerous flexural cracks in the mortar on the tension side of the beam until interface debonding occurred between the concrete surface and mortar. The interface debonding patterns differed slightly between beams BS–EA and BS–CA. Beam BS–EA, which was anchored only in the end block, exhibited either a separation or spalling of the mortar overlay only at the mid-point of the beam after the tensile rebar yielded. The composite action of the FRP rod and mortar overlay was diminished by the pull-out failure of the FRP rod. Beam BS–CA, which was anchored along the entire beam length, developed horizontal cracks in the concrete and mortar overlay interface along the entire span, but the mortar overlay did not fully separate from the bottom of the beam. These facts indicate that the anchor bolts inserted in the mortar contributed to the stress distribution and the composite action between the overlaid material and the concrete. 3.1.2. Load–deflection relationship Fig. 5 shows the load–deflection relationships of nonstrengthened and strengthened specimens with different anchoring schemes. The load–deflection relationship of the strengthened BS–EA and BS–CA specimens showed identical behaviors to that of the BC specimen before the

Fig. 4. Failure patterns of specimens under static loads.

80

80

60

60

Load (kN)

Loads (kN)

D.-Y. Moon et al. / Construction and Building Materials 21 (2007) 1636–1646

40 BC

1641

40 BC(rebar) BS-CA(rebar)

BS-CA

20

20

BS-EA

BS-EA(rebar) BS-CA(FRP rod)

Theory(BC)

BS-EA(FRP rod)

Theory(BS series)

0

0 0

20

40

60

80

Displacement (mm)

0

2000

4000

6000

8000

10000

Strain (X10-6)

Fig. 5. Load–deflection relationship.

Fig. 6. Load–strain relationship of reinforcing steel bar and FRP rod.

reinforcing bars yielded. However, after the yielding point of the reinforcing steel bars in the BS series, the stiffness and yield load of the strengthened beams were slightly greater than those of the BC specimen. The strengthened specimen BS–CA failed owing to a relatively ductile failure mode that is more often compared to beam BS–EA; this was caused by a gradually progressive debonding of the FRP rod in the mortar overlay after post-peak region. The ductility of the test beam was defined as a deflection ratio at the ultimate loads and yield loads. The failure loads for the strengthened specimens are shown in Table 3. Even though the same amount of FRP rod was applied, the BS– EA and BS–CA specimens increased in strength by 42% and 56%, respectively. These results indicate that the anchoring scheme that spanned the entire specimen (specimen BS–CA) was more effective than the scheme in which only the end block was anchored (specimen BS–EA).

between the strengthening materials and their surrounding materials or the stress concentrations in the strengthening materials. Beam BS–EA, which was initially perfectly bonded to the mortar overlay, showed a strain lag after the rebar yielded, which was caused by the pull-out failure of the FRP rod. For beam BS–CA, the rebar strain was relatively small as compared to the deformation of the FRP rod from the initial loading state. This phenomenon originated from the stress concentration at the mid-span of the beam. Therefore, the anchoring scheme of beam BS–EA was more effective and would ensure better composite action up to the yield load of the reinforcing bars. However, when the purpose of the strengthening is either to increase the ultimate strength or to control the failure mode, the anchoring scheme adopted in beam BS–CA would be more effective.

3.1.3. Load–strain relationships of the rebar and FRP rod The load–strain relationships of the FRP rod are shown in Fig. 6. The strain profiles of the strengthened beams BS– EA and BS–CA were very similar to the strain profiles of the rebar up to the yield loads. An initial conspicuous deformation of the FRP rod in beam BS–EA was observed 20 kN after flexural cracking. Then the strain of the strengthening material abruptly increased. This differed from the strain of the FRP rod in beam BS–CA, which increased proportionally from the initial loading state. Thus the anchoring scheme of beam BS–CA adequately resisted external loads without introducing the mid-span pull-out failure of the strengthening material that was observed for beam BS–EA. 3.1.4. Strain profile in the beam section Experimentally obtained strain profiles of the concrete, rebar, and FRP rod in the mid-span beam section are shown in Fig. 7 to examine the relative effectiveness of the composite action in the strengthened beam. Since the strengthening materials were assumed to be perfectly bonded to the mortar overlay, the discrepancy between the linearity of the strain profile and the strain compatibility for each load resulted from either cumulative slips that existed in the interface

3.1.5. Simplified moment–curvature relationship Time and effort are required to determine the load-carrying capacity and load–deflection relationship of strengthened beams using a nonlinear finite element analysis. This is because these parameters are functions of the type of loading, the type of strengthening, and the restraint conditions. Elastic beam theory is too simplistic to yield realistic results, yet nonlinear finite element analysis is too complex for practical design purposes. In this study, the simplified moment–curvature relationship proposed in the CEB-FIP Model Code 1990[13] was adopted and modified to assess the moment–curvature relationship of a beam strengthened with FRP rod. If a deteriorated concrete member repaired on the preexisted cracks with epoxy resin and then strengthened with externally bonded FRP is subjected to a bending moment, the following stages are observed: – Stage 0–1: the idealized uncracked stage In this stage, the repaired cracks and the role of the reinforcement can be neglected – Stage 1–2: the crack-formation stage The first cracks deeply penetrate into the compression area. The subsequent cracks will have smaller lengths, because the cross-section is not fully stressed, due to

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BC(21.7) BC(40.3) BC(48.1)

Beam Depth (cm)

22cm

25cm

25

1.25cm

2.5cm

Rebar

FRP rod

-2000

0

2000

4000

6000

8000

10000

Strain (X10-6)

(a) Beam BC 25 BS-EA(20.6)

BS-CA(21.9)

BS-EA(40.3)

BS-CA(43.5)

BS-EA(49.0) BS-EA(57.1)

2000

4000

6000 Strain(X10-6)

8000 10000

Beam Depth (cm)

Beam Depth (cm)

25

-1.25 -2000 0

-1.2 5

BS-CA(49.7) BS-CA(57.2)

-1.25 -2000 0

(b) Beam BS-EA

2000

4000 6000 Strain(X10-6)

8000 10000

(c) Beam BS-CA Fig. 7. Strain profile in beam section.

the influence of the first cracks. Further cracks will occur, which are limited to the reinforcement area. – Stage 2–3: stabilized cracking stage No new cracks appear any more. The existing cracks widen. – Stage 3–4: rebars’s yielding stage The reinforcement steel yields. The curvature abruptly increases, whereas the increase of bending moment is relatively slight. – Stage 4–5: failure stage The curvature and bending moment linearly increase, and then finally the strengthened FRP either fails by debonding on concrete surface or ruptures. The moment–curvature relation can be constructed using the characteristic points, depicted in Fig. 8. In order to calculate the (M, 1/r) combinations for these points, material properties have to be supplied. Fig. 9 gives relations for the stress–strain relations of concrete, reinforcing steel and FRP. The simplified moment curvature relationship of the strengthened beam depicted in Fig. 8 can be computed with the following procedure.

M

4 3 3'

Δ1/r ts

1.3M r 1 Mr

2 Naked bar in tensile zone

1/r Fig. 8. Conceptual moment–curvature relationship of strengthened beam.

3.1.5.1. Flexural crack-formation. The cracking moment is M r ¼ W 1  fr

ð1Þ

where W1 is the section modulus of the uncracked section, fr is the flexural tensile strength of the concrete 0:7 b =100Þ (fr ¼ ft 1þ1:5ðh 0:7 Þ based on the CEB-FIP Model Code 1:5ðh =100Þ b

D.-Y. Moon et al. / Construction and Building Materials 21 (2007) 1636–1646

σc

σs

σ frp

fs

fFRP

1643

fc εc

ε cu =3.5%

εs

(a) concrete

(b) rebar

ε FRP (c) FRP

Fig. 9. Idealized stress–strain relation for concrete, steel and FRP.

1990[13] and ft ¼ 2:12  lnð1 þ fc0 =10Þ MPa. During the cracking phase, the strain on the bottom face is er = fr/ Ec. Thus the curvature is 1=r ¼

er ð1=2hÞ

ð2Þ

concrete had reached the value fc0 . The compatibility of the deformations requires that (see Fig. 10) ec Cb ¼ ð3Þ ey d  C b and because of the force equilibrium, 0:85fc0  a  b ¼ As  fy þ AFRP  ffrp

3.1.5.2. Stabilized cracks. The flexural cracks penetrate deeply into the compression zone. 3.1.5.3. Rebar yield. The dotted line in Fig. 8 is a theoretical line, for the case that concrete is only ably to sustain compression (no tension stiffening). For the sake of simplicity, we assumed that the stress in the compression area of the

ð4Þ

Now the yielding moment of the rebar of strengthened beam follows from   As  fy þ AFRP  ffrp M y ¼ As  fy d  þ AFRP 1:7fc0  b   As  fy þ AFRP  ffrp  ffrp h  ð5Þ 1:7fc0  b

Fig. 10. Strengthened RC section at failure.

Table 4 Fatigue test results Specimen

Fatigue Test Maxium loading size (kN)

Failure pattern

Nf

BC-60 BC-70 BC-80 BS-EA-60 BS–EA-70 BS–EA-80 BS–CA-60 BS–CA-70 BS–CA-80

28.8 33.6 38.4 40.8 47.6 54.4 45.0 52.5 60.0

– – – – – – – – –

597,543 121,426 11,179 686,214 158,241 30,988 785,083 236,869 51,754

Propagation of initial cracks at 1st loading cycle Intensive flexural cracks in mid-point of beam Similar failure pattern with BC70 Interface debonding and spalling of mortar overlay Similar failure pattern with BS–EA-60 Similar failure pattern with BS–EA-60 Flexural failure and similar pattern with BC series Similar failure pattern with BS–CA-60 Similar failure pattern with BS–CA-60

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D.-Y. Moon et al. / Construction and Building Materials 21 (2007) 1636–1646

and the corresponding curvature follows from   fc0 b 1=r ¼ ey =d   D1=rts As  fy þ AFRP  ffrp

ð6Þ

where As and AFRP are the area of the reinforcing steel bars and the FRPs, respectively, b is the unit slab width, d is the distance from the tension steel to the compression face, fy is the yield strength, fc0 is the concrete strength, and ffrp is the stress of the strengthening FRP when the rebar starts to yield. In the CEB-FIP Model Code 1990, the moment curvature relationship is described in an empirical manner. The tension stiffening effect represented as the discrep-

ancy between line 2–3 and line 2–3 0 in Fig. 8, is formulated as   Mr ð7Þ D1=rts ¼ ð1=r2r  1=r1r Þbp M where 1/r1r is the curvature in the uncracked state of the strengthened beam at cracking moment Mr, 1/r2r is the curvature in the uncracked state of the unstrengthened beam at cracking moment Mr, M is the external moment, and

80 70 Static test results of BC

Load(kN)

60 1

50 40

100

10000

1000

100000

30 10

20 10 0

0

10

20

30

40

50

60

Displacement (mm)

(a) BC-70 (Nf =121,426) 80 Static

70

Load (kN)

60

100000

50

10

1

1000

10000 150000

40 30 20 10 0

0

10

20 30 40 Displacement (mm)

50

60

50

60

(b) BS-EA-70 (Nf =158,241) 80 Static

70 10

Load (tonf)

60

1

50

100 1000 200000

40 30 20 10 0

0

10

20 30 40 Displacement (mm)

(c) BS - CA -70 (Nf =236,869) Fig. 11. Typical fatigue failure patterns.

Fig. 12. Cyclic load–deflection relationship.

D.-Y. Moon et al. / Construction and Building Materials 21 (2007) 1636–1646

bp is the general reducing factor for concrete tensile strength. 3.1.5.4. Failure of the strengthened materials. The ultimate moment is reached when either the strain of the FRP reaches the ultimate tensile strain or the compressive strain of concrete in top fiber reaches the ultimate value ecu = 0.0035, as shown in Fig. 9. The ultimate flexural moment of strengthened concrete beam is   As  fy þ AFRP  /FRP fFRP M u ¼ As  fy d  1:7fc0  b   As  fy þ AFRP  /FRP fFRP þ AFRP  /FRP fFRP h  ð8Þ 1:7fc0  b   fc0 b 1=r ¼ ecu = ð9Þ As  fy þ AFRP  /FRP fFRP This moment–curvature relation can be converted into load–displacement relation. Fig. 5 compares the test results and theoretical results predicted by the simplified model proposed in the CEB-FIP Model Code 1990. Reasonably good

agreements were obtained. In general, the model predictions showed that the stiffness and strength of the strengthened beams in the pre-peak region were almost the same as the load–deflection curve. Therefore, this assumption and simplified model can be used for strengthening designs and predicting the load–deflection relationship of beams. 3.2. Fatigue response 3.2.1. Failure Patterns A summary of the test results is shown in Table 4, and the failure patterns of each specimen at a stress level of 60% are illustrated in Fig. 11. The non-strengthened specimens (BC60, -70 and -80) developed flexural cracks similar to the crack patterns of beam BC under static loads, and finally failed after the macro-flexural cracks widened at the midspan, as shown in Fig. 11(a). Horizontal interface cracks were not observed in beam series BS–CA, unlike beam series BC-CA, which was subjected to monotonic loads. Horizontal debonding cracks between the concrete/mortar interface were widely propagated in beam series BS–EA.

4

4

BC -80 BC -70 BC -60

BS -EA -80 3. 5

Compliance(mm/tonf)

3 2.5 2 1.5 1 0.5

BS -EA-70 BS -EA-60

3 2. 5 2 1. 5 1 0. 5

1

100

10000

0

1 000000

1

100

10000

N

N

(b) BS-EA Series

(a) BC Series 4 B S -C A -80 B S-C A -70 B S-C A -60

3.5

Compliance(mm/tonf)

Compliance(mm/tonf)

3.5

0

1645

3 2.5 2 1.5 1 0.5 0

1

100

10000

N

(c) BS - CA Series Fig. 13. Variation of compliance.

1000000

1000000

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D.-Y. Moon et al. / Construction and Building Materials 21 (2007) 1636–1646

3.2.2. Structural performance according to load cycle Load-cumulative deflection relationships corresponding to the load cycles of the beams at a stress level of 70% are illustrated in Fig. 12. Strengthened beams BS–EA-70 (Nf = 158,241) and BS–CA-70 (Nf = 236,869) had longer life cycles than did beam BC-70 (Nf = 121,426). The maximum accumulation deflections of specimens BC-70, BS–EA-70, and BS–CA-70 subjected to cyclic loads were 30, 21.6, and 30.6 mm, respectively. The beams strengthened with FRP rod displayed similar behaviors under the other stress levels. The compliance method is effective for determining the fatigue response of brittle materials. The compliance can be calculated from a load–deflection curve or from a load-crack mouth-opening displacement curve. In this study, the compliance was defined as C ¼ Pd from a load– deflection curve. The compliance, represented by a function of the crack length, increased greatly at the initial loading state, and then increased more gradually afterwards. This indicates a stabilized crack state. Finally, the compliance increased rapidly at the development of fatigue failure, as shown in Fig. 13. The compliance variation of the beams changed suddenly at the initial loading state, and the corresponding results indicate that beam damage occurred owing to the initial cyclic loads. In addition, the rate of compliance for beam BS–EA was larger than that of beam BS–CA. This was caused by the superior compliance control capacity of beam BS–CA, which concentrated the mechanical cracks in the mid-span of the specimen. 3.2.3. S–N Relationship The strengthened beams had an improved endurance limit as well as load-carrying capacity for cyclic loads. When the fatigue limit cycles were regarded as 2 · 106 cycles, the endurance limit of the BC specimen was 58%, while the endurance limits of the strengthened specimens BS–EA and BS–CA were 60% and 62%, respectively. The endurance limit of BS–CA series beams was 4% higher than that of an unstrengthened beam. The S–N relationship of the beams based on the test results is depicted in Fig. 14.

Stress level (S)

1

0.8

0.6

BC BS-EA BS-CA

0.4 1000

10000

100000

Numberofcycles (Nf) Fig. 14. S–N relationship.

1000000

4. Conclusions The results presented in this paper lead to the following conclusions. Beams strengthened with FRP rod can have a substantially increased load-carrying capacity and flexural stiffness, but the cracking patterns and failure mode of the strengthened beams depend on the anchoring scheme. From the static test results, the strengthened specimens showed a 40–50% improvement in their ultimate strength. Beam BS–CA, which was anchored through its entire span length, proved to be efficient from the viewpoint of strength, crack control, and energy dissipation. Also, the fatigue tests suggested that the strengthened beams were more efficient at fatigue resistance as compared to BC beams. At the same stress level, the BA–CA beam series showed a remarkable structural enhancement that resisted fatigue loads, because the stress was more effectively distributed in the beams under the service load state. Acknowledgement This work is supported by the R&D Program (C105B1030001-05B0303-000 and C105D201000105D0201-00230) of the Korea Institute of Construction and Transportation Technology Evaluation and Planning (KICTTEP). References [1] Teng JG, Chen JF, Smith ST, Lam L. FRP-strengthened RC structures. John Wiley & Sons, LTD; 2002. [2] Arduini M, Tommaso AD, Nanni A. Brittle failure in FRP plate and sheet bonded beams. ACI Struct J 1997;94(4). [3] Arduini M, Nanni A. Parametric study of beams with externally bonded FRP reinforcement. ACI Struct J 1997;94(4). [4] Oh H, Sim J, Meyer C. Experimental assessment of bridge deck panels strengthened with carbon fiber sheets. Compos Part B: Eng 2003;34(6):527–38. [5] Arockiasamy M, Sowrirajan R, Shahawy M, Beitelman TE. Repair of damaged pretensioned solid slab using CFRP laminates. In: Taerwe L, editor. Non-metallic (FRP) reinforcement for concrete structures, RILEM; 1995. p. 492–500. [6] Buyukozturk O, Hearing B. Failure behaviour of precracked concrete beams retrofitted with FRP. J Compos Constr 1998;2(3):138–44. [7] Almusallam TH, Al-Salloum YA. Ultimate strength prediction for RC beams externally strengthened by composite Materials. Compos Part B: Eng 2001;32(6):609–19. [8] De Lorenzis L. Strengthening of the structures with near surface mounted FRProds. University of Missouri-Rolla; 2000. p. 1–153. [9] De Lorenzis L, Nanni A, Tegola ALa. Flexural and shear strengthening of reinforced concrete structures with near surface mounted FRProds. Proceeding of the third international conference on advanced composite materials in bridges and structures 2000:521–8. [10] Pecee M, Manfredi G, Cosenza E. Experimental response and code models of GFRPRC beams in bending. J Comp Constr 2000;4(4):182–90. [11] Plevris N, Triantafillou TC, Veneziano D. Reliability of RC members strengthened with CFRP laminates. J. Struct. Eng. 1995;121(7): 1037–44. [12] Toutanji H, Deng Y. Deflection and crack-width prediction of concrete beams reinforced with glass FRP rods. Constr Build Mater 2003;17(1):69–74. [13] CEB-FIP model code 1990, 1992, CEB-FIP.